Re: Questions about the Equivalence Principle (EP) and GR

[Alan Grayson]

Did Einstein "derive" the field equation using the 5 postulates of GR, or 
did he guess what they had to be based on what the postulates implied? I 
ask this because I recall reading that the field equations published in his 
1916 paper were those he had rejected around 1913. How could the final 
equations be "derived" if they were rejected earlier? The fact that he 
later adds the cosmological constant to satisfy a stable universe seems to 
suggest he was making guesses based on what he thought the postulates 
implied. AG

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Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Wednesday, April 24, 2019 at 8:59:52 PM UTC-5, Brent wrote:
>
>
>
> On 4/24/2019 6:36 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 24, 2019 at 6:46:49 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/24/2019 4:17 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: 



 On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:



 On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>
>
>
> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>
> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
> the metric tensor is a Kronecker delta function. But I could swear that 
> the 
> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>
>
> What's odd about that??? Flat space is just special case of curved 
> space in which the curvature is zero.
>
> Brent
>

 *Sure, but he seems to be saying that the Kronecker delta is the metric 
 tensor for curved space. Isn't that how you interpret his comment?*


 No.?? After he goes thru the derivation with delta function in it, then 
 he says it's different for a curve?? space.

 Brent

>>>
>>> *I just reviewed it again. That's not my reading. In any event, it's not 
>>> clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't 
>>> really help either since you end up with the Lorentz metric which is far 
>>> from Euclidean intuition for demonstrating deviations from flatness. 
>>> Further, there are transformations that keep spacetime flat with NON-zero 
>>> off diagonal elements, such as a simple rotation. AG??*
>>>
>>
>>
>> *Using the Lorentz metric, how is "flat" spacetime defined 
>> mathematically? AG *
>>
>>
>> The general definition is that the Riemann tensor is zero.?? This is 
>> independent of what coordinate system is used.?? 
>> https://en.wikipedia.org/wiki/Riemann_curvature_tensor
>>
>> If the Lorentz metric applies globally the space is flat.
>>
>> Brent
>>
>
> Are the double question marks significant in some way, or typos? AG 
>
> They are some glitch in my email program which puts in extra ??? It is 
> mysteriously inconsistent.
>
> Brent
>
>
I can't imagine interfacing with Google Groups via anything else (like any 
email system) but its own web interface.

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Wednesday, April 24, 2019 at 6:17:14 PM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 



 On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

 *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
 the metric tensor is a Kronecker delta function. But I could swear that 
 the 
 diagonal of -1,1,1,1 represents flat space in SR. AG??*


 What's odd about that??? Flat space is just special case of curved 
 space in which the curvature is zero.

 Brent

>>>
>>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>>> tensor for curved space. Isn't that how you interpret his comment?*
>>>
>>>
>>> No.?? After he goes thru the derivation with delta function in it, then 
>>> he says it's different for a curve?? space.
>>>
>>> Brent
>>>
>>
>> *I just reviewed it again. That's not my reading. In any event, it's not 
>> clear what he means, and using Bruno's suggestion, t' --> it,  doesn't 
>> really help either since you end up with the Lorentz metric which is far 
>> from Euclidean intuition for demonstrating deviations from flatness. 
>> Further, there are transformations that keep spacetime flat with NON-zero 
>> off diagonal elements, such as a simple rotation. AG *
>>
>
> *Using the Lorentz metric, how is "flat" spacetime defined mathematically? 
> AG *
>



See https://en.wikipedia.org/wiki/Metric_tensor#Examples

Euclidean metric vs.
Lorentzian metrics  "In flat Minkowski space 
 ..."

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/24/2019 6:36 PM, agrayson2...@gmail.com wrote:



On Wednesday, April 24, 2019 at 6:46:49 PM UTC-6, Brent wrote:



On 4/24/2019 4:17 PM, agrays...@gmail.com  wrote:



On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6,
agrays...@gmail.com wrote:



On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:



On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:



On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:



On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

*Here's something odd. At 9:45 in Susskind's
Lecture 2 on GR, he says the metric tensor is a
Kronecker delta function. But I could swear that
the diagonal of -1,1,1,1 represents flat space in
SR. AG??*


What's odd about that??? Flat space is just special
case of curved space in which the curvature is zero.

Brent


*Sure, but he seems to be saying that the Kronecker
delta is the metric tensor for curved space. Isn't that
how you interpret his comment?*


No.?? After he goes thru the derivation with delta
function in it, then he says it's different for a curve??
space.

Brent


*I just reviewed it again. That's not my reading. In any
event, it's not clear what he means, and using Bruno's
suggestion, t' --> it,?? doesn't really help either since you
end up with the Lorentz metric which is far from Euclidean
intuition for demonstrating deviations from flatness.
Further, there are transformations that keep spacetime flat
with NON-zero off diagonal elements, such as a simple
rotation. AG??*


*Using the Lorentz metric, how is "flat" spacetime defined
mathematically? AG
*



The general definition is that the Riemann tensor is zero.?? This
is independent of what coordinate system is used.??
https://en.wikipedia.org/wiki/Riemann_curvature_tensor


If the Lorentz metric applies globally the space is flat.

Brent


Are the double question marks significant in some way, or typos? AG

They are some glitch in my email program which puts in extra ??? It is 
mysteriously inconsistent.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 6:46:49 PM UTC-6, Brent wrote:
>
>
>
> On 4/24/2019 4:17 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 



 On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

 *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
 the metric tensor is a Kronecker delta function. But I could swear that 
 the 
 diagonal of -1,1,1,1 represents flat space in SR. AG??*


 What's odd about that??? Flat space is just special case of curved 
 space in which the curvature is zero.

 Brent

>>>
>>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>>> tensor for curved space. Isn't that how you interpret his comment?*
>>>
>>>
>>> No.?? After he goes thru the derivation with delta function in it, then 
>>> he says it's different for a curve?? space.
>>>
>>> Brent
>>>
>>
>> *I just reviewed it again. That's not my reading. In any event, it's not 
>> clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't 
>> really help either since you end up with the Lorentz metric which is far 
>> from Euclidean intuition for demonstrating deviations from flatness. 
>> Further, there are transformations that keep spacetime flat with NON-zero 
>> off diagonal elements, such as a simple rotation. AG??*
>>
>
>
> *Using the Lorentz metric, how is "flat" spacetime defined mathematically? 
> AG *
>
>
> The general definition is that the Riemann tensor is zero.?? This is 
> independent of what coordinate system is used.?? 
> https://en.wikipedia.org/wiki/Riemann_curvature_tensor
>
> If the Lorentz metric applies globally the space is flat.
>
> Brent
>

Are the double question marks significant in some way, or typos? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/24/2019 4:17 PM, agrayson2...@gmail.com wrote:



On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com 
wrote:




On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:



On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:



On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:



On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

*Here's something odd. At 9:45 in Susskind's Lecture 2
on GR, he says the metric tensor is a Kronecker delta
function. But I could swear that the diagonal of
-1,1,1,1 represents flat space in SR. AG??*


What's odd about that??? Flat space is just special case
of curved space in which the curvature is zero.

Brent


*Sure, but he seems to be saying that the Kronecker delta is
the metric tensor for curved space. Isn't that how you
interpret his comment?*


No.?? After he goes thru the derivation with delta function in
it, then he says it's different for a curve?? space.

Brent


*I just reviewed it again. That's not my reading. In any event,
it's not clear what he means, and using Bruno's suggestion, t' -->
it,?? doesn't really help either since you end up with the Lorentz
metric which is far from Euclidean intuition for demonstrating
deviations from flatness. Further, there are transformations that
keep spacetime flat with NON-zero off diagonal elements, such as a
simple rotation. AG *


*Using the Lorentz metric, how is "flat" spacetime defined 
mathematically? AG

*



The general definition is that the Riemann tensor is zero.?? This is 
independent of what coordinate system is used.

https://en.wikipedia.org/wiki/Riemann_curvature_tensor

If the Lorentz metric applies globally the space is flat.

Brent



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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 6:04:43 PM UTC-6, Brent wrote:
>
>
>
> On 4/24/2019 4:11 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>>
>>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
>>> the metric tensor is a Kronecker delta function. But I could swear that the 
>>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>>
>>>
>>> What's odd about that??? Flat space is just special case of curved space 
>>> in which the curvature is zero.
>>>
>>> Brent
>>>
>>
>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>> tensor for curved space. Isn't that how you interpret his comment?*
>>
>>
>> No.?? After he goes thru the derivation with delta function in it, then 
>> he says it's different for a curve?? space.
>>
>> Brent
>>
>
> *I just reviewed it again. That's not my reading. In any event, it's not 
> clear what he means, and using Bruno's suggestion, t' --> it,?? doesn't 
> really help either since you end up with the Lorentz metric which is far 
> from Euclidean intuition for demonstrating deviations from flatness. *
>
>
> It was NOT demonstrating deviation from flatness.??
>

*I know. He just offered a final comment that deviations from flatness 
corresponds to non-zero off diagonal elements, so it got me wondering how 
flatness is mathematically defined for a Lorentz metric. I agree I should 
focus on the reference I posted. AG*
 

> I don't know what the guy was intending to demonstrate but he started with 
> assuming flatness, got a metric, and then remarked that it's different for 
> curve space.?? So what's your problem??? Read
>
> arXiv:1608.05752v1 [physics.hist-ph] 19 Aug 2016
>
> and stop fussing about some video.
>
> Brent
>
> *Further, there are transformations that keep spacetime flat with NON-zero 
> off diagonal elements, such as a simple rotation. AG??*
> -- 
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>
>
>

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/24/2019 4:11 PM, agrayson2...@gmail.com wrote:



On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:



On 4/21/2019 7:35 PM, agrays...@gmail.com  wrote:



On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:



On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:

*Here's something odd. At 9:45 in Susskind's Lecture 2 on
GR, he says the metric tensor is a Kronecker delta function.
But I could swear that the diagonal of -1,1,1,1 represents
flat space in SR. AG??*


What's odd about that??? Flat space is just special case of
curved space in which the curvature is zero.

Brent


*Sure, but he seems to be saying that the Kronecker delta is the
metric tensor for curved space. Isn't that how you interpret his
comment?*


No.?? After he goes thru the derivation with delta function in it,
then he says it's different for a curve?? space.

Brent


*I just reviewed it again. That's not my reading. In any event, it's 
not clear what he means, and using Bruno's suggestion, t' --> it,?? 
doesn't really help either since you end up with the Lorentz metric 
which is far from Euclidean intuition for demonstrating deviations 
from flatness. *


It was NOT demonstrating deviation from flatness.?? I don't know what the 
guy was intending to demonstrate but he started with assuming flatness, 
got a metric, and then remarked that it's different for curve space.?? So 
what's your problem??? Read


arXiv:1608.05752v1 [physics.hist-ph] 19 Aug 2016

and stop fussing about some video.

Brent
*Further, there are transformations that keep spacetime flat with 
NON-zero off diagonal elements, such as a simple rotation. AG *

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.
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.

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 5:11:13 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/21/2019 7:35 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>>
>>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
>>> the metric tensor is a Kronecker delta function. But I could swear that the 
>>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>>
>>>
>>> What's odd about that??? Flat space is just special case of curved space 
>>> in which the curvature is zero.
>>>
>>> Brent
>>>
>>
>> *Sure, but he seems to be saying that the Kronecker delta is the metric 
>> tensor for curved space. Isn't that how you interpret his comment?*
>>
>>
>> No.?? After he goes thru the derivation with delta function in it, then 
>> he says it's different for a curve?? space.
>>
>> Brent
>>
>
> *I just reviewed it again. That's not my reading. In any event, it's not 
> clear what he means, and using Bruno's suggestion, t' --> it,  doesn't 
> really help either since you end up with the Lorentz metric which is far 
> from Euclidean intuition for demonstrating deviations from flatness. 
> Further, there are transformations that keep spacetime flat with NON-zero 
> off diagonal elements, such as a simple rotation. AG *
>

*Using the Lorentz metric, how is "flat" spacetime defined mathematically? 
AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 3:34:28 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 7:35 PM, agrays...@gmail.com  wrote:
>
>
>
> On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/21/2019 6:31 PM, agrays...@gmail.com wrote:
>>
>> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
>> metric tensor is a Kronecker delta function. But I could swear that the 
>> diagonal of -1,1,1,1 represents flat space in SR. AG??*
>>
>>
>> What's odd about that??? Flat space is just special case of curved space 
>> in which the curvature is zero.
>>
>> Brent
>>
>
> *Sure, but he seems to be saying that the Kronecker delta is the metric 
> tensor for curved space. Isn't that how you interpret his comment?*
>
>
> No.?? After he goes thru the derivation with delta function in it, then he 
> says it's different for a curve?? space.
>
> Brent
>

*I just reviewed it again. That's not my reading. In any event, it's not 
clear what he means, and using Bruno's suggestion, t' --> it,  doesn't 
really help either since you end up with the Lorentz metric which is far 
from Euclidean intuition for demonstrating deviations from flatness. 
Further, there are transformations that keep spacetime flat with NON-zero 
off diagonal elements, such as a simple rotation. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/21/2019 7:35 PM, agrayson2...@gmail.com wrote:



On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:



On 4/21/2019 6:31 PM, agrays...@gmail.com  wrote:

*Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he
says the metric tensor is a Kronecker delta function. But I could
swear that the diagonal of -1,1,1,1 represents flat space in SR. AG *


What's odd about that??? Flat space is just special case of curved
space in which the curvature is zero.

Brent


*Sure, but he seems to be saying that the Kronecker delta is the 
metric tensor for curved space. Isn't that how you interpret his comment?*


No.?? After he goes thru the derivation with delta function in it, then 
he says it's different for a curve?? space.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 11:29:36 AM UTC-6, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, April 24, 2019 at 11:06:10 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 23 Apr 2019, at 13:39, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 20 Apr 2019, at 23:14, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:


 On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:



 On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>
> Sorry, I don't remember what, if anything, I intended to text.
>
> I'm not expert on how Einstein arrived at his famous field equations.  
> I know that he insisted on them being tensor equations so that they would 
> have the same form in all coordinate systems.  That may sound like a 
> mathematical technicality, but it is really to ensure that the things in 
> the equation, the tensors, could have a physical interpretation.  He also 
> limited himself to second order differentials, probably as a matter of 
> simplicity.  And he excluded torsion, but I don't know why.  And of 
> course 
> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>
> Brent
>

 Here's a link which might help;

  https://arxiv.org/pdf/1608.05752.pdf



 Yes. That is helpful.

 The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>
>>>
>>> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” 
>>> are the coefficients needed to ensure un non-planner (curved) metric, and 
>>> they can be use to define the curvature.
>>>
>>> Bruno 
>>>
>>
>> *Thanks for your time, but I don't think you have a clue what the issues 
>> are here. And, as a alleged expert in logic, it puts your other claims in 
>> jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
>> delta as the leading multiplicative factor in his definition of the Metric 
>> Tensor, which implies all off diagonal terms are zero. And even if that 
>> term were omitted, your reference to Pythagorus leaves much to be desired. 
>> In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
>> Euclidean space where the Pythagorean theorem applies. How does a diagonal 
>> signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
>> elements have anything to do with a departure from flat space under 
>> Lorentz's metric? AG *
>>
>>
>>
>> Oops sorry. Since long I do relativity only in its euclidian form, 
>> through the transformation t' := it. (I being the square root of -1). This 
>> makes Minkowski euclidean again. I should have mentioned this.
>>
>> Bruno
>>
>
>  
> *How does it make Minkowski euclidean if you're not dealing with 
> spacetime. Euclidean and departures from flat require real coordinates. AG*
>

*Using transformation t' --> it  yields a pseudo-Euclidean or 
pseudo-Minkowski space, and can't be used to explain the off-diagonal 
elements of the metric tensor as indicative of lack of Euclidean flatness. 
AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 24, 2019 at 11:06:10 AM UTC-6, Bruno Marchal wrote:
>
>
> On 23 Apr 2019, at 13:39, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 20 Apr 2019, at 23:14, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:

 Sorry, I don't remember what, if anything, I intended to text.

 I'm not expert on how Einstein arrived at his famous field equations.  
 I know that he insisted on them being tensor equations so that they would 
 have the same form in all coordinate systems.  That may sound like a 
 mathematical technicality, but it is really to ensure that the things in 
 the equation, the tensors, could have a physical interpretation.  He also 
 limited himself to second order differentials, probably as a matter of 
 simplicity.  And he excluded torsion, but I don't know why.  And of course 
 he knew it had to reproduce Newtonian gravity in the weak/slow limit.

 Brent

>>>
>>> Here's a link which might help;
>>>
>>>  https://arxiv.org/pdf/1608.05752.pdf
>>>
>>>
>>>
>>> Yes. That is helpful.
>>>
>>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>
>> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are 
>> the coefficients needed to ensure un non-planner (curved) metric, and they 
>> can be use to define the curvature.
>>
>> Bruno 
>>
>
> *Thanks for your time, but I don't think you have a clue what the issues 
> are here. And, as a alleged expert in logic, it puts your other claims in 
> jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
> delta as the leading multiplicative factor in his definition of the Metric 
> Tensor, which implies all off diagonal terms are zero. And even if that 
> term were omitted, your reference to Pythagorus leaves much to be desired. 
> In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
> Euclidean space where the Pythagorean theorem applies. How does a diagonal 
> signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
> elements have anything to do with a departure from flat space under 
> Lorentz's metric? AG *
>
>
>
> Oops sorry. Since long I do relativity only in its euclidian form, through 
> the transformation t' := it. (I being the square root of -1). This makes 
> Minkowski euclidean again. I should have mentioned this.
>
> Bruno
>

 
*How does it make Minkowski euclidean if you're not dealing with spacetime. 
Euclidean and departures from flat require real coordinates. AG*

-- 
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Re: Questions about the Equivalence Principle (EP) and GR

[Bruno Marchal]

> On 23 Apr 2019, at 13:39, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
> 
>> On 20 Apr 2019, at 23:14, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>> 
>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> 
>>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>> Sorry, I don't remember what, if anything, I intended to text.
>>> 
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>> 
>>> Brent
>>> 
>>> Here's a link which might help;
>>> 
>>>  https://arxiv.org/pdf/1608.05752.pdf 
>> 
>> Yes. That is helpful.
>> 
>> The following (long!) video can also help (well, it did help me)
>> 
>> https://www.youtube.com/watch?v=foRPKAKZWx8 
>> 
>> 
>> 
>> Bruno
>> 
>> I've been viewing this video. I don't see how he established that the metric 
>> tensor is a correction for curved spacetime. AG 
> 
> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are the 
> coefficients needed to ensure un non-planner (curved) metric, and they can be 
> use to define the curvature.
> 
> Bruno 
> 
> Thanks for your time, but I don't think you have a clue what the issues are 
> here. And, as a alleged expert in logic, it puts your other claims in 
> jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
> delta as the leading multiplicative factor in his definition of the Metric 
> Tensor, which implies all off diagonal terms are zero. And even if that term 
> were omitted, your reference to Pythagorus leaves much to be desired. In SR 
> we're dealing with a 4 dim space with the Lorentz metric, not a Euclidean 
> space where the Pythagorean theorem applies. How does a diagonal signature of 
> -1,1,1,1 imply flat space? Why would non-zero off diagonal elements have 
> anything to do with a departure from flat space under Lorentz's metric? AG 


Oops sorry. Since long I do relativity only in its euclidian form, through the 
transformation t' := it. (I being the square root of -1). This makes Minkowski 
euclidean again. I should have mentioned this.

Bruno



> 
> 
> 
> 
> 
>> 
>> 
>> 
>>> 
>>> AG
>>> 
>>> On 4/18/2019 7:59 AM, agrays...@gmail.com <> wrote:
 
 
 On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com <> 
 wrote:
 I see no new text in this message. AG
  
 Brent; if you have time, please reproduce the text you intended. 
 
 I recall reading that before Einstein published his GR paper, he used a 
 trial and error method to determine the final field equations (as he raced 
 for the correct ones in competition with Hilbert, who may have arrived at 
 them first).  So it's hard to imagine a mathematical methodology which 
 produces them. If you have any articles that attempt to explain how the 
 field equations are derived, I'd really like to explore this aspect of GR 
 and get some "satisfaction". I can see how he arrived at some principles, 
 such as geodesic motion, by applying the Least Action Principle, or how he 
 might have intuited that matter/energy effects the geometry of spacetime, 
 but from these principles it's baffling how he arrived at the field 
 equations. 
 
