subject:"RE\: How does acceleration curve space\? Can anyone provide an answer\?"

Brent,

What problem do you think P-time has in SR? I see none. Have you been 
following my discussion with Jesse as to why it is possible to correlate 
proper times (the twins own actual ages) 1:1 for the twins all along their 
worldlines in a frame independent way simply by comparing the relativistic 
descriptions of BOTH twins?

I think your problem is that you are trying to explain P-time from WITHIN 
some particular relativistic frame. I agree that simply doesn't work, but 
that's not the way to look at it. One needs to know both frames. When this 
known a 1:1 correlation can always be found, at that is the same p-time, 
the same present moment...

Edgar

On Saturday, February 22, 2014 1:08:20 AM UTC-5, Brent wrote:
>
> On 2/21/2014 3:48 PM, Russell Standish wrote: 
> > On Fri, Feb 21, 2014 at 03:11:56PM -0800, meekerdb wrote: 
> >> Just to clarify, it is *space* that is flat, but spacetime is still 
> >> curved, i.e. expansion of the universe is accelerating. 
> >> 
> > That could only be true in one particular inertial reference 
> > frame? Surely, it can't be the case that spacetime is flat along all 
> > space-like trajectories, whilst at the same time being curved along 
> > time-like trajectories. 
>
> The metric for a isotropic, homogenous universe (FRW) is 
>
>  ds^2 = dt^2 - a(t)^2{dr^2/(1-kr^2) + r^2[dtheta^2 + sin(theta)^2 
> dphi^2]} 
>
>Where a(t) must satisfy the Friedman equations. 
>
>  (da/dt)^2 - (8/3)piG*a^2 = -k 
>
>  (d^2a/dt^2) = -(4/3)piG(rho + 3p)a(t) 
>
> For k=0 the space part {...} is just Euclidean.  But it's not a flat 
> spacetime because of 
> the time dependent a(t)^2 factor. 
>
> > 
> > If so, then the orthogonal time axis that makes the spatial subspace 
> > flat could be a candidate for Edgar's mysterious p-time. 
>
> Yes, I suggested to Edgar that the coordinate time in co-moving 
> coordinates, which is what 
> t is in the FRW equation, could serve as a physically distinguished time. 
>  A global 
> simultaneity is defined by the same value of a(t) everywhere.  But of 
> course that doesn't 
> solve his problem, which occurs already in special relativity. 
>
> Brent 
>
> > 
> > Cheers 
> > 
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

Jesse,

But from the links you yourself provide:
http://adsabs.harvard.edu/abs/1985AmJPh..53..661O

To quote from the abstract:

If a heavy object with rest mass M moves past you with a velocity 
comparable to the speed of light, you will be attracted gravitationally 
towards its path as though it had an increased mass. If the relativistic 
increase in active gravitational mass is measured by the transverse (and 
longitudinal) velocities which such a moving mass induces in test particles 
initially at rest near its path, then we find, with this definition, that 
Mrel=γ(1+β^2)M. Therefore, in the ultrarelativistic limit, the active 
gravitational mass of a moving body, measured in this way, is not γM but is 
approximately 2γM.
So this reference from the Harvard physics dept. says that the active 
gravitational mass of a relativistically moving particle DOES INCREASE and 
has a stronger gravitational attraction to what it is moving relative to.

So that seems to contradict your own conclusion.

Clearly from Harvard, the increased mass (relativistic mass) of a moving 
object DOES have an increased gravitational attraction. So since 
gravitational attraction is due to curvature of spacetime one can say that 
from the POV (the frame) of the stationary observer, the moving object must 
be curving spacetime more.

Correct?

Edgar




Read more: http://www.physicsforums.com 

On Wednesday, February 19, 2014 10:32:07 AM UTC-5, jessem wrote:
>
> The curvature of spacetime is understood in a coordinate-invariant way, in 
> terms of the proper time and proper length along paths through spacetime, 
> so it doesn't depend at all on what coordinate system you use to describe 
> things. Physicists do sometimes talk about the "curvature of space" 
> distinct from the curvature of spacetime, I'm not sure if you meant to 
> distinguish the two or were treating them as synonymous. But defining the 
> curvature of space depends on picking a simultaneity convention which 
> divides 4D spacetime into a series of 3D slices, and then defining the 
> curvature of each slice in terms of proper length along spacelike paths 
> confined to that slice. So the "curvature of space" is 
> coordinate-dependent, since different simultaneity conventions = different 
> slices with different curvatures.
>
> I don't know if there's any meaningful sense in which picking a coordinate 
> system where an object has a higher velocity means it curves space 
> "more"--if there is, it would presumably depend on a choice to restrict the 
> analysis to some family of coordinate systems where each possible velocity 
> would be associated with a particular choice of simultaneity convention, 
> rather than using any of the arbitrary smooth coordinate systems (with 
> arbitrary simultaneity conventions) that are permitted in general 
> relativity.
>
> I found some discussion of the issue of how velocity relates to curvature 
> and gravitational "force" on these pages:
>
>
> http://physics.stackexchange.com/questions/95023/does-a-moving-object-curve-space-time-as-its-velocity-increases
>
> http://www.physicsforums.com/showthread.php?t=602644
>
>
> On Wed, Feb 19, 2014 at 9:15 AM, Edgar L. Owen 
> > wrote:
>
>> Russell, Brent, Jesse, et al,
>>
>> The "increased kinetic energy of the particle" is not due to its 
>> acceleration but to its relative velocity to some observer. Mass also 
>> increases with relative velocity, but that apparent increase in mass is 
>> only with respect to some observer the motion is relative to. In fact all 
>> kinetic energy is only with respect to relative velocity with some observer 
>> frame.
>>
>> So this means that any increased curvature of space from that increased 
>> kinetic energy and increased mass should be only with respect to observers 
>> it is in relative motion with respect to.
>>
>> So in this case we seem to have a case in which the curvature of space is 
>> relative rather than being absolute.
>>
>> Would you not agree?
>>
>> Edgar
>>
>>
>>
>> On Tuesday, February 18, 2014 4:44:58 PM UTC-5, Russell Standish wrote:
>>>
>>> On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote: 
>>> > On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen  
>>> wrote: 
>>> > 
>>> > > 
>>> > > >> You say that "You can tell if spacetime is curved or not by 
>>> observing 
>>> > >> if light moves in a straight line or not." and then you say that 
>>> light does 
>>> > >> NOT travel in a straight line in the accelerating elevator example 
>>> you give. 
>>> > >> 
>>> > > 
>>> > > > So, by your terminology, does that mean that the acceleration of 
>>> the 
>>> > > elevator IS curving space ? 
>>> > > 
>>> > 
>>> > You should stop talking about "space", it's "4D spacetime"; but yes 
>>> it's 
>>> > curved, although if you were inside that sealed elevator you couldn't 
>>> tell 
>>> > if the curvature was caused by rockets accelerating the elevator in 
>>> deep 
>>> > space or if it was caused by the Earth's gravity. Acceleration is 
>>> abs

Re: How does acceleration curve space? Can anyone provide an answer?

John,

First Linde didn't "prove" eternal inflation as you claim. Eternal 
inflation is a theory. In fact you yourself admit this when you write "IF 
Linde is correct..".

Basically the bounding problem of any physical infinity is that it would 
take infinite energy over infinite time to 'achieve' (though it is not 
really something subject to being achieved since by definition it's the 
result of an unending process) which I don't think anyone agrees exists. 
Though, on second thought judging by some of the other nonsense they 
believe, there is probably some physicist somewhere that believes in 
anything.

The other approach, which you hint at, is that even if a physical infinity 
existed it would be unobservable. And since we can make a good case that 
only observables exist (or their direct effects) we can say that even if a 
physical infinite existed it wouldn't actually exist.

Edgar




On Saturday, February 22, 2014 1:13:14 PM UTC-5, John Clark wrote:
>
> On Sat, Feb 22, 2014 at 8:41 AM, Edgar L. Owen 
> > wrote:
>
> > I hate it when otherwise intelligent physicists use infinite in the 
>> sense of just really really big!
>>
>
> I hate that too, in fact I take pride in not using the word "infinite" 
> unless a proper subset of the thing can be put into a one to one 
> correspondence with the entire thing; and as a result I sometime struggle 
> to come up with the correct word when "astronomical" seems too small but 
> "infinite" is too big. But I stand by what I said, the CMBR data is 
> consistent with the universe being infinite and not just very very very 
> big. Of course that doesn't prove it is in fact infinite but it doesn't 
> rule it out either.
>
> > There simply are and can be no physical infinities. 
>>
>
> Nobody has found a infinite number of any physical object, but even if 
> there were such things how would we know?  
>
> > It's an impossible notion by its very definition.
>
>
> Physical infinity might not exist, but if it doesn't it wouldn't be 
> because it was impossible by its very definition.
>
> > However it is simply impossible for anything physical to be "literally 
>> infinite" when the nature of infinity as an unending PROCESS (forever add 
>> +1) 
>>
>
> Maybe, maybe not. Alan Guth's Inflation theory is by far the most 
> successful in modern cosmology, it solves many problems that have plagued 
> the Big Bang idea such as the horizon problem and the flatness problem. 
> Guth postulated an inflation field (sometimes called a inflation substance) 
> that for a very brief time caused the universe to expand exponentially, 
> astronomically (insert a stronger word if you can find one) faster than the 
> speed of light. This doesn't violate Relativity because Einstein only 
> talked about how fast things could move in space not on how fast space 
> itself could expand. Guth said the field was such that after a short time 
> the inflation field (or substance) decayed away in a process somewhat 
> analogous to radioactive half life, and after the decay the universe 
> expanded at a much much more leisurely pace.
>
> But then Andre Linde proved that for Guth's idea to work the inflation 
> field had to expand faster than it decayed, Linde called it "Eternal 
> Inflation". Linde showed that for every volume in which the inflation field 
> decays away 2 other volumes don't decay. So one universe becomes 3, the 
> field decays in one universe but not in the other 2, then both of those two 
> universes splits in 3 again and the inflation field decays away in one and 
> doesn't decay in 2 others, and it goes on forever. So what we call "The Big 
> Bang" isn't the beginning of everything it's just the end of inflation in 
> our particular part of the universe. So according to Linde this field 
> created one Big Bang, then 2, then 4, then 8, then 16 etc in a unending 
> PROCESS.
>
> If Linde is correct then each universe that a Big Bang creates may or may 
> not be infinitely large, but it doesn't really matter because there are a 
> infinite (and not just astronomical) number of them.
>
>   John K Clark
>
>
>  
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-22 Thread John Clark

On Sat, Feb 22, 2014 at 8:41 AM, Edgar L. Owen  wrote:

> I hate it when otherwise intelligent physicists use infinite in the sense
> of just really really big!
>

I hate that too, in fact I take pride in not using the word "infinite"
unless a proper subset of the thing can be put into a one to one
correspondence with the entire thing; and as a result I sometime struggle
to come up with the correct word when "astronomical" seems too small but
"infinite" is too big. But I stand by what I said, the CMBR data is
consistent with the universe being infinite and not just very very very
big. Of course that doesn't prove it is in fact infinite but it doesn't
rule it out either.

> There simply are and can be no physical infinities.
>

Nobody has found a infinite number of any physical object, but even if
there were such things how would we know?

> It's an impossible notion by its very definition.

Physical infinity might not exist, but if it doesn't it wouldn't be because
it was impossible by its very definition.

> However it is simply impossible for anything physical to be "literally
> infinite" when the nature of infinity as an unending PROCESS (forever add
> +1)
>

Maybe, maybe not. Alan Guth's Inflation theory is by far the most
successful in modern cosmology, it solves many problems that have plagued
the Big Bang idea such as the horizon problem and the flatness problem.
Guth postulated an inflation field (sometimes called a inflation substance)
that for a very brief time caused the universe to expand exponentially,
astronomically (insert a stronger word if you can find one) faster than the
speed of light. This doesn't violate Relativity because Einstein only
talked about how fast things could move in space not on how fast space
itself could expand. Guth said the field was such that after a short time
the inflation field (or substance) decayed away in a process somewhat
analogous to radioactive half life, and after the decay the universe
expanded at a much much more leisurely pace.

But then Andre Linde proved that for Guth's idea to work the inflation
field had to expand faster than it decayed, Linde called it "Eternal
Inflation". Linde showed that for every volume in which the inflation field
decays away 2 other volumes don't decay. So one universe becomes 3, the
field decays in one universe but not in the other 2, then both of those two
universes splits in 3 again and the inflation field decays away in one and
doesn't decay in 2 others, and it goes on forever. So what we call "The Big
Bang" isn't the beginning of everything it's just the end of inflation in
our particular part of the universe. So according to Linde this field
created one Big Bang, then 2, then 4, then 8, then 16 etc in a unending
PROCESS.

If Linde is correct then each universe that a Big Bang creates may or may
not be infinitely large, but it doesn't really matter because there are a
infinite (and not just astronomical) number of them.

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-22 Thread Richard Ruquist

On Sat, Feb 22, 2014 at 8:41 AM, Edgar L. Owen  wrote:

> John,
>
> Yes, that's my understanding, but that wasn't clear in your original post.
>
> However it is simply impossible for anything physical to be "literally
> infinite" when the nature of infinity as an unending PROCESS (forever add
> +1) rather than an actual number is understood.
>
> I hate it when otherwise intelligent physicists use infinite in the sense
> of just really really big!
>
> There simply are and can be no physical infinities. It's an impossible
> notion by its very definition.
>
> Edgar
>


Even worse Edgar when physicists substitute -1/12 for infinity.
Mathematica apparently rules our universe. Richard


>
> On Friday, February 21, 2014 2:16:48 PM UTC-5, John Clark wrote:
>>
>> On Fri, Feb 21, 2014 at 12:03 PM, Edgar L. Owen  wrot
>>
>> > I don't see how your CMB spot example works. Any 'spots' = features
>>> would not necessarily be caused by gravitation but could be caused by
>>> initial inhomogeneities as space itself expanded. Those are not necessarily
>>> ruled out. So I don't think your conclusion necessarily follows unless
>>> completely homogeneity is assumed, which it isn't in other theories such as
>>> brane traces and even enormously magnified = inflated quantum phenomena.
>>>
>>
>> No, complete homogeneity is not assumed. Quantum Mechanics says that an
>> unimaginably short time after the Big Bang the tiny cosmic fireball would
>> be very very homogenous but due to Heisenberg's Uncertainty Principle not
>> perfectly so, some parts of the fireball would be very slightly hotter and
>> denser than others. And the great thing about Quantum Mechanics is it
>> allows you to calculate numbers about all this, it can tell you just how
>> big the region would be and just how much denser and hotter it should be
>> and it can tell you how common variations from the norm will be. As the
>> universe expands these once tiny regions would enlarge too, and given
>> enough time gravity could make them grow too because slightly denser
>> regions would suck matter in from places that were slightly less dense so
>> with enough time there is no limit on how big they could get.
>>
>> But when we're looking at the CMBR we know how much variation to expect
>> from Heisenberg and we know that gravity had only 380,000 years to make
>> them bigger. And so we can figure out not just how large the biggest spots
>> should be but also how common spots of all sizes should be. And what we
>> predict the spectrum of spot sizes should be is exactly the same as what we
>> do in fact see. But we'd see something different if space were not flat,
>> the picture would be distorted and we'd see a different distribution of hot
>> and cold spots on the CMBR. But we see no such distortion so the Universe
>> at the largest scale must be flat, or at least nearly so, it's flat to at
>> least one part in 100,000 and could be absolutely flat.
>>
>> So regardless of how big our telescopes get at best the most of our
>> Universe we will ever observe is 0.0001% because 13.8 billion years is not
>> enough time for light from more distant parts of our universe to reach us.
>> And current observations are consistent with the universe being not merely
>> astronomically large but literally infinite.
>>
>>   John K Clark
>>
>>
>>
>>
>>
>>
>>
>>
>>  --
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Re: How does acceleration curve space? Can anyone provide an answer?