 AG
 
 
 On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
 
 
 On 4/17/2019 5:20 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:
> 
> 
> On 4/17/2019 12:36 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/17/2019 7:37 AM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/16/2019 6:14 PM, agrays...@gmail.com <> wrote:
 
 
 On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
 <>wrote:
 
 
 On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
 
 
 On 4/16/2019 11:41 AM, agrays...@gmail.com <> wrote:
> 
> 
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
> 
>

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 23, 2019 at 4:00:26 AM UTC-6, Bruno Marchal wrote:
>
>
> On 20 Apr 2019, at 23:14, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>>
>>> Sorry, I don't remember what, if anything, I intended to text.
>>>
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>>
>>> Brent
>>>
>>
>> Here's a link which might help;
>>
>>  https://arxiv.org/pdf/1608.05752.pdf
>>
>>
>>
>> Yes. That is helpful.
>>
>> The following (long!) video can also help (well, it did help me)
>>
>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>
>>
>> Bruno
>>
>
> *I've been viewing this video. I don't see how he established that the 
> metric tensor is a correction for curved spacetime. AG *
>
>
> ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are 
> the coefficients needed to ensure un non-planner (curved) metric, and they 
> can be use to define the curvature.
>
> Bruno 
>

*Thanks for your time, but I don't think you have a clue what the issues 
are here. And, as a alleged expert in logic, it puts your other claims in 
jeopardy. Firstly, in the video you offered, the presenter has a Kronecker 
delta as the leading multiplicative factor in his definition of the Metric 
Tensor, which implies all off diagonal terms are zero. And even if that 
term were omitted, your reference to Pythagorus leaves much to be desired. 
In SR we're dealing with a 4 dim space with the Lorentz metric, not a 
Euclidean space where the Pythagorean theorem applies. How does a diagonal 
signature of -1,1,1,1 imply flat space? Why would non-zero off diagonal 
elements have anything to do with a departure from flat space under 
Lorentz's metric? AG *

>
>
>
>
>
>
>>
>>
>>
>> AG
>>
>>>
>>> On 4/18/2019 7:59 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
>>> wrote: 

 *I see no new text in this message. AG*

>>>  
>>> Brent; if you have time, please reproduce the text you intended. 
>>>
>>> I recall reading that before Einstein published his GR paper, he used a 
>>> trial and error method to determine the final field equations (as he raced 
>>> for the correct ones in competition with Hilbert, who may have arrived at 
>>> them first).  So it's hard to imagine a mathematical methodology which 
>>> produces them. If you have any articles that attempt to explain how the 
>>> field equations are derived, I'd really like to explore this aspect of GR 
>>> and get some "satisfaction". I can see how he arrived at some principles, 
>>> such as geodesic motion, by applying the Least Action Principle, or how he 
>>> might have intuited that matter/energy effects the geometry of spacetime, 
>>> but from these principles it's baffling how he arrived at the field 
>>> equations. 
>>>
>>> AG
>>>


 On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 



 On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, 
>>> agrays...@gmail.com wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>

Re: Questions about the Equivalence Principle (EP) and GR

[Bruno Marchal]

> On 21 Apr 2019, at 08:07, Philip Thrift  wrote:
> 
> 
> 
> On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com wrote:
> 
> 
> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
> 
>> On 19 Apr 2019, at 04:08, agrays...@gmail.com <> wrote:
>> 
>> 
>> 
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>> Sorry, I don't remember what, if anything, I intended to text.
>> 
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would have 
>> the same form in all coordinate systems.  That may sound like a mathematical 
>> technicality, but it is really to ensure that the things in the equation, 
>> the tensors, could have a physical interpretation.  He also limited himself 
>> to second order differentials, probably as a matter of simplicity.  And he 
>> excluded torsion, but I don't know why.  And of course he knew it had to 
>> reproduce Newtonian gravity in the weak/slow limit.
>> 
>> Brent
>> 
>> Here's a link which might help;
>> 
>>  https://arxiv.org/pdf/1608.05752.pdf 
> 
> Yes. That is helpful.
> 
> The following (long!) video can also help (well, it did help me)
> 
> https://www.youtube.com/watch?v=foRPKAKZWx8 
> 
> 
> 
> Bruno
> 
> I've been viewing this video. I don't see how he established that the metric 
> tensor is a correction for curved spacetime. AG 
> 
> 
> 
> 
> The physicists' vocabulary can be baffling (at least it is to me).
> 
> I think the basic thing though is that the Einstein Field Equations (EFE) is 
> not - in a sense - absolute. EFE is relative.
> 
> Once one has established a coordinate system/metric (c-sys1) for "the world" 
> independently, then EFE(c-sys1) provides a recipe for making predictions 
> within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) calculates 
> predictions in c-sys2.
> 
> There is no absolute c-sys for "the world”.

Right. 

Like there is no absolute universal machine for the mindscape, including the 
world. Physics is not just coordinate independent, it is observer independent, 
and even more deeply (with mechanism) universal machine independent. That’s why 
we can use arithmetic, or combinator, or any Turing complete theory, any 
“phi_i”,  for the ontology for the “theory of everything”. 

Bruno



> 
> - pt
> 
> 
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everything-list+unsubscr...@googlegroups.com 
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Re: Questions about the Equivalence Principle (EP) and GR

[Bruno Marchal]

> On 20 Apr 2019, at 23:14, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
> 
>> On 19 Apr 2019, at 04:08, agrays...@gmail.com  wrote:
>> 
>> 
>> 
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>> Sorry, I don't remember what, if anything, I intended to text.
>> 
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would have 
>> the same form in all coordinate systems.  That may sound like a mathematical 
>> technicality, but it is really to ensure that the things in the equation, 
>> the tensors, could have a physical interpretation.  He also limited himself 
>> to second order differentials, probably as a matter of simplicity.  And he 
>> excluded torsion, but I don't know why.  And of course he knew it had to 
>> reproduce Newtonian gravity in the weak/slow limit.
>> 
>> Brent
>> 
>> Here's a link which might help;
>> 
>>  https://arxiv.org/pdf/1608.05752.pdf 
> 
> Yes. That is helpful.
> 
> The following (long!) video can also help (well, it did help me)
> 
> https://www.youtube.com/watch?v=foRPKAKZWx8 
> 
> 
> 
> Bruno
> 
> I've been viewing this video. I don't see how he established that the metric 
> tensor is a correction for curved spacetime. AG 

ds^2 = dx^2 + dy^2 is Pythagorus theorem, in the plane. The “g_mu,nu” are the 
coefficients needed to ensure un non-planner (curved) metric, and they can be 
use to define the curvature.

Bruno 





> 
> 
> 
>> 
>> AG
>> 
>> On 4/18/2019 7:59 AM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com <> 
>>> wrote:
>>> I see no new text in this message. AG
>>>  
>>> Brent; if you have time, please reproduce the text you intended. 
>>> 
>>> I recall reading that before Einstein published his GR paper, he used a 
>>> trial and error method to determine the final field equations (as he raced 
>>> for the correct ones in competition with Hilbert, who may have arrived at 
>>> them first).  So it's hard to imagine a mathematical methodology which 
>>> produces them. If you have any articles that attempt to explain how the 
>>> field equations are derived, I'd really like to explore this aspect of GR 
>>> and get some "satisfaction". I can see how he arrived at some principles, 
>>> such as geodesic motion, by applying the Least Action Principle, or how he 
>>> might have intuited that matter/energy effects the geometry of spacetime, 
>>> but from these principles it's baffling how he arrived at the field 
>>> equations. 
>>> 
>>> AG
>>> 
>>> 
>>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/17/2019 5:20 PM, agrays...@gmail.com <> wrote:
 
 
 On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:
 
 
 On 4/17/2019 12:36 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:
> 
> 
> On 4/17/2019 7:37 AM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/16/2019 6:14 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com <> 
>>> wrote:
>>> 
>>> 
>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com <> wrote:
 
 
 On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
 
 
 On 4/15/2019 7:14 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com <> 
> wrote:
> 
> 
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
> 
> 
> On 4/11/2019 9:33 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/11/2019 4:53 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com <> wrote:
> 
> 
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative 
> at that point in spacetime is zero. Does this make any sense?
 
 Sort of. 
 
 
 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So 
 spacetime has a non zero curvature an

Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Sunday, April 21, 2019 at 6:59:25 PM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Sunday, April 21, 2019 at 5:54:33 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/21/2019 2:20 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/20/2019 2:14 PM, agrays...@gmail.com wrote:
>>>
>>> The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>
>>>
>>> The metric tensor is the quantified embodiment of curved spacetime.  But 
>>> How else would you define curvature, if not with the metric?
>>>
>>> Brent
>>>
>>
>> *At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
>> leading term. So all cross terms will be zero in its matrix representation. 
>> *
>>
>>
>> But then he says that in a curved space g_mn must be something else, that 
>> does have cross terms.   I don't find his presentation very enlightening.  
>> He ends up wit ds^2 = g_m_n dx^r dx^sHe doesn't even have the indices 
>> match as in Einstein's summation forumula.
>>
>> Bren
>>
>
> Thanks. I'm going on to Susskind's lectures on GR.  AG
>
>>
>> *Listen; this is pure mathematics. If what he calls the metric tensor is 
>> the general correction for curved spacetime, it can be proven 
>> mathematically, strictly by mathematics. What I see is a hand-waving 
>> argument at best! Ball in your court. AG *
>> -- 
>>
>>
>>
Theoretical physics is all hand-waving in a sense: One can take speaker X's 
formulation of GR in one vocabulary and speaker Y's formulation of GR in 
another vocabulary. and one is as good as the other it they produce the 
same predictions. 

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 8:07:28 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 6:31 PM, agrays...@gmail.com  wrote:
>
> *Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
> metric tensor is a Kronecker delta function. But I could swear that the 
> diagonal of -1,1,1,1 represents flat space in SR. AG *
>
>
> What's odd about that?  Flat space is just special case of curved space in 
> which the curvature is zero.
>
> Brent
>

*Sure, but he seems to be saying that the Kronecker delta is the metric 
tensor for curved space. Isn't that how you interpret his comment? AG *

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/21/2019 6:31 PM, agrayson2...@gmail.com wrote:
*Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says 
the metric tensor is a Kronecker delta function. But I could swear 
that the diagonal of -1,1,1,1 represents flat space in SR. AG *


What's odd about that?  Flat space is just special case of curved space 
in which the curvature is zero.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 5:59:25 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Sunday, April 21, 2019 at 5:54:33 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/21/2019 2:20 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/20/2019 2:14 PM, agrays...@gmail.com wrote:
>>>
>>> The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>
>>>
>>> The metric tensor is the quantified embodiment of curved spacetime.  But 
>>> How else would you define curvature, if not with the metric?
>>>
>>> Brent
>>>
>>
>> *At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
>> leading term. So all cross terms will be zero in its matrix representation. 
>> *
>>
>>
>> But then he says that in a curved space g_mn must be something else, that 
>> does have cross terms.   I don't find his presentation very enlightening.  
>> He ends up wit ds^2 = g_m_n dx^r dx^sHe doesn't even have the indices 
>> match as in Einstein's summation forumula.
>>
>> Brent
>>
>
> Thanks. I'm going on to Susskind's lectures on GR.  AG
>

*Here's something odd. At 9:45 in Susskind's Lecture 2 on GR, he says the 
metric tensor is a Kronecker delta function. But I could swear that the 
diagonal of -1,1,1,1 represents flat space in SR. AG *

>
>> *Listen; this is pure mathematics. If what he calls the metric tensor is 
>> the general correction for curved spacetime, it can be proven 
>> mathematically, strictly by mathematics. What I see is a hand-waving 
>> argument at best! Ball in your court. AG *
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
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>> email to everyth...@googlegroups.com.
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>>
>>
>>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 5:54:33 PM UTC-6, Brent wrote:
>
>
>
> On 4/21/2019 2:20 AM, agrays...@gmail.com  wrote:
>
>
>
> On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/20/2019 2:14 PM, agrays...@gmail.com wrote:
>>
>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>
>> The metric tensor is the quantified embodiment of curved spacetime.  But 
>> How else would you define curvature, if not with the metric?
>>
>> Brent
>>
>
> *At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
> leading term. So all cross terms will be zero in its matrix representation. 
> *
>
>
> But then he says that in a curved space g_mn must be something else, that 
> does have cross terms.   I don't find his presentation very enlightening.  
> He ends up wit ds^2 = g_m_n dx^r dx^sHe doesn't even have the indices 
> match as in Einstein's summation forumula.
>
> Bren
>

Thanks. I'm going on to Susskind's lectures on GR.  AG

>
> *Listen; this is pure mathematics. If what he calls the metric tensor is 
> the general correction for curved spacetime, it can be proven 
> mathematically, strictly by mathematics. What I see is a hand-waving 
> argument at best! Ball in your court. AG *
> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everyth...@googlegroups.com .
> To post to this group, send email to everyth...@googlegroups.com 
> .
> Visit this group at https://groups.google.com/group/everything-list.
> For more options, visit https://groups.google.com/d/optout.
>
>
>

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/21/2019 2:20 AM, agrayson2...@gmail.com wrote:



On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote:



On 4/20/2019 2:14 PM, agrays...@gmail.com  wrote:


The following (long!) video can also help (well, it did help me)

https://www.youtube.com/watch?v=foRPKAKZWx8



Bruno


*I've been viewing this video. I don't see how he established
that the metric tensor is a correction for curved spacetime. AG *


The metric tensor is the quantified embodiment of curved
spacetime.  But How else would you define curvature, if not with
the metric?

Brent


*At 49:42 he defines the metric tensor. It has a Kronecker delta as 
the leading term. So all cross terms will be zero in its matrix 
representation. *


But then he says that in a curved space g_mn must be something else, 
that does have cross terms.   I don't find his presentation very 
enlightening.  He ends up wit ds^2 = g_m_n dx^r dx^s    He doesn't even 
have the indices match as in Einstein's summation forumula.


Bren

*Listen; this is pure mathematics. If what he calls the metric tensor 
is the general correction for curved spacetime, it can be proven 
mathematically, strictly by mathematics. What I see is a hand-waving 
argument at best! Ball in your court. AG *

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.
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.

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Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Sunday, April 21, 2019 at 5:23:33 AM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Sunday, April 21, 2019 at 12:07:07 AM UTC-6, Philip Thrift wrote:
>>
>>
>>
>> On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com 
>> wrote:
>>>
>>>
>>>
>>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:


 On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:



 On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>
> Sorry, I don't remember what, if anything, I intended to text.
>
> I'm not expert on how Einstein arrived at his famous field equations.  
> I know that he insisted on them being tensor equations so that they would 
> have the same form in all coordinate systems.  That may sound like a 
> mathematical technicality, but it is really to ensure that the things in 
> the equation, the tensors, could have a physical interpretation.  He also 
> limited himself to second order differentials, probably as a matter of 
> simplicity.  And he excluded torsion, but I don't know why.  And of 
> course 
> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>
> Brent
>

 Here's a link which might help;

  https://arxiv.org/pdf/1608.05752.pdf



 Yes. That is helpful.

 The following (long!) video can also help (well, it did help me)

 https://www.youtube.com/watch?v=foRPKAKZWx8


 Bruno

>>>
>>> *I've been viewing this video. I don't see how he established that the 
>>> metric tensor is a correction for curved spacetime. AG *
>>>


>>
>>
>> The physicists' vocabulary can be baffling (at least it is to me).
>>
>> I think the basic thing though is that the Einstein Field Equations (EFE) 
>> is not - in a sense - absolute. EFE is relative.
>>
>> Once one has established a coordinate system/metric (c-sys1) for "the 
>> world" independently, then EFE(c-sys1) provides a recipe for making 
>> predictions within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) 
>> calculates predictions in c-sys2.
>>
>> There is no absolute c-sys for "the world".
>>
>> - pt
>>
>
> I don't follow your argument. GR satisfies the Principle of General 
> Covariance since it's written in tensor form, and tensors transform 
> covariantly. Whether the video shows what is alleged as the metric tensor 
> is truly a representation of departure from flatness is an entirely 
> different matter, as I explained to Brent. AG 
>


I think that the first thing is that there is no such thing as an a priori 
"flat" geometry. 

We take certain phenomenon - like the path a light beam takes when there is 
no mass around - and then define that is what a "straight line" is. There 
is no a priori thing that is a "straight line". From that a "flat" 
coordinate system is defined.

And then EFE takes it from there. It provides a recipe for how light beam 
paths change when matter is nearby.

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Sunday, April 21, 2019 at 12:07:07 AM UTC-6, Philip Thrift wrote:
>
>
>
> On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:

 Sorry, I don't remember what, if anything, I intended to text.

 I'm not expert on how Einstein arrived at his famous field equations.  
 I know that he insisted on them being tensor equations so that they would 
 have the same form in all coordinate systems.  That may sound like a 
 mathematical technicality, but it is really to ensure that the things in 
 the equation, the tensors, could have a physical interpretation.  He also 
 limited himself to second order differentials, probably as a matter of 
 simplicity.  And he excluded torsion, but I don't know why.  And of course 
 he knew it had to reproduce Newtonian gravity in the weak/slow limit.

 Brent

>>>
>>> Here's a link which might help;
>>>
>>>  https://arxiv.org/pdf/1608.05752.pdf
>>>
>>>
>>>
>>> Yes. That is helpful.
>>>
>>> The following (long!) video can also help (well, it did help me)
>>>
>>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>>
>>>
>>> Bruno
>>>
>>
>> *I've been viewing this video. I don't see how he established that the 
>> metric tensor is a correction for curved spacetime. AG *
>>
>>>
>>>
>
>
> The physicists' vocabulary can be baffling (at least it is to me).
>
> I think the basic thing though is that the Einstein Field Equations (EFE) 
> is not - in a sense - absolute. EFE is relative.
>
> Once one has established a coordinate system/metric (c-sys1) for "the 
> world" independently, then EFE(c-sys1) provides a recipe for making 
> predictions within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) 
> calculates predictions in c-sys2.
>
> There is no absolute c-sys for "the world".
>
> - pt
>

I don't follow your argument. GR satisfies the Principle of General 
Covariance since it's written in tensor form, and tensors transform 
covariantly. Whether the video shows what is alleged as the metric tensor 
is truly a representation of departure from flatness is an entirely 
different matter, as I explained to Brent. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, April 20, 2019 at 9:51:13 PM UTC-6, Brent wrote:
>
>
>
> On 4/20/2019 2:14 PM, agrays...@gmail.com  wrote:
>
> The following (long!) video can also help (well, it did help me)
>>
>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>
>>
>> Bruno
>>
>
> *I've been viewing this video. I don't see how he established that the 
> metric tensor is a correction for curved spacetime. AG *
>
>
> The metric tensor is the quantified embodiment of curved spacetime.  How 
> else would you define curvature, if not with the metric?
>
> Brent
>

*At 49:42 he defines the metric tensor. It has a Kronecker delta as the 
leading term. So all cross terms will be zero in its matrix representation. 
Listen; this is pure mathematics. If what he calls the metric tensor is the 
general correction for curved spacetime, it can be proven mathematically, 
strictly by mathematics. What I see is a hand-waving argument at best! Ball 
in your court. AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Saturday, April 20, 2019 at 4:14:27 PM UTC-5, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 19 Apr 2019, at 04:08, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>>
>>> Sorry, I don't remember what, if anything, I intended to text.
>>>
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>>
>>> Brent
>>>
>>
>> Here's a link which might help;
>>
>>  https://arxiv.org/pdf/1608.05752.pdf
>>
>>
>>
>> Yes. That is helpful.
>>
>> The following (long!) video can also help (well, it did help me)
>>
>> https://www.youtube.com/watch?v=foRPKAKZWx8
>>
>>
>> Bruno
>>
>
> *I've been viewing this video. I don't see how he established that the 
> metric tensor is a correction for curved spacetime. AG *
>
>>
>>


The physicists' vocabulary can be baffling (at least it is to me).

I think the basic thing though is that the Einstein Field Equations (EFE) 
is not - in a sense - absolute. EFE is relative.

Once one has established a coordinate system/metric (c-sys1) for "the 
world" independently, then EFE(c-sys1) provides a recipe for making 
predictions within c-sys1. Change c-sys1 to c-sys2, and EFE(c-sys2) 
calculates predictions in c-sys2.

There is no absolute c-sys for "the world".

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/20/2019 2:14 PM, agrayson2...@gmail.com wrote:


The following (long!) video can also help (well, it did help me)

https://www.youtube.com/watch?v=foRPKAKZWx8



Bruno


*I've been viewing this video. I don't see how he established that the 
metric tensor is a correction for curved spacetime. AG *


The metric tensor is the quantified embodiment of curved spacetime. How 
else would you define curvature, if not with the metric?


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, April 19, 2019 at 2:53:00 AM UTC-6, Bruno Marchal wrote:
>
>
> On 19 Apr 2019, at 04:08, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>
>> Sorry, I don't remember what, if anything, I intended to text.
>>
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would 
>> have the same form in all coordinate systems.  That may sound like a 
>> mathematical technicality, but it is really to ensure that the things in 
>> the equation, the tensors, could have a physical interpretation.  He also 
>> limited himself to second order differentials, probably as a matter of 
>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>
>> Brent
>>
>
> Here's a link which might help;
>
>  https://arxiv.org/pdf/1608.05752.pdf
>
>
>
> Yes. That is helpful.
>
> The following (long!) video can also help (well, it did help me)
>
> https://www.youtube.com/watch?v=foRPKAKZWx8
>
>
> Bruno
>

*I've been viewing this video. I don't see how he established that the 
metric tensor is a correction for curved spacetime. AG *

>
>
>
>
> AG
>
>>
>> On 4/18/2019 7:59 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>> *I see no new text in this message. AG*
>>>
>>  
>> Brent; if you have time, please reproduce the text you intended. 
>>
>> I recall reading that before Einstein published his GR paper, he used a 
>> trial and error method to determine the final field equations (as he raced 
>> for the correct ones in competition with Hilbert, who may have arrived at 
>> them first).  So it's hard to imagine a mathematical methodology which 
>> produces them. If you have any articles that attempt to explain how the 
>> field equations are derived, I'd really like to explore this aspect of GR 
>> and get some "satisfaction". I can see how he arrived at some principles, 
>> such as geodesic motion, by applying the Least Action Principle, or how he 
>> might have intuited that matter/energy effects the geometry of spacetime, 
>> but from these principles it's baffling how he arrived at the field 
>> equations. 
>>
>> AG
>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 



 On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:



 On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>
>
>
> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, 
>> agrays...@gmail.com wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a 
>>> tangent space where the metric tensor is diagonalized and its 
>>> derivative at 
>>> that point in spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given 
>> coordinate system and some arbitrary point in a non-empty 
>> spacetime. So 
>> spacetime has a non zero curvature and the derivative of the 
>> metric tensor 
>> is generally

Re: Questions about the Equivalence Principle (EP) and GR

[Bruno Marchal]

> On 19 Apr 2019, at 04:08, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
> Sorry, I don't remember what, if anything, I intended to text.
> 
> I'm not expert on how Einstein arrived at his famous field equations.  I know 
> that he insisted on them being tensor equations so that they would have the 
> same form in all coordinate systems.  That may sound like a mathematical 
> technicality, but it is really to ensure that the things in the equation, the 
> tensors, could have a physical interpretation.  He also limited himself to 
> second order differentials, probably as a matter of simplicity.  And he 
> excluded torsion, but I don't know why.  And of course he knew it had to 
> reproduce Newtonian gravity in the weak/slow limit.
> 
> Brent
> 
> Here's a link which might help;
> 
>  https://arxiv.org/pdf/1608.05752.pdf 

Yes. That is helpful.

The following (long!) video can also help (well, it did help me)

https://www.youtube.com/watch?v=foRPKAKZWx8 



Bruno



> 
> AG
> 
> On 4/18/2019 7:59 AM, agrays...@gmail.com  wrote:
>> 
>> 
>> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com <> 
>> wrote:
>> I see no new text in this message. AG
>>  
>> Brent; if you have time, please reproduce the text you intended. 
>> 
>> I recall reading that before Einstein published his GR paper, he used a 
>> trial and error method to determine the final field equations (as he raced 
>> for the correct ones in competition with Hilbert, who may have arrived at 
>> them first).  So it's hard to imagine a mathematical methodology which 
>> produces them. If you have any articles that attempt to explain how the 
>> field equations are derived, I'd really like to explore this aspect of GR 
>> and get some "satisfaction". I can see how he arrived at some principles, 
>> such as geodesic motion, by applying the Least Action Principle, or how he 
>> might have intuited that matter/energy effects the geometry of spacetime, 
>> but from these principles it's baffling how he arrived at the field 
>> equations. 
>> 
>> AG
>> 
>> 
>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/17/2019 5:20 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/17/2019 12:36 PM, agrays...@gmail.com <> wrote:
 
 
 On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:
 
 
 On 4/17/2019 7:37 AM, agrays...@gmail.com <> wrote:
> 
> 
> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
> 
> 
> On 4/16/2019 6:14 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com <> 
>> wrote:
>> 
>> 
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/16/2019 11:41 AM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com <> wrote:
 
 
 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 <>wrote:
 
 
 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
 
 
 On 4/11/2019 9:33 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:
> 
> 
> On 4/11/2019 4:53 PM, agrays...@gmail.com <> wrote:
>> 
>> 
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/11/2019 1:58 PM, agrays...@gmail.com <> wrote:
 
 
 He might have been referring to a transformation to a tangent 
 space where the metric tensor is diagonalized and its derivative 
 at that point in spacetime is zero. Does this make any sense?
>>> 
>>> Sort of. 
>>> 
>>> 
>>> Yeah, that's what he's doing. He's assuming a given coordinate 
>>> system and some arbitrary point in a non-empty spacetime. So 
>>> spacetime has a non zero curvature and the derivative of the metric 
>>> tensor is generally non-zero at that arbitrary point, however small 
>>> we assume the region around that point. But applying the EEP, we 
>>> can transform to the tangent space at that point to diagonalize 
>>>   the metric 
>>> tensor and have its derivative as zero at that point. Does THIS 
>>> make sense? AG
>> 
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>> 
>> Brent
>> 
>> But i

Re: Questions about the Equivalence Principle (EP) and GR

[Russell Standish]

On Thu, Apr 18, 2019 at 09:13:34PM -0700, agrayson2...@gmail.com wrote:
> 
> 
> On Thursday, April 18, 2019 at 9:20:36 PM UTC-6, agrays...@gmail.com wrote:
> 
> 
> 
> On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com 
> wrote:
> 
> 
> 
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
> 
> Sorry, I don't remember what, if anything, I intended to text.
> 
> I'm not expert on how Einstein arrived at his famous field
> equations.  I know that he insisted on them being tensor equations
> so that they would have the same form in all coordinate systems. 
> That may sound like a mathematical technicality, but it is really
> to ensure that the things in the equation, the tensors, could have
> a physical interpretation.  He also limited himself to second 
> order
> differentials, probably as a matter of simplicity.  And he 
> excluded
> torsion, but I don't know why.  And of course he knew it had to
> reproduce Newtonian gravity in the weak/slow limit.
> 
> Brent
> 
> 
> Here's a link which might help;
> 
>  https://arxiv.org/pdf/1608.05752.pdf
> 
> AG
> 
> 
> I'm coming to the view that what I have been seeking these many years -
> namely, a mathematical derivation of Einstein's field equations, somewhat
> like a mathematical theorem -- doesn't exist. It's more a case of a set of
> highly subtle physical intuitions about how the universe functions, which,
> when cobbled together, result in the field equations. For this reason, 
> most
> alleged explanations of GR involve, at some point, essentially pulling the
> field equations out of the proverbial hat.  As with the Principle of
> Relativity and the Least Action Principle, the latter say applied to
> asserting geodesic motion for freely falling bodies, they're not provable
> as "true", but assuming them "false" would be a dead-end for physics and
> would, as well, make our lives miserable. AG
> 
> 
> One possible exception to the above is the Einstein-Hilbert Principle of Least
> Action, from which, it is alleges, Einstein's field equations can be derived.
> 
>  https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action
> 
> But what it is, and how it would work, is above my pay grade. Maybe someone
> here can shed some light on this topic. 
> 
> AG

Roy Frieden has a derivation of Einstein's field equations from his
Fisher information principle - sorry its above my pay grade too, so
don't ask me to explain, but it could be related to you Hilbert action
derivation.


@Book{Frieden98,
  author =   {B. Roy Frieden},
  title ={Physics from Fisher Information: a unification},
  publisher ={Cambridge UP},
  year = 1998,
  address =  {Cambridge}
}

-- 


Dr Russell StandishPhone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Senior Research Fellowhpco...@hpcoders.com.au
Economics, Kingston University http://www.hpcoders.com.au


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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/18/2019 8:20 PM, agrayson2...@gmail.com wrote:



On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com 
wrote:




On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:

Sorry, I don't remember what, if anything, I intended to text.

I'm not expert on how Einstein arrived at his famous field
equations.  I know that he insisted on them being tensor
equations so that they would have the same form in all
coordinate systems.  That may sound like a mathematical
technicality, but it is really to ensure that the things in
the equation, the tensors, could have a physical
interpretation.  He also limited himself to second order
differentials, probably as a matter of simplicity.  And he
excluded torsion, but I don't know why.  And of course he knew
it had to reproduce Newtonian gravity in the weak/slow limit.

Brent


Here's a link which might help;

https://arxiv.org/pdf/1608.05752.pdf


AG


I'm coming to the view that what I have been seeking these many years 
- namely, a mathematical derivation of Einstein's field equations, 
somewhat like a mathematical theorem -- doesn't exist. It's more a 
case of a set of highly subtle physical intuitions about how the 
universe functions, which, when cobbled together, result in the field 
equations. For this reason, most alleged explanations of GR involve, 
at some point, essentially pulling the field equations out of the 
proverbial hat.  As with the Principle of Relativity and the Least 
Action Principle, the latter say applied to asserting geodesic motion 
for freely falling bodies, they're not provable as "true", but 
assuming them "false" would be a dead-end for physics and would, as 
well, make our lives miserable. AG


As in all science, the proof of the pudding is in the eating.

Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 9:20:36 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com 
> wrote:
>>
>>
>>
>> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>>
>>> Sorry, I don't remember what, if anything, I intended to text.
>>>
>>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>>> know that he insisted on them being tensor equations so that they would 
>>> have the same form in all coordinate systems.  That may sound like a 
>>> mathematical technicality, but it is really to ensure that the things in 
>>> the equation, the tensors, could have a physical interpretation.  He also 
>>> limited himself to second order differentials, probably as a matter of 
>>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>>
>>> Brent
>>>
>>
>> Here's a link which might help;
>>
>>  https://arxiv.org/pdf/1608.05752.pdf
>>
>> AG
>>
>
> I'm coming to the view that what I have been seeking these many years - 
> namely, a mathematical derivation of Einstein's field equations, somewhat 
> like a mathematical theorem -- doesn't exist. It's more a case of a set of 
> highly subtle physical intuitions about how the universe functions, which, 
> when cobbled together, result in the field equations. For this reason, most 
> alleged explanations of GR involve, at some point, essentially pulling the 
> field equations out of the proverbial hat.  As with the Principle of 
> Relativity and the Least Action Principle, the latter say applied to 
> asserting geodesic motion for freely falling bodies, they're not provable 
> as "true", but assuming them "false" would be a dead-end for physics and 
> would, as well, make our lives miserable. AG
>

One possible exception to the above is the Einstein-Hilbert Principle of 
Least Action, from which, it is alleges, Einstein's field equations can be 
derived.

 https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action

But what it is, and how it would work, is above my pay grade. Maybe someone 
here can shed some light on this topic. 

AG

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

Very interesting.  Thanks.

Brent

On 4/18/2019 7:08 PM, agrayson2...@gmail.com wrote:

Here's a link which might help;

https://arxiv.org/pdf/1608.05752.pdf

AG


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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 8:08:58 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>>
>> Sorry, I don't remember what, if anything, I intended to text.
>>
>> I'm not expert on how Einstein arrived at his famous field equations.  I 
>> know that he insisted on them being tensor equations so that they would 
>> have the same form in all coordinate systems.  That may sound like a 
>> mathematical technicality, but it is really to ensure that the things in 
>> the equation, the tensors, could have a physical interpretation.  He also 
>> limited himself to second order differentials, probably as a matter of 
>> simplicity.  And he excluded torsion, but I don't know why.  And of course 
>> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>>
>> Brent
>>
>
> Here's a link which might help;
>
>  https://arxiv.org/pdf/1608.05752.pdf
>
> AG
>

I'm coming to the view that what I have been seeking these many years - 
namely, a mathematical derivation of Einstein's field equations, somewhat 
like a mathematical theorem -- doesn't exist. It's more a case of a set of 
highly subtle physical intuitions about how the universe functions, which, 
when cobbled together, result in the field equations. For this reason, most 
alleged explanations of GR involve, at some point, essentially pulling the 
field equations out of the proverbial hat.  As with the Principle of 
Relativity and the Least Action Principle, the latter say applied to 
asserting geodesic motion for freely falling bodies, they're not provable 
as "true", but assuming them "false" would be a dead-end for physics and 
would, as well, make our lives miserable. AG

-- 
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 18, 2019 at 6:53:33 PM UTC-6, Brent wrote:
>
> Sorry, I don't remember what, if anything, I intended to text.
>
> I'm not expert on how Einstein arrived at his famous field equations.  I 
> know that he insisted on them being tensor equations so that they would 
> have the same form in all coordinate systems.  That may sound like a 
> mathematical technicality, but it is really to ensure that the things in 
> the equation, the tensors, could have a physical interpretation.  He also 
> limited himself to second order differentials, probably as a matter of 
> simplicity.  And he excluded torsion, but I don't know why.  And of course 
> he knew it had to reproduce Newtonian gravity in the weak/slow limit.
>
> Brent
>

Here's a link which might help;

 https://arxiv.org/pdf/1608.05752.pdf

AG

>
> On 4/18/2019 7:59 AM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>> *I see no new text in this message. AG*
>>
>  
> Brent; if you have time, please reproduce the text you intended. 
>
> I recall reading that before Einstein published his GR paper, he used a 
> trial and error method to determine the final field equations (as he raced 
> for the correct ones in competition with Hilbert, who may have arrived at 
> them first).  So it's hard to imagine a mathematical methodology which 
> produces them. If you have any articles that attempt to explain how the 
> field equations are derived, I'd really like to explore this aspect of GR 
> and get some "satisfaction". I can see how he arrived at some principles, 
> such as geodesic motion, by applying the Least Action Principle, or how he 
> might have intuited that matter/energy effects the geometry of spacetime, 
> but from these principles it's baffling how he arrived at the field 
> equations. 
>
> AG
>
>>
>>
>> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 



 On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:



 On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>
>
>
> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 



 On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



 On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent 
>> space where the metric tensor is diagonalized and its derivative 
>> at that 
>> point in spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate 
> system and some arbitrary point in a non-empty spacetime. So 
> spacetime has 
> a non zero curvature and the derivative of the metric tensor is 
> generally 
> non-zero at that arbitrary point, however small we assume the 
> region around 
> that point. But applying the EEP, we can transform to the tangent 
> space at 
> that point to diagonalize the metric tensor and have its 
> derivative as zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a 
> Riemannian space.
>
> Brent
>

 But isn't it weird 

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

Sorry, I don't remember what, if anything, I intended to text.

I'm not expert on how Einstein arrived at his famous field equations.  I 
know that he insisted on them being tensor equations so that they would 
have the same form in all coordinate systems. That may sound like a 
mathematical technicality, but it is really to ensure that the things in 
the equation, the tensors, could have a physical interpretation.  He 
also limited himself to second order differentials, probably as a matter 
of simplicity.  And he excluded torsion, but I don't know why.  And of 
course he knew it had to reproduce Newtonian gravity in the weak/slow limit.


Brent

On 4/18/2019 7:59 AM, agrayson2...@gmail.com wrote:



On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com 
wrote:


*I see no new text in this message. AG*

Brent; if you have time, please reproduce the text you intended.

I recall reading that before Einstein published his GR paper, he used 
a trial and error method to determine the final field equations (as he 
raced for the correct ones in competition with Hilbert, who may have 
arrived at them first).  So it's hard to imagine a mathematical 
methodology which produces them. If you have any articles that attempt 
to explain how the field equations are derived, I'd really like to 
explore this aspect of GR and get some "satisfaction". I can see how 
he arrived at some principles, such as geodesic motion, by applying 
the Least Action Principle, or how he might have intuited that 
matter/energy effects the geometry of spacetime, but from these 
principles it's baffling how he arrived at the field equations.


AG



On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:



On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:



On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:



On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:



On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent
wrote:



On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6,
Brent wrote:



On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:39:11 PM
UTC-6, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:10:16 PM
UTC-6, Brent wrote:



On 4/16/2019 11:41 AM,
agrays...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59
PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM,
agrays...@gmail.com wrote:



On Friday, April 12, 2019 at
5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019
at 10:56:08 PM UTC-6, Brent
wrote:



On 4/11/2019 9:33 PM,
agrays...@gmail.com wrote:



On Thursday, April 11,
2019 at 7:12:17 PM
UTC-6, Brent wrote:



On 4/11/2019 4:53
PM,
agrays...@gmail.com
wrote:



On Thursday, April
11, 2019 at
4:37:39 PM UTC-6,
Brent wrote:



On 4/11/2019
1:58 PM,
agrays...@gmail.com
wrote:





He might
have
been
referring
to a
transformation
to a
tangent
space
where
the
metric
tensor
  

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 7:16:45 PM UTC-6, agrays...@gmail.com wrote:
>
> *I see no new text in this message. AG*
>
 
Brent; if you have time, please reproduce the text you intended. 

I recall reading that before Einstein published his GR paper, he used a 
trial and error method to determine the final field equations (as he raced 
for the correct ones in competition with Hilbert, who may have arrived at 
them first).  So it's hard to imagine a mathematical methodology which 
produces them. If you have any articles that attempt to explain how the 
field equations are derived, I'd really like to explore this aspect of GR 
and get some "satisfaction". I can see how he arrived at some principles, 
such as geodesic motion, by applying the Least Action Principle, or how he 
might have intuited that matter/energy effects the geometry of spacetime, 
but from these principles it's baffling how he arrived at the field 
equations. 

AG

>
>
> On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/17/2019 5:20 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 



 On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative 
> at that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So 
 spacetime has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the 
 region around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its 
 derivative as zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test 
>>> particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces 
>>> on it, it will deviate from the geodesic in the tangent space 
>>> coordinates.  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting 
>> on test particle, I assume the trajectory appears identical to an 
>> external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime 
>> points. If 
>> this is true, it's sti

Re: Questions about the Equivalence Principle (EP) and GR

[Bruno Marchal]

> On 17 Apr 2019, at 01:41, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 4/16/2019 7:56 AM, agrayson2...@gmail.com  
> wrote:
>> 
>> 
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>> 
>> 
>> On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:
>>> 
>>> 
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>>> 
>>> 
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com <> wrote:
 
 
 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:
 
 
 On 4/11/2019 4:53 PM, agrays...@gmail.com <> wrote:
> 
> 
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:
> 
> 
> On 4/11/2019 1:58 PM, agrays...@gmail.com <> wrote:
>>> 
>>> 
>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that 
>>> point in spacetime is zero. Does this make any sense?
>> 
>> Sort of. 
>> 
>> 
>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>> and some arbitrary point in a non-empty spacetime. So spacetime has a 
>> non zero curvature and the derivative of the metric tensor is generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around that point. But applying the EEP, we can  
>>transform to the tangent space at that point to 
>> diagonalize the metric tensor and have its derivative as zero at that 
>> point. Does THIS make sense? AG
> 
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
> 
> Brent
> 
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
> 
 It doesn't put it in free-fall.  If the particle has EM forces on it, it 
 will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.
 
 Brent
 
 In both cases, with and without non-gravitational forces acting on test 
 particle, I assume the trajectory appears identical to an external 
 observer, before and after coordinate transformation to the tangent plane 
 at some point; all that's changed are the labels of spacetime points. If 
 this is true, it's still hard to see why changing labels can remove the 
 gravitational forces. And what does this buy us? AG
>>> 
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces. 
>>> 
>>> If gravity is a fictitious force produced by the choice of coordinate 
>>> system, in its absence (due to a change in coordinate system) how does GR 
>>> explain motion? Test particles move on geodesics in the absence of 
>>> non-gravitational forces, but why do they move at all? AG
>>> 
>>> Maybe GR assumes motion but doesn't explain it. AG 
>> 
>> The sciences do not try to explain, they hardly even try to  interpret, they 
>> mainly make models. By a model is meant a  mathematical construct which, 
>> with the addition of certain verbal  interpretations, describes observed 
>> phenomena. The justification of  such a mathematical construct is solely and 
>> precisely that it is  expected to work.
>> --—John von Neumann
>> 
>> This is straight out of the "shut up and calculate" school, and I don't 
>> completely buy it. E.g., the Principle of Relativity and Least Action 
>> Principle give strong indications of not only how the universe works, but 
>> why. That is, they're somewhat explanatory in nature. AG
> 
> Fine, then take them as explanations.  But to ask that they be explained is 
> to misunderstand their status.  It's possible that they could be explained; 
> but only by finding a more fundamental theory that includes them as 
> consequences or special cases.  Whatever theory is fundamental cannot have an 
> explanation in the sense you want because then it would not be fundamental.

Indeed. 

And with Mechanism, any Turing-complete theory can be chosen as fundamental, 
because we can’t explain them from less (provably so).

Then, physics becomes a sum on all histories, and the least action principle 
should be derivable from its quantum structure imposed by incompleteness on 
observation (defined by some variant of []p & p).

We cannot explained what we are starting from.

Bruno


> 
> Brent
> 
> -- 
> You received this message because you are subscribed to the G

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

*I see no new text in this message. AG*

On Wednesday, April 17, 2019 at 7:00:55 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 5:20 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 12:36 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 



 On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



 On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent 
 space where the metric tensor is diagonalized and its derivative 
 at that 
 point in spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate 
>>> system and some arbitrary point in a non-empty spacetime. So 
>>> spacetime has 
>>> a non zero curvature and the derivative of the metric tensor is 
>>> generally 
>>> non-zero at that arbitrary point, however small we assume the 
>>> region around 
>>> that point. But applying the EEP, we can transform to the tangent 
>>> space at 
>>> that point to diagonalize the metric tensor and have its derivative 
>>> as zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a 
>>> Riemannian space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle 
>> in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on 
>> it, it will deviate from the geodesic in the tangent space 
>> coordinates.  
>> The transformation is just adapting the coordinates to the local 
>> free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on 
> test particle, I assume the trajectory appears identical to an 
> external 
> observer, before and after coordinate transformation to the tangent 
> plane 
> at some point; all that's changed are the labels of spacetime points. 
> If 
> this is true, it's still hard to see why changing labels can remove 
> the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made 
> fictitious 
> forces appear; just like when you use a merry-go-round as your 
> reference 
> frame you get coriolis forces.  
>

 If gravity is a fictitious force produced by the choice of 
 coordinate system, in its absence (due to a change in coordinate 
 system) 
 how does GR explain motion? Test particles move on geodesics in the 
 absence 
 of non-gravitational forces, but why do they move at all? AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  
>>> interpret, they mainly make models. By a model is meant a  mathematical 
>

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/17/2019 5:20 PM, agrayson2...@gmail.com wrote:



On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:



On 4/17/2019 12:36 PM, agrays...@gmail.com  wrote:



On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:



On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:



On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6,
agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6,
Brent wrote:



On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6,
Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com
wrote:



On Friday, April 12, 2019 at 5:48:23 AM
UTC-6, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at
10:56:08 PM UTC-6, Brent wrote:



On 4/11/2019 9:33 PM,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at
7:12:17 PM UTC-6, Brent wrote:



On 4/11/2019 4:53 PM,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019
at 4:37:39 PM UTC-6, Brent
wrote:



On 4/11/2019 1:58 PM,
agrays...@gmail.com wrote:





He might have
been referring to
a transformation
to a tangent
space where the
metric tensor is
diagonalized and
its derivative at
that point in
spacetime is
zero. Does this
make any sense?


Sort of.



Yeah, that's what he's
doing. He's assuming a
given coordinate
system and some
arbitrary point in a
non-empty spacetime.
So spacetime has a non
zero curvature and the
derivative of the
metric tensor is
generally non-zero at
that arbitrary point,
however small we
assume the region
around that point. But
applying the EEP, we
can transform to the
tangent space at that
point to diagonalize
the metric tensor and
have its derivative as
zero at that point.
Does THIS make sense? AG


Yep.  That's pretty
much the defining
characteristic of a
Riemannian space.

Brent


But isn't it weird that
changing labels on
spacetime points by
transforming coordinates
has the result of putting
the test particle in local
free fall, when it wasn't
prior to the
transformation? AG


It doesn't put it in
free-fall.  If the particle
has EM forc

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 5:11:55 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 12:36 PM, agrays...@gmail.com  wrote:
>
>
>
> On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/17/2019 7:37 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent 
>>> space where the metric tensor is diagonalized and its derivative at 
>>> that 
>>> point in spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate 
>> system and some arbitrary point in a non-empty spacetime. So 
>> spacetime has 
>> a non zero curvature and the derivative of the metric tensor is 
>> generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent 
>> space at 
>> that point to diagonalize the metric tensor and have its derivative 
>> as zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a 
>> Riemannian space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle 
> in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on 
> it, it will deviate from the geodesic in the tangent space 
> coordinates.  
> The transformation is just adapting the coordinates to the local 
> free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on 
 test particle, I assume the trajectory appears identical to an 
 external 
 observer, before and after coordinate transformation to the tangent 
 plane 
 at some point; all that's changed are the labels of spacetime points. 
 If 
 this is true, it's still hard to see why changing labels can remove 
 the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your 
 reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of 
>>> coordinate system, in its absence (due to a change in coordinate 
>>> system) 
>>> how does GR explain motion? Test particles move on geodesics in the 
>>> absence 
>>> of non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  
>> interpret, they mainly make models. By a model is meant a  mathematical 
>> construct which, with the addition of certain verbal  interpretations, 
>> describes observed phenomena. The justification of  such a mathematical 
>> construct is solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>>
>>> Another problem is the inconsistency 

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/17/2019 12:36 PM, agrayson2...@gmail.com wrote:



On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:



On 4/17/2019 7:37 AM, agrays...@gmail.com  wrote:



On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:



On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6,
agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent
wrote:



On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6,
Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM
UTC-6, Brent wrote:



On 4/11/2019 9:33 PM,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at
7:12:17 PM UTC-6, Brent wrote:



On 4/11/2019 4:53 PM,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at
4:37:39 PM UTC-6, Brent wrote:



On 4/11/2019 1:58 PM,
agrays...@gmail.com wrote:





He might have been
referring to a
transformation to a
tangent space where
the metric tensor is
diagonalized and its
derivative at that
point in spacetime is
zero. Does this make
any sense?