John,

Yes, that's my understanding, but that wasn't clear in your original post.

However it is simply impossible for anything physical to be "literally 
infinite" when the nature of infinity as an unending PROCESS (forever add 
+1) rather than an actual number is understood.

I hate it when otherwise intelligent physicists use infinite in the sense 
of just really really big!

There simply are and can be no physical infinities. It's an impossible 
notion by its very definition.

Edgar

On Friday, February 21, 2014 2:16:48 PM UTC-5, John Clark wrote:
>
> On Fri, Feb 21, 2014 at 12:03 PM, Edgar L. Owen 
> > wrot
>
> > I don't see how your CMB spot example works. Any 'spots' = features 
>> would not necessarily be caused by gravitation but could be caused by 
>> initial inhomogeneities as space itself expanded. Those are not necessarily 
>> ruled out. So I don't think your conclusion necessarily follows unless 
>> completely homogeneity is assumed, which it isn't in other theories such as 
>> brane traces and even enormously magnified = inflated quantum phenomena.
>>
>
> No, complete homogeneity is not assumed. Quantum Mechanics says that an 
> unimaginably short time after the Big Bang the tiny cosmic fireball would 
> be very very homogenous but due to Heisenberg's Uncertainty Principle not 
> perfectly so, some parts of the fireball would be very slightly hotter and 
> denser than others. And the great thing about Quantum Mechanics is it 
> allows you to calculate numbers about all this, it can tell you just how 
> big the region would be and just how much denser and hotter it should be 
> and it can tell you how common variations from the norm will be. As the 
> universe expands these once tiny regions would enlarge too, and given 
> enough time gravity could make them grow too because slightly denser 
> regions would suck matter in from places that were slightly less dense so 
> with enough time there is no limit on how big they could get.
>
> But when we're looking at the CMBR we know how much variation to expect 
> from Heisenberg and we know that gravity had only 380,000 years to make 
> them bigger. And so we can figure out not just how large the biggest spots 
> should be but also how common spots of all sizes should be. And what we 
> predict the spectrum of spot sizes should be is exactly the same as what we 
> do in fact see. But we'd see something different if space were not flat, 
> the picture would be distorted and we'd see a different distribution of hot 
> and cold spots on the CMBR. But we see no such distortion so the Universe 
> at the largest scale must be flat, or at least nearly so, it's flat to at 
> least one part in 100,000 and could be absolutely flat.  
>
> So regardless of how big our telescopes get at best the most of our 
> Universe we will ever observe is 0.0001% because 13.8 billion years is not 
> enough time for light from more distant parts of our universe to reach us. 
> And current observations are consistent with the universe being not merely 
> astronomically large but literally infinite.
>
>   John K Clark
>
>
>
>
>  
>
>  
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread meekerdb


On 2/21/2014 3:48 PM, Russell Standish wrote:

On Fri, Feb 21, 2014 at 03:11:56PM -0800, meekerdb wrote:

Just to clarify, it is *space* that is flat, but spacetime is still
curved, i.e. expansion of the universe is accelerating.


That could only be true in one particular inertial reference
frame? Surely, it can't be the case that spacetime is flat along all
space-like trajectories, whilst at the same time being curved along
time-like trajectories.


The metric for a isotropic, homogenous universe (FRW) is

ds^2 = dt^2 - a(t)^2{dr^2/(1-kr^2) + r^2[dtheta^2 + sin(theta)^2 dphi^2]}

  Where a(t) must satisfy the Friedman equations.

(da/dt)^2 - (8/3)piG*a^2 = -k

(d^2a/dt^2) = -(4/3)piG(rho + 3p)a(t)

For k=0 the space part {...} is just Euclidean.  But it's not a flat spacetime because of 
the time dependent a(t)^2 factor.




If so, then the orthogonal time axis that makes the spatial subspace
flat could be a candidate for Edgar's mysterious p-time.


Yes, I suggested to Edgar that the coordinate time in co-moving coordinates, which is what 
t is in the FRW equation, could serve as a physically distinguished time.  A global 
simultaneity is defined by the same value of a(t) everywhere.  But of course that doesn't 
solve his problem, which occurs already in special relativity.


Brent



Cheers



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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread Russell Standish

On Fri, Feb 21, 2014 at 03:11:56PM -0800, meekerdb wrote:
> 
> Just to clarify, it is *space* that is flat, but spacetime is still
> curved, i.e. expansion of the universe is accelerating.
> 

That could only be true in one particular inertial reference
frame? Surely, it can't be the case that spacetime is flat along all
space-like trajectories, whilst at the same time being curved along
time-like trajectories.

If so, then the orthogonal time axis that makes the spatial subspace
flat could be a candidate for Edgar's mysterious p-time.

Cheers

-- 


Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread meekerdb

On 2/21/2014 8:50 AM, John Clark wrote:
Astronomers proved that, although there are certainly local variations, on the very
largest scale the universe is in general flat. They did this by looking at the Cosmic
Microwave Background Radiation (CMBR), it is the most distant and oldest thing we have
ever seen and was formed just 380,000 years after the Big Bang, so if we look at a map
of that background radiation the largest structure we could see on it would be 380,000
light years across, spots larger than this wouldn't have had enough time to form because
nothing, not even gravity can move faster than light, a larger lump wouldn't even have
enough time to know it was a lump. So how large would a object 13.8 billion light years
away appear to us if it's size was 380,000 light years across? The answer is one degree
of arc, but ONLY if the universe is flat. If it's not flat and parallel lines converge
or diverge then the image of the largest structures we can see in the CMBR could appear
to be larger or smaller than one degree depending on how the image was distorted, and
that would depend on if the universe is positively or negatively curved. But we see no
distortion at all, in this way the WMAP and Planck satellite proved that the universe is
in general flat, or at least isn't curved much, over a distance of 13.8 billion light
years if the universe curves at all it is less than one part in 100,000.

Just to clarify, it is *space* that is flat, but spacetime is still curved, i.e. expansion
of the universe is accelerating.

Brent

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread John Clark

On Fri, Feb 21, 2014 at 12:03 PM, Edgar L. Owen  wrot

> I don't see how your CMB spot example works. Any 'spots' = features would
> not necessarily be caused by gravitation but could be caused by initial
> inhomogeneities as space itself expanded. Those are not necessarily ruled
> out. So I don't think your conclusion necessarily follows unless completely
> homogeneity is assumed, which it isn't in other theories such as brane
> traces and even enormously magnified = inflated quantum phenomena.
>

No, complete homogeneity is not assumed. Quantum Mechanics says that an
unimaginably short time after the Big Bang the tiny cosmic fireball would
be very very homogenous but due to Heisenberg's Uncertainty Principle not
perfectly so, some parts of the fireball would be very slightly hotter and
denser than others. And the great thing about Quantum Mechanics is it
allows you to calculate numbers about all this, it can tell you just how
big the region would be and just how much denser and hotter it should be
and it can tell you how common variations from the norm will be. As the
universe expands these once tiny regions would enlarge too, and given
enough time gravity could make them grow too because slightly denser
regions would suck matter in from places that were slightly less dense so
with enough time there is no limit on how big they could get.

But when we're looking at the CMBR we know how much variation to expect
from Heisenberg and we know that gravity had only 380,000 years to make
them bigger. And so we can figure out not just how large the biggest spots
should be but also how common spots of all sizes should be. And what we
predict the spectrum of spot sizes should be is exactly the same as what we
do in fact see. But we'd see something different if space were not flat,
the picture would be distorted and we'd see a different distribution of hot
and cold spots on the CMBR. But we see no such distortion so the Universe
at the largest scale must be flat, or at least nearly so, it's flat to at
least one part in 100,000 and could be absolutely flat.

So regardless of how big our telescopes get at best the most of our
Universe we will ever observe is 0.0001% because 13.8 billion years is not
enough time for light from more distant parts of our universe to reach us.
And current observations are consistent with the universe being not merely
astronomically large but literally infinite.

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread Edgar L. Owen

John,

I don't see how your CMB spot example works. Any 'spots' = features would 
not necessarily be caused by gravitation but could be caused by initial 
inhomogeneities as space itself expanded. Those are not necessarily ruled 
out. So I don't think your conclusion necessarily follows unless completely 
homogeneity is assumed, which it isn't in other theories such as brane 
traces and even enormously magnified = inflated quantum phenomena.

Edgar

 

On Friday, February 21, 2014 11:50:27 AM UTC-5, John Clark wrote:
>
>
>
>
> On Wed, Feb 19, 2014 at 1:09 PM, Jesse Mazer 
> > wrote:
>
> >> It's true that SR says nothing about gravity, but incorrect that it 
>>> deals only with "objects in uniform motion". Special relativity can handle 
>>> acceleration just fine too, either by analyzing it in the context of an 
>>> inertial frame, or by using a non-inertial coordinate system like Rindler 
>>> coordinates. See for example this section of the Usenet Physics FAQ, hosted 
>>> on the site of physicist John Baez:
>>>
>>
>> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html
>>
>> "It is a common misconception that Special Relativity cannot handle 
>> accelerating objects or accelerating reference frames.  It is claimed that 
>> general relativity is required because special relativity only applies to 
>> inertial frames.  This is not true.  Special relativity treats accelerating 
>> frames differently from inertial frames but can still deal with them. 
>>  Accelerating objects can be dealt with without even calling upon 
>> accelerating frames."
>>
>>  Are you claiming the above is incorrect?
>>
>
> No, you are entirely correct, I was being sloppy. But you still need 
> General Relativity if gravity is involved.
>  
>
>>  >> If you could never tell experimentally if spacetime was curved or 
>>> not then the very idea of curved spacetime would become an idea as as 
>>> useless as the concept of the luminiferous aether.
>>>
>>
>> > I didn't say in the post you're responding to that "you could never 
>> tell experimentally if spacetime was curved or not", I said you couldn't 
>> tell *if* you were only measuring the laws of physics to the first order,
>>
>
> I was assuming you were talking about things like tidal effects, but you 
> can tell if spacetime is curved even without that. Euclidean spacetime is 
> flat while non euclidean spacetime is curved, and according to General 
> Relativity matter tells spacetime how to curve and spacetime tells matter 
> how to move. On the surface of the spherical Earth an ant, or even one of 
> Abbott's 2D creatures from his novel "Flatland", could tell that the 
> surface it was crawling over was not flat by measuring the angles of a 
> triangle, if they added up to more than 180 degrees then the surface must 
> have a positive curvature like  the surface of a sphere and the 2D creature 
> would know that this must be true even if it was curved in a third 
> direction that the creature couldn't visualize. And if the angles of a 
> triangle added up to less than 180 degrees the creature would know that the 
> surface must have a negative curvature like the surface of a saddle. 
>
> Astronomers proved that, although there are certainly local variations, on 
> the very largest scale the universe is in general flat. They did this by 
> looking at the Cosmic Microwave Background Radiation (CMBR), it is the most 
> distant and oldest thing we have ever seen and was formed just 380,000 
> years after the Big Bang, so if we look at a map of that background 
> radiation the largest structure we could see on it would be 380,000 light 
> years across, spots larger than this wouldn't have had enough time to form 
> because nothing, not even gravity can move faster than light, a larger lump 
> wouldn't even have enough time to know it was a lump. So how large would a 
> object 13.8 billion light years away appear to us if it's size was 380,000 
> light years across? The answer is one degree of arc, but ONLY if the 
> universe is flat. If it's not flat and parallel lines converge or diverge 
> then the image of the largest structures we can see in the CMBR could 
> appear to be larger or smaller than one degree depending on how the image 
> was distorted, and that would depend on if the universe is positively or 
> negatively curved.  But we see no distortion at all, in this way the WMAP 
> and Planck satellite proved that the universe is in general flat, or at 
> least isn't curved much, over a distance of 13.8 billion light years if the 
> universe curves at all it is less than one part in 100,000.
>  
>
>> >> Pick any 3 points inside that sealed elevator. Place a Laser pointer 
>>> at each of the 3 points and form a triangle with the light beams. Measure 
>>> the 3 angles of the triangle in degrees. Add up the 3 measurements. If the 
>>> sum comes out to be exactly 180 then you know that the spacetime within 
>>> your sealed elevator is flat.
>>>
>>
>> > Do you have any

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread John Clark

On Wed, Feb 19, 2014 at 1:09 PM, Jesse Mazer  wrote:

>> It's true that SR says nothing about gravity, but incorrect that it
>> deals only with "objects in uniform motion". Special relativity can handle
>> acceleration just fine too, either by analyzing it in the context of an
>> inertial frame, or by using a non-inertial coordinate system like Rindler
>> coordinates. See for example this section of the Usenet Physics FAQ, hosted
>> on the site of physicist John Baez:
>>
>
> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html
>
> "It is a common misconception that Special Relativity cannot handle
> accelerating objects or accelerating reference frames.  It is claimed that
> general relativity is required because special relativity only applies to
> inertial frames.  This is not true.  Special relativity treats accelerating
> frames differently from inertial frames but can still deal with them.
>  Accelerating objects can be dealt with without even calling upon
> accelerating frames."
>
>  Are you claiming the above is incorrect?
>

No, you are entirely correct, I was being sloppy. But you still need
General Relativity if gravity is involved.

> >> If you could never tell experimentally if spacetime was curved or not
>> then the very idea of curved spacetime would become an idea as as useless
>> as the concept of the luminiferous aether.
>>
>
> > I didn't say in the post you're responding to that "you could never tell
> experimentally if spacetime was curved or not", I said you couldn't tell
> *if* you were only measuring the laws of physics to the first order,
>

I was assuming you were talking about things like tidal effects, but you
can tell if spacetime is curved even without that. Euclidean spacetime is
flat while non euclidean spacetime is curved, and according to General
Relativity matter tells spacetime how to curve and spacetime tells matter
how to move. On the surface of the spherical Earth an ant, or even one of
Abbott's 2D creatures from his novel "Flatland", could tell that the
surface it was crawling over was not flat by measuring the angles of a
triangle, if they added up to more than 180 degrees then the surface must
have a positive curvature like  the surface of a sphere and the 2D creature
would know that this must be true even if it was curved in a third
direction that the creature couldn't visualize. And if the angles of a
triangle added up to less than 180 degrees the creature would know that the
surface must have a negative curvature like the surface of a saddle.