Sort of.



Yeah, that's what he's
doing. He's assuming a
given coordinate system and
some arbitrary point in a
non-empty spacetime. So
spacetime has a non zero
curvature and the
derivative of the metric
tensor is generally
non-zero at that arbitrary
point, however small we
assume the region around
that point. But applying
the EEP, we can transform
to the tangent space at
that point to diagonalize
the metric tensor and have
its derivative as zero at
that point. Does THIS make
sense? AG


Yep.  That's pretty much the
defining characteristic of a
Riemannian space.

Brent


But isn't it weird that changing
labels on spacetime points by
transforming coordinates has the
result of putting the test
particle in local free fall,
when it wasn't prior to the
transformation? AG


It doesn't put it in free-fall. 
If the particle has EM forces on
it, it will deviate from the
geodesic in the tangent space
coordinates. The transformation
is just adapting the coordinates
to the local free-fall which
removes gravity as a force...but
not other forces.

Brent


In both cases, with and without
non-gravitational forces acting on
test particle, I assume the
trajectory appears identical to an
external observer, before and after
coordinat

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, April 17, 2019 at 1:02:09 PM UTC-6, Brent wrote:
>
>
>
> On 4/17/2019 7:37 AM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 6:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 



 On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



 On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent 
>> space where the metric tensor is diagonalized and its derivative at 
>> that 
>> point in spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate 
> system and some arbitrary point in a non-empty spacetime. So 
> spacetime has 
> a non zero curvature and the derivative of the metric tensor is 
> generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent 
> space at 
> that point to diagonalize the metric tensor and have its derivative 
> as zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a 
> Riemannian space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle 
 in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on 
 it, it will deviate from the geodesic in the tangent space 
 coordinates.  
 The transformation is just adapting the coordinates to the local 
 free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on 
>>> test particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent 
>>> plane 
>>> at some point; all that's changed are the labels of spacetime points. 
>>> If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made 
>>> fictitious 
>>> forces appear; just like when you use a merry-go-round as your 
>>> reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does 
>> GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  
> interpret, they mainly make models. By a model is meant a  mathematical 
> construct which, with the addition of certain verbal  interpretations, 
> describes observed phenomena. The justification of  such a mathematical 
> construct is solely and precisely that it is  expected to work.
> --—John von Neumann
>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am 
> merely pointing out the inconsi

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/17/2019 7:37 AM, agrayson2...@gmail.com wrote:



On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:



On 4/16/2019 6:14 PM, agrays...@gmail.com  wrote:



On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6,
agrays...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:



On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM
UTC-6, Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com
wrote:



On Thursday, April 11, 2019 at 7:12:17 PM
UTC-6, Brent wrote:



On 4/11/2019 4:53 PM,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at
4:37:39 PM UTC-6, Brent wrote:



On 4/11/2019 1:58 PM,
agrays...@gmail.com wrote:





He might have been
referring to a
transformation to a tangent
space where the metric
tensor is diagonalized and
its derivative at that
point in spacetime is zero.
Does this make any sense?


Sort of.



Yeah, that's what he's doing.
He's assuming a given coordinate
system and some arbitrary point
in a non-empty spacetime. So
spacetime has a non zero
curvature and the derivative of
the metric tensor is generally
non-zero at that arbitrary
point, however small we assume
the region around that point.
But applying the EEP, we can
transform to the tangent space
at that point to diagonalize the
metric tensor and have its
derivative as zero at that
point. Does THIS make sense? AG


Yep.  That's pretty much the
defining characteristic of a
Riemannian space.

Brent


But isn't it weird that changing
labels on spacetime points by
transforming coordinates has the
result of putting the test particle
in local free fall, when it wasn't
prior to the transformation? AG


It doesn't put it in free-fall.  If
the particle has EM forces on it, it
will deviate from the geodesic in the
tangent space coordinates.  The
transformation is just adapting the
coordinates to the local free-fall
which removes gravity as a force...but
not other forces.

Brent


In both cases, with and without
non-gravitational forces acting on test
particle, I assume the trajectory appears
identical to an external observer, before
and after coordinate transformation to the
tangent plane at some point; all that's
changed are the labels of spacetime
points. If this is true, it's still hard
to see why changing labels can remove the
gravitational forces. And what does this
buy us? AG


You're looking at it the wrong way around. 
There never were any gravitational forces,
just your choice of coordinate system made
fictitious forces appear; just like when
you use a merry-go-round as your reference
frame you g

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative at 
> that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So spacetime 
 has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on 
>>> it, it will deviate from the geodesic in the tangent space coordinates. 
>>>  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on 
>> test particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made 
>> fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

 Maybe GR assumes motion but doesn't explain it. AG 


 The sciences do not try to explain, they hardly even try to  interpret, 
 they mainly make models. By a model is meant a  mathematical construct 
 which, with the addition of certain verbal  interpretations, describes 
 observed phenomena. The justification of  such a mathematical construct is 
 solely and precisely that it is  expected to work.
 --—John von Neumann


> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

 It's said that consistency is the hobgoblin of small minds. I am merely 
 pointing out the inconsistency of the gravitational force with the other 
 forces. Maybe gravity is just different. AG 


 That's one possibility, e.g entropic gravity.


>  
>
>> What is gets you is it enforces and explains the equivalence 
>> principle.  And of course Einstein's theory a

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:21:32 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:25 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 5:41:35 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/16/2019 7:56 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 

 ...
 If gravity is a fictitious force produced by the choice of coordinate 
 system, in its absence (due to a change in coordinate system)* how 
 does GR explain motion?* Test particles move on geodesics in the 
 absence of non-gravitational forces, but * why do they move at all?* AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  interpret, 
>>> they mainly make models. By a model is meant a  mathematical construct 
>>> which, with the addition of certain verbal  interpretations, describes 
>>> observed phenomena. The justification of  such a mathematical construct is 
>>> solely and precisely that it is  expected to work.
>>> --—John von Neumann
>>>
>>
>> *This is straight out of the "shut up and calculate" school, and I don't 
>> completely buy it. E.g., the Principle of Relativity and Least Action 
>> Principle give strong indications of not only how the universe works, but 
>> why. That is, they're somewhat explanatory in nature. AG*
>>
>>
>> Fine, then take them as explanations.  But to ask that they be explained 
>> is to misunderstand their status.  It's possible that they could be 
>> explained; but only by finding a more fundamental theory that includes them 
>> as consequences or special cases.  Whatever theory is fundamental cannot 
>> have an explanation in the sense you want because then it would not be 
>> fundamental.
>>
>> Brent
>>
>
> *I don't think I asked them to be explained, and I don't think*
> * I misunderstand their status. In the examples I gave, the principles are 
> pretty fundamental and nonetheless seem to explain something substantive 
> about the universe even though they're not part of a deeper theory. AG *
>
>
> You wrote, "...how does GR explain motion? Test particles move on 
> geodesics in the absence of non-gravitational forces, but why do they move 
> at all?"
>
> GR hypothesizes that force-free motion of test particles is along 
> geodesics.  In 4-space they "move" because there is a time coordinate and a 
> particle is by definition something that persists in time (in contrast to 
> an "event").
>
> Brent
>

*Yes, I asked for an explanation of motion in the context of GR, but my 
response to Von Neumann was NOT meant in that context; namely, that physics 
sometimes DOES give explanations in what we could consider fundamental 
theories. But particles can hypothetically persist at a fixed time and 
still be particles. I don't think GR says anything about WHY test particles 
move, other than to postulate HOW they move; along geodesics. By 
distinction, our other force theories do IMO explain WHY particles move. 
AG *

> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everyth...@googlegroups.com .
> To post to this group, send email to everyth...@googlegroups.com 
> .
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> For more options, visit https://groups.google.com/d/optout.
>
>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 9:15:40 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 6:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>>
>>
>> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 



 On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



 On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
 wrote: 
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent 
> space where the metric tensor is diagonalized and its derivative at 
> that 
> point in spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate 
 system and some arbitrary point in a non-empty spacetime. So spacetime 
 has 
 a non zero curvature and the derivative of the metric tensor is 
 generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent 
 space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a 
 Riemannian space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on 
>>> it, it will deviate from the geodesic in the tangent space coordinates. 
>>>  
>>> The transformation is just adapting the coordinates to the local 
>>> free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on 
>> test particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent 
>> plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made 
>> fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

 Maybe GR assumes motion but doesn't explain it. AG 


 The sciences do not try to explain, they hardly even try to  interpret, 
 they mainly make models. By a model is meant a  mathematical construct 
 which, with the addition of certain verbal  interpretations, describes 
 observed phenomena. The justification of  such a mathematical construct is 
 solely and precisely that it is  expected to work.
 --—John von Neumann


> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

 It's said that consistency is the hobgoblin of small minds. I am merely 
 pointing out the inconsistency of the gravitational force with the other 
 forces. Maybe gravity is just different. AG 


 That's one possibility, e.g entropic gravity.


>  
>
>> What is gets you is it enforces and explains the equivalence 
>> principle.  And of course Einstein's theory a

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/16/2019 6:25 PM, agrayson2...@gmail.com wrote:



On Tuesday, April 16, 2019 at 5:41:35 PM UTC-6, Brent wrote:



On 4/16/2019 7:56 AM, agrays...@gmail.com  wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:

...
If gravity is a fictitious force produced by the choice
of coordinate system, in its absence (due to a change in
coordinate system)*how does GR explain motion?* Test
particles move on geodesics in the absence of
non-gravitational forces, but *why do they move at all?* AG


Maybe GR assumes motion but doesn't explain it. AG


The sciences do not try to explain, they hardly even try to 
interpret, they mainly make models. By a model is meant a 
mathematical construct which, with the addition of certain
verbal  interpretations, describes observed phenomena. The
justification of such a mathematical construct is solely and
precisely that it is  expected to work.
    --—John von Neumann


*This is straight out of the "shut up and calculate" school, and
I don't completely buy it. E.g., the Principle of Relativity and
Least Action Principle give strong indications of not only how
the universe works, but why. That is, they're somewhat
explanatory in nature. AG*


Fine, then take them as explanations.  But to ask that they be
explained is to misunderstand their status.  It's possible that
they could be explained; but only by finding a more fundamental
theory that includes them as consequences or special cases. 
Whatever theory is fundamental cannot have an explanation in the
sense you want because then it would not be fundamental.

Brent


*I don't think I asked them to be explained, and I don't think** I 
misunderstand their status. In the examples I gave, the principles are 
pretty fundamental and nonetheless seem to explain something 
substantive about the universe even though they're not part of a 
deeper theory. AG

*


You wrote, "...how does GR explain motion? Test particles move on 
geodesics in the absence of non-gravitational forces, but why do they 
move at all?"


GR hypothesizes that force-free motion of test particles is along 
geodesics.  In 4-space they "move" because there is a time coordinate 
and a particle is by definition something that persists in time (in 
contrast to an "event").


Brent





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.
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.

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/16/2019 6:14 PM, agrayson2...@gmail.com wrote:



On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com 
wrote:




On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:



On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM UTC-6,
Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM
UTC-6, Brent wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com
wrote:



On Thursday, April 11, 2019 at 4:37:39 PM
UTC-6, Brent wrote:



On 4/11/2019 1:58 PM,
agrays...@gmail.com wrote:





He might have been referring to
a transformation to a tangent
space where the metric tensor is
diagonalized and its derivative
at that point in spacetime is
zero. Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's
assuming a given coordinate system
and some arbitrary point in a
non-empty spacetime. So spacetime has
a non zero curvature and the
derivative of the metric tensor is
generally non-zero at that arbitrary
point, however small we assume the
region around that point. But
applying the EEP, we can transform to
the tangent space at that point to
diagonalize the metric tensor and
have its derivative as zero at that
point. Does THIS make sense? AG


Yep.  That's pretty much the defining
characteristic of a Riemannian space.

Brent


But isn't it weird that changing labels on
spacetime points by transforming
coordinates has the result of putting the
test particle in local free fall, when it
wasn't prior to the transformation? AG


It doesn't put it in free-fall.  If the
particle has EM forces on it, it will
deviate from the geodesic in the tangent
space coordinates.  The transformation is
just adapting the coordinates to the local
free-fall which removes gravity as a
force...but not other forces.

Brent


In both cases, with and without
non-gravitational forces acting on test
particle, I assume the trajectory appears
identical to an external observer, before and
after coordinate transformation to the tangent
plane at some point; all that's changed are the
labels of spacetime points. If this is true,
it's still hard to see why changing labels can
remove the gravitational forces. And what does
this buy us? AG


You're looking at it the wrong way around. 
There never were any gravitational forces, just
your choice of coordinate system made fictitious
forces appear; just like when you use a
merry-go-round as your reference frame you get
coriolis forces.


If gravity is a fictitious force produced by the
choice of coordinate system, in its absence (due to
a change in coordinate system) how does GR explain
motion? Test particles move on geodesics in the
absence of non-gravitational forces, but why do they
move at all? AG


Maybe GR assumes motion but doesn't explain it. AG


The sciences do not try to explain, they hardly even try
to  interpret, they mainly make models. By a model is
meant a  mathematical construct which, with the addition
of certai

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 5:41:35 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 7:56 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that 
>>> point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>> and some arbitrary point in a non-empty spacetime. So spacetime has a 
>> non 
>> zero curvature and the derivative of the metric tensor is generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent space 
>> at 
>> that point to diagonalize the metric tensor and have its derivative as 
>> zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, 
> it will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on test 
 particle, I assume the trajectory appears identical to an external 
 observer, before and after coordinate transformation to the tangent plane 
 at some point; all that's changed are the labels of spacetime points. If 
 this is true, it's still hard to see why changing labels can remove the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of coordinate 
>>> system, in its absence (due to a change in coordinate system) how does GR 
>>> explain motion? Test particles move on geodesics in the absence of 
>>> non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  interpret, 
>> they mainly make models. By a model is meant a  mathematical construct 
>> which, with the addition of certain verbal  interpretations, describes 
>> observed phenomena. The justification of  such a mathematical construct is 
>> solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>
> *This is straight out of the "shut up and calculate" school, and I don't 
> completely buy it. E.g., the Principle of Relativity and Least Action 
> Principle give strong indications of not only how the universe works, but 
> why. That is, they're somewhat explanatory in nature. AG*
>
>
> Fine, then take them as explanations.  But to ask that they be explained 
> is to misunderstand their status.  It's possible that they could be 
> explained; but only by finding a more fundamental theory that includes them 
> as consequences or special cases.  Whatever theory is fundamental cannot 
> have an explanation in the sense you want because then it would not be 
> fundamental.
>
> Brent
>

*I don't think I asked them to be explained, and I don't think** I 
misunderstand their status. In the examples I gave, the principles are 
pretty fundamental and nonetheless seem to explain something substantive 
about the universe even though they're not part of a deeper theory. AG *

-- 
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving ema

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 6:39:11 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/16/2019 11:41 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>>> wrote: 



 On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent space 
 where the metric tensor is diagonalized and its derivative at that 
 point in 
 spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate 
>>> system and some arbitrary point in a non-empty spacetime. So spacetime 
>>> has 
>>> a non zero curvature and the derivative of the metric tensor is 
>>> generally 
>>> non-zero at that arbitrary point, however small we assume the region 
>>> around 
>>> that point. But applying the EEP, we can transform to the tangent space 
>>> at 
>>> that point to diagonalize the metric tensor and have its derivative as 
>>> zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>>> space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on it, 
>> it will deviate from the geodesic in the tangent space coordinates.  The 
>> transformation is just adapting the coordinates to the local free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on 
> test particle, I assume the trajectory appears identical to an external 
> observer, before and after coordinate transformation to the tangent plane 
> at some point; all that's changed are the labels of spacetime points. If 
> this is true, it's still hard to see why changing labels can remove the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made 
> fictitious 
> forces appear; just like when you use a merry-go-round as your reference 
> frame you get coriolis forces.  
>

 If gravity is a fictitious force produced by the choice of coordinate 
 system, in its absence (due to a change in coordinate system) how does GR 
 explain motion? Test particles move on geodesics in the absence of 
 non-gravitational forces, but why do they move at all? AG

>>>
>>> Maybe GR assumes motion but doesn't explain it. AG 
>>>
>>>
>>> The sciences do not try to explain, they hardly even try to  interpret, 
>>> they mainly make models. By a model is meant a  mathematical construct 
>>> which, with the addition of certain verbal  interpretations, describes 
>>> observed phenomena. The justification of  such a mathematical construct is 
>>> solely and precisely that it is  expected to work.
>>> --—John von Neumann
>>>
>>>
 Another problem is the inconsistency of the fictitious gravitational 
 force, and how the other forces function; EM, Strong, and Weak, which 
 apparently can't be removed by changes in coordinates systems. AG

>>>
>>> It's said that consistency is the hobgoblin of small minds. I am merely 
>>> pointing out the inconsistency of the gravitational force with the other 
>>> forces. Maybe gravity is just different. AG 
>>>
>>>
>>> That's one possibility, e.g entropic gravity.
>>>
>>>
  

> What is gets you is it enforces and explains the equivalence 
> principle.  And of course Einstein's theory also correctly predicted the 
> bending of light, gravitational waves, time dilation and the precession 
> of 
> the perhelion of Mercury.
>

 I was referring earlier just to the transformation to the tangent 
 space; what specifically does it buy us; why would we want 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 16, 2019 at 6:10:16 PM UTC-6, Brent wrote:
>
>
>
> On 4/16/2019 11:41 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/15/2019 7:14 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 



 On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that 
>>> point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>> and some arbitrary point in a non-empty spacetime. So spacetime has a 
>> non 
>> zero curvature and the derivative of the metric tensor is generally 
>> non-zero at that arbitrary point, however small we assume the region 
>> around 
>> that point. But applying the EEP, we can transform to the tangent space 
>> at 
>> that point to diagonalize the metric tensor and have its derivative as 
>> zero 
>> at that point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, 
> it will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

 In both cases, with and without non-gravitational forces acting on test 
 particle, I assume the trajectory appears identical to an external 
 observer, before and after coordinate transformation to the tangent plane 
 at some point; all that's changed are the labels of spacetime points. If 
 this is true, it's still hard to see why changing labels can remove the 
 gravitational forces. And what does this buy us? AG


 You're looking at it the wrong way around.  There never were any 
 gravitational forces, just your choice of coordinate system made 
 fictitious 
 forces appear; just like when you use a merry-go-round as your reference 
 frame you get coriolis forces.  

>>>
>>> If gravity is a fictitious force produced by the choice of coordinate 
>>> system, in its absence (due to a change in coordinate system) how does GR 
>>> explain motion? Test particles move on geodesics in the absence of 
>>> non-gravitational forces, but why do they move at all? AG
>>>
>>
>> Maybe GR assumes motion but doesn't explain it. AG 
>>
>>
>> The sciences do not try to explain, they hardly even try to  interpret, 
>> they mainly make models. By a model is meant a  mathematical construct 
>> which, with the addition of certain verbal  interpretations, describes 
>> observed phenomena. The justification of  such a mathematical construct is 
>> solely and precisely that it is  expected to work.
>> --—John von Neumann
>>
>>
>>> Another problem is the inconsistency of the fictitious gravitational 
>>> force, and how the other forces function; EM, Strong, and Weak, which 
>>> apparently can't be removed by changes in coordinates systems. AG
>>>
>>
>> It's said that consistency is the hobgoblin of small minds. I am merely 
>> pointing out the inconsistency of the gravitational force with the other 
>> forces. Maybe gravity is just different. AG 
>>
>>
>> That's one possibility, e.g entropic gravity.
>>
>>
>>>  
>>>
 What is gets you is it enforces and explains the equivalence 
 principle.  And of course Einstein's theory also correctly predicted the 
 bending of light, gravitational waves, time dilation and the precession of 
 the perhelion of Mercury.

>>>
>>> I was referring earlier just to the transformation to the tangent space; 
>>> what specifically does it buy us; why would we want to execute this 
>>> particular transformation? AG 
>>>
>>
>> For one thing, you know the acceleration due to non-gravitational forces 
>> in this frame.  
>>
>
> *IIUC, the tangent space is a vector space which has elements with 
> const

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/16/2019 11:41 AM, agrayson2...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent
wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6,
Brent wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:





He might have been referring to a
transformation to a tangent space where
the metric tensor is diagonalized and its
derivative at that point in spacetime is
zero. Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a
given coordinate system and some arbitrary
point in a non-empty spacetime. So spacetime
has a non zero curvature and the derivative of
the metric tensor is generally non-zero at
that arbitrary point, however small we assume
the region around that point. But applying the
EEP, we can transform to the tangent space at
that point to diagonalize the metric tensor
and have its derivative as zero at that point.
Does THIS make sense? AG


Yep.  That's pretty much the defining
characteristic of a Riemannian space.

Brent


But isn't it weird that changing labels on
spacetime points by transforming coordinates has
the result of putting the test particle in local
free fall, when it wasn't prior to the
transformation? AG


It doesn't put it in free-fall.  If the particle has
EM forces on it, it will deviate from the geodesic
in the tangent space coordinates.  The
transformation is just adapting the coordinates to
the local free-fall which removes gravity as a
force...but not other forces.

Brent


In both cases, with and without non-gravitational forces
acting on test particle, I assume the trajectory appears
identical to an external observer, before and after
coordinate transformation to the tangent plane at some
point; all that's changed are the labels of spacetime
points. If this is true, it's still hard to see why
changing labels can remove the gravitational forces. And
what does this buy us? AG


You're looking at it the wrong way around. There never
were any gravitational forces, just your choice of
coordinate system made fictitious forces appear; just
like when you use a merry-go-round as your reference
frame you get coriolis forces.


If gravity is a fictitious force produced by the choice of
coordinate system, in its absence (due to a change in
coordinate system) how does GR explain motion? Test particles
move on geodesics in the absence of non-gravitational forces,
but why do they move at all? AG


Maybe GR assumes motion but doesn't explain it. AG


The sciences do not try to explain, they hardly even try to
interpret, they mainly make models. By a model is meant a
mathematical construct which, with the addition of certain verbal 
interpretations, describes observed phenomena. The justification
of  such a mathematical construct is solely and precisely that it
is  expected to work.
    --—John von Neumann



Another problem is the inconsistency of the fictitious
gravitational force, and how the other forces function; EM,
Strong, and Weak, which apparently can't be removed by
changes in coordinates systems. AG


It's said that consistency is the hobgoblin of small minds. I am
merely pointing out the inconsistency of the gravitational force
with the other forces. Maybe gravity is just different. AG


That's one possibility, e.g entropic gravity.



What is gets you is it enforces and explains the
equivalence principle.  And of course Einstein's theory
also correctly predicted the bending of light,
gravitational waves, time dilation and the precession of
the perhelion of Mercury.


I was referring earlier just

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/16/2019 7:56 AM, agrayson2...@gmail.com wrote:



On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:



On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6,
agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent
wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6,
Brent wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:





He might have been referring to a
transformation to a tangent space where
the metric tensor is diagonalized and its
derivative at that point in spacetime is
zero. Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a
given coordinate system and some arbitrary
point in a non-empty spacetime. So spacetime
has a non zero curvature and the derivative of
the metric tensor is generally non-zero at
that arbitrary point, however small we assume
the region around that point. But applying the
EEP, we can transform to the tangent space at
that point to diagonalize the metric tensor
and have its derivative as zero at that point.
Does THIS make sense? AG


Yep.  That's pretty much the defining
characteristic of a Riemannian space.

Brent


But isn't it weird that changing labels on
spacetime points by transforming coordinates has
the result of putting the test particle in local
free fall, when it wasn't prior to the
transformation? AG


It doesn't put it in free-fall.  If the particle has
EM forces on it, it will deviate from the geodesic
in the tangent space coordinates.  The
transformation is just adapting the coordinates to
the local free-fall which removes gravity as a
force...but not other forces.

Brent


In both cases, with and without non-gravitational forces
acting on test particle, I assume the trajectory appears
identical to an external observer, before and after
coordinate transformation to the tangent plane at some
point; all that's changed are the labels of spacetime
points. If this is true, it's still hard to see why
changing labels can remove the gravitational forces. And
what does this buy us? AG


You're looking at it the wrong way around. There never
were any gravitational forces, just your choice of
coordinate system made fictitious forces appear; just
like when you use a merry-go-round as your reference
frame you get coriolis forces.


If gravity is a fictitious force produced by the choice of
coordinate system, in its absence (due to a change in
coordinate system) how does GR explain motion? Test particles
move on geodesics in the absence of non-gravitational forces,
but why do they move at all? AG


Maybe GR assumes motion but doesn't explain it. AG


The sciences do not try to explain, they hardly even try to
interpret, they mainly make models. By a model is meant a
mathematical construct which, with the addition of certain verbal 
interpretations, describes observed phenomena. The justification
of  such a mathematical construct is solely and precisely that it
is  expected to work.
    --—John von Neumann


*This is straight out of the "shut up and calculate" school, and I 
don't completely buy it. E.g., the Principle of Relativity and Least 
Action Principle give strong indications of not only how the universe 
works, but why. That is, they're somewhat explanatory in nature. AG*


Fine, then take them as explanations.  But to ask that they be explained 
is to misunderstand their status.  It's possible that they could be 
explained; but only by finding a more fundamental theory that includes 
them as consequences or special cases.  Whatever theory is fundamental 
cannot have an explanation in the sense you want because then it would 
not be fundamental.


Brent

--
You received this message because you are subscribed to the Google Groups 
"Everything List" group.
To unsubscribe from this group and stop receiving emails fr

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  interpret, 
> they mainly make models. By a model is meant a  mathematical construct 
> which, with the addition of certain verbal  interpretations, describes 
> observed phenomena. The justification of  such a mathematical construct is 
> solely and precisely that it is  expected to work.
> --—John von Neumann
>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>
> That's one possibility, e.g entropic gravity.
>
>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>
> For one thing, you know the acceleration due to non-gravitational forces 
> in this frame.  
>

*IIUC, the tangent space is a vector space which has elements with constant 
t.  So its elements are linear combinations of t, x, y, and z. How do you 
get accelerations from such sums (even if t is not constant)? AG*

So you can transform to it, put in the accelerations, and transform back. 
>

*I see no way to put the accelerations into the tangent space 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 9:26:59 PM UTC-6, Brent wrote:
>
>
>
> On 4/15/2019 7:14 PM, agrays...@gmail.com  wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote: 
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>
> The sciences do not try to explain, they hardly even try to  interpret, 
> they mainly make models. By a model is meant a  mathematical construct 
> which, with the addition of certain verbal  interpretations, describes 
> observed phenomena. The justification of  such a mathematical construct is 
> solely and precisely that it is  expected to work.
> --—John von Neumann
>

*This is straight out of the "shut up and calculate" school, and I don't 
completely buy it. E.g., the Principle of Relativity and Least Action 
Principle give strong indications of not only how the universe works, but 
why. That is, they're somewhat explanatory in nature. AG*
  

>
>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>
> That's one possibility, e.g entropic gravity.
>
>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>
> For one thing, you know the acceleration due to non-gravitational forces 
> in this frame.  So you can transform to it, put in the accelerations, and 
> transform back.  

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/15/2019 8:08 PM, agrayson2...@gmail.com wrote:



On Monday, April 15, 2019 at 8:14:35 PM UTC-6, agrays...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agray...@gmail.com
wrote:



On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent
wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6,
Brent wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:





He might have been referring to a
transformation to a tangent space where
the metric tensor is diagonalized and its
derivative at that point in spacetime is
zero. Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a
given coordinate system and some arbitrary
point in a non-empty spacetime. So spacetime
has a non zero curvature and the derivative of
the metric tensor is generally non-zero at that
arbitrary point, however small we assume the
region around that point. But applying the EEP,
we can transform to the tangent space at that
point to diagonalize the metric tensor and have
its derivative as zero at that point. Does THIS
make sense? AG


Yep.  That's pretty much the defining
characteristic of a Riemannian space.

Brent


But isn't it weird that changing labels on spacetime
points by transforming coordinates has the result of
putting the test particle in local free fall, when
it wasn't prior to the transformation? AG


It doesn't put it in free-fall.  If the particle has
EM forces on it, it will deviate from the geodesic in
the tangent space coordinates.  The transformation is
just adapting the coordinates to the local free-fall
which removes gravity as a force...but not other forces.

Brent


In both cases, with and without non-gravitational forces
acting on test particle, I assume the trajectory appears
identical to an external observer, before and after
coordinate transformation to the tangent plane at some
point; all that's changed are the labels of spacetime
points. If this is true, it's still hard to see why
changing labels can remove the gravitational forces. And
what does this buy us? AG


You're looking at it the wrong way around.  There never
were any gravitational forces, just your choice of
coordinate system made fictitious forces appear; just like
when you use a merry-go-round as your reference frame you
get coriolis forces.


If gravity is a fictitious force produced by the choice of
coordinate system, in its absence (due to a change in
coordinate system) how does GR explain motion? Test particles
move on geodesics in the absence of non-gravitational forces,
but why do they move at all? AG


Maybe GR assumes motion but doesn't explain it. AG


Another problem is the inconsistency of the fictitious
gravitational force, and how the other forces function; EM,
Strong, and Weak, which apparently can't be removed by changes
in coordinates systems. AG


It's said that consistency is the hobgoblin of small minds. I am
merely pointing out the inconsistency of the gravitational force
with the other forces. Maybe gravity is just different. AG


What is gets you is it enforces and explains the
equivalence principle.  And of course Einstein's theory
also correctly predicted the bending of light,
gravitational waves, time dilation and the precession of
the perhelion of Mercury.


I was referring earlier just to the transformation to the
tangent space; what specifically does it buy us; why would we
want to execute this particular transformation? AG


Brent


*I could be mistaken, I usually am, but ISTM that labeling all points 
in spacetime as (t, x, y, z) makes no sense since there is no 
universal clock in GR. Each observer has his own clock in GR. No 
"Bird's Eye" observer GR. So what could the same t for all spatial 
points mean, or increasing t's as time evolves? AG*


The "t" in the coor

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/15/2019 7:14 PM, agrayson2...@gmail.com wrote:



On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:



On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent
wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:





He might have been referring to a
transformation to a tangent space where the
metric tensor is diagonalized and its
derivative at that point in spacetime is zero.
Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a given
coordinate system and some arbitrary point in a
non-empty spacetime. So spacetime has a non zero
curvature and the derivative of the metric tensor
is generally non-zero at that arbitrary point,
however small we assume the region around that
point. But applying the EEP, we can transform to
the tangent space at that point to diagonalize the
metric tensor and have its derivative as zero at
that point. Does THIS make sense? AG


Yep.  That's pretty much the defining characteristic
of a Riemannian space.

Brent


But isn't it weird that changing labels on spacetime
points by transforming coordinates has the result of
putting the test particle in local free fall, when it
wasn't prior to the transformation? AG


It doesn't put it in free-fall.  If the particle has EM
forces on it, it will deviate from the geodesic in the
tangent space coordinates.  The transformation is just
adapting the coordinates to the local free-fall which
removes gravity as a force...but not other forces.

Brent


In both cases, with and without non-gravitational forces
acting on test particle, I assume the trajectory appears
identical to an external observer, before and after
coordinate transformation to the tangent plane at some point;
all that's changed are the labels of spacetime points. If
this is true, it's still hard to see why changing labels can
remove the gravitational forces. And what does this buy us? AG


You're looking at it the wrong way around.  There never were
any gravitational forces, just your choice of coordinate
system made fictitious forces appear; just like when you use a
merry-go-round as your reference frame you get coriolis forces.


If gravity is a fictitious force produced by the choice of
coordinate system, in its absence (due to a change in coordinate
system) how does GR explain motion? Test particles move on
geodesics in the absence of non-gravitational forces, but why do
they move at all? AG


Maybe GR assumes motion but doesn't explain it. AG


The sciences do not try to explain, they hardly even try to interpret, 
they mainly make models. By a model is meant a mathematical construct 
which, with the addition of certain verbal interpretations, describes 
observed phenomena. The justification of such a mathematical construct 
is solely and precisely that it is expected to work.

    --—John von Neumann



Another problem is the inconsistency of the fictitious
gravitational force, and how the other forces function; EM,
Strong, and Weak, which apparently can't be removed by changes in
coordinates systems. AG


It's said that consistency is the hobgoblin of small minds. I am 
merely pointing out the inconsistency of the gravitational force with 
the other forces. Maybe gravity is just different. AG


That's one possibility, e.g entropic gravity.



What is gets you is it enforces and explains the equivalence
principle.  And of course Einstein's theory also correctly
predicted the bending of light, gravitational waves, time
dilation and the precession of the perhelion of Mercury.


I was referring earlier just to the transformation to the tangent
space; what specifically does it buy us; why would we want to
execute this particular transformation? AG



For one thing, you know the acceleration due to non-gravitational forces 
in this frame.  So you can transform to it, put in the accelerations, 
and transform back.  So all the "gravitation" is in the transform.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 15, 2019 at 8:14:35 PM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>>>
>>>
>>>
>>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 



 On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:



 On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space 
>> where the metric tensor is diagonalized and its derivative at that point 
>> in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system 
> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
> zero curvature and the derivative of the metric tensor is generally 
> non-zero at that arbitrary point, however small we assume the region 
> around 
> that point. But applying the EEP, we can transform to the tangent space 
> at 
> that point to diagonalize the metric tensor and have its derivative as 
> zero 
> at that point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian 
> space.
>
> Brent
>

 But isn't it weird that changing labels on spacetime points by 
 transforming coordinates has the result of putting the test particle in 
 local free fall, when it wasn't prior to the transformation? AG 

 It doesn't put it in free-fall.  If the particle has EM forces on it, 
 it will deviate from the geodesic in the tangent space coordinates.  The 
 transformation is just adapting the coordinates to the local free-fall 
 which removes gravity as a force...but not other forces.

 Brent

>>>
>>> In both cases, with and without non-gravitational forces acting on test 
>>> particle, I assume the trajectory appears identical to an external 
>>> observer, before and after coordinate transformation to the tangent plane 
>>> at some point; all that's changed are the labels of spacetime points. If 
>>> this is true, it's still hard to see why changing labels can remove the 
>>> gravitational forces. And what does this buy us? AG
>>>
>>>
>>> You're looking at it the wrong way around.  There never were any 
>>> gravitational forces, just your choice of coordinate system made fictitious 
>>> forces appear; just like when you use a merry-go-round as your reference 
>>> frame you get coriolis forces.  
>>>
>>
>> If gravity is a fictitious force produced by the choice of coordinate 
>> system, in its absence (due to a change in coordinate system) how does GR 
>> explain motion? Test particles move on geodesics in the absence of 
>> non-gravitational forces, but why do they move at all? AG
>>
>
> Maybe GR assumes motion but doesn't explain it. AG 
>
>>
>> Another problem is the inconsistency of the fictitious gravitational 
>> force, and how the other forces function; EM, Strong, and Weak, which 
>> apparently can't be removed by changes in coordinates systems. AG
>>
>
> It's said that consistency is the hobgoblin of small minds. I am merely 
> pointing out the inconsistency of the gravitational force with the other 
> forces. Maybe gravity is just different. AG 
>
>>
>>  
>>
>>> What is gets you is it enforces and explains the equivalence principle.  
>>> And of course Einstein's theory also correctly predicted the bending of 
>>> light, gravitational waves, time dilation and the precession of the 
>>> perhelion of Mercury.
>>>
>>
>> I was referring earlier just to the transformation to the tangent space; 
>> what specifically does it buy us; why would we want to execute this 
>> particular transformation? AG 
>>
>>>
>>> Brent
>>>
>>
*I could be mistaken, I usually am, but ISTM that labeling all points in 
spacetime as (t, x, y, z) makes no sense since there is no universal clock 
in GR. Each observer has his own clock in GR. No "Bird's Eye" observer GR. 
So what could the same t for all spatial points mean, or increasing t's as 
time evolves? AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Friday, April 12, 2019 at 5:48:23 AM UTC-6, agrays...@gmail.com wrote:
>
>
>
> On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>>
>>
>>
>> On 4/11/2019 9:33 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 



 On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:


>>
> He might have been referring to a transformation to a tangent space 
> where the metric tensor is diagonalized and its derivative at that point 
> in 
> spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


 Yeah, that's what he's doing. He's assuming a given coordinate system 
 and some arbitrary point in a non-empty spacetime. So spacetime has a non 
 zero curvature and the derivative of the metric tensor is generally 
 non-zero at that arbitrary point, however small we assume the region 
 around 
 that point. But applying the EEP, we can transform to the tangent space at 
 that point to diagonalize the metric tensor and have its derivative as 
 zero 
 at that point. Does THIS make sense? AG


 Yep.  That's pretty much the defining characteristic of a Riemannian 
 space.

 Brent

>>>
>>> But isn't it weird that changing labels on spacetime points by 
>>> transforming coordinates has the result of putting the test particle in 
>>> local free fall, when it wasn't prior to the transformation? AG 
>>>
>>> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
>>> will deviate from the geodesic in the tangent space coordinates.  The 
>>> transformation is just adapting the coordinates to the local free-fall 
>>> which removes gravity as a force...but not other forces.
>>>
>>> Brent
>>>
>>
>> In both cases, with and without non-gravitational forces acting on test 
>> particle, I assume the trajectory appears identical to an external 
>> observer, before and after coordinate transformation to the tangent plane 
>> at some point; all that's changed are the labels of spacetime points. If 
>> this is true, it's still hard to see why changing labels can remove the 
>> gravitational forces. And what does this buy us? AG
>>
>>
>> You're looking at it the wrong way around.  There never were any 
>> gravitational forces, just your choice of coordinate system made fictitious 
>> forces appear; just like when you use a merry-go-round as your reference 
>> frame you get coriolis forces.  
>>
>
> If gravity is a fictitious force produced by the choice of coordinate 
> system, in its absence (due to a change in coordinate system) how does GR 
> explain motion? Test particles move on geodesics in the absence of 
> non-gravitational forces, but why do they move at all? AG
>

Maybe GR assumes motion but doesn't explain it. AG 

>
> Another problem is the inconsistency of the fictitious gravitational 
> force, and how the other forces function; EM, Strong, and Weak, which 
> apparently can't be removed by changes in coordinates systems. AG
>

It's said that consistency is the hobgoblin of small minds. I am merely 
pointing out the inconsistency of the gravitational force with the other 
forces. Maybe gravity is just different. AG 

>
>  
>
>> What is gets you is it enforces and explains the equivalence principle.  
>> And of course Einstein's theory also correctly predicted the bending of 
>> light, gravitational waves, time dilation and the precession of the 
>> perhelion of Mercury.
>>
>
> I was referring earlier just to the transformation to the tangent space; 
> what specifically does it buy us; why would we want to execute this 
> particular transformation? AG 
>
>>
>> Brent
>>
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 10:56:08 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent space 
 where the metric tensor is diagonalized and its derivative at that point 
 in 
 spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>>> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
>>> zero curvature and the derivative of the metric tensor is generally 
>>> non-zero at that arbitrary point, however small we assume the region around 
>>> that point. But applying the EEP, we can transform to the tangent space at 
>>> that point to diagonalize the metric tensor and have its derivative as zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>>> space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
>> will deviate from the geodesic in the tangent space coordinates.  The 
>> transformation is just adapting the coordinates to the local free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on test 
> particle, I assume the trajectory appears identical to an external 
> observer, before and after coordinate transformation to the tangent plane 
> at some point; all that's changed are the labels of spacetime points. If 
> this is true, it's still hard to see why changing labels can remove the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made fictitious 
> forces appear; just like when you use a merry-go-round as your reference 
> frame you get coriolis forces.  
>

If gravity is a fictitious force produced by the choice of coordinate 
system, in its absence (due to a change in coordinate system) how does GR 
explain motion? Test particles move on geodesics in the absence of 
non-gravitational forces, but why do they move at all? AG

Another problem is the inconsistency of the fictitious gravitational force, 
and how the other forces function; EM, Strong, and Weak, which apparently 
can't be removed by changes in coordinates systems. AG

 

> What is gets you is it enforces and explains the equivalence principle.  
> And of course Einstein's theory also correctly predicted the bending of 
> light, gravitational waves, time dilation and the precession of the 
> perhelion of Mercury.
>

I was referring earlier just to the transformation to the tangent space; 
what specifically does it buy us; why would we want to execute this 
particular transformation? AG 

>
> Brent
>

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Re: Questions about the Equivalence Principle (EP) and GR

[Philip Thrift]

On Thursday, April 11, 2019 at 11:56:08 PM UTC-5, Brent wrote:
>
>
>
> On 4/11/2019 9:33 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 4:53 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>>
>>>
>
 He might have been referring to a transformation to a tangent space 
 where the metric tensor is diagonalized and its derivative at that point 
 in 
 spacetime is zero. Does this make any sense? 


 Sort of.  

>>>
>>>
>>> Yeah, that's what he's doing. He's assuming a given coordinate system 
>>> and some arbitrary point in a non-empty spacetime. So spacetime has a non 
>>> zero curvature and the derivative of the metric tensor is generally 
>>> non-zero at that arbitrary point, however small we assume the region around 
>>> that point. But applying the EEP, we can transform to the tangent space at 
>>> that point to diagonalize the metric tensor and have its derivative as zero 
>>> at that point. Does THIS make sense? AG
>>>
>>>
>>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>>> space.
>>>
>>> Brent
>>>
>>
>> But isn't it weird that changing labels on spacetime points by 
>> transforming coordinates has the result of putting the test particle in 
>> local free fall, when it wasn't prior to the transformation? AG 
>>
>> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
>> will deviate from the geodesic in the tangent space coordinates.  The 
>> transformation is just adapting the coordinates to the local free-fall 
>> which removes gravity as a force...but not other forces.
>>
>> Brent
>>
>
> In both cases, with and without non-gravitational forces acting on test 
> particle, I assume the trajectory appears identical to an external 
> observer, before and after coordinate transformation to the tangent plane 
> at some point; all that's changed are the labels of spacetime points. If 
> this is true, it's still hard to see why changing labels can remove the 
> gravitational forces. And what does this buy us? AG
>
>
> You're looking at it the wrong way around.  There never were any 
> gravitational forces, just your choice of coordinate system made fictitious 
> forces appear; just like when you use a merry-go-round as your reference 
> frame you get coriolis forces.  What is gets you is it enforces and 
> explains the equivalence principle.  And of course Einstein's theory also 
> correctly predicted the bending of light, gravitational waves, time 
> dilation and the precession of the perhelion of Mercury.
>
> Brent
>



One would think (has anyone ever used it?) the Einstein Toolkit - 
https://einsteintoolkit.org/ - (the one platform I've heard about) takes 
care of all the coordinate management.

https://einsteintoolkit.org/thornguide/CactusBase/CoordBase/documentation.html
 

- pt

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/11/2019 9:33 PM, agrayson2...@gmail.com wrote:



On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:



On 4/11/2019 4:53 PM, agrays...@gmail.com  wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:





He might have been referring to a transformation to a
tangent space where the metric tensor is diagonalized
and its derivative at that point in spacetime is zero.
Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a given
coordinate system and some arbitrary point in a non-empty
spacetime. So spacetime has a non zero curvature and the
derivative of the metric tensor is generally non-zero at
that arbitrary point, however small we assume the region
around that point. But applying the EEP, we can transform to
the tangent space at that point to diagonalize the metric
tensor and have its derivative as zero at that point. Does
THIS make sense? AG


Yep.  That's pretty much the defining characteristic of a
Riemannian space.

Brent


But isn't it weird that changing labels on spacetime points by
transforming coordinates has the result of putting the test
particle in local free fall, when it wasn't prior to the
transformation? AG


It doesn't put it in free-fall.  If the particle has EM forces on
it, it will deviate from the geodesic in the tangent space
coordinates.  The transformation is just adapting the coordinates
to the local free-fall which removes gravity as a force...but not
other forces.