Astronomers proved that, although there are certainly local variations, on
the very largest scale the universe is in general flat. They did this by
looking at the Cosmic Microwave Background Radiation (CMBR), it is the most
distant and oldest thing we have ever seen and was formed just 380,000
years after the Big Bang, so if we look at a map of that background
radiation the largest structure we could see on it would be 380,000 light
years across, spots larger than this wouldn't have had enough time to form
because nothing, not even gravity can move faster than light, a larger lump
wouldn't even have enough time to know it was a lump. So how large would a
object 13.8 billion light years away appear to us if it's size was 380,000
light years across? The answer is one degree of arc, but ONLY if the
universe is flat. If it's not flat and parallel lines converge or diverge
then the image of the largest structures we can see in the CMBR could
appear to be larger or smaller than one degree depending on how the image
was distorted, and that would depend on if the universe is positively or
negatively curved.  But we see no distortion at all, in this way the WMAP
and Planck satellite proved that the universe is in general flat, or at
least isn't curved much, over a distance of 13.8 billion light years if the
universe curves at all it is less than one part in 100,000.

> >> Pick any 3 points inside that sealed elevator. Place a Laser pointer at
>> each of the 3 points and form a triangle with the light beams. Measure the
>> 3 angles of the triangle in degrees. Add up the 3 measurements. If the sum
>> comes out to be exactly 180 then you know that the spacetime within your
>> sealed elevator is flat.
>>
>
> > Do you have any reference for the idea that this is a valid way to
> measure spacetime curvature in general relativity?
>

The following quote is from:
https://www.e-education.psu.edu/astro801/content/l10_p7.html

"In principle, if there was a large enough triangular object in the
universe and you could measure its interior angles, you could determine the
local geometry of the Universe. There are other tests you could also
conceive. For example, in our familiar flat geometry, two parallel lines
remain parallel for their entire length. In a spherical geometry, parallel
lines converge, and in a hyperbolic geometry parallel lines diverge. Note
that if the Universe is spherical, if you could travel in one direction
l

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-21 Thread LizR

Would it be correct to say that the equivalence principle is another way of
saying that gravitational and inertial masses are the same? Which I believe
some theories indicate they may not be.

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-20 Thread meekerdb

On 2/19/2014 10:09 AM, Jesse Mazer wrote:

On Wed, Feb 19, 2014 at 12:42 PM, John Clark > wrote:

> There is no sense in which an observer in an accelerating elevator in
the flat
spacetime of special relativity could correctly conclude that spacetime
has any
"curvature"

What you say is true but only according to Einstein's 1905 Special
Relativity
because that theory says nothing about gravity and only deals with special
cases,
objects in uniform motion; that's why it's called "special".

It's true that SR says nothing about gravity, but incorrect that it deals only with
"objects in uniform motion". Special relativity can handle acceleration just fine too,
either by analyzing it in the context of an inertial frame, or by using a non-inertial
coordinate system like Rindler coordinates. See for example this section of the Usenet
Physics FAQ, hosted on the site of physicist John Baez:

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

"It is a common misconception that Special Relativity cannot handle accelerating objects
or accelerating reference frames. It is claimed that general relativity is required
because special relativity only applies to inertial frames. This is not true. Special
relativity treats accelerating frames differently from inertial frames but can still
deal with them. Accelerating objects can be dealt with without even calling upon
accelerating frames."

Are you claiming the above is incorrect?

If you could never tell experimentally if spacetime was curved or not then
the very
idea of curved spacetime would become an idea as as useless as the concept
of the
luminiferous aether.

I didn't say in the post you're responding to that "you could never tell experimentally
if spacetime was curved or not", I said you couldn't tell *if* you were only measuring
the laws of physics to the first order, and *if* were only measuring in an
infinitesimally small region, both of which are conditions for the equivalence principle
to apply (as mentioned in the references I provided at
https://groups.google.com/d/msg/everything-list/xOpw-X9J2MY/wTDTy1Dr7s4J ). I said
specifically that the guy in the elevator *could* measure curvature if he wasn't
restricted in such ways: "In fact the observer inside the elevator should have ways of
measuring curvature if he can measure second-order effects, or if the size of the
elevator is taken as non-infinitesimal, and in either case he could definitely conclude
that spacetime was *not* curved within an elevator accelerating in flat SR spacetime".

But you can tell. Pick any 3 points inside that sealed elevator. Place a
Laser
pointer at each of the 3 points and form a triangle with the light beams.
Measure
the 3 angles of the triangle in degrees. Add up the 3 measurements. If the
sum comes
out to be exactly 180 then you know that the spacetime within your sealed
elevator
is flat.

Do you have any reference for the idea that this is a valid way to measure spacetime
curvature in general relativity? According to a poster at
http://www.physicsforums.com/showthread.php?t=454705 who I've found to be quite
knowledgeable on the subject of GR, "To measure actual curvature, rather than 'non
inertial motion through spacetime', J.L. Synge has a proof in his book on GR that you
need a minimum of 5 points. He then defines an idealized 5 point curvature detector. I
don't know how easy it is to get this book, but I don't really want to type in the whole
discussion. It is fun though - he even carries it out to producing ideal rods, trying to
arrange them in a certain way, and the last one minutely fails to fit if there is actual
curvature."

Presumably this is referring to the section on p. 408 of "Relativity: The General
Theory" which you can see a brief excerpt of here:
http://books.google.com/books?id=CqoNAQAAIAAJ&focus=searchwithinvolume&q=detector

I would also guess that one of the conditions needed for building a valid curvature
detector would be that all the components are in free-fall, though without having that
section of the book available I can't verify that this is true for the one suggested by
Synge.

The guy in an upward accelerating elevator in Minkowski space can measure the difference
in clock rate between a clock at the top of the elevator and one at the bottom and infer a
gravitational field, i.e. a non-flat metric:

ds^2=(1+gz/c^2)dt^2 - dx^2 - dy^2 - dz^2

Or even simpler he can toss one clock up and catch it (so it follows a geodesic for a
short time) and compare the interval to a clock he continued to hold. But what the
equivalence principle says is that */within a sufficiently small region/* acceleration is
indistinguishable from a uniform gravitational field. It doesn't say that acceleration IS
a gravitational field. And in fact they are obviously different as soon as y

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread Jesse Mazer

On Wed, Feb 19, 2014 at 12:42 PM, John Clark  wrote:

>
>

>
>  > There is no sense in which an observer in an accelerating elevator in
>> the flat spacetime of special relativity could correctly conclude that
>> spacetime has any "curvature"
>>
>
> What you say is true but only according to Einstein's 1905 Special
> Relativity because that theory says nothing about gravity and only deals
> with special cases, objects in uniform motion; that's why it's called
> "special".
>

It's true that SR says nothing about gravity, but incorrect that it deals
only with "objects in uniform motion". Special relativity can handle
acceleration just fine too, either by analyzing it in the context of an
inertial frame, or by using a non-inertial coordinate system like Rindler
coordinates. See for example this section of the Usenet Physics FAQ, hosted
on the site of physicist John Baez:

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

"It is a common misconception that Special Relativity cannot handle
accelerating objects or accelerating reference frames.  It is claimed that
general relativity is required because special relativity only applies to
inertial frames.  This is not true.  Special relativity treats accelerating
frames differently from inertial frames but can still deal with them.
 Accelerating objects can be dealt with without even calling upon
accelerating frames."

Are you claiming the above is incorrect?

>
>
> If you could never tell experimentally if spacetime was curved or not then
> the very idea of curved spacetime would become an idea as as useless as the
> concept of the luminiferous aether.
>

I didn't say in the post you're responding to that "you could never tell
experimentally if spacetime was curved or not", I said you couldn't tell
*if* you were only measuring the laws of physics to the first order, and
*if* were only measuring in an infinitesimally small region, both of which
are conditions for the equivalence principle to apply (as mentioned in the
references I provided at
https://groups.google.com/d/msg/everything-list/xOpw-X9J2MY/wTDTy1Dr7s4J ).
I said specifically that the guy in the elevator *could* measure curvature
if he wasn't restricted in such ways: "In fact the observer inside the
elevator should have ways of measuring curvature if he can measure
second-order effects, or if the size of the elevator is taken as
non-infinitesimal, and in either case he could definitely conclude that
spacetime was *not* curved within an elevator accelerating in flat SR
spacetime".

> But you can tell. Pick any 3 points inside that sealed elevator. Place a
> Laser pointer at each of the 3 points and form a triangle with the light
> beams. Measure the 3 angles of the triangle in degrees. Add up the 3
> measurements. If the sum comes out to be exactly 180 then you know that the
> spacetime within your sealed elevator is flat.
>

Do you have any reference for the idea that this is a valid way to measure
spacetime curvature in general relativity? According to a poster at
http://www.physicsforums.com/showthread.php?t=454705 who I've found to be
quite knowledgeable on the subject of GR, "To measure actual curvature,
rather than 'non inertial motion through spacetime', J.L. Synge has a proof
in his book on GR that you need a minimum of 5 points. He then defines an
idealized 5 point curvature detector. I don't know how easy it is to get
this book, but I don't really want to type in the whole discussion. It is
fun though - he even carries it out to producing ideal rods, trying to
arrange them in a certain way, and the last one minutely fails to fit if
there is actual curvature."

Presumably this is referring to the section on p. 408 of "Relativity: The
General Theory" which you can see a brief excerpt of here:
http://books.google.com/books?id=CqoNAQAAIAAJ&focus=searchwithinvolume&q=detector

I would also guess that one of the conditions needed for building a valid
curvature detector would be that all the components are in free-fall,
though without having that section of the book available I can't verify
that this is true for the one suggested by Synge.

Jesse

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread John Clark

On Wed, Feb 19, 2014 at 12:35 AM, Jesse Mazer  wrote:

>> You should stop talking about "space", it's "4D spacetime"; but yes it's
>> curved, although if you were inside that sealed elevator you couldn't tell
>> if the curvature was caused by rockets accelerating the elevator in deep
>> space or if it was caused by the Earth's gravity. Acceleration is absolute
>> in that there is no need to look outside your reference frame to detect it,
>> but according to General Relativity there is no way to tell the difference
>> between it and being in a gravitational field.
>>
>
> You are simply incorrect here, John.
>

No Jesse I am not.

> There is no sense in which an observer in an accelerating elevator in the
> flat spacetime of special relativity could correctly conclude that
> spacetime has any "curvature"
>

What you say is true but only according to Einstein's 1905 Special
Relativity because that theory says nothing about gravity and only deals
with special cases, objects in uniform motion; that's why it's called
"special". It is NOT true according to  Einsteins much more comprehensive
1916 General Relativity which includes gravity and nonuniform motion and
pressure and much more; that's why it's called "General".

If you could never tell experimentally if spacetime was curved or not then
the very idea of curved spacetime would become an idea as as useless as the
concept of the luminiferous aether. But you can tell. Pick any 3 points
inside that sealed elevator. Place a Laser pointer at each of the 3 points
and form a triangle with the light beams. Measure the 3 angles of the
triangle in degrees. Add up the 3 measurements. If the sum comes out to be
exactly 180 then you know that the spacetime within your sealed elevator is
flat. If the sum comes out as any number other than 180 then you know that
the spacetime within your sealed elevator is not flat; but unless you take
into consideration tidal effects (which will always occur in a
gravitational field if the elevator is not infinitesimally small) you will
not know if the spacetime curvature was caused by gravity or by a rocket.

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread Jesse Mazer

The curvature of spacetime is understood in a coordinate-invariant way, in
terms of the proper time and proper length along paths through spacetime,
so it doesn't depend at all on what coordinate system you use to describe
things. Physicists do sometimes talk about the "curvature of space"
distinct from the curvature of spacetime, I'm not sure if you meant to
distinguish the two or were treating them as synonymous. But defining the
curvature of space depends on picking a simultaneity convention which
divides 4D spacetime into a series of 3D slices, and then defining the
curvature of each slice in terms of proper length along spacelike paths
confined to that slice. So the "curvature of space" is
coordinate-dependent, since different simultaneity conventions = different
slices with different curvatures.

I don't know if there's any meaningful sense in which picking a coordinate
system where an object has a higher velocity means it curves space
"more"--if there is, it would presumably depend on a choice to restrict the
analysis to some family of coordinate systems where each possible velocity
would be associated with a particular choice of simultaneity convention,
rather than using any of the arbitrary smooth coordinate systems (with
arbitrary simultaneity conventions) that are permitted in general
relativity.

I found some discussion of the issue of how velocity relates to curvature
and gravitational "force" on these pages:

http://physics.stackexchange.com/questions/95023/does-a-moving-object-curve-space-time-as-its-velocity-increases

http://www.physicsforums.com/showthread.php?t=602644


On Wed, Feb 19, 2014 at 9:15 AM, Edgar L. Owen  wrote:

> Russell, Brent, Jesse, et al,
>
> The "increased kinetic energy of the particle" is not due to its
> acceleration but to its relative velocity to some observer. Mass also
> increases with relative velocity, but that apparent increase in mass is
> only with respect to some observer the motion is relative to. In fact all
> kinetic energy is only with respect to relative velocity with some observer
> frame.
>
> So this means that any increased curvature of space from that increased
> kinetic energy and increased mass should be only with respect to observers
> it is in relative motion with respect to.
>
> So in this case we seem to have a case in which the curvature of space is
> relative rather than being absolute.
>
> Would you not agree?
>
> Edgar
>
>
>
> On Tuesday, February 18, 2014 4:44:58 PM UTC-5, Russell Standish wrote:
>>
>> On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote:
>> > On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen 
>> wrote:
>> >
>> > >
>> > > >> You say that "You can tell if spacetime is curved or not by
>> observing
>> > >> if light moves in a straight line or not." and then you say that
>> light does
>> > >> NOT travel in a straight line in the accelerating elevator example
>> you give.
>> > >>
>> > >
>> > > > So, by your terminology, does that mean that the acceleration of
>> the
>> > > elevator IS curving space ?
>> > >
>> >
>> > You should stop talking about "space", it's "4D spacetime"; but yes
>> it's
>> > curved, although if you were inside that sealed elevator you couldn't
>> tell
>> > if the curvature was caused by rockets accelerating the elevator in
>> deep
>> > space or if it was caused by the Earth's gravity. Acceleration is
>> absolute
>> > in that there is no need to look outside your reference frame to detect
>> it,
>> > but according to General Relativity there is no way to tell the
>> difference
>> > between it and being in a gravitational field.
>> >
>> >
>> > > > It seems like you might be saying that the acceleration does curve
>> space
>> > >
>> >
>> > Yes.
>> >
>>
>> In which theory? IIUC, acceleration of an infinitesimal point particle
>> does not change the curvature of space. And acceleration of a massive
>> particle only changes the curvature by the amount due to the increased
>> kinetic energy of the particle.
>>
>>
>> --
>>
>> 
>>
>> Prof Russell Standish  Phone 0425 253119 (mobile)
>> Principal, High Performance Coders
>> Visiting Professor of Mathematics  hpc...@hpcoders.com.au
>> University of New South Wales  http://www.hpcoders.com.au
>> 
>>
>>
>  --
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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread Edgar L. Owen

Russell, Brent, Jesse, et al,

The "increased kinetic energy of the particle" is not due to its 
acceleration but to its relative velocity to some observer. Mass also 
increases with relative velocity, but that apparent increase in mass is 
only with respect to some observer the motion is relative to. In fact all 
kinetic energy is only with respect to relative velocity with some observer 
frame.

So this means that any increased curvature of space from that increased 
kinetic energy and increased mass should be only with respect to observers 
it is in relative motion with respect to.