Brent


In both cases, with and without non-gravitational forces acting on 
test particle, I assume the trajectory appears identical to an 
external observer, before and after coordinate transformation to the 
tangent plane at some point; all that's changed are the labels of 
spacetime points. If this is true, it's still hard to see why changing 
labels can remove the gravitational forces. And what does this buy us? AG


You're looking at it the wrong way around.  There never were any 
gravitational forces, just your choice of coordinate system made 
fictitious forces appear; just like when you use a merry-go-round as 
your reference frame you get coriolis forces.  What is gets you is it 
enforces and explains the equivalence principle.  And of course 
Einstein's theory also correctly predicted the bending of light, 
gravitational waves, time dilation and the precession of the perhelion 
of Mercury.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 7:12:17 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 4:53 PM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/11/2019 1:58 PM, agrays...@gmail.com wrote:
>>
>>

>>> He might have been referring to a transformation to a tangent space 
>>> where the metric tensor is diagonalized and its derivative at that point in 
>>> spacetime is zero. Does this make any sense? 
>>>
>>>
>>> Sort of.  
>>>
>>
>>
>> Yeah, that's what he's doing. He's assuming a given coordinate system and 
>> some arbitrary point in a non-empty spacetime. So spacetime has a non zero 
>> curvature and the derivative of the metric tensor is generally non-zero at 
>> that arbitrary point, however small we assume the region around that point. 
>> But applying the EEP, we can transform to the tangent space at that point 
>> to diagonalize the metric tensor and have its derivative as zero at that 
>> point. Does THIS make sense? AG
>>
>>
>> Yep.  That's pretty much the defining characteristic of a Riemannian 
>> space.
>>
>> Brent
>>
>
> But isn't it weird that changing labels on spacetime points by 
> transforming coordinates has the result of putting the test particle in 
> local free fall, when it wasn't prior to the transformation? AG 
>
> It doesn't put it in free-fall.  If the particle has EM forces on it, it 
> will deviate from the geodesic in the tangent space coordinates.  The 
> transformation is just adapting the coordinates to the local free-fall 
> which removes gravity as a force...but not other forces.
>
> Brent
>

In both cases, with and without non-gravitational forces acting on test 
particle, I assume the trajectory appears identical to an external 
observer, before and after coordinate transformation to the tangent plane 
at some point; all that's changed are the labels of spacetime points. If 
this is true, it's still hard to see why changing labels can remove the 
gravitational forces. And what does this buy us? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/11/2019 4:53 PM, agrayson2...@gmail.com wrote:



On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:



On 4/11/2019 1:58 PM, agrays...@gmail.com  wrote:





He might have been referring to a transformation to a
tangent space where the metric tensor is diagonalized and
its derivative at that point in spacetime is zero. Does this
make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a given coordinate
system and some arbitrary point in a non-empty spacetime. So
spacetime has a non zero curvature and the derivative of the
metric tensor is generally non-zero at that arbitrary point,
however small we assume the region around that point. But
applying the EEP, we can transform to the tangent space at that
point to diagonalize the metric tensor and have its derivative as
zero at that point. Does THIS make sense? AG


Yep.  That's pretty much the defining characteristic of a
Riemannian space.

Brent


But isn't it weird that changing labels on spacetime points by 
transforming coordinates has the result of putting the test particle 
in local free fall, when it wasn't prior to the transformation? AG


It doesn't put it in free-fall.  If the particle has EM forces on it, it 
will deviate from the geodesic in the tangent space coordinates.  The 
transformation is just adapting the coordinates to the local free-fall 
which removes gravity as a force...but not other forces.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, April 11, 2019 at 4:37:39 PM UTC-6, Brent wrote:
>
>
>
> On 4/11/2019 1:58 PM, agrays...@gmail.com  wrote:
>
>
>>>
>> He might have been referring to a transformation to a tangent space where 
>> the metric tensor is diagonalized and its derivative at that point in 
>> spacetime is zero. Does this make any sense? 
>>
>>
>> Sort of.  
>>
>
>
> Yeah, that's what he's doing. He's assuming a given coordinate system and 
> some arbitrary point in a non-empty spacetime. So spacetime has a non zero 
> curvature and the derivative of the metric tensor is generally non-zero at 
> that arbitrary point, however small we assume the region around that point. 
> But applying the EEP, we can transform to the tangent space at that point 
> to diagonalize the metric tensor and have its derivative as zero at that 
> point. Does THIS make sense? AG
>
>
> Yep.  That's pretty much the defining characteristic of a Riemannian space.
>
> Brent
>

But isn't it weird that changing labels on spacetime points by transforming 
coordinates has the result of putting the test particle in local free fall, 
when it wasn't prior to the transformation? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/11/2019 1:58 PM, agrayson2...@gmail.com wrote:





He might have been referring to a transformation to a tangent
space where the metric tensor is diagonalized and its derivative
at that point in spacetime is zero. Does this make any sense?


Sort of.



Yeah, that's what he's doing. He's assuming a given coordinate system 
and some arbitrary point in a non-empty spacetime. So spacetime has a 
non zero curvature and the derivative of the metric tensor is 
generally non-zero at that arbitrary point, however small we assume 
the region around that point. But applying the EEP, we can transform 
to the tangent space at that point to diagonalize the metric tensor 
and have its derivative as zero at that point. Does THIS make sense? AG


Yep.  That's pretty much the defining characteristic of a Riemannian space.

Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 11:09:36 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 6:52 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 6:41:52 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 5:20 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 12:47 PM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 



 On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:



 On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>
>
>
> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>
>
>
> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
> wrote: 
>>
>> In GR, is there a distinction between coordinate systems and frames 
>> of reference? AG??
>>
>
> Here's the problem; there's a GR expert known to some members of this 
> list, who claims GR does NOT distinguish coordinate systems from frames 
> of 
> reference. He also claims that given an arbitrary coordinate system on a 
> manifold, and any given point in space-time, it's possible to find a 
> transformation from the given coordinate system (and using Einstein's 
> Equivalence Principle), to another coordinate system which is locally 
> flat 
> at the arbitrarily given point in space-time. This implies that a test 
> particle is in free fall at that point in space-time. But how can 
> changing 
> labels on space-time points, change the physical properties of a test 
> particle at some arbitrarily chosen point in space-time? I believe that 
> such a transformation implies a DIFFERENT frame of reference, in motion, 
> possibly accelerated, from the original frame or coordinate system. Am I 
> correct? TIA, AG
>
>
> You're right that a coordinate system is just a function for labeling 
> points and, while is may make the equations messy or simple, it doesn't 
> change the physics.?? If you have two different coordinate systems the 
> transformation between them may be arbitrarily complicated.?? But your 
> last 
> sentence referring to motion as distinguishing a coordinate transform 
> from 
> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
> spacetime, block universe there's no difference between an accelerated 
> reference frame and one defined by coordinates that are not geodesic.
>
> Brent
>

 Suppose the test particle is on a geodesic path in one coordinate 
 system, but in another it's on an approximately flat 4D surface at some 
 point in the transformed coordinate system. 


 A geodesic is a physically defined path, one of extremal length.  It's 
 independent of coordinate systems and reference frames.  If a geodesic is 
 not a geodesic in your transformed coordinate system, then you've done 
 something wrong in transforming the metric.

 Brent

>>>
>>> It would clarify the situation if you would state the acceptable before 
>>> and after states of a coordinate transformation that puts the test particle 
>>> in a locally flat region for some chosen point in the transformed 
>>> coordinate system. AG 
>>>
>>>
>>> Like "geodesic" being "locally flat" is a physical characteristic of the 
>>> spacetime.  It's just part of being a Riemannian space that there is a 
>>> sufficiently small region around any point that is "flat".  This is the 
>>> mathematical correlate of Einstein's equivalence principle.  So it is not 
>>> the coordinate system or any transformation that "puts the particle in a 
>>> flat region".  It's just a property of the space being smooth and 
>>> differentiable so that even a curved spacetime at every point has a flat 
>>> tangent space.
>>>
>>> Brent
>>>
>>
>> What you're saying is pretty easy to understand. So I wonder why the 
>> "expert" I was discussing this with, claimed something about a 
>> transformation existing from one coordinate system to another, to make the 
>> particle to be locally in an inertial condition, when that's always the 
>> case?  Do you have any idea what he was referring to? AG
>>
>>
>> Well, it's not always the case.  There are other forces that can act on a 
>> particle besides gravity.  So the the fact that you can always transform to 
>> a free-falling local reference frame and eliminate "gravitational force" 
>> doesn't mean that a particle may not be accelerated by EM or other forces.
>>
>> Brent
>>
>
> He might have been referring to a transformation to a tangent space where 
> the metric tensor is diagonalized and its derivative at that point in 
> spacetime is zero. Does this make any sense? 
>
>
> Sort of.  
>


Yeah, that's what he's doing. He's assuming a given coordinate system and 
some arbitrary point in a non-empty spacetime. So spacetime ha

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/9/2019 6:52 PM, agrayson2...@gmail.com wrote:



On Tuesday, April 9, 2019 at 6:41:52 PM UTC-6, Brent wrote:



On 4/9/2019 5:20 PM, agrays...@gmail.com  wrote:



On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote:



On 4/9/2019 12:47 PM, agrays...@gmail.com wrote:



On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:



On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:



On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent
wrote:



On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:



On Monday, April 8, 2019 at 11:16:25 PM UTC-6,
agrays...@gmail.com wrote:

In GR, is there a distinction between
coordinate systems and frames of reference? AG??


Here's the problem; there's a GR expert known to
some members of this list, who claims GR does NOT
distinguish coordinate systems from frames of
reference. He also claims that given an arbitrary
coordinate system on a manifold, and any given
point in space-time, it's possible to find a
transformation from the given coordinate system
(and using Einstein's Equivalence Principle), to
another coordinate system which is locally flat at
the arbitrarily given point in space-time. This
implies that a test particle is in free fall at
that point in space-time. But how can changing
labels on space-time points, change the physical
properties of a test particle at some arbitrarily
chosen point in space-time? I believe that such a
transformation implies a DIFFERENT frame of
reference, in motion, possibly accelerated, from
the original frame or coordinate system. Am I
correct? TIA, AG


You're right that a coordinate system is just a
function for labeling points and, while is may make
the equations messy or simple, it doesn't change
the physics.?? If you have two different coordinate
systems the transformation between them may be
arbitrarily complicated.?? But your last sentence
referring to motion as distinguishing a coordinate
transform from a reference frame seems to have
slipped into a 3D picture.?? In a 4D spacetime,
block universe there's no difference between an
accelerated reference frame and one defined by
coordinates that are not geodesic.

Brent


Suppose the test particle is on a geodesic path in one
coordinate system, but in another it's on an
approximately flat 4D surface at some point in the
transformed coordinate system.


A geodesic is a physically defined path, one of extremal
length.  It's independent of coordinate systems and
reference frames.  If a geodesic is not a geodesic in
your transformed coordinate system, then you've done
something wrong in transforming the metric.

Brent


It would clarify the situation if you would state the
acceptable before and after states of a coordinate
transformation that puts the test particle in a locally flat
region for some chosen point in the transformed coordinate
system. AG


Like "geodesic" being "locally flat" is a physical
characteristic of the spacetime.  It's just part of being a
Riemannian space that there is a sufficiently small region
around any point that is "flat".  This is the mathematical
correlate of Einstein's equivalence principle.  So it is not
the coordinate system or any transformation that "puts the
particle in a flat region".  It's just a property of the
space being smooth and differentiable so that even a curved
spacetime at every point has a flat tangent space.

Brent


What you're saying is pretty easy to understand. So I wonder why
the "expert" I was discussing this with, claimed something about
a transformation existing from one coordinate system to another,
to make the particle to be locally in an inertial condition, when
that's always the case?  Do you have any idea what he was
referring to? AG


Well, it's not always the case.  There are other forces that can
act on a particle besides gravity.  So the the fact that you can
always transform to a free-falling local reference frame and
eliminate "gravitational force" doesn't mean that a particle may
not be accelerated by EM or other forces.

Brent


He might have been referring to a transf

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 6:41:52 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 5:20 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 12:47 PM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 



 On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:



 On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
 wrote: 
>
> In GR, is there a distinction between coordinate systems and frames of 
> reference? AG??
>

 Here's the problem; there's a GR expert known to some members of this 
 list, who claims GR does NOT distinguish coordinate systems from frames of 
 reference. He also claims that given an arbitrary coordinate system on a 
 manifold, and any given point in space-time, it's possible to find a 
 transformation from the given coordinate system (and using Einstein's 
 Equivalence Principle), to another coordinate system which is locally flat 
 at the arbitrarily given point in space-time. This implies that a test 
 particle is in free fall at that point in space-time. But how can changing 
 labels on space-time points, change the physical properties of a test 
 particle at some arbitrarily chosen point in space-time? I believe that 
 such a transformation implies a DIFFERENT frame of reference, in motion, 
 possibly accelerated, from the original frame or coordinate system. Am I 
 correct? TIA, AG


 You're right that a coordinate system is just a function for labeling 
 points and, while is may make the equations messy or simple, it doesn't 
 change the physics.?? If you have two different coordinate systems the 
 transformation between them may be arbitrarily complicated.?? But your 
 last 
 sentence referring to motion as distinguishing a coordinate transform from 
 a reference frame seems to have slipped into a 3D picture.?? In a 4D 
 spacetime, block universe there's no difference between an accelerated 
 reference frame and one defined by coordinates that are not geodesic.

 Brent

>>>
>>> Suppose the test particle is on a geodesic path in one coordinate 
>>> system, but in another it's on an approximately flat 4D surface at some 
>>> point in the transformed coordinate system. 
>>>
>>>
>>> A geodesic is a physically defined path, one of extremal length.  It's 
>>> independent of coordinate systems and reference frames.  If a geodesic is 
>>> not a geodesic in your transformed coordinate system, then you've done 
>>> something wrong in transforming the metric.
>>>
>>> Brent
>>>
>>
>> It would clarify the situation if you would state the acceptable before 
>> and after states of a coordinate transformation that puts the test particle 
>> in a locally flat region for some chosen point in the transformed 
>> coordinate system. AG 
>>
>>
>> Like "geodesic" being "locally flat" is a physical characteristic of the 
>> spacetime.  It's just part of being a Riemannian space that there is a 
>> sufficiently small region around any point that is "flat".  This is the 
>> mathematical correlate of Einstein's equivalence principle.  So it is not 
>> the coordinate system or any transformation that "puts the particle in a 
>> flat region".  It's just a property of the space being smooth and 
>> differentiable so that even a curved spacetime at every point has a flat 
>> tangent space.
>>
>> Brent
>>
>
> What you're saying is pretty easy to understand. So I wonder why the 
> "expert" I was discussing this with, claimed something about a 
> transformation existing from one coordinate system to another, to make the 
> particle to be locally in an inertial condition, when that's always the 
> case?  Do you have any idea what he was referring to? AG
>
>
> Well, it's not always the case.  There are other forces that can act on a 
> particle besides gravity.  So the the fact that you can always transform to 
> a free-falling local reference frame and eliminate "gravitational force" 
> doesn't mean that a particle may not be accelerated by EM or other forces.
>
> Brent
>

He might have been referring to a transformation to a tangent space where 
the metric tensor is diagonalized and its derivative at that point in 
spacetime is zero. Does this make any sense? I am not sure what initial 
conditions he assumed for the test particle, whether or not it was under 
the influence of non gravitational forces. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/9/2019 5:20 PM, agrayson2...@gmail.com wrote:



On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote:



On 4/9/2019 12:47 PM, agrays...@gmail.com  wrote:



On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:



On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:



On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:



On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:



On Monday, April 8, 2019 at 11:16:25 PM UTC-6,
agrays...@gmail.com wrote:

In GR, is there a distinction between coordinate
systems and frames of reference? AG??


Here's the problem; there's a GR expert known to some
members of this list, who claims GR does NOT
distinguish coordinate systems from frames of
reference. He also claims that given an arbitrary
coordinate system on a manifold, and any given point in
space-time, it's possible to find a transformation from
the given coordinate system (and using Einstein's
Equivalence Principle), to another coordinate system
which is locally flat at the arbitrarily given point in
space-time. This implies that a test particle is in
free fall at that point in space-time. But how can
changing labels on space-time points, change the
physical properties of a test particle at some
arbitrarily chosen point in space-time? I believe that
such a transformation implies a DIFFERENT frame of
reference, in motion, possibly accelerated, from the
original frame or coordinate system. Am I correct? TIA, AG


You're right that a coordinate system is just a function
for labeling points and, while is may make the equations
messy or simple, it doesn't change the physics.?? If you
have two different coordinate systems the transformation
between them may be arbitrarily complicated.?? But your
last sentence referring to motion as distinguishing a
coordinate transform from a reference frame seems to
have slipped into a 3D picture.?? In a 4D spacetime,
block universe there's no difference between an
accelerated reference frame and one defined by
coordinates that are not geodesic.

Brent


Suppose the test particle is on a geodesic path in one
coordinate system, but in another it's on an approximately
flat 4D surface at some point in the transformed coordinate
system.


A geodesic is a physically defined path, one of extremal
length.  It's independent of coordinate systems and reference
frames.  If a geodesic is not a geodesic in your transformed
coordinate system, then you've done something wrong in
transforming the metric.

Brent


It would clarify the situation if you would state the acceptable
before and after states of a coordinate transformation that puts
the test particle in a locally flat region for some chosen point
in the transformed coordinate system. AG


Like "geodesic" being "locally flat" is a physical characteristic
of the spacetime.  It's just part of being a Riemannian space that
there is a sufficiently small region around any point that is
"flat".  This is the mathematical correlate of Einstein's
equivalence principle.  So it is not the coordinate system or any
transformation that "puts the particle in a flat region".  It's
just a property of the space being smooth and differentiable so
that even a curved spacetime at every point has a flat tangent space.

Brent


What you're saying is pretty easy to understand. So I wonder why the 
"expert" I was discussing this with, claimed something about a 
transformation existing from one coordinate system to another, to make 
the particle to be locally in an inertial condition, when that's 
always the case?  Do you have any idea what he was referring to? AG


Well, it's not always the case.  There are other forces that can act on 
a particle besides gravity.  So the the fact that you can always 
transform to a free-falling local reference frame and eliminate 
"gravitational force" doesn't mean that a particle may not be 
accelerated by EM or other forces.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 2:40:16 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 12:47 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 11:55 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
>>> wrote: 

 In GR, is there a distinction between coordinate systems and frames of 
 reference? AG??

>>>
>>> Here's the problem; there's a GR expert known to some members of this 
>>> list, who claims GR does NOT distinguish coordinate systems from frames of 
>>> reference. He also claims that given an arbitrary coordinate system on a 
>>> manifold, and any given point in space-time, it's possible to find a 
>>> transformation from the given coordinate system (and using Einstein's 
>>> Equivalence Principle), to another coordinate system which is locally flat 
>>> at the arbitrarily given point in space-time. This implies that a test 
>>> particle is in free fall at that point in space-time. But how can changing 
>>> labels on space-time points, change the physical properties of a test 
>>> particle at some arbitrarily chosen point in space-time? I believe that 
>>> such a transformation implies a DIFFERENT frame of reference, in motion, 
>>> possibly accelerated, from the original frame or coordinate system. Am I 
>>> correct? TIA, AG
>>>
>>>
>>> You're right that a coordinate system is just a function for labeling 
>>> points and, while is may make the equations messy or simple, it doesn't 
>>> change the physics.?? If you have two different coordinate systems the 
>>> transformation between them may be arbitrarily complicated.?? But your last 
>>> sentence referring to motion as distinguishing a coordinate transform from 
>>> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
>>> spacetime, block universe there's no difference between an accelerated 
>>> reference frame and one defined by coordinates that are not geodesic.
>>>
>>> Brent
>>>
>>
>> Suppose the test particle is on a geodesic path in one coordinate system, 
>> but in another it's on an approximately flat 4D surface at some point in 
>> the transformed coordinate system. 
>>
>>
>> A geodesic is a physically defined path, one of extremal length.  It's 
>> independent of coordinate systems and reference frames.  If a geodesic is 
>> not a geodesic in your transformed coordinate system, then you've done 
>> something wrong in transforming the metric.
>>
>> Brent
>>
>
> It would clarify the situation if you would state the acceptable before 
> and after states of a coordinate transformation that puts the test particle 
> in a locally flat region for some chosen point in the transformed 
> coordinate system. AG 
>
>
> Like "geodesic" being "locally flat" is a physical characteristic of the 
> spacetime.  It's just part of being a Riemannian space that there is a 
> sufficiently small region around any point that is "flat".  This is the 
> mathematical correlate of Einstein's equivalence principle.  So it is not 
> the coordinate system or any transformation that "puts the particle in a 
> flat region".  It's just a property of the space being smooth and 
> differentiable so that even a curved spacetime at every point has a flat 
> tangent space.
>
> Brent
>

What you're saying is pretty easy to understand. So I wonder why the 
"expert" I was discussing this with, claimed something about a 
transformation existing from one coordinate system to another, to make the 
particle to be locally in an inertial condition, when that's always the 
case?  Do you have any idea what he was referring to? AG

>
>
>> Doesn't this represent a change in the physics via a change in labeling 
>> the space-time points?  How is this possible without a change in the frame 
>> of reference, and if so, how would that be described if not by 
>> acceleration? AG
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "Everything List" group.
>> To unsubscribe from this group and stop receiving emails from it, send an 
>> email to everyth...@googlegroups.com.
>> To post to this group, send email to everyth...@googlegroups.com.
>> Visit this group at https://groups.google.com/group/everything-list.
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>>
>>
>> -- 
> You received this message because you are subscribed to the Google Groups 
> "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an 
> email to everyth...@googlegroups.com .
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>
>
>

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You received this message because you are s

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/9/2019 12:47 PM, agrayson2...@gmail.com wrote:



On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:



On 4/9/2019 11:55 AM, agrays...@gmail.com  wrote:



On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:



On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:



On Monday, April 8, 2019 at 11:16:25 PM UTC-6,
agrays...@gmail.com wrote:

In GR, is there a distinction between coordinate systems
and frames of reference? AG??