So in this case we seem to have a case in which the curvature of space is 
relative rather than being absolute.

Would you not agree?

Edgar



On Tuesday, February 18, 2014 4:44:58 PM UTC-5, Russell Standish wrote:
>
> On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote: 
> > On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen 
> > > 
> wrote: 
> > 
> > > 
> > > >> You say that "You can tell if spacetime is curved or not by 
> observing 
> > >> if light moves in a straight line or not." and then you say that 
> light does 
> > >> NOT travel in a straight line in the accelerating elevator example 
> you give. 
> > >> 
> > > 
> > > > So, by your terminology, does that mean that the acceleration of the 
> > > elevator IS curving space ? 
> > > 
> > 
> > You should stop talking about "space", it's "4D spacetime"; but yes it's 
> > curved, although if you were inside that sealed elevator you couldn't 
> tell 
> > if the curvature was caused by rockets accelerating the elevator in deep 
> > space or if it was caused by the Earth's gravity. Acceleration is 
> absolute 
> > in that there is no need to look outside your reference frame to detect 
> it, 
> > but according to General Relativity there is no way to tell the 
> difference 
> > between it and being in a gravitational field. 
> > 
> > 
> > > > It seems like you might be saying that the acceleration does curve 
> space 
> > > 
> > 
> > Yes. 
> > 
>
> In which theory? IIUC, acceleration of an infinitesimal point particle 
> does not change the curvature of space. And acceleration of a massive 
> particle only changes the curvature by the amount due to the increased 
> kinetic energy of the particle. 
>
>
> -- 
>
>  
>
> Prof Russell Standish  Phone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
> University of New South Wales  http://www.hpcoders.com.au 
>  
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread LizR

Sorry I should have read on before making that last post.

It would appear that acceleration alone doesn't curve space, the only
curvature involved is that due to the mass/energy involved.

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-19 Thread LizR

On 19 February 2014 13:30, Russell Standish  wrote:

> > Acceleration of a point particle doesn't cause light crossing the
> > particle to bend (because it's a point) but accel of a larger object
> > does because light takes time to cross the object.
>
> I'm sure the particle size is not relevant. A point-like concentration
> of mass-energy will still curve spacetime with an approximate 1/r^2.
>

We aren't talking about the curvature caused by the mass/energy. That's
assumed to exist. We're talking about curvature caused by acceleration, or
more likely (I think) not caused by it.

>
> > But surely this doesn't mean space-time is really curved, or does it?
> > Or is space-time curvature relative to an observer (surely not) ???
>
> Spacetime curvature is independent of the observer - in the sense that
> it is a rank 2 tensor, although its components will vary according to
> the observer's reference frame (just like your x,y coordinates change
> whenever I move around my house).
>
> I'm unsure whether my comment about kinetic energy contributing to
> curvature is correct though. In the particle's instantaneous inertial
> reference frame, the kinetic energy is always zero. Maybe Brent or
> someone else could comment.
>
> Isn't this just the mass increased with velocity measured by an observer
moving at a different speed?

The question is, does acceleration curve space? It causes effects that are
the same as gravity, but I would imagine it doesn't actually curve space.
Or does it?

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread Jesse Mazer

On Tue, Feb 18, 2014 at 1:28 PM, John Clark  wrote:

> On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen  wrote:
>
>>
>> >> You say that "You can tell if spacetime is curved or not by observing
>>> if light moves in a straight line or not." and then you say that light does
>>> NOT travel in a straight line in the accelerating elevator example you give.
>>>
>>
>> > So, by your terminology, does that mean that the acceleration of the
>> elevator IS curving space ?
>>
>
> You should stop talking about "space", it's "4D spacetime"; but yes it's
> curved, although if you were inside that sealed elevator you couldn't tell
> if the curvature was caused by rockets accelerating the elevator in deep
> space or if it was caused by the Earth's gravity. Acceleration is absolute
> in that there is no need to look outside your reference frame to detect it,
> but according to General Relativity there is no way to tell the difference
> between it and being in a gravitational field.
>

You are simply incorrect here, John. There is no sense in which an observer
in an accelerating elevator in the flat spacetime of special relativity
could correctly conclude that spacetime has any "curvature"--the fact that
light curves relative to a coordinate system where the elevator is at rest
is completely irrelevant, since there's no principle of physics that says
curved light paths imply curved spacetime. In fact the observer inside the
elevator should have ways of measuring curvature if he can measure
second-order effects, or if the size of the elevator is taken as
non-infinitesimal, and in either case he could definitely conclude that
spacetime was *not* curved within an elevator accelerating in flat SR
spacetime. The equivalence principle only says there's no way to tell the
difference between acceleration and gravity *if* you only look at a
first-order approximation to the equations of physics in your region, and
*if* your region is infinitesimally small. But in that case there's no way
for you to measure spacetime curvature at all, so there's no valid reason
for concluding that spacetime in your region is curved.

Jesse

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread meekerdb

On 2/18/2014 4:30 PM, Russell Standish wrote:

On Wed, Feb 19, 2014 at 11:57:21AM +1300, LizR wrote:

On 19/02/2014, Russell Standish wrote:

In which theory? IIUC, acceleration of an infinitesimal point particle
does not change the curvature of space. And acceleration of a massive
particle only changes the curvature by the amount due to the increased
kinetic energy of the particle.

Acceleration of a point particle doesn't cause light crossing the
particle to bend (because it's a point) but accel of a larger object
does because light takes time to cross the object.

I'm sure the particle size is not relevant. A point-like concentration
of mass-energy will still curve spacetime with an approximate 1/r^2.

But surely this doesn't mean space-time is really curved, or does it?
Or is space-time curvature relative to an observer (surely not) ???

Spacetime curvature is independent of the observer - in the sense that
it is a rank 2 tensor, although its components will vary according to
the observer's reference frame (just like your x,y coordinates change
whenever I move around my house).

I'm unsure whether my comment about kinetic energy contributing to
curvature is correct though. In the particle's instantaneous inertial
reference frame, the kinetic energy is always zero. Maybe Brent or
someone else could comment.

Of course things don't just accelerate all by themselves. John Clark seems to think that
just measuring in an accelerating frame warps spacetime, which as Russell points out is
not consistent with curvature being an invariant. When a mass accelerates, conservation
laws require that stress-energy be conserved. So from the standpoint of Einstein's
equation the right side T_a_b is just getting rearranged. No mass-energy is created. So
we can consider the case of two masses (one an elevator if you like) connected by a long
spring and oscillating together and apart. Locally the curvature of spacetime must change
to reflect their changing positions. Their gravitationl effect will be greater than if
they were not moving because they and the spring have more stress-energy. But there is no
net increase due to the acceleration per se. Note that the system does not radiate
gravitational waves because it is only bipolar and gravity waves are quadrupole.

Brent

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread Russell Standish

On Wed, Feb 19, 2014 at 11:57:21AM +1300, LizR wrote:
> On 19/02/2014, Russell Standish  wrote:
> >
> > In which theory? IIUC, acceleration of an infinitesimal point particle
> > does not change the curvature of space. And acceleration of a massive
> > particle only changes the curvature by the amount due to the increased
> > kinetic energy of the particle.
> 
> Acceleration of a point particle doesn't cause light crossing the
> particle to bend (because it's a point) but accel of a larger object
> does because light takes time to cross the object.

I'm sure the particle size is not relevant. A point-like concentration
of mass-energy will still curve spacetime with an approximate 1/r^2.

> 
> But surely this doesn't mean space-time is really curved, or does it?
> Or is space-time curvature relative to an observer (surely not) ???
> 

Spacetime curvature is independent of the observer - in the sense that
it is a rank 2 tensor, although its components will vary according to
the observer's reference frame (just like your x,y coordinates change
whenever I move around my house).

I'm unsure whether my comment about kinetic energy contributing to
curvature is correct though. In the particle's instantaneous inertial
reference frame, the kinetic energy is always zero. Maybe Brent or
someone else could comment.

-- 

Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread ghibbsa


On Tuesday, February 18, 2014 9:44:58 PM UTC, Russell Standish wrote:
>
> On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote: 
> > On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen 
> > > 
> wrote: 
> > 
> > > 
> > > >> You say that "You can tell if spacetime is curved or not by 
> observing 
> > >> if light moves in a straight line or not." and then you say that 
> light does 
> > >> NOT travel in a straight line in the accelerating elevator example 
> you give. 
> > >> 
> > > 
> > > > So, by your terminology, does that mean that the acceleration of the 
> > > elevator IS curving space ? 
> > > 
> > 
> > You should stop talking about "space", it's "4D spacetime"; but yes it's 
> > curved, although if you were inside that sealed elevator you couldn't 
> tell 
> > if the curvature was caused by rockets accelerating the elevator in deep 
> > space or if it was caused by the Earth's gravity. Acceleration is 
> absolute 
> > in that there is no need to look outside your reference frame to detect 
> it, 
> > but according to General Relativity there is no way to tell the 
> difference 
> > between it and being in a gravitational field. 
> > 
> > 
> > > > It seems like you might be saying that the acceleration does curve 
> space 
> > > 
> > 
> > Yes. 
> > 
>
> In which theory? IIUC, acceleration of an infinitesimal point particle 
> does not change the curvature of space. And acceleration of a massive 
> particle only changes the curvature by the amount due to the increased 
> kinetic energy of the particle. 
>
>
> Hi Russell -  isn't the equivalence principle for acceleration vs falling 
> approximate for theoretical purposes only? It's only really the case for 
> two point particles, or not? 

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread LizR

On 19/02/2014, Russell Standish  wrote:
>
> In which theory? IIUC, acceleration of an infinitesimal point particle
> does not change the curvature of space. And acceleration of a massive
> particle only changes the curvature by the amount due to the increased
> kinetic energy of the particle.

Acceleration of a point particle doesn't cause light crossing the
particle to bend (because it's a point) but accel of a larger object
does because light takes time to cross the object.

But surely this doesn't mean space-time is really curved, or does it?
Or is space-time curvature relative to an observer (surely not) ???

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread Russell Standish

On Tue, Feb 18, 2014 at 01:28:09PM -0500, John Clark wrote:
> On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen  wrote:
> 
> >
> > >> You say that "You can tell if spacetime is curved or not by observing
> >> if light moves in a straight line or not." and then you say that light does
> >> NOT travel in a straight line in the accelerating elevator example you 
> >> give.
> >>
> >
> > > So, by your terminology, does that mean that the acceleration of the
> > elevator IS curving space ?
> >
> 
> You should stop talking about "space", it's "4D spacetime"; but yes it's
> curved, although if you were inside that sealed elevator you couldn't tell
> if the curvature was caused by rockets accelerating the elevator in deep
> space or if it was caused by the Earth's gravity. Acceleration is absolute
> in that there is no need to look outside your reference frame to detect it,
> but according to General Relativity there is no way to tell the difference
> between it and being in a gravitational field.
> 
> 
> > > It seems like you might be saying that the acceleration does curve space
> >
> 
> Yes.
> 

In which theory? IIUC, acceleration of an infinitesimal point particle
does not change the curvature of space. And acceleration of a massive
particle only changes the curvature by the amount due to the increased
kinetic energy of the particle.


-- 


Prof Russell Standish  Phone 0425 253119 (mobile)
Principal, High Performance Coders
Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread LizR

On 19/02/2014, John Clark  wrote:
>
> No, the curvature of both is equally fundamental and equally real. However
> it is true that General Relativity talks about a particular type of
> acceleration called "Proper Acceleration", it is the acceleration of
> something relative to an observer in free fall (also called relative to a
> observer in a inertial frame). So gravity does not cause Proper
> Acceleration, you'd need a rocket for that, and anyone in free fall has a
> Proper Acceleration of zero (if you're in free fall you're not accelerating
> relative to the free falling skydiver next to you).

Is this something to do with deviating from geodesics?

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-18 Thread John Clark

On Sun, Feb 16, 2014 at 12:54 PM, Edgar L. Owen  wrote:

>
> >> You say that "You can tell if spacetime is curved or not by observing
>> if light moves in a straight line or not." and then you say that light does
>> NOT travel in a straight line in the accelerating elevator example you give.
>>
>
> > So, by your terminology, does that mean that the acceleration of the
> elevator IS curving space ?
>

You should stop talking about "space", it's "4D spacetime"; but yes it's
curved, although if you were inside that sealed elevator you couldn't tell
if the curvature was caused by rockets accelerating the elevator in deep
space or if it was caused by the Earth's gravity. Acceleration is absolute
in that there is no need to look outside your reference frame to detect it,
but according to General Relativity there is no way to tell the difference
between it and being in a gravitational field.

> > It seems like you might be saying that the acceleration does curve space
>

Yes.

> > And if that is true can we then say that the curvature of space is not
> absolute and the same for all observers, but is frame dependent, at least
> in the case of acceleration curving space?
>

All observers will agree that spacetime inside the elevator is curved but
they might not know if the curvature was cause by rockets or a
gravitational field.
But there are 2 things that all observers in any frame will agree on, the
measured speed of light and the distance between two events in spacetime.

> > And can we say this is a basic difference between the curvature of space
> by gravitation and by acceleration, that the curvature of space by
> gravitation is absolute in this sense,
>

No, the curvature of both is equally fundamental and equally real. However
it is true that General Relativity talks about a particular type of
acceleration called "Proper Acceleration", it is the acceleration of
something relative to an observer in free fall (also called relative to a
observer in a inertial frame). So gravity does not cause Proper
Acceleration, you'd need a rocket for that, and anyone in free fall has a
Proper Acceleration of zero (if you're in free fall you're not accelerating
relative to the free falling skydiver next to you).

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-17 Thread Edgar L. Owen

Craig,

If I understand you it sounds close to my theory of Xperience which I just 
described in my other reply to you on the "What are numbers..." topic.

Please refer to that..

Edgar



On Sunday, February 16, 2014 4:49:57 PM UTC-5, Craig Weinberg wrote:
>
>
>
> On Sunday, February 16, 2014 1:23:32 PM UTC-5, Edgar L. Owen wrote:
>>
>> Craig,
>>
>> But how can elemental computation "arise out of even more primitive 
>> sensory-motive qualities" and "supervene on an even more primordial 
>> possibility of aesthetic appreciation and intentional participation" since 
>> those seem to be human dependent attributes?
>>
>
> They only seem to be human dependent attributes because we are human. If 
> the cells and molecules our bodies are made of had no sensory capabilities, 
> certainly there would be no reason to develop any such capabilities. What 
> our immune system or digestive system does is far more important and 
> complex than what humans primitively do in their environment.
>  
>
>>
>> Aren't you confusing human mental MODELS of reality (to which your 
>> comments might apply) with the actual human independent reality which human 
>> minds make their internal models of? That seems like a much more reasonable 
>> view of reality...
>>
>
> While human experience does model non-human experiences, I do not think 
> that it makes sense to say that it is, itself a "model" of anything. There 
> are experiences which are independent of human experience, but there are 
> not necessarily any phenomena which are independent of all experience. As 
> far as I can tell, there is no meaningful difference between a phenomenon 
> which can never be detected or inferred in any way and nothingness or 
> non-existence.
>
> If we are talking about local views of reality only, then sure, the 
> experiences which our body tells us are other bodies or objects are indeed 
> so alien to our own perception, on such wildly different scales, that 
> figuratively we could consider our experience a model of the phenomenon, 
> but literally there is no model, only a presentation of the relation of our 
> own experience to others.
>
> Craig
>  
>
>>
>> Edgar
>>
>>
>>
>> On Sunday, February 16, 2014 1:05:15 PM UTC-5, Craig Weinberg wrote:
>>>
>>>
>>>
>>> On Sunday, February 16, 2014 12:32:35 PM UTC-5, Edgar L. Owen wrote:

 Craig,

 I agree with your idea in one sense, that actually space and clock time 
 are just computational relationships between events, specifically the 
 dimensional aspects of those events, rather than the actual physical 
 background to events that is usually assumed.

 In my book on Reality, I point out the reasons why it's more reasonable 
 to assume that spaceclocktime is something that arises out of elemental 
 computational events in discrete fragments, rather than existing as a 
 fixed, pre-existing background to events.

>>>
>>> I agree, except that I see elemental computation also as something that 
>>> arises out of even more primitive sensory-motive qualities disentangling 
>>> into localized fugues which precede even qualities of discreteness or 
>>> linear sequence. 
>>>

 The advantage of this approach is that it enables a conceptual 
 unification of quantum theory and GR; immediately resolves all quantum 
 paradoxes (which are paradoxical only with respect to the fixed, 
 pre-existing background space mistakenly assumed); and provides a clear 
 explanation of the source and necessity of quantum randomness. 

>>>
 Strangely no one here seems interested in how this happens, even to 
 criticize it!

>>>
>>> Yes, I am very familiar with the feeling ;)  I have only a superficial 
>>> understanding of QT and GR, so I wouldn't be the one to criticize 
>>> technically. My objection is only that whatever primordial form or function 
>>> can be conceived of as absolute must supervene on an even more primordial 
>>> possibility of aesthetic appreciation and intentional participation.
>>>
>>> Craig
>>>  
>>>
  

>>>
 Edgar

 On Sunday, February 16, 2014 8:35:32 AM UTC-5, Craig Weinberg wrote:
>
>
>
> On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:
>>
>> Russell,
>>
>> No, the proper understanding is that gravitation and curved space are 
>> EQUIVALENT. Both are produced by the presence of mass-energy (and 
>> stress).
>>
>
> I would say that gravity and curved space are metaphorical rather than 
> literal. The literal phenomenon is that the inertial frame of sensible 
> external relations is what is being curved. It is literally the 
> experience 
> of stress - of seriousness and realism which is seen from the outside as 
> exaggerated irreversibility and inevitability. Mass-energy is the public 
> token which represents sensory-motive. Space/density is the dual of mass, 
> time/duration is the dual

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Craig Weinberg

On Sunday, February 16, 2014 1:23:32 PM UTC-5, Edgar L. Owen wrote:
>
> Craig,
>
> But how can elemental computation "arise out of even more primitive 
> sensory-motive qualities" and "supervene on an even more primordial 
> possibility of aesthetic appreciation and intentional participation" since 
> those seem to be human dependent attributes?
>

They only seem to be human dependent attributes because we are human. If 
the cells and molecules our bodies are made of had no sensory capabilities, 
certainly there would be no reason to develop any such capabilities. What 
our immune system or digestive system does is far more important and 
complex than what humans primitively do in their environment.

>
> Aren't you confusing human mental MODELS of reality (to which your 
> comments might apply) with the actual human independent reality which human 
> minds make their internal models of? That seems like a much more reasonable 
> view of reality...
>

While human experience does model non-human experiences, I do not think 
that it makes sense to say that it is, itself a "model" of anything. There 
are experiences which are independent of human experience, but there are 
not necessarily any phenomena which are independent of all experience. As 
far as I can tell, there is no meaningful difference between a phenomenon 
which can never be detected or inferred in any way and nothingness or 
non-existence.

If we are talking about local views of reality only, then sure, the 
experiences which our body tells us are other bodies or objects are indeed 
so alien to our own perception, on such wildly different scales, that 
figuratively we could consider our experience a model of the phenomenon, 
but literally there is no model, only a presentation of the relation of our 
own experience to others.

Craig

>
> Edgar
>
>
>
> On Sunday, February 16, 2014 1:05:15 PM UTC-5, Craig Weinberg wrote:
>>
>>
>>
>> On Sunday, February 16, 2014 12:32:35 PM UTC-5, Edgar L. Owen wrote:
>>>
>>> Craig,
>>>
>>> I agree with your idea in one sense, that actually space and clock time 
>>> are just computational relationships between events, specifically the 
>>> dimensional aspects of those events, rather than the actual physical 
>>> background to events that is usually assumed.
>>>
>>> In my book on Reality, I point out the reasons why it's more reasonable 
>>> to assume that spaceclocktime is something that arises out of elemental 
>>> computational events in discrete fragments, rather than existing as a 
>>> fixed, pre-existing background to events.
>>>
>>
>> I agree, except that I see elemental computation also as something that 
>> arises out of even more primitive sensory-motive qualities disentangling 
>> into localized fugues which precede even qualities of discreteness or 
>> linear sequence. 
>>
>>>
>>> The advantage of this approach is that it enables a conceptual 
>>> unification of quantum theory and GR; immediately resolves all quantum 
>>> paradoxes (which are paradoxical only with respect to the fixed, 
>>> pre-existing background space mistakenly assumed); and provides a clear 
>>> explanation of the source and necessity of quantum randomness. 
>>>
>>
>>> Strangely no one here seems interested in how this happens, even to 
>>> criticize it!
>>>
>>
>> Yes, I am very familiar with the feeling ;)  I have only a superficial 
>> understanding of QT and GR, so I wouldn't be the one to criticize 
>> technically. My objection is only that whatever primordial form or function 
>> can be conceived of as absolute must supervene on an even more primordial 
>> possibility of aesthetic appreciation and intentional participation.
>>
>> Craig
>>  
>>
>>>  
>>>
>>
>>> Edgar
>>>
>>> On Sunday, February 16, 2014 8:35:32 AM UTC-5, Craig Weinberg wrote:

 On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:
>
> Russell,
>
> No, the proper understanding is that gravitation and curved space are 
> EQUIVALENT. Both are produced by the presence of mass-energy (and stress).
>

 I would say that gravity and curved space are metaphorical rather than 
 literal. The literal phenomenon is that the inertial frame of sensible 
 external relations is what is being curved. It is literally the experience 
 of stress - of seriousness and realism which is seen from the outside as 
 exaggerated irreversibility and inevitability. Mass-energy is the public 
 token which represents sensory-motive. Space/density is the dual of mass, 
 time/duration is the dual of energy.

 Mass-energy doesn't produce anything except externalized reflections of 
 phenomenal experiences. Gravitation and curved space describe the back end 
 of the sensory-motor (not motive because its externalized) relations which 
 are interphenomenal, automatic, and unattended on all frames but the 
 primordial one.

 Craig

>
> You say "Motion through

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Edgar L. Owen

Craig,

But how can elemental computation "arise out of even more primitive 
sensory-motive qualities" and "supervene on an even more primordial 
possibility of aesthetic appreciation and intentional participation" since 
those seem to be human dependent attributes?

Aren't you confusing human mental MODELS of reality (to which your comments 
might apply) with the actual human independent reality which human minds 
make their internal models of? That seems like a much more reasonable view 
of reality...

Edgar



On Sunday, February 16, 2014 1:05:15 PM UTC-5, Craig Weinberg wrote:
>
>
>
> On Sunday, February 16, 2014 12:32:35 PM UTC-5, Edgar L. Owen wrote:
>>
>> Craig,
>>
>> I agree with your idea in one sense, that actually space and clock time 
>> are just computational relationships between events, specifically the 
>> dimensional aspects of those events, rather than the actual physical 
>> background to events that is usually assumed.
>>
>> In my book on Reality, I point out the reasons why it's more reasonable 
>> to assume that spaceclocktime is something that arises out of elemental 
>> computational events in discrete fragments, rather than existing as a 
>> fixed, pre-existing background to events.
>>
>
> I agree, except that I see elemental computation also as something that 
> arises out of even more primitive sensory-motive qualities disentangling 
> into localized fugues which precede even qualities of discreteness or 
> linear sequence. 
>
>>
>> The advantage of this approach is that it enables a conceptual 
>> unification of quantum theory and GR; immediately resolves all quantum 
>> paradoxes (which are paradoxical only with respect to the fixed, 
>> pre-existing background space mistakenly assumed); and provides a clear 
>> explanation of the source and necessity of quantum randomness. 
>>
>
>> Strangely no one here seems interested in how this happens, even to 
>> criticize it!
>>
>
> Yes, I am very familiar with the feeling ;)  I have only a superficial 
> understanding of QT and GR, so I wouldn't be the one to criticize 
> technically. My objection is only that whatever primordial form or function 
> can be conceived of as absolute must supervene on an even more primordial 
> possibility of aesthetic appreciation and intentional participation.
>
> Craig
>  
>
>>  
>>
>
>> Edgar
>>
>> On Sunday, February 16, 2014 8:35:32 AM UTC-5, Craig Weinberg wrote:
>>>
>>>
>>>
>>> On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:

 Russell,

 No, the proper understanding is that gravitation and curved space are 
 EQUIVALENT. Both are produced by the presence of mass-energy (and stress).

>>>
>>> I would say that gravity and curved space are metaphorical rather than 
>>> literal. The literal phenomenon is that the inertial frame of sensible 
>>> external relations is what is being curved. It is literally the experience 
>>> of stress - of seriousness and realism which is seen from the outside as 
>>> exaggerated irreversibility and inevitability. Mass-energy is the public 
>>> token which represents sensory-motive. Space/density is the dual of mass, 
>>> time/duration is the dual of energy.
>>>
>>> Mass-energy doesn't produce anything except externalized reflections of 
>>> phenomenal experiences. Gravitation and curved space describe the back end 
>>> of the sensory-motor (not motive because its externalized) relations which 
>>> are interphenomenal, automatic, and unattended on all frames but the 
>>> primordial one.
>>>
>>> Craig
>>>  
>>>

 You say "Motion through curved space appears as acceleration in a flat 
 tangent space."

 Are you saying then that acceleration from a rising elevator is "motion 
 through curved space"?

 That was my original question but I don't know what your answer is from 
 your post..

 Edgar





 On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:
>
> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
> > All, 
> > 
> > By the Principle of Equivalence acceleration is equivalent to 
> gravitation. 
> > 
> > Gravitation curves space. 
>
> No - curved space generates the phenomena of gravitation. 
>
> It is sometimes said that "matter curves space". 
>
> > 
> > So doesn't this mean acceleration should also curve space? If not, 
> why not? 
> > 
>
> Motion through curved space appears as acceleration in a flat tangent 
> space. 
>
> > If not, doesn't that violate the Equivalence Principle? 
>
>
> No. 
>
>
> -- 
>
> 
>  
>
> Prof Russell Standish  Phone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
> University of New Sou

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Craig Weinberg



On Sunday, February 16, 2014 12:32:35 PM UTC-5, Edgar L. Owen wrote:
>
> Craig,
>
> I agree with your idea in one sense, that actually space and clock time 
> are just computational relationships between events, specifically the 
> dimensional aspects of those events, rather than the actual physical 
> background to events that is usually assumed.
>
> In my book on Reality, I point out the reasons why it's more reasonable to 
> assume that spaceclocktime is something that arises out of elemental 
> computational events in discrete fragments, rather than existing as a 
> fixed, pre-existing background to events.
>

I agree, except that I see elemental computation also as something that 
arises out of even more primitive sensory-motive qualities disentangling 
into localized fugues which precede even qualities of discreteness or 
linear sequence. 

>
> The advantage of this approach is that it enables a conceptual unification 
> of quantum theory and GR; immediately resolves all quantum paradoxes (which 
> are paradoxical only with respect to the fixed, pre-existing background 
> space mistakenly assumed); and provides a clear explanation of the source 
> and necessity of quantum randomness. 
>

> Strangely no one here seems interested in how this happens, even to 
> criticize it!
>

Yes, I am very familiar with the feeling ;)  I have only a superficial 
understanding of QT and GR, so I wouldn't be the one to criticize 
technically. My objection is only that whatever primordial form or function 
can be conceived of as absolute must supervene on an even more primordial 
possibility of aesthetic appreciation and intentional participation.

Craig
 

>  
>

> Edgar
>
> On Sunday, February 16, 2014 8:35:32 AM UTC-5, Craig Weinberg wrote:
>>
>>
>>
>> On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:
>>>
>>> Russell,
>>>
>>> No, the proper understanding is that gravitation and curved space are 
>>> EQUIVALENT. Both are produced by the presence of mass-energy (and stress).
>>>
>>
>> I would say that gravity and curved space are metaphorical rather than 
>> literal. The literal phenomenon is that the inertial frame of sensible 
>> external relations is what is being curved. It is literally the experience 
>> of stress - of seriousness and realism which is seen from the outside as 
>> exaggerated irreversibility and inevitability. Mass-energy is the public 
>> token which represents sensory-motive. Space/density is the dual of mass, 
>> time/duration is the dual of energy.
>>
>> Mass-energy doesn't produce anything except externalized reflections of 
>> phenomenal experiences. Gravitation and curved space describe the back end 
>> of the sensory-motor (not motive because its externalized) relations which 
>> are interphenomenal, automatic, and unattended on all frames but the 
>> primordial one.
>>
>> Craig
>>  
>>
>>>
>>> You say "Motion through curved space appears as acceleration in a flat 
>>> tangent space."
>>>
>>> Are you saying then that acceleration from a rising elevator is "motion 
>>> through curved space"?
>>>
>>> That was my original question but I don't know what your answer is from 
>>> your post..
>>>
>>> Edgar
>>>
>>>
>>>
>>>
>>>
>>> On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:

 On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
 > All, 
 > 
 > By the Principle of Equivalence acceleration is equivalent to 
 gravitation. 
 > 
 > Gravitation curves space. 

 No - curved space generates the phenomena of gravitation. 

 It is sometimes said that "matter curves space". 

 > 
 > So doesn't this mean acceleration should also curve space? If not, 
 why not? 
 > 

 Motion through curved space appears as acceleration in a flat tangent 
 space. 

 > If not, doesn't that violate the Equivalence Principle? 


 No. 


 -- 

 
  

 Prof Russell Standish  Phone 0425 253119 (mobile) 
 Principal, High Performance Coders 
 Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
 University of New South Wales  http://www.hpcoders.com.au 
 
  


>>>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Edgar L. Owen

John,

You say that "You can tell if spacetime is curved or not by observing if 
light moves in a straight line or not." and then you say that light does 
NOT travel in a straight line in the accelerating elevator example you give.

So, by your terminology, does that mean that the acceleration of the 
elevator IS curving space or not?

It seems like you might be saying that the acceleration does curve space 
but only in its own frame. Would that be an accurate way to state your 
understanding?

And if that is true can we then say that the curvature of space is not 
absolute and the same for all observers, but is frame dependent, at least 
in the case of acceleration curving space? 

And can we say this is a basic difference between the curvature of space by 
gravitation and by acceleration, that the curvature of space by gravitation 
is absolute in this sense, but the curvature of space by acceleration is 
relative in the sense it is true only for the accelerating frame?