Here's the problem; there's a GR expert known to some
members of this list, who claims GR does NOT distinguish
coordinate systems from frames of reference. He also claims
that given an arbitrary coordinate system on a manifold, and
any given point in space-time, it's possible to find a
transformation from the given coordinate system (and using
Einstein's Equivalence Principle), to another coordinate
system which is locally flat at the arbitrarily given point
in space-time. This implies that a test particle is in free
fall at that point in space-time. But how can changing
labels on space-time points, change the physical properties
of a test particle at some arbitrarily chosen point in
space-time? I believe that such a transformation implies a
DIFFERENT frame of reference, in motion, possibly
accelerated, from the original frame or coordinate system.
Am I correct? TIA, AG


You're right that a coordinate system is just a function for
labeling points and, while is may make the equations messy or
simple, it doesn't change the physics.?? If you have two
different coordinate systems the transformation between them
may be arbitrarily complicated.?? But your last sentence
referring to motion as distinguishing a coordinate transform
from a reference frame seems to have slipped into a 3D
picture.?? In a 4D spacetime, block universe there's no
difference between an accelerated reference frame and one
defined by coordinates that are not geodesic.

Brent


Suppose the test particle is on a geodesic path in one coordinate
system, but in another it's on an approximately flat 4D surface
at some point in the transformed coordinate system.


A geodesic is a physically defined path, one of extremal length. 
It's independent of coordinate systems and reference frames.  If a
geodesic is not a geodesic in your transformed coordinate system,
then you've done something wrong in transforming the metric.

Brent


It would clarify the situation if you would state the acceptable 
before and after states of a coordinate transformation that puts the 
test particle in a locally flat region for some chosen point in the 
transformed coordinate system. AG


Like "geodesic" being "locally flat" is a physical characteristic of the 
spacetime.  It's just part of being a Riemannian space that there is a 
sufficiently small region around any point that is "flat".  This is the 
mathematical correlate of Einstein's equivalence principle.  So it is 
not the coordinate system or any transformation that "puts the particle 
in a flat region".  It's just a property of the space being smooth and 
differentiable so that even a curved spacetime at every point has a flat 
tangent space.


Brent




Doesn't this represent a change in the physics via a change in
labeling the space-time points?  How is this possible without a
change in the frame of reference, and if so, how would that be
described if not by acceleration? AG
-- 
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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 1:35:34 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 11:55 AM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 4/9/2019 7:52 AM, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com 
>> wrote: 
>>>
>>> In GR, is there a distinction between coordinate systems and frames of 
>>> reference? AG??
>>>
>>
>> Here's the problem; there's a GR expert known to some members of this 
>> list, who claims GR does NOT distinguish coordinate systems from frames of 
>> reference. He also claims that given an arbitrary coordinate system on a 
>> manifold, and any given point in space-time, it's possible to find a 
>> transformation from the given coordinate system (and using Einstein's 
>> Equivalence Principle), to another coordinate system which is locally flat 
>> at the arbitrarily given point in space-time. This implies that a test 
>> particle is in free fall at that point in space-time. But how can changing 
>> labels on space-time points, change the physical properties of a test 
>> particle at some arbitrarily chosen point in space-time? I believe that 
>> such a transformation implies a DIFFERENT frame of reference, in motion, 
>> possibly accelerated, from the original frame or coordinate system. Am I 
>> correct? TIA, AG
>>
>>
>> You're right that a coordinate system is just a function for labeling 
>> points and, while is may make the equations messy or simple, it doesn't 
>> change the physics.?? If you have two different coordinate systems the 
>> transformation between them may be arbitrarily complicated.?? But your last 
>> sentence referring to motion as distinguishing a coordinate transform from 
>> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
>> spacetime, block universe there's no difference between an accelerated 
>> reference frame and one defined by coordinates that are not geodesic.
>>
>> Brent
>>
>
> Suppose the test particle is on a geodesic path in one coordinate system, 
> but in another it's on an approximately flat 4D surface at some point in 
> the transformed coordinate system. 
>
>
> A geodesic is a physically defined path, one of extremal length.  It's 
> independent of coordinate systems and reference frames.  If a geodesic is 
> not a geodesic in your transformed coordinate system, then you've done 
> something wrong in transforming the metric.
>
> Brent
>

It would clarify the situation if you would state the acceptable before and 
after states of a coordinate transformation that puts the test particle in 
a locally flat region for some chosen point in the transformed coordinate 
system. AG 

>
> Doesn't this represent a change in the physics via a change in labeling 
> the space-time points?  How is this possible without a change in the frame 
> of reference, and if so, how would that be described if not by 
> acceleration? AG
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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/9/2019 11:55 AM, agrayson2...@gmail.com wrote:



On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:



On 4/9/2019 7:52 AM, agrays...@gmail.com  wrote:



On Monday, April 8, 2019 at 11:16:25 PM UTC-6,
agrays...@gmail.com wrote:

In GR, is there a distinction between coordinate systems and
frames of reference? AG??


Here's the problem; there's a GR expert known to some members of
this list, who claims GR does NOT distinguish coordinate systems
from frames of reference. He also claims that given an arbitrary
coordinate system on a manifold, and any given point in
space-time, it's possible to find a transformation from the given
coordinate system (and using Einstein's Equivalence Principle),
to another coordinate system which is locally flat at the
arbitrarily given point in space-time. This implies that a test
particle is in free fall at that point in space-time. But how can
changing labels on space-time points, change the physical
properties of a test particle at some arbitrarily chosen point in
space-time? I believe that such a transformation implies a
DIFFERENT frame of reference, in motion, possibly accelerated,
from the original frame or coordinate system. Am I correct? TIA, AG


You're right that a coordinate system is just a function for
labeling points and, while is may make the equations messy or
simple, it doesn't change the physics.?? If you have two different
coordinate systems the transformation between them may be
arbitrarily complicated.?? But your last sentence referring to
motion as distinguishing a coordinate transform from a reference
frame seems to have slipped into a 3D picture.?? In a 4D
spacetime, block universe there's no difference between an
accelerated reference frame and one defined by coordinates that
are not geodesic.

Brent


Suppose the test particle is on a geodesic path in one coordinate 
system, but in another it's on an approximately flat 4D surface at 
some point in the transformed coordinate system.


A geodesic is a physically defined path, one of extremal length. It's 
independent of coordinate systems and reference frames.  If a geodesic 
is not a geodesic in your transformed coordinate system, then you've 
done something wrong in transforming the metric.


Brent

Doesn't this represent a change in the physics via a change in 
labeling the space-time points?  How is this possible without a change 
in the frame of reference, and if so, how would that be described if 
not by acceleration? AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, April 9, 2019 at 12:05:11 PM UTC-6, Brent wrote:
>
>
>
> On 4/9/2019 7:52 AM, agrays...@gmail.com  wrote:
>
>
>
> On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com wrote: 
>>
>> In GR, is there a distinction between coordinate systems and frames of 
>> reference? AG??
>>
>
> Here's the problem; there's a GR expert known to some members of this 
> list, who claims GR does NOT distinguish coordinate systems from frames of 
> reference. He also claims that given an arbitrary coordinate system on a 
> manifold, and any given point in space-time, it's possible to find a 
> transformation from the given coordinate system (and using Einstein's 
> Equivalence Principle), to another coordinate system which is locally flat 
> at the arbitrarily given point in space-time. This implies that a test 
> particle is in free fall at that point in space-time. But how can changing 
> labels on space-time points, change the physical properties of a test 
> particle at some arbitrarily chosen point in space-time? I believe that 
> such a transformation implies a DIFFERENT frame of reference, in motion, 
> possibly accelerated, from the original frame or coordinate system. Am I 
> correct? TIA, AG
>
>
> You're right that a coordinate system is just a function for labeling 
> points and, while is may make the equations messy or simple, it doesn't 
> change the physics.?? If you have two different coordinate systems the 
> transformation between them may be arbitrarily complicated.?? But your last 
> sentence referring to motion as distinguishing a coordinate transform from 
> a reference frame seems to have slipped into a 3D picture.?? In a 4D 
> spacetime, block universe there's no difference between an accelerated 
> reference frame and one defined by coordinates that are not geodesic.
>
> Brent
>

Suppose the test particle is on a geodesic path in one coordinate system, 
but in another it's on an approximately flat 4D surface at some point in 
the transformed coordinate system. Doesn't this represent a change in the 
physics via a change in labeling the space-time points?  How is this 
possible without a change in the frame of reference, and if so, how would 
that be described if not by acceleration? AG

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 4/9/2019 7:52 AM, agrayson2...@gmail.com wrote:



On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com wrote:

In GR, is there a distinction between coordinate systems and
frames of reference? AG


Here's the problem; there's a GR expert known to some members of this 
list, who claims GR does NOT distinguish coordinate systems from 
frames of reference. He also claims that given an arbitrary coordinate 
system on a manifold, and any given point in space-time, it's possible 
to find a transformation from the given coordinate system (and using 
Einstein's Equivalence Principle), to another coordinate system which 
is locally flat at the arbitrarily given point in space-time. This 
implies that a test particle is in free fall at that point in 
space-time. But how can changing labels on space-time points, change 
the physical properties of a test particle at some arbitrarily chosen 
point in space-time? I believe that such a transformation implies a 
DIFFERENT frame of reference, in motion, possibly accelerated, from 
the original frame or coordinate system. Am I correct? TIA, AG


You're right that a coordinate system is just a function for labeling 
points and, while is may make the equations messy or simple, it doesn't 
change the physics.?? If you have two different coordinate systems the 
transformation between them may be arbitrarily complicated.?? But your 
last sentence referring to motion as distinguishing a coordinate 
transform from a reference frame seems to have slipped into a 3D 
picture.?? In a 4D spacetime, block universe there's no difference 
between an accelerated reference frame and one defined by coordinates 
that are not geodesic.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Monday, April 8, 2019 at 11:16:25 PM UTC-6, agrays...@gmail.com wrote:
>
> In GR, is there a distinction between coordinate systems and frames of 
> reference? AG 
>

Here's the problem; there's a GR expert known to some members of this list, 
who claims GR does NOT distinguish coordinate systems from frames of 
reference. He also claims that given an arbitrary coordinate system on a 
manifold, and any given point in space-time, it's possible to find a 
transformation from the given coordinate system (and using Einstein's 
Equivalence Principle), to another coordinate system which is locally flat 
at the arbitrarily given point in space-time. This implies that a test 
particle is in free fall at that point in space-time. But how can changing 
labels on space-time points, change the physical properties of a test 
particle at some arbitrarily chosen point in space-time? I believe that 
such a transformation implies a DIFFERENT frame of reference, in motion, 
possibly accelerated, from the original frame or coordinate system. Am I 
correct? TIA, AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

In GR, is there a distinction between coordinate systems and frames of 
reference? AG 

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 3/27/2019 9:34 AM, agrayson2...@gmail.com wrote:


Look at the paper by Gupta and Padmanabhan that I linked to.



*I looked through your posts here and do not find these papers. Please 
post the links. I want to spend more time reading relevant articles, 
than asking questions. AG*


arXiv:physics/9710036v1

Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 5:08:15 PM UTC-6, smitra wrote:
>
> On 26-03-2019 20:29, agrays...@gmail.com  wrote: 
> > On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote: 
> > 
> >> On Tue, Mar 26, 2019 at 1:14 PM  wrote: 
> >> 
> >>> _> How do the mathematicians prove it?_ 
> >> 
> >> Mathematicians can't prove that a physical theory is correct, all 
> >> they can do is show that changing the coordinate system (for example 
> >> by rotating the X and Y axis) does not result in different physical 
> >> predictions. Only exparament can tell you if the predictions is 
> >> right, or at least mostly right. 
> >> 
> >> John K Clark 
> > 
> > I'm not asking if GR is correct; rather, whether it is covariant. 
> > Moreover, for SR we can prove covariance, since under the LT, the law 
> > of physics don't change and the SoL is c in any inertial frame. ME are 
> > also invariant under the LT.  AG 
> > 
>
> There are many ways one can do this, the most elegant way is to start 
> with a Lagrangian of a field theory and then demand that it be invariant 
> under general coordinate transforms, which requires factors of the 
> square root of the determinant of the metric tensor to be inserted to 
> compensate for the Jacobian of a coordinate transform. This seemingly 
> rather trivial insertion, will yield the field equations of GR as far as 
> the coupling with the fields desribed by the field theory are concerned. 
>
> Compare this with the way you can derive the Maxwell equations from 
> scratch. You start of a scalar field theory, that is invariant under 
> global gauge transforms phi ---> exp(i alpha) phi. And then you make the 
> constant alpha an arbitrary function of space-time, which destroys the 
> invariance due to derivatives generating additional terms. But you can 
> compensate for these derivatives by including a gauge potential. This 
> then yields the coupling of the scalar field to a new field that we can 
> call the electromagnetic field, and this field will have its own gauge 
> invariant term proportional to the field strength tensor squared. 
>
> So, as Paul Davies puts it, in principle mathematically gifted cave men 
> who had never done any experiments involving electromagnetism and 
> gravity could have deduced the Maxwell equations and the Einstein 
> equations of GR from scratch based only on mathematical elegance. 
>
> Saibal 
>

*As I just told Brent, I think I should spend more time reading relevant 
articles, *
*than asking questions. With that objective, please post some links 
describing *
*the methods you reference above, and the article with Davies quote. TIA, 
AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 7:58:11 PM UTC-6, Brent wrote:
>
>
>
> On 3/26/2019 12:29 PM, agrays...@gmail.com  wrote:
>
>
>
> On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote: 
>>
>> On Tue, Mar 26, 2019 at 1:14 PM  wrote:
>>
>> *> How do the mathematicians prove it?*
>>
>>
>> Mathematicians can't prove that a physical theory is correct, all they 
>> can do is show that changing the coordinate system (for example by rotating 
>> the X and Y axis) does not result in different physical predictions. Only 
>> exparament can tell you if the predictions is right, or at least mostly 
>> right.  
>>
>> John K Clark
>>
>
> I'm not asking if GR is correct; rather, whether it is covariant. 
> Moreover, for SR we can prove covariance, since under the LT, the law of 
> physics don't change and the SoL is c in any inertial frame. ME are also 
> invariant under the LT.  AG
>
>
> Look at the paper by Gupta and Padmanabhan that I linked to.  
>


*I looked through your posts here and do not find these papers. Please post 
the links. I want to spend more time reading relevant articles, than asking 
questions. AG*
 

> The equations are written a manifestly covariant form, so no "proof" is 
> relevant.  
>

*That's what I need to grasp; what is a covariant form and why it's 
sufficient to establish covariance, or frame independence of the laws of 
physics. AG *

But the equations are local, partial differential equations.  So when you 
> want to calculate something that involves radiation (and accelerating a 
> mass produced gravitational radiation), even though the local equations are 
> covariant the solution depends on an integral equation over the past motion 
> of the body.  Since that motion can be, ex hypothesi, arbitrary, there's no 
> general transformation between two reference systems that have gone through 
> arbitrary motions in the past.
>
> Brent 
>

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 3/26/2019 12:29 PM, agrayson2...@gmail.com wrote:



On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:

On Tue, Mar 26, 2019 at 1:14 PM > wrote:

/> How do the mathematicians prove it?/


Mathematicians can't prove that a physical theory is correct, all
they can do is show that changing the coordinate system (for
example by rotating the X and Y axis) does not result in different
physical predictions. Only exparament can tell you if the
predictions is right, or at least mostly right.

John K Clark


I'm not asking if GR is correct; rather, whether it is covariant. 
Moreover, for SR we can prove covariance, since under the LT, the law 
of physics don't change and the SoL is c in any inertial frame. ME are 
also invariant under the LT.  AG


Look at the paper by Gupta and Padmanabhan that I linked to.  The 
equations are written a manifestly covariant form, so no "proof" is 
relevant.  But the equations are local, partial differential equations.  
So when you want to calculate something that involves radiation (and 
accelerating a mass produced gravitational radiation), even though the 
local equations are covariant the solution depends on an integral 
equation over the past motion of the body.  Since that motion can be, ex 
hypothesi, arbitrary, there's no general transformation between two 
reference systems that have gone through arbitrary motions in the past.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 3/26/2019 6:14 AM, agrayson2...@gmail.com wrote:



On Tuesday, March 26, 2019 at 6:28:18 AM UTC-6, John Clark wrote:

On Tue, Mar 26, 2019 at 4:40 AM > wrote:

>>>Einstein never said everything is relative. Unlike
velocity there is such a thing as absolute
acceleration, if that were not true the Twin Paradox
could not be resolved.


/>> But in GR don't the field equations take the same form
in all frames, including accelerating frames, which if I
understand correctly,* IS* the Principle of Relativity?
TIA, AG/


*> Clark, how about an answer?*


*Sir yes sir!* Saying the field equations are the same form in all
reference frames is just another way of saying the fundamental
laws of physics are the same everywhere, and if they weren't the
same everywhere General Relativity would be a very bad theory. It
took Einstein 10 years to find equations that fit these invariant
requirements so that in every reference frame the spacetime
distance between 2 events is the same, and in every reference
frame absolute acceleration exists but absolute motion does not,
and every frame is accelerating except for one moving through flat
spacetime (aka a zero gravitational field) in a straight path, and
for every curved spacetime path there must be a force being
applied unless that particular spacetime curve happens to be a
geodesic.

John K Clark


*TY! But what still puzzles me is that, according to Brent, there is 
no general transformation from one accelerating frame to another 
accelerating frame (only a local LT). So, although the field equations 
are claimed to be the same in all frames, accelerating or not, how 
does one prove that without applying a general (non existent!) 
transformation? TIA, AG

*


Look at Appendix C of this very nice paper arXiv:physics/9710036v1 It 
derives the covariant equations for the field of an arbitrarily moving 
charge.


Brent

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Re: Questions about the Equivalence Principle (EP) and GR

[smitra]

On 26-03-2019 20:29, agrayson2...@gmail.com wrote:

On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:


On Tue, Mar 26, 2019 at 1:14 PM  wrote:


_> How do the mathematicians prove it?_


Mathematicians can't prove that a physical theory is correct, all
they can do is show that changing the coordinate system (for example
by rotating the X and Y axis) does not result in different physical
predictions. Only exparament can tell you if the predictions is
right, or at least mostly right.

John K Clark


I'm not asking if GR is correct; rather, whether it is covariant.
Moreover, for SR we can prove covariance, since under the LT, the law
of physics don't change and the SoL is c in any inertial frame. ME are
also invariant under the LT.  AG



There are many ways one can do this, the most elegant way is to start 
with a Lagrangian of a field theory and then demand that it be invariant 
under general coordinate transforms, which requires factors of the 
square root of the determinant of the metric tensor to be inserted to 
compensate for the Jacobian of a coordinate transform. This seemingly 
rather trivial insertion, will yield the field equations of GR as far as 
the coupling with the fields desribed by the field theory are concerned.


Compare this with the way you can derive the Maxwell equations from 
scratch. You start of a scalar field theory, that is invariant under 
global gauge transforms phi ---> exp(i alpha) phi. And then you make the 
constant alpha an arbitrary function of space-time, which destroys the 
invariance due to derivatives generating additional terms. But you can 
compensate for these derivatives by including a gauge potential. This 
then yields the coupling of the scalar field to a new field that we can 
call the electromagnetic field, and this field will have its own gauge 
invariant term proportional to the field strength tensor squared.


So, as Paul Davies puts it, in principle mathematically gifted cave men 
who had never done any experiments involving electromagnetism and 
gravity could have deduced the Maxwell equations and the Einstein 
equations of GR from scratch based only on mathematical elegance.


Saibal

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 11:29:08 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 1:14 PM > wrote:
>
> *> How do the mathematicians prove it?*
>
>
> Mathematicians can't prove that a physical theory is correct, all they can 
> do is show that changing the coordinate system (for example by rotating the 
> X and Y axis) does not result in different physical predictions. Only 
> exparament can tell you if the predictions is right, or at least mostly 
> right.  
>
> John K Clark
>

I'm not asking if GR is correct; rather, whether it is covariant. Moreover, 
for SR we can prove covariance, since under the LT, the law of physics 
don't change and the SoL is c in any inertial frame. ME are also invariant 
under the LT.  AG

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Re: Questions about the Equivalence Principle (EP) and GR

[John Clark]

On Tue, Mar 26, 2019 at 1:14 PM  wrote:

*> How do the mathematicians prove it?*


Mathematicians can't prove that a physical theory is correct, all they can
do is show that changing the coordinate system (for example by rotating the
X and Y axis) does not result in different physical predictions. Only
exparament can tell you if the predictions is right, or at least mostly
right.

John K Clark






> For more options, visit https://groups.google.com/d/optout.
>

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 10:36:03 AM UTC-6, John Clark wrote:
>
> By the way, just  2 weeks ago the best test ever made of Einstein's 
> Equivalence Principle was performed in a gravitational field one million 
> times greater than Earth's and Einstein passed the test with flying 
> colors.  
>
> Test of the Einstein Equivalence Principle near the Galactic Center 
> Supermassive Black Hole 
>   
>
> John K Clark
>

I read an article about that yesterday. AG 

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 9:35:41 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 9:14 AM > wrote:
>
> *>* *although the field equations are claimed to be the same in all 
>> frames, accelerating or not, how does one prove that*
>>
>
> Mathematicians prove things Physicists don't. Physicists show that some 
> ideas are less wrong than others and they do that by determining how 
> closely the idea conforms with experimental observation. So far at least 
> General Relativity has conformed very very well. 
>
>  John K Clark
>

Thanks, but that's very far removed from a viable explanation of covariance 
as a property of the GR field equations. How do the mathematicians prove 
it? You know, Einstein worked with the best of them, such as Grossman and 
Hilbert. They must have been very satisfied that covariance was an 
established, provable property. Do you have a clue how that might be done 
-- to establish covariance? AG 

>
>  
>

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Re: Questions about the Equivalence Principle (EP) and GR

[John Clark]

By the way, just  2 weeks ago the best test ever made of Einstein's
Equivalence Principle was performed in a gravitational field one million
times greater than Earth's and Einstein passed the test with flying
colors.

Test of the Einstein Equivalence Principle near the Galactic Center
Supermassive Black Hole


John K Clark

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Re: Questions about the Equivalence Principle (EP) and GR

[John Clark]

On Tue, Mar 26, 2019 at 9:14 AM  wrote:

*>* *although the field equations are claimed to be the same in all frames,
> accelerating or not, how does one prove that*
>

Mathematicians prove things Physicists don't. Physicists show that some
ideas are less wrong than others and they do that by determining how
closely the idea conforms with experimental observation. So far at least
General Relativity has conformed very very well.

 John K Clark

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Tuesday, March 26, 2019 at 6:28:18 AM UTC-6, John Clark wrote:
>
> On Tue, Mar 26, 2019 at 4:40 AM > wrote:
>
> >>>Einstein never said everything is relative. Unlike velocity there is 
 such a thing as absolute acceleration, if that were not true the Twin 
 Paradox could not be resolved.