Edgar

On Friday, February 14, 2014 3:44:47 PM UTC-5, John Clark wrote:
>
> On Thu, Feb 13, 2014 at 8:39 PM, Edgar L. Owen 
> > wrote:
>
> > The accelerating elevator is in deep space. There are no tidal forces.
>>
>
> You can tell if spacetime is curved or not by observing if light moves in 
> a straight line or not. If you were in deep space and the elevator was 
> accelerating at 1g due to a attached rocket and you turned on a laser 
> pointer that was aimed parallel to the floor you would notice that the 
> light would not hit the spot directly across because by the time it took 
> the light beam to cross the elevator the elevator would be moving faster 
> upward than when the light beam started it's journey due to the 
> acceleration. Thus you would observe the light beam hit a spot slightly 
> below where it would have hit if the light moved in a straight line, so you 
> would conclude that spacetime inside the elevator was curved. 
>
> If the elevator was not in deep space but was just sitting on the surface 
> of the Earth you would make the exact same observation and make the same 
> conclusion about the curvature of spacetime. So you'd know spacetime was 
> curved but unless the elevator had a window you wouldn't know if it was 
> because it was in deep space being accelerated by a rocket at 1g or because 
> it was sitting still on the surface of the Earth in the planet's 1g gravity 
> field.
>
>   John K Clark
>
>
>
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Edgar L. Owen

Craig,

I agree with your idea in one sense, that actually space and clock time are 
just computational relationships between events, specifically the 
dimensional aspects of those events, rather than the actual physical 
background to events that is usually assumed.

In my book on Reality, I point out the reasons why it's more reasonable to 
assume that spaceclocktime is something that arises out of elemental 
computational events in discrete fragments, rather than existing as a 
fixed, pre-existing background to events.

The advantage of this approach is that it enables a conceptual unification 
of quantum theory and GR; immediately resolves all quantum paradoxes (which 
are paradoxical only with respect to the fixed, pre-existing background 
space mistakenly assumed); and provides a clear explanation of the source 
and necessity of quantum randomness.

Strangely no one here seems interested in how this happens, even to 
criticize it!

Edgar

On Sunday, February 16, 2014 8:35:32 AM UTC-5, Craig Weinberg wrote:
>
>
>
> On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:
>>
>> Russell,
>>
>> No, the proper understanding is that gravitation and curved space are 
>> EQUIVALENT. Both are produced by the presence of mass-energy (and stress).
>>
>
> I would say that gravity and curved space are metaphorical rather than 
> literal. The literal phenomenon is that the inertial frame of sensible 
> external relations is what is being curved. It is literally the experience 
> of stress - of seriousness and realism which is seen from the outside as 
> exaggerated irreversibility and inevitability. Mass-energy is the public 
> token which represents sensory-motive. Space/density is the dual of mass, 
> time/duration is the dual of energy.
>
> Mass-energy doesn't produce anything except externalized reflections of 
> phenomenal experiences. Gravitation and curved space describe the back end 
> of the sensory-motor (not motive because its externalized) relations which 
> are interphenomenal, automatic, and unattended on all frames but the 
> primordial one.
>
> Craig
>  
>
>>
>> You say "Motion through curved space appears as acceleration in a flat 
>> tangent space."
>>
>> Are you saying then that acceleration from a rising elevator is "motion 
>> through curved space"?
>>
>> That was my original question but I don't know what your answer is from 
>> your post..
>>
>> Edgar
>>
>>
>>
>>
>>
>> On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:
>>>
>>> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
>>> > All, 
>>> > 
>>> > By the Principle of Equivalence acceleration is equivalent to 
>>> gravitation. 
>>> > 
>>> > Gravitation curves space. 
>>>
>>> No - curved space generates the phenomena of gravitation. 
>>>
>>> It is sometimes said that "matter curves space". 
>>>
>>> > 
>>> > So doesn't this mean acceleration should also curve space? If not, why 
>>> not? 
>>> > 
>>>
>>> Motion through curved space appears as acceleration in a flat tangent 
>>> space. 
>>>
>>> > If not, doesn't that violate the Equivalence Principle? 
>>>
>>>
>>> No. 
>>>
>>>
>>> -- 
>>>
>>> 
>>>  
>>>
>>> Prof Russell Standish  Phone 0425 253119 (mobile) 
>>> Principal, High Performance Coders 
>>> Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
>>> University of New South Wales  http://www.hpcoders.com.au 
>>> 
>>>  
>>>
>>>
>>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread John Clark

On Sat, Feb 15, 2014 at 3:17 PM, LizR  wrote:

>
> >>> Einstein couldn't be classed as witless
>>> He claimed atoms were the littlelest
>>> When they did a bit of splittin' em
>>> It scared everybody shitless.
>>>
>>
>>  >> A Quantum Mechanic's vacation
>>  Left his colleagues in dire consternation
>>  Though tests had shown
>>  His speed was well known
>>  His position was pure speculation
>>
> > There ain't half been some clever bastards
> Probably got help from their mum
>
> There ain't half been some clever bastards
> Now that we've had some
> Let's hope that there's lots more to come.
>


There was a young lady named Bright
Who traveled much faster than light
She left one day
In a relative way
And returned the previous night

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-16 Thread Craig Weinberg



On Thursday, February 13, 2014 8:22:50 PM UTC-5, Edgar L. Owen wrote:
>
> Russell,
>
> No, the proper understanding is that gravitation and curved space are 
> EQUIVALENT. Both are produced by the presence of mass-energy (and stress).
>

I would say that gravity and curved space are metaphorical rather than 
literal. The literal phenomenon is that the inertial frame of sensible 
external relations is what is being curved. It is literally the experience 
of stress - of seriousness and realism which is seen from the outside as 
exaggerated irreversibility and inevitability. Mass-energy is the public 
token which represents sensory-motive. Space/density is the dual of mass, 
time/duration is the dual of energy.

Mass-energy doesn't produce anything except externalized reflections of 
phenomenal experiences. Gravitation and curved space describe the back end 
of the sensory-motor (not motive because its externalized) relations which 
are interphenomenal, automatic, and unattended on all frames but the 
primordial one.

Craig
 

>
> You say "Motion through curved space appears as acceleration in a flat 
> tangent space."
>
> Are you saying then that acceleration from a rising elevator is "motion 
> through curved space"?
>
> That was my original question but I don't know what your answer is from 
> your post..
>
> Edgar
>
>
>
>
>
> On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:
>>
>> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
>> > All, 
>> > 
>> > By the Principle of Equivalence acceleration is equivalent to 
>> gravitation. 
>> > 
>> > Gravitation curves space. 
>>
>> No - curved space generates the phenomena of gravitation. 
>>
>> It is sometimes said that "matter curves space". 
>>
>> > 
>> > So doesn't this mean acceleration should also curve space? If not, why 
>> not? 
>> > 
>>
>> Motion through curved space appears as acceleration in a flat tangent 
>> space. 
>>
>> > If not, doesn't that violate the Equivalence Principle? 
>>
>>
>> No. 
>>
>>
>> -- 
>>
>>  
>>
>> Prof Russell Standish  Phone 0425 253119 (mobile) 
>> Principal, High Performance Coders 
>> Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
>> University of New South Wales  http://www.hpcoders.com.au 
>>  
>>
>>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-15 Thread LizR

On 16 February 2014 09:35,  wrote:

> Limericks?
>

No, I just put a quote at the end of my post... Seems I can't do anything
without starting a trend.

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-15 Thread spudboy100



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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-15 Thread LizR

On 16 February 2014 06:07, John Clark  wrote:

> On Fri, Feb 14, 2014 at 3:49 PM, LizR  wrote:
>
> > Einstein couldn't be classed as witless
>> He claimed atoms were the littlelest
>> When they did a bit of splittin' em
>> It scared everybody shitless.
>>
>
>  A Quantum Mechanic's vacation
>  Left his colleagues in dire consternation
>  Though tests had shown
>  His speed was well known
>  His position was pure speculation
>
> There ain't half been some clever bastards
Probably got help from their mum

There ain't half been some clever bastards
Now that we've had some
Let's hope that there's lots more to come.

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-15 Thread John Clark

On Fri, Feb 14, 2014 at 3:49 PM, LizR  wrote:

> Einstein couldn't be classed as witless
> He claimed atoms were the littlelest
> When they did a bit of splittin' em
> It scared everybody shitless.
>

 A Quantum Mechanic's vacation
 Left his colleagues in dire consternation
 Though tests had shown
 His speed was well known
 His position was pure speculation

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-14 Thread meekerdb


On 2/14/2014 12:39 PM, John Mikes wrote:
Asks the agnostic: if there is a 'flat tangent space' - how did it "curl up"? (isn't 
that our distorted view (or words) only?)

 ((Matter did it?? how??))


We know the equations and they make accurate predictions.  We're agnostic about 
"how?".

 if curved space generates the phenomena of gravitation how 
is the curvature oriented so that the
 resulting gravitation has a definite direction? Is the 
'curvature' aim-oriented? (like a linear growth?)


Curvature can have a direction.  But it is not just space that is curved, it is 
spacetime.  Gravitational acceleration near the Earth comes from the time difference at 
different radii.



(The gravitation theorem of Istvan Vass in the early 50's Commi Hungary called for the 
unkilekiness of 'pulling' from afar,
vs. the likeliness of pushing. In his view everything is pushing in all directions and 
the 'push' dies in 'mass'. So wherever
a large mess gets in the way of the 'push' it blocks it, allowing the rest of the 
directions to work pushing, resulting in a "PULL"-like effect from the direction of the 
mass.
towards the big mass. The Commi authorities disallowed publication, even working on the 
theorem.)


Regardless of "the authorities" I've heard of the theory (it's one most physics majors 
come up with at some time).  It has several problems, e.g. there should be lower 
gravitational acceleration on the side of the Earth facing the Sun since the Sun would be 
'shielding' the 'push'.  There should be an observable directional difference due to 
motion through the pushing medium.


Brent

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-14 Thread LizR

On 15 February 2014 09:44, John Clark  wrote:

> On Thu, Feb 13, 2014 at 8:39 PM, Edgar L. Owen  wrote:
>
> > The accelerating elevator is in deep space. There are no tidal forces.
>>
>
> You can tell if spacetime is curved or not by observing if light moves in
> a straight line or not. If you were in deep space and the elevator was
> accelerating at 1g due to a attached rocket and you turned on a laser
> pointer that was aimed parallel to the floor you would notice that the
> light would not hit the spot directly across because by the time it took
> the light beam to cross the elevator the elevator would be moving faster
> upward than when the light beam started it's journey due to the
> acceleration. Thus you would observe the light beam hit a spot slightly
> below where it would have hit if the light moved in a straight line, so you
> would conclude that spacetime inside the elevator was curved.
>
> I know this is bad forum form, but for once I will just post in order to
say...

DAMN good point I'd completely forgotten that.



Actually I'll round out my post  with a quote (from memory, due to
laziness) from Ian Dury's song "There ain't half been some clever bastards"

Einstein couldn't be classed as witless
He claimed atoms were the littlelest
When they did a bit of splittin' em
It scared everybody shitless.

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-14 Thread John Clark

On Thu, Feb 13, 2014 at 8:39 PM, Edgar L. Owen  wrote:

> The accelerating elevator is in deep space. There are no tidal forces.
>

You can tell if spacetime is curved or not by observing if light moves in a
straight line or not. If you were in deep space and the elevator was
accelerating at 1g due to a attached rocket and you turned on a laser
pointer that was aimed parallel to the floor you would notice that the
light would not hit the spot directly across because by the time it took
the light beam to cross the elevator the elevator would be moving faster
upward than when the light beam started it's journey due to the
acceleration. Thus you would observe the light beam hit a spot slightly
below where it would have hit if the light moved in a straight line, so you
would conclude that spacetime inside the elevator was curved.

If the elevator was not in deep space but was just sitting on the surface
of the Earth you would make the exact same observation and make the same
conclusion about the curvature of spacetime. So you'd know spacetime was
curved but unless the elevator had a window you wouldn't know if it was
because it was in deep space being accelerated by a rocket at 1g or because
it was sitting still on the surface of the Earth in the planet's 1g gravity
field.

  John K Clark

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-14 Thread LizR

The "pushing theory of gravity" is an interesting one which crops up
occasionally (even in science fiction, at least when written by the
wonderful Barrington Bayley). I have a feeling there is some fundamental
flaw with it, but I can't recall if I just imagined that, or actually read
it somewhere...


On 15 February 2014 09:39, John Mikes  wrote:

> Asks the agnostic: if there is a 'flat tangent space' - how did it "curl
> up"? (isn't that our distorted view (or words) only?)
>  ((Matter did it?? how??))
>  if curved space generates the phenomena of
> gravitation how is the curvature oriented so that the
>  resulting gravitation has a definite
> direction? Is the 'curvature' aim-oriented? (like a linear growth?)
> (The gravitation theorem of Istvan Vass in the early 50's Commi Hungary
> called for the unkilekiness of 'pulling' from afar,
> vs. the likeliness of pushing. In his view everything is pushing in all
> directions and the 'push' dies in 'mass'. So wherever
> a large mess gets in the way of the 'push' it blocks it, allowing the rest
> of the directions to work pushing, resulting in a "PULL"-like effect from
> the direction of the mass.
> towards the big mass. The Commi authorities disallowed publication, even
> working on the theorem.)
> John Mikes
>
>
> On Thu, Feb 13, 2014 at 7:41 PM, Russell Standish 
> wrote:
>
>> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote:
>> > All,
>> >
>> > By the Principle of Equivalence acceleration is equivalent to
>> gravitation.
>> >
>> > Gravitation curves space.
>>
>> No - curved space generates the phenomena of gravitation.
>>
>> It is sometimes said that "matter curves space".
>>
>> >
>> > So doesn't this mean acceleration should also curve space? If not, why
>> not?
>> >
>>
>> Motion through curved space appears as acceleration in a flat tangent
>> space.
>>
>> > If not, doesn't that violate the Equivalence Principle?
>>
>>
>> No.
>>
>>
>> --
>>
>>
>> 
>> Prof Russell Standish  Phone 0425 253119 (mobile)
>> Principal, High Performance Coders
>> Visiting Professor of Mathematics  hpco...@hpcoders.com.au
>> University of New South Wales  http://www.hpcoders.com.au
>>
>> 
>>
>> --
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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-14 Thread John Mikes

Asks the agnostic: if there is a 'flat tangent space' - how did it "curl
up"? (isn't that our distorted view (or words) only?)
 ((Matter did it?? how??))
 if curved space generates the phenomena of
gravitation how is the curvature oriented so that the
 resulting gravitation has a definite
direction? Is the 'curvature' aim-oriented? (like a linear growth?)
(The gravitation theorem of Istvan Vass in the early 50's Commi Hungary
called for the unkilekiness of 'pulling' from afar,
vs. the likeliness of pushing. In his view everything is pushing in all
directions and the 'push' dies in 'mass'. So wherever
a large mess gets in the way of the 'push' it blocks it, allowing the rest
of the directions to work pushing, resulting in a "PULL"-like effect from
the direction of the mass.
towards the big mass. The Commi authorities disallowed publication, even
working on the theorem.)
John Mikes

On Thu, Feb 13, 2014 at 7:41 PM, Russell Standish wrote:

> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote:
> > All,
> >
> > By the Principle of Equivalence acceleration is equivalent to
> gravitation.
> >
> > Gravitation curves space.
>
> No - curved space generates the phenomena of gravitation.
>
> It is sometimes said that "matter curves space".
>
> >
> > So doesn't this mean acceleration should also curve space? If not, why
> not?
> >
>
> Motion through curved space appears as acceleration in a flat tangent
> space.
>
> > If not, doesn't that violate the Equivalence Principle?
>
>
> No.
>
>
> --
>
>
> 
> Prof Russell Standish  Phone 0425 253119 (mobile)
> Principal, High Performance Coders
> Visiting Professor of Mathematics  hpco...@hpcoders.com.au
> University of New South Wales  http://www.hpcoders.com.au
>
> 
>
> --
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> "Everything List" group.
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> email to everything-list+unsubscr...@googlegroups.com.
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Re: How does acceleration curve space? Can anyone provide an answer?