>>>
>>> *>> But in GR don't the field equations take the same form in all 
>>> frames, including accelerating frames, which if I understand correctly, IS 
>>> the Principle of Relativity? TIA, AG*
>>>
>>
>> *> Clark, how about an answer?*
>>
>
> *Sir yes sir!* Saying the field equations are the same form in all 
> reference frames is just another way of saying the fundamental laws of 
> physics are the same everywhere, and if they weren't the same 
> everywhere General Relativity would be a very bad theory. It took Einstein 
> 10 years to find equations that fit these invariant requirements so that in 
> every reference frame the spacetime distance between 2 events is the same, 
> and in every reference frame absolute acceleration exists but absolute 
> motion does not, and every frame is accelerating except for one moving 
> through flat spacetime (aka a zero gravitational field) in a straight path, 
> and for every curved spacetime path there must be a force being applied 
> unless that particular spacetime curve happens to be a geodesic. 
>
> John K Clark
>

*TY! But what still puzzles me is that, according to Brent, there is no 
general transformation from one accelerating frame to another accelerating 
frame (only a local LT). So, although the field equations are claimed to be 
the same in all frames, accelerating or not, how does one prove that 
without applying a general (non existent!) transformation? TIA, AG *

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Re: Questions about the Equivalence Principle (EP) and GR

[John Clark]

On Tue, Mar 26, 2019 at 4:40 AM  wrote:

>>>Einstein never said everything is relative. Unlike velocity there is
>>> such a thing as absolute acceleration, if that were not true the Twin
>>> Paradox could not be resolved.
>>>
>>
>> *>> But in GR don't the field equations take the same form in all frames,
>> including accelerating frames, which if I understand correctly, IS the
>> Principle of Relativity? TIA, AG*
>>
>
> *> Clark, how about an answer?*
>

*Sir yes sir!* Saying the field equations are the same form in all
reference frames is just another way of saying the fundamental laws of
physics are the same everywhere, and if they weren't the same
everywhere General Relativity would be a very bad theory. It took Einstein
10 years to find equations that fit these invariant requirements so that in
every reference frame the spacetime distance between 2 events is the same,
and in every reference frame absolute acceleration exists but absolute
motion does not, and every frame is accelerating except for one moving
through flat spacetime (aka a zero gravitational field) in a straight path,
and for every curved spacetime path there must be a force being applied
unless that particular spacetime curve happens to be a geodesic.

John K Clark

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 11:13:06 PM UTC-6, agrays...@gmail.com 
wrote:
>
>
>
> On Wednesday, March 20, 2019 at 10:08:53 AM UTC-6, John Clark wrote:
>>
>> On Wed, Mar 20, 2019 at 9:16 AM  wrote:
>>
>> * > how does GR establish the Principle of Relativity (for accelerating 
>>> frames)? AG *
>>>
>>
>> It doesn't, Einstein never said everything is relative. Unlike velocity 
>> there is such a thing as absolute acceleration, if that were not true the 
>> Twin Paradox could not be resolved.
>>
>> John K Clark
>>
>
> But in GR don't the field equations take the same form in all frames, 
> including accelerating frames, which if I understand correctly,* IS* the 
> Principle of Relativity? TIA, AG
>

*Clark, how about an answer? If the GR field equations have the same form 
in all frames, including accelerating frames, isn't this what we call the 
Principle of Relativity? AG*

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Saturday, March 23, 2019 at 2:19:39 PM UTC-6, Brent wrote:
>
>
>
> On 3/23/2019 5:45 AM, agrays...@gmail.com  wrote:
>
>
>
> On Thursday, March 21, 2019 at 12:40:13 AM UTC-6, smitra wrote: 
>>
>> On 21-03-2019 06:21, agrays...@gmail.com wrote: 
>> > On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote: 
>> > 
>> >> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote: 
>> >> 
>> >> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote: 
>> >> 
>> >> On 3/19/2019 9:32 AM, John Clark wrote: 
>> >> 
>> >> On Tue, Mar 19, 2019 at 4:50 AM  wrote: 
>> >> 
>> >>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A 
>> >> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND 
>> >> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY. 
>> >> IS THIS TRUE? TIA, AG 
>> >> 
>> >> Einstein's breakthrough, what he called "the happiest thought of my 
>> >> life" was when he realized a man in a falling elevator will not feel 
>> >> gravity but a man in a accelerating elevator will. In other words an 
>> >> accelerating frame and gravity are the same thing, that's why it's 
>> >> called the Equivalence Principle. 
>> > 
>> >  I wonder if Einstein ever considered whether a charged particle in 
>> > the falling radiate would radiate? 
>> > 
>> >  Brent 
>> > 
>> > Because of your typos, at first I thought you were joking. Well, maybe 
>> > it was a joke, but for me it sounds like a damned good question. I 
>> > surmise that a charged particle accelerating due to gravity does NOT 
>> > radiate energy, but why? AG 
>> > 
>> >  Sorry about the typos.   Yes, it does seem paradoxical.  Here's a 
>> > paper that purports to solve the problem. 
>> > 
>> > THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON: 
>> > A SIMPLE DERIVATION 
>> > 
>> > Camila de Almeida [1], Alberto Saa [2] 
>> > (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this 
>> > version, v5)) 
>> > 
>> >> We show, by exploring some elementary consequences of the covariance 
>> >> of Maxwell's equations under general coordinate transformations, 
>> >> that, despite inertial observers can indeed detect electromagnetic 
>> >> radiation emitted from a uniformly accelerated charge, comoving 
>> >> observers will see only a static electric field. This simple 
>> >> analysis can help understanding one of the most celebrated paradoxes 
>> >> of last century. 
>> > 
>> >  Comments: 
>> >  Revtex, 6 pages, 2 figures. v2: Some small 
>> corrections. v3: 
>> > Citation of a earlier paper included. v4: Some stylistic changes. v5: 
>> > Final version to appear in AJP 
>> > 
>> >  Subjects: 
>> >  Classical Physics (physics.class-ph); General 
>> Relativity and 
>> > Quantum Cosmology (gr-qc) 
>> > 
>> >  Journal reference: 
>> >  Am.J.Phys. 74 (2006) 154-158 
>> > 
>> >  DOI: 
>> >  10.1119/1.2162548 [4] 
>> > 
>> >  Cite as: 
>> >  arXiv:physics/0506049 [5] [physics.class-ph] 
>> > 
>> >  (or arXiv:physics/0506049v5 [6] [physics.class-ph] for 
>> this 
>> > version) 
>> > 
>> >  And another paper that looks at possible experimental evidence. 
>> > 
>> > ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEIN'S 
>> > EQUIVALENCE PRINCIPLE 
>> > 
>> > Gerold Gründler [7] 
>> > (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this 
>> > version, v3)) 
>> > 
>> >> According to Larmor's formula, accelerated electric charges radiate 
>> >> electromagnetic waves. Hence charges should radiate, if they are in 
>> >> free fall in gravitational fields, and they should not radiate if 
>> >> they are supported at rest in gravitational fields. But according to 
>> >> Einstein's equivalence principle, charges in free fall should not 
>> >> radiate, while charges supported at rest in gravitational fields 
>> >> should radiate. In this article we point out indirect experimental 
>> >> evidence, indicating that the equivalence principle is correct, 
>> >> while the traditional interpretation of Larmor's formula must be 
>> >> amended. 
>> > 
>> >  Subjects: 
>> >  General Physics (physics.gen-ph) 
>> > 
>> >  Cite as: 
>> >  arXiv:1509.08757 [9] [physics.gen-ph] 
>> > 
>> >  (or arXiv:1509.08757v3 [10] [physics.gen-ph] for this 
>> version) 
>> > 
>> >  However, I don't find them entirely convincing.  We know that double 
>> > stars, which are orbiting one another in free-fall, radiate 
>> > gravitational waves.  Are we to suppose that if one or both of them 
>> > had an electrical charge that there would be no EM radiation? 
>> > 
>> >  Brent 
>> > 
>> > IF WE GO BACK TO CLASSICAL E&M, WHERE DOES THE EM RADIATION COME FROM 
>> > WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CAN'T COME FROM 
>> > THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOUL

Re: Questions about the Equivalence Principle (EP) and GR

['Brent Meeker' via Everything List]

On 3/23/2019 5:45 AM, agrayson2...@gmail.com wrote:



On Thursday, March 21, 2019 at 12:40:13 AM UTC-6, smitra wrote:

On 21-03-2019 06:21, agrays...@gmail.com  wrote:
> On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote:
>
>> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote:
>>
>> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote:
>>
>> On 3/19/2019 9:32 AM, John Clark wrote:
>>
>> On Tue, Mar 19, 2019 at 4:50 AM  wrote:
>>
>>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A
>> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND
>> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY.
>> IS THIS TRUE? TIA, AG
>>
>> Einstein's breakthrough, what he called "the happiest thought
of my
>> life" was when he realized a man in a falling elevator will not
feel
>> gravity but a man in a accelerating elevator will. In other
words an
>> accelerating frame and gravity are the same thing, that's why it's
>> called the Equivalence Principle.
>
>  I wonder if Einstein ever considered whether a charged particle in
> the falling radiate would radiate?
>
>  Brent
>
> Because of your typos, at first I thought you were joking. Well,
maybe
> it was a joke, but for me it sounds like a damned good question. I
> surmise that a charged particle accelerating due to gravity does
NOT
> radiate energy, but why? AG
>
>  Sorry about the typos.   Yes, it does seem paradoxical.  Here's a
> paper that purports to solve the problem.
>
> THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE
HORIZON:
> A SIMPLE DERIVATION
>
> Camila de Almeida [1], Alberto Saa [2]
> (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this
> version, v5))
>
>> We show, by exploring some elementary consequences of the
covariance
>> of Maxwell's equations under general coordinate transformations,
>> that, despite inertial observers can indeed detect electromagnetic
>> radiation emitted from a uniformly accelerated charge, comoving
>> observers will see only a static electric field. This simple
>> analysis can help understanding one of the most celebrated
paradoxes
>> of last century.
>
>  Comments:
>  Revtex, 6 pages, 2 figures. v2: Some small
corrections. v3:
> Citation of a earlier paper included. v4: Some stylistic
changes. v5:
> Final version to appear in AJP
>
>  Subjects:
>  Classical Physics (physics.class-ph); General
Relativity and
> Quantum Cosmology (gr-qc)
>
>  Journal reference:
>  Am.J.Phys. 74 (2006) 154-158
>
>  DOI:
>  10.1119/1.2162548 [4]
>
>  Cite as:
>  arXiv:physics/0506049 [5] [physics.class-ph]
>
>  (or arXiv:physics/0506049v5 [6]
[physics.class-ph] for this
> version)
>
>  And another paper that looks at possible experimental evidence.
>
> ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEIN'S
> EQUIVALENCE PRINCIPLE
>
> Gerold Gründler [7]
> (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this
> version, v3))
>
>> According to Larmor's formula, accelerated electric charges
radiate
>> electromagnetic waves. Hence charges should radiate, if they
are in
>> free fall in gravitational fields, and they should not radiate if
>> they are supported at rest in gravitational fields. But
according to
>> Einstein's equivalence principle, charges in free fall should not
>> radiate, while charges supported at rest in gravitational fields
>> should radiate. In this article we point out indirect experimental
>> evidence, indicating that the equivalence principle is correct,
>> while the traditional interpretation of Larmor's formula must be
>> amended.
>
>  Subjects:
>  General Physics (physics.gen-ph)
>
>  Cite as:
>  arXiv:1509.08757 [9] [physics.gen-ph]
>
>  (or arXiv:1509.08757v3 [10] [physics.gen-ph]
for this version)
>
>  However, I don't find them entirely convincing.  We know that
double
> stars, which are orbiting one another in free-fall, radiate
> gravitational waves.  Are we to suppose that if one or both of them
> had an electrical charge that there would be no EM radiation?
>
>  Brent
>
> IF WE GO BACK TO CLASSICAL E&M, WHERE DOES THE EM RADIATION COME
FROM
> WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CAN'T COME FROM
> THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD IMPLY LOSS OF
 

Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Wednesday, March 20, 2019 at 10:08:53 AM UTC-6, John Clark wrote:
>
> On Wed, Mar 20, 2019 at 9:16 AM > wrote:
>
> * > how does GR establish the Principle of Relativity (for accelerating 
>> frames)? AG *
>>
>
> It doesn't, Einstein never said everything is relative. Unlike velocity 
> there is such a thing as absolute acceleration, if that were not true the 
> Twin Paradox could not be resolved.
>
> John K Clark
>

In the TP we're comparing an inertial frame with an accelerating frame; not 
the general case I was referring to for accelerating frames. But I'm 
confused, again. Don't Einstein's field equations take the same form in all 
frames, and isn't this the Principle of Relativity for gravity? AG

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Re: Questions about the Equivalence Principle (EP) and GR

[agrayson2000]

On Thursday, March 21, 2019 at 12:40:13 AM UTC-6, smitra wrote:
>
> On 21-03-2019 06:21, agrays...@gmail.com  wrote: 
> > On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote: 
> > 
> >> On 3/20/2019 3:07 AM, agrays...@gmail.com wrote: 
> >> 
> >> On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote: 
> >> 
> >> On 3/19/2019 9:32 AM, John Clark wrote: 
> >> 
> >> On Tue, Mar 19, 2019 at 4:50 AM  wrote: 
> >> 
> >>> I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A 
> >> GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND 
> >> LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY. 
> >> IS THIS TRUE? TIA, AG 
> >> 
> >> Einstein's breakthrough, what he called "the happiest thought of my 
> >> life" was when he realized a man in a falling elevator will not feel 
> >> gravity but a man in a accelerating elevator will. In other words an 
> >> accelerating frame and gravity are the same thing, that's why it's 
> >> called the Equivalence Principle. 
> > 
> >  I wonder if Einstein ever considered whether a charged particle in 
> > the falling radiate would radiate? 
> > 
> >  Brent 
> > 
> > Because of your typos, at first I thought you were joking. Well, maybe 
> > it was a joke, but for me it sounds like a damned good question. I 
> > surmise that a charged particle accelerating due to gravity does NOT 
> > radiate energy, but why? AG 
> > 
> >  Sorry about the typos.   Yes, it does seem paradoxical.  Here's a 
> > paper that purports to solve the problem. 
> > 
> > THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON: 
> > A SIMPLE DERIVATION 
> > 
> > Camila de Almeida [1], Alberto Saa [2] 
> > (Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this 
> > version, v5)) 
> > 
> >> We show, by exploring some elementary consequences of the covariance 
> >> of Maxwell's equations under general coordinate transformations, 
> >> that, despite inertial observers can indeed detect electromagnetic 
> >> radiation emitted from a uniformly accelerated charge, comoving 
> >> observers will see only a static electric field. This simple 
> >> analysis can help understanding one of the most celebrated paradoxes 
> >> of last century. 
> > 
> >  Comments: 
> >  Revtex, 6 pages, 2 figures. v2: Some small corrections. 
> v3: 
> > Citation of a earlier paper included. v4: Some stylistic changes. v5: 
> > Final version to appear in AJP 
> > 
> >  Subjects: 
> >  Classical Physics (physics.class-ph); General 
> Relativity and 
> > Quantum Cosmology (gr-qc) 
> > 
> >  Journal reference: 
> >  Am.J.Phys. 74 (2006) 154-158 
> > 
> >  DOI: 
> >  10.1119/1.2162548 [4] 
> > 
> >  Cite as: 
> >  arXiv:physics/0506049 [5] [physics.class-ph] 
> > 
> >  (or arXiv:physics/0506049v5 [6] [physics.class-ph] for 
> this 
> > version) 
> > 
> >  And another paper that looks at possible experimental evidence. 
> > 
> > ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEIN'S 
> > EQUIVALENCE PRINCIPLE 
> > 
> > Gerold Gründler [7] 
> > (Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this 
> > version, v3)) 
> > 
> >> According to Larmor's formula, accelerated electric charges radiate 
> >> electromagnetic waves. Hence charges should radiate, if they are in 
> >> free fall in gravitational fields, and they should not radiate if 
> >> they are supported at rest in gravitational fields. But according to 
> >> Einstein's equivalence principle, charges in free fall should not 
> >> radiate, while charges supported at rest in gravitational fields 
> >> should radiate. In this article we point out indirect experimental 
> >> evidence, indicating that the equivalence principle is correct, 
> >> while the traditional interpretation of Larmor's formula must be 
> >> amended. 
> > 
> >  Subjects: 
> >  General Physics (physics.gen-ph) 
> > 
> >  Cite as: 
> >  arXiv:1509.08757 [9] [physics.gen-ph] 
> > 
> >  (or arXiv:1509.08757v3 [10] [physics.gen-ph] for this 
> version) 
> > 
> >  However, I don't find them entirely convincing.  We know that double 
> > stars, which are orbiting one another in free-fall, radiate 
> > gravitational waves.  Are we to suppose that if one or both of them 
> > had an electrical charge that there would be no EM radiation? 
> > 
> >  Brent 
> > 
> > IF WE GO BACK TO CLASSICAL E&M, WHERE DOES THE EM RADIATION COME FROM 
> > WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CAN'T COME FROM 
> > THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD IMPLY LOSS OF 
> > MASS OR CHARGE OF THE ELECTRON, WHICH IS NEVER CLAIMED. SO IT MUST 
> > COME FROM THE EM FIELD CAUSING THE ACCELERATION. NOW IF WE GO TO THE 
> > CASE OF GRAVITY WITHOUT ANY EM SOURCE FIELDS, AND WE STILL GET EM 
> > RADI

Re: Questions about the Equivalence Principle (EP) and GR

[smitra]

On 21-03-2019 06:21, agrayson2...@gmail.com wrote:

On Wednesday, March 20, 2019 at 12:51:18 PM UTC-6, Brent wrote:


On 3/20/2019 3:07 AM, agrays...@gmail.com wrote:

On Tuesday, March 19, 2019 at 7:23:29 PM UTC-6, Brent wrote:

On 3/19/2019 9:32 AM, John Clark wrote:

On Tue, Mar 19, 2019 at 4:50 AM  wrote:


I SUPPOSE EINSTEIN STARTED WITH THE MOTIVATION OF FINDING A

GENERAL TRANSFORMATION FROM ONE ACCELERATING FRAME TO ANOTHER, AND
LATER GAVE UP ON THIS PROJECT AND SETTLED FOR A THEORY OF GRAVITY.
IS THIS TRUE? TIA, AG

Einstein's breakthrough, what he called "the happiest thought of my
life" was when he realized a man in a falling elevator will not feel
gravity but a man in a accelerating elevator will. In other words an
accelerating frame and gravity are the same thing, that's why it's
called the Equivalence Principle.


 I wonder if Einstein ever considered whether a charged particle in
the falling radiate would radiate?

 Brent

Because of your typos, at first I thought you were joking. Well, maybe
it was a joke, but for me it sounds like a damned good question. I
surmise that a charged particle accelerating due to gravity does NOT
radiate energy, but why? AG

 Sorry about the typos.   Yes, it does seem paradoxical.  Here's a
paper that purports to solve the problem.

THE RADIATION OF A UNIFORMLY ACCELERATED CHARGE IS BEYOND THE HORIZON:
A SIMPLE DERIVATION

Camila de Almeida [1], Alberto Saa [2]
(Submitted on 6 Jun 2005 (v1 [3]), last revised 2 Dec 2005 (this
version, v5))


We show, by exploring some elementary consequences of the covariance
of Maxwell's equations under general coordinate transformations,
that, despite inertial observers can indeed detect electromagnetic
radiation emitted from a uniformly accelerated charge, comoving
observers will see only a static electric field. This simple
analysis can help understanding one of the most celebrated paradoxes
of last century.


Comments:
Revtex, 6 pages, 2 figures. v2: Some small corrections. v3:
Citation of a earlier paper included. v4: Some stylistic changes. v5:
Final version to appear in AJP

Subjects:
Classical Physics (physics.class-ph); General Relativity and
Quantum Cosmology (gr-qc)

Journal reference:
Am.J.Phys. 74 (2006) 154-158

DOI:
10.1119/1.2162548 [4]

Cite as:
arXiv:physics/0506049 [5] [physics.class-ph]

(or arXiv:physics/0506049v5 [6] [physics.class-ph] for this
version)

 And another paper that looks at possible experimental evidence.

ELECTRICAL CHARGES IN GRAVITATIONAL FIELDS, AND EINSTEIN'S
EQUIVALENCE PRINCIPLE

Gerold Gründler [7]
(Submitted on 14 Sep 2015 (v1 [8]), last revised 12 Oct 2015 (this
version, v3))


According to Larmor's formula, accelerated electric charges radiate
electromagnetic waves. Hence charges should radiate, if they are in
free fall in gravitational fields, and they should not radiate if
they are supported at rest in gravitational fields. But according to
Einstein's equivalence principle, charges in free fall should not
radiate, while charges supported at rest in gravitational fields
should radiate. In this article we point out indirect experimental
evidence, indicating that the equivalence principle is correct,
while the traditional interpretation of Larmor's formula must be
amended.


Subjects:
General Physics (physics.gen-ph)

Cite as:
arXiv:1509.08757 [9] [physics.gen-ph]

(or arXiv:1509.08757v3 [10] [physics.gen-ph] for this version)

 However, I don't find them entirely convincing.  We know that double
stars, which are orbiting one another in free-fall, radiate
gravitational waves.  Are we to suppose that if one or both of them
had an electrical charge that there would be no EM radiation?

 Brent

IF WE GO BACK TO CLASSICAL E&M, WHERE DOES THE EM RADIATION COME FROM
WHICH IS EMITTED FOR ACCELERATING PARTICLES? IT CAN'T COME FROM
THE SELF FIELD OF, SAY, AN ELECTRON, SINCE THAT WOULD IMPLY LOSS OF
MASS OR CHARGE OF THE ELECTRON, WHICH IS NEVER CLAIMED. SO IT MUST
COME FROM THE EM FIELD CAUSING THE ACCELERATION. NOW IF WE GO TO THE
CASE OF GRAVITY WITHOUT ANY EM SOURCE FIELDS, AND WE STILL GET EM
RADIATION DUE TO THE ACCELERATION, WHERE DOES IT COME FROM? AG


It comes from the self-force, see here:

https://arxiv.org/abs/0905.2391

Saibal

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