On 14 February 2014 14:39, Edgar L. Owen  wrote:

> Liz,
>
> As usual, you are late to the party.
>

And I see you haven't lost any of your wit and charm.

>
> The accelerating elevator is in deep space. There are no tidal forces.
>

The tidal forces are for the non-accelerating elevator resting on the
surface of the Earth.

>
> The tidal forces of EARTH'S gravitation on the man standing on earth are
> negligible and can be ignored. They are just the difference in
> gravitational pull on his head and feet.
>

Plus as I mentioned the fact that the gravitational field of the Earth is
centred on the centre of the Earth. Hence the tidal force has two
components, a vertical one you just described and a horizontal one that I
mentioned.

The point of the exercise was to answer the question of whether
acceleration curves space, and if not, whether that violates the
equivalence principle. Hence *all* points of comparison are relevant.

But in any case, hopefully you now know that acceleration doesn't curve
space, and that this doesn't violate the equivalence principle.

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Re: How does acceleration curve space? Can anyone provide an answer?

The equivalence principle only works for infinitesimal regions because any
gravitational field will vary from point to point, while acceleration is
uniform.

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Re: How does acceleration curve space? Can anyone provide an answer?

On Thu, Feb 13, 2014 at 8:30 PM, Edgar L. Owen  wrote:

> Jesse,
>
> The accelerating floor of an elevator the size of a planet is not "an
> infinitesimal neighborhood of a point in spacetime". So that comment of
> yours does not apply.
>

It seems to me it should apply, since you asked "If not doesn't that
violate the Principle of Equivalence?"--I think the answer is no, because
the equivalence principle only deals with infinitesimal regions in
gravitational fields, it doesn't say anything about planet-sized elevators
accelerating in deep space being equivalent to planet-sized elevators in a
gravitational field, and thus there is no violation of the principle if
effects of curved spacetime are seen in the latter but not the former.
Unless you were just asking whether a planet-sized elevator accelerating in
deep space would see the same first-order laws as are seen in an
infinitesimal elevator in a gravitational field--in that case they *would*
see the same first-order laws, but no first-order effects of "warped space"
would be seen by the observer in the infinitesimal elevator in the gravity
field, so we shouldn't expect any to be seen in the planet-sized elevator
in deep space either.

>
> So based on that understanding, is space warped by the acceleration of
> the planet sized sized elevator or not?
>
>
No, not if it's massless as you assumed in your thought-experiment. Only
mass/energy curves spacetime, acceleration on its own does not.

Jesse

>
>
>
> On Thursday, February 13, 2014 7:51:00 PM UTC-5, jessem wrote:
>>
>>
>>
>> On Thu, Feb 13, 2014 at 7:41 PM, Edgar L. Owen  wrote:
>>
>>> Jesse, Brent, Liz, et al,
>>>
>>> Free fall in a gravitational field is NOT acceleration. Standing on the
>>> surface of the earth IS acceleration because only then is the acceleration
>>> of gravity felt as such.
>>>
>>
>> Yes, that's why I equated inertial motion in flat spacetime with freefall
>> in a gravitational field--"Bob" could be either one in my example. I also
>> equated accelerated motion in flat spacetime with non-freefall in a
>> gravitational field--"Alice" could be either one in my example, note where
>> I said she'd observe the same thing "regardless of whether she's
>> accelerating through Bob's region in flat spacetime, or passing through his
>> region because he's in free-fall while she is not (say, she's standing on a
>> platform resting on a pole embedded in the Earth below, while Bob falls
>> past her)."
>>
>>
>>
>>> Now imagine that elevator is enormous, the size of a planet (but assume
>>> also in this thought experiment that it has no mass and thus has no
>>> gravitational effect).
>>>
>>
>> The equivalence principle simply doesn't apply to large regions of space
>> where tidal forces can be observed, mathematically it only applies in the
>> infinitesimal neighborhood of a point in spacetime, though in practice if
>> your measuring instruments aren't too precise a reasonably small space like
>> an elevator should be OK (at least in the Earth's gravitational field--in
>> the gravitational field of a black hole even an elevator would be too large
>> because there'd be a significant tidal force between the top and bottom).
>> See the discussion about how tidal forces spoil any attempt to make the
>> equivalence principle work in a non-infinitesimal region at
>> http://www.einstein-online.info/spotlights/equivalence_principle
>>
>> Jesse
>>
>>
>>> On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote:

 On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen wrote:

> All,
>
> By the Principle of Equivalence acceleration is equivalent to
> gravitation.
>

 Too vague. A more precise statement is that in an observer in free-fall
 in a gravitational field can define a "local inertial frame" in an
 infinitesimally small neighborhood of spacetime around them, and that if
 the laws of physics are expressed in the coordinates of this frame, they
 will look just like the corresponding equations in flat SR spacetime,
 though only in the first-order approximation to the equations (i.e.
 eliminating all derivatives beyond the first derivatives). See for example:
 http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and
 http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and
 http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5

 Even though the curvature disappears in the first order terms, it
 remains in the higher order terms, whereas curvature is really zero in all
 terms for an accelerating observer in flat spacetime. So, the answer to
 your question is that acceleration does not in itself cause spacetime
 curvature, SR can handle acceleration just fine as discussed at
 http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html, but 
 this isn't a violation of the equivalence principle since the
 mathematical formulation of the principle dea

Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-13 Thread Russell Standish

On Thu, Feb 13, 2014 at 05:22:50PM -0800, Edgar L. Owen wrote:
> Russell,
> 
> No, the proper understanding is that gravitation and curved space are 
> EQUIVALENT. Both are produced by the presence of mass-energy (and stress).

In General Relativity, gravitation is not a force, but rather a
pseudo-force (like a kind of illusion) caused by curvature of space.

I also suspect that mass-energy is an effect of spacetime being
curved, but that is not the usual picture. The usual picture is:

mass-energy-stress => curved spacetime => gravitation

summed up by "matter causes space to curve, curved space tells matter
how to move".

> 
> You say "Motion through curved space appears as acceleration in a flat 
> tangent space."
> 
> Are you saying then that acceleration from a rising elevator is "motion 
> through curved space"?
> 

No. The rising lift could just as easily be acelerating in flat space
due to electromagnetic forces acting through a cable, say.

But a lift in free fall in curved space (ie following a geodesic) will
appear to be accelerating (in its tangent space), and we describe the
pseudo force that appears to be causing that apparent acceleration as "gravity".

> That was my original question but I don't know what your answer is from 
> your post..
> 

Your original post of 13th Feb is shown below. You started by
asserting "Gravitation curves space", and you went downhill from there.

> Edgar
> 
> 
> 
> 
> 
> On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:
> >
> > On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
> > > All, 
> > > 
> > > By the Principle of Equivalence acceleration is equivalent to 
> > gravitation. 
> > > 
> > > Gravitation curves space. 
> >
> > No - curved space generates the phenomena of gravitation. 
> >
> > It is sometimes said that "matter curves space". 
> >
> > > 
> > > So doesn't this mean acceleration should also curve space? If not, why 
> > not? 
> > > 
> >
> > Motion through curved space appears as acceleration in a flat tangent 
> > space. 
> >
> > > If not, doesn't that violate the Equivalence Principle? 
> >
> >
> > No. 
> >
> >
> > -- 
> >
> > 
> >  
> >
> > Prof Russell Standish  Phone 0425 253119 (mobile) 
> > Principal, High Performance Coders 
> > Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
> > University of New South Wales  http://www.hpcoders.com.au 
> > 
> >  
> >
> >
> 
> -- 
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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: How does acceleration curve space? Can anyone provide an answer?

Liz,

As usual, you are late to the party.

The accelerating elevator is in deep space. There are no tidal forces.

The tidal forces of EARTH'S gravitation on the man standing on earth are 
negligible and can be ignored. They are just the difference in 
gravitational pull on his head and feet. 

Of course the tidal forces of the MOON on the man on earth are measurable 
but those are not part of my example.

So tidal forces can be ignored.

Edgar



On Thursday, February 13, 2014 8:07:46 PM UTC-5, Liz R wrote:
>
> Yeah, tidal forces make a measurable difference between the guy on a 
> planet and the accelerating elevator guy. Basically a planet is (more or 
> less) spherical, so the gravity field isn't uniform over the flat floor of 
> hte elevator, but pulls slightly towards the centre of the sphere. With 
> sensitive enough instruments you could tell that two objects falling on 
> either side of the elevator aren't moving along parallel courses, and hence 
> tell the two cases apart.
>
> The equivalence principle also assumes that gravitational and inertial 
> mass are the same, which (although accurate to a very high degree) may turn 
> out to not be exactly identical. (See the works of E.E. "Doc" Smith for 
> what that would mean!)
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

Jesse,

The accelerating floor of an elevator the size of a planet is not "an 
infinitesimal neighborhood of a point in spacetime". So that comment of 
yours does not apply.

And I don't see any tidal forces at play here since the entire floor of the 
elevator is accelerating 'upward' (just in the direction of the 
acceleration since there is no absolute up and down) at the same rate and 
there are NO gravitational fields in deep space where the elevator is. So I 
don't see your tidal force comment being relevant.

So based on that understanding, is space warped by the acceleration of 
the planet sized sized elevator or not? And if so what is the form of that 
warpage? Is there a planet sized warping, or not?

Edgar




On Thursday, February 13, 2014 7:51:00 PM UTC-5, jessem wrote:
>
>
>
> On Thu, Feb 13, 2014 at 7:41 PM, Edgar L. Owen 
> > wrote:
>
>> Jesse, Brent, Liz, et al,
>>
>> Free fall in a gravitational field is NOT acceleration. Standing on the 
>> surface of the earth IS acceleration because only then is the acceleration 
>> of gravity felt as such.
>>
>
> Yes, that's why I equated inertial motion in flat spacetime with freefall 
> in a gravitational field--"Bob" could be either one in my example. I also 
> equated accelerated motion in flat spacetime with non-freefall in a 
> gravitational field--"Alice" could be either one in my example, note where 
> I said she'd observe the same thing "regardless of whether she's 
> accelerating through Bob's region in flat spacetime, or passing through his 
> region because he's in free-fall while she is not (say, she's standing on a 
> platform resting on a pole embedded in the Earth below, while Bob falls 
> past her)."
>
>
>
>> Now imagine that elevator is enormous, the size of a planet (but assume 
>> also in this thought experiment that it has no mass and thus has no 
>> gravitational effect).
>>
>
> The equivalence principle simply doesn't apply to large regions of space 
> where tidal forces can be observed, mathematically it only applies in the 
> infinitesimal neighborhood of a point in spacetime, though in practice if 
> your measuring instruments aren't too precise a reasonably small space like 
> an elevator should be OK (at least in the Earth's gravitational field--in 
> the gravitational field of a black hole even an elevator would be too large 
> because there'd be a significant tidal force between the top and bottom). 
> See the discussion about how tidal forces spoil any attempt to make the 
> equivalence principle work in a non-infinitesimal region at 
> http://www.einstein-online.info/spotlights/equivalence_principle
>
> Jesse
>
>
>> On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote:
>>>
>>>
>>>
>>> On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen  wrote:
>>>
 All,

 By the Principle of Equivalence acceleration is equivalent to 
 gravitation.

>>>
>>> Too vague. A more precise statement is that in an observer in free-fall 
>>> in a gravitational field can define a "local inertial frame" in an 
>>> infinitesimally small neighborhood of spacetime around them, and that if 
>>> the laws of physics are expressed in the coordinates of this frame, they 
>>> will look just like the corresponding equations in flat SR spacetime, 
>>> though only in the first-order approximation to the equations (i.e. 
>>> eliminating all derivatives beyond the first derivatives). See for example: 
>>> http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and 
>>> http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and 
>>> http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5
>>>
>>> Even though the curvature disappears in the first order terms, it 
>>> remains in the higher order terms, whereas curvature is really zero in all 
>>> terms for an accelerating observer in flat spacetime. So, the answer to 
>>> your question is that acceleration does not in itself cause spacetime 
>>> curvature, SR can handle acceleration just fine as discussed at 
>>> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html , 
>>> but this isn't a violation of the equivalence principle since the 
>>> mathematical formulation of the principle deals only with first-order terms.
>>>
>>> Jesse
>>>
>>>
>>>  -- 
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Re: How does acceleration curve space? Can anyone provide an answer?

Russell,

No, the proper understanding is that gravitation and curved space are 
EQUIVALENT. Both are produced by the presence of mass-energy (and stress).

You say "Motion through curved space appears as acceleration in a flat 
tangent space."

Are you saying then that acceleration from a rising elevator is "motion 
through curved space"?

That was my original question but I don't know what your answer is from 
your post..

Edgar





On Thursday, February 13, 2014 7:41:09 PM UTC-5, Russell Standish wrote:
>
> On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote: 
> > All, 
> > 
> > By the Principle of Equivalence acceleration is equivalent to 
> gravitation. 
> > 
> > Gravitation curves space. 
>
> No - curved space generates the phenomena of gravitation. 
>
> It is sometimes said that "matter curves space". 
>
> > 
> > So doesn't this mean acceleration should also curve space? If not, why 
> not? 
> > 
>
> Motion through curved space appears as acceleration in a flat tangent 
> space. 
>
> > If not, doesn't that violate the Equivalence Principle? 
>
>
> No. 
>
>
> -- 
>
>  
>
> Prof Russell Standish  Phone 0425 253119 (mobile) 
> Principal, High Performance Coders 
> Visiting Professor of Mathematics  hpc...@hpcoders.com.au 
> University of New South Wales  http://www.hpcoders.com.au 
>  
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

Yeah, tidal forces make a measurable difference between the guy on a planet
and the accelerating elevator guy. Basically a planet is (more or less)
spherical, so the gravity field isn't uniform over the flat floor of hte
elevator, but pulls slightly towards the centre of the sphere. With
sensitive enough instruments you could tell that two objects falling on
either side of the elevator aren't moving along parallel courses, and hence
tell the two cases apart.

The equivalence principle also assumes that gravitational and inertial mass
are the same, which (although accurate to a very high degree) may turn out
to not be exactly identical. (See the works of E.E. "Doc" Smith for what
that would mean!)

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Re: How does acceleration curve space? Can anyone provide an answer?

On Thu, Feb 13, 2014 at 7:41 PM, Edgar L. Owen  wrote:

> Jesse, Brent, Liz, et al,
>
> Free fall in a gravitational field is NOT acceleration. Standing on the
> surface of the earth IS acceleration because only then is the acceleration
> of gravity felt as such.
>

Yes, that's why I equated inertial motion in flat spacetime with freefall
in a gravitational field--"Bob" could be either one in my example. I also
equated accelerated motion in flat spacetime with non-freefall in a
gravitational field--"Alice" could be either one in my example, note where
I said she'd observe the same thing "regardless of whether she's
accelerating through Bob's region in flat spacetime, or passing through his
region because he's in free-fall while she is not (say, she's standing on a
platform resting on a pole embedded in the Earth below, while Bob falls
past her)."

> Now imagine that elevator is enormous, the size of a planet (but assume
> also in this thought experiment that it has no mass and thus has no
> gravitational effect).
>

The equivalence principle simply doesn't apply to large regions of space
where tidal forces can be observed, mathematically it only applies in the
infinitesimal neighborhood of a point in spacetime, though in practice if
your measuring instruments aren't too precise a reasonably small space like
an elevator should be OK (at least in the Earth's gravitational field--in
the gravitational field of a black hole even an elevator would be too large
because there'd be a significant tidal force between the top and bottom).
See the discussion about how tidal forces spoil any attempt to make the
equivalence principle work in a non-infinitesimal region at
http://www.einstein-online.info/spotlights/equivalence_principle

Jesse

> On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote:
>>
>>
>>
>> On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen  wrote:
>>
>>> All,
>>>
>>> By the Principle of Equivalence acceleration is equivalent to
>>> gravitation.
>>>
>>
>> Too vague. A more precise statement is that in an observer in free-fall
>> in a gravitational field can define a "local inertial frame" in an
>> infinitesimally small neighborhood of spacetime around them, and that if
>> the laws of physics are expressed in the coordinates of this frame, they
>> will look just like the corresponding equations in flat SR spacetime,
>> though only in the first-order approximation to the equations (i.e.
>> eliminating all derivatives beyond the first derivatives). See for example:
>> http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and
>> http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and
>> http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5
>>
>> Even though the curvature disappears in the first order terms, it remains
>> in the higher order terms, whereas curvature is really zero in all terms
>> for an accelerating observer in flat spacetime. So, the answer to your
>> question is that acceleration does not in itself cause spacetime curvature,
>> SR can handle acceleration just fine as discussed at
>> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html ,
>> but this isn't a violation of the equivalence principle since the
>> mathematical formulation of the principle deals only with first-order terms.
>>
>> Jesse
>>
>>
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Re: How does acceleration curve space? Can anyone provide an answer?

Jesse, Brent, Liz, et al,

Free fall in a gravitational field is NOT acceleration. Standing on the 
surface of the earth IS acceleration because only then is the acceleration 
of gravity felt as such.

Given that, let me clarify my example:

Observer A is standing on the surface of earth. He experiences a continual 
1g acceleration BECAUSE earth's gravitation warps space around the earth.

Observer B is standing in an accelerating elevator out in gravity free 
space. He also experiences the same 1g acceleration.

Now imagine that elevator is enormous, the size of a planet (but assume 
also in this thought experiment that it has no mass and thus has no 
gravitational effect).

OK, the whole planet sized massless elevator is continually accelerating so 
that observer B feels a 1g acceleration.

Now is the acceleration felt by observer B because the acceleration of the 
planet sized elevator warps space? Note the same 1 g acceleration would be 
felt everywhere on that planet sized surface.

If so, what is the shape of that space curvature/warp? Does it extend 
across the entire planet sized elevator surface?

If not doesn't that violate the Principle of Equivalence? And mean 
acceleration is not really equivalent to gravitation?

Can anyone explain?

Edgar

On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote:
>
>
>
> On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen 
> > wrote:
>
>> All,
>>
>> By the Principle of Equivalence acceleration is equivalent to gravitation.
>>
>
> Too vague. A more precise statement is that in an observer in free-fall in 
> a gravitational field can define a "local inertial frame" in an 
> infinitesimally small neighborhood of spacetime around them, and that if 
> the laws of physics are expressed in the coordinates of this frame, they 
> will look just like the corresponding equations in flat SR spacetime, 
> though only in the first-order approximation to the equations (i.e. 
> eliminating all derivatives beyond the first derivatives). See for example: 
> http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and 
> http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and 
> http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5
>
> Even though the curvature disappears in the first order terms, it remains 
> in the higher order terms, whereas curvature is really zero in all terms 
> for an accelerating observer in flat spacetime. So, the answer to your 
> question is that acceleration does not in itself cause spacetime curvature, 
> SR can handle acceleration just fine as discussed at 
> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html , 
> but this isn't a violation of the equivalence principle since the 
> mathematical formulation of the principle deals only with first-order terms.
>
> Jesse
>
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-13 Thread Russell Standish

On Thu, Feb 13, 2014 at 09:22:18AM -0800, Edgar L. Owen wrote:
> All,
> 
> By the Principle of Equivalence acceleration is equivalent to gravitation.
> 
> Gravitation curves space.

No - curved space generates the phenomena of gravitation.

It is sometimes said that "matter curves space".

> 
> So doesn't this mean acceleration should also curve space? If not, why not?
> 

Motion through curved space appears as acceleration in a flat tangent space.

> If not, doesn't that violate the Equivalence Principle?


No.


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Visiting Professor of Mathematics  hpco...@hpcoders.com.au
University of New South Wales  http://www.hpcoders.com.au


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Re: How does acceleration curve space? Can anyone provide an answer?

Brent,

Correction. That should be Unruh radiation or the Unruh effect, not Uruh.

Edgar


On Thursday, February 13, 2014 6:18:00 PM UTC-5, Brent wrote:
>
>  On 2/13/2014 2:55 PM, LizR wrote:
>  
> I didn't really imagine that an acceleration-caused event horizon warps 
> space (particularly since it will, I think, generally be a long way from 
> the accelerating observer?) I wouldn't imagine that acceleration in itself 
> warps space...?
> But I *do *seem to recall that the accel-caused EH emits Hawking 
> radiation, which is ... interesting, at least.
>  
>
> Sort of.  It's called Uruh radiation.  It's frame dependent in that the 
> guy accelerating sees the vacuum as a thermal bath and can detect it, but 
> to the guy not accelerating it appears that the detector is emitting the 
> radiation it registers.  Robert Wald has a thorough discussion of the 
> phenomena.  Its somewhat controversial and there have been proposals to 
> detect its effect on highly accelerated particles in cyclotrons.
>
> Brent
>
>  
>
> On 14 February 2014 11:31, Jesse Mazer  >wrote:
>
>> In this case the horizon is basically just the edge of a light cone, and 
>> a continuously-accelerating observer can indefinitely avoid crossing into 
>> this light cone (see the top diagram at 
>> https://en.wikipedia.org/wiki/Rindler_coordinates -- x=0 is the edge of 
>> the light cone, while the curve labeled x=0.2 would be the worldline of 
>> such an accelerating observer, similarly with x=0.4, x=0.6 etc.) Naturally 
>> any light cone behaves like an event horizon in the sense that once you 
>> cross into it, there's no way to ever get out of it without moving faster 
>> than light. But such a "Rindler horizon" is not considered a true event 
>> horizon, if I remember the terminology correctly--an event horizon is 
>> specifically defined as a boundary between points where all worldlines 
>> crossing through those points are guaranteed to hit a singularity, and 
>> points where some worldlines can avoid doing so forever. 
>>
>>  Jesse 
>>
>>
>>
>> On Thu, Feb 13, 2014 at 4:56 PM, meekerdb 
>> > wrote:
>>
>>> The event horizon due to acceleration is just relative to the one 
>>> accelerated.  I doesn't warp space, so there's no reason it should interact 
>>> with anything.
>>>
>>> Brent
>>>
>>  
>  

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Re: How does acceleration curve space? Can anyone provide an answer?


On 2/13/2014 3:27 PM, LizR wrote:
On 14 February 2014 12:22, meekerdb mailto:meeke...@verizon.net>> 
wrote:


On 2/13/2014 3:01 PM, LizR wrote:

On 14 February 2014 11:55, LizR mailto:lizj...@gmail.com>> wrote:

I wouldn't imagine that acceleration in itself warps space...?


Actually I take that back. A pair of neutron stars in close orbit (both
accelerating under their mutual gravity) /do/ warp space, presumably due to 
their
motion.

(...I think!)

The stress energy warps space and its value is greater due to their orbital 
motion
compared to them being stationary.  But I don't think their acceleration 
per se
contributes.  In fact due to their orbital motion they will radiate away 
energy as
gravity waves.


It was the gravity waves I was thinking of. That is to say, I believe very large masses 
orbitting each other radiate gravity waves because of their orbital motion, hence hence 
gravity waves are, or at least can be in this situation, an "acceleration-caused warping 
of space" ... as per the original question.


Or have I got that wrong?


No, I think that's right.  It's like EM: A charged particle causes a field. An 
acceleration causes a wave in the field caused by the particle.


Brent

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Re: How does acceleration curve space? Can anyone provide an answer?

On 14 February 2014 12:22, meekerdb  wrote:

>  On 2/13/2014 3:01 PM, LizR wrote:
>
>  On 14 February 2014 11:55, LizR  wrote:
>
>> I wouldn't imagine that acceleration in itself warps space...?
>>
>
> Actually I take that back. A pair of neutron stars in close orbit (both
> accelerating under their mutual gravity) *do* warp space, presumably due
> to their motion.
>
>  (...I think!)
>
> The stress energy warps space and its value is greater due to their
> orbital motion compared to them being stationary.  But I don't think their
> acceleration per se contributes.  In fact due to their orbital motion they
> will radiate away energy as gravity waves.
>

It was the gravity waves I was thinking of. That is to say, I believe very
large masses orbitting each other radiate gravity waves because of their
orbital motion, hence hence gravity waves are, or at least can be in this
situation, an "acceleration-caused warping of space" ... as per the
original question.

Or have I got that wrong?

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Re: How does acceleration curve space? Can anyone provide an answer?


On 2/13/2014 3:01 PM, LizR wrote:

On 14 February 2014 11:55, LizR mailto:lizj...@gmail.com>> 
wrote:

I wouldn't imagine that acceleration in itself warps space...?


Actually I take that back. A pair of neutron stars in close orbit (both accelerating 
under their mutual gravity) /do/ warp space, presumably due to their motion.


(...I think!)


The stress energy warps space and its value is greater due to their orbital motion 
compared to them being stationary.  But I don't think their acceleration per se 
contributes.  In fact due to their orbital motion they will radiate away energy as gravity 
waves.


Brent

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Re: How does acceleration curve space? Can anyone provide an answer?


On 2/13/2014 2:55 PM, LizR wrote:
I didn't really imagine that an acceleration-caused event horizon warps space 
(particularly since it will, I think, generally be a long way from the accelerating 
observer?) I wouldn't imagine that acceleration in itself warps space...?
But I /do /seem to recall that the accel-caused EH emits Hawking radiation, which is ... 
interesting, at least.


Sort of.  It's called Uruh radiation.  It's frame dependent in that the guy accelerating 
sees the vacuum as a thermal bath and can detect it, but to the guy not accelerating it 
appears that the detector is emitting the radiation it registers.  Robert Wald has a 
thorough discussion of the phenomena.  Its somewhat controversial and there have been 
proposals to detect its effect on highly accelerated particles in cyclotrons.


Brent




On 14 February 2014 11:31, Jesse Mazer > wrote:


In this case the horizon is basically just the edge of a light cone, and a
continuously-accelerating observer can indefinitely avoid crossing into 
this light
cone (see the top diagram at 
https://en.wikipedia.org/wiki/Rindler_coordinates --
x=0 is the edge of the light cone, while the curve labeled x=0.2 would be 
the
worldline of such an accelerating observer, similarly with x=0.4, x=0.6 
etc.)
Naturally any light cone behaves like an event horizon in the sense that 
once you
cross into it, there's no way to ever get out of it without moving faster 
than
light. But such a "Rindler horizon" is not considered a true event horizon, 
if I
remember the terminology correctly--an event horizon is specifically 
defined as a
boundary between points where all worldlines crossing through those points 
are
guaranteed to hit a singularity, and points where some worldlines can avoid 
doing so
forever.

Jesse



On Thu, Feb 13, 2014 at 4:56 PM, meekerdb mailto:meeke...@verizon.net>> wrote:

The event horizon due to acceleration is just relative to the one 
accelerated.
 I doesn't warp space, so there's no reason it should interact with 
anything.

Brent



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Re: How does acceleration curve space? Can anyone provide an answer?

On 14 February 2014 11:55, LizR  wrote:

> I wouldn't imagine that acceleration in itself warps space...?
>

Actually I take that back. A pair of neutron stars in close orbit (both
accelerating under their mutual gravity) *do* warp space, presumably due to
their motion.

(...I think!)

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Re: How does acceleration curve space? Can anyone provide an answer?

I didn't really imagine that an acceleration-caused event horizon warps
space (particularly since it will, I think, generally be a long way from
the accelerating observer?) I wouldn't imagine that acceleration in itself
warps space...?
But I *do *seem to recall that the accel-caused EH emits Hawking radiation,
which is ... interesting, at least.


On 14 February 2014 11:31, Jesse Mazer  wrote:

> In this case the horizon is basically just the edge of a light cone, and a
> continuously-accelerating observer can indefinitely avoid crossing into
> this light cone (see the top diagram at
> https://en.wikipedia.org/wiki/Rindler_coordinates -- x=0 is the edge of
> the light cone, while the curve labeled x=0.2 would be the worldline of
> such an accelerating observer, similarly with x=0.4, x=0.6 etc.) Naturally
> any light cone behaves like an event horizon in the sense that once you
> cross into it, there's no way to ever get out of it without moving faster
> than light. But such a "Rindler horizon" is not considered a true event
> horizon, if I remember the terminology correctly--an event horizon is
> specifically defined as a boundary between points where all worldlines
> crossing through those points are guaranteed to hit a singularity, and
> points where some worldlines can avoid doing so forever.
>
> Jesse
>
>
>
> On Thu, Feb 13, 2014 at 4:56 PM, meekerdb  wrote:
>
>> The event horizon due to acceleration is just relative to the one
>> accelerated.  I doesn't warp space, so there's no reason it should interact
>> with anything.
>>
>> Brent
>>
>> On 2/13/2014 12:41 PM, LizR wrote:
>>
>>> Acceleration does cause the formation of an event horizon, I believe,
>>> which might be considered to couple it with gravity (in an unexpected way).
>>>
>>
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Re: How does acceleration curve space? Can anyone provide an answer?

In this case the horizon is basically just the edge of a light cone, and a
continuously-accelerating observer can indefinitely avoid crossing into
this light cone (see the top diagram at
https://en.wikipedia.org/wiki/Rindler_coordinates -- x=0 is the edge of the
light cone, while the curve labeled x=0.2 would be the worldline of such an
accelerating observer, similarly with x=0.4, x=0.6 etc.) Naturally any
light cone behaves like an event horizon in the sense that once you cross
into it, there's no way to ever get out of it without moving faster than
light. But such a "Rindler horizon" is not considered a true event horizon,
if I remember the terminology correctly--an event horizon is specifically
defined as a boundary between points where all worldlines crossing through
those points are guaranteed to hit a singularity, and points where some
worldlines can avoid doing so forever.

Jesse

On Thu, Feb 13, 2014 at 4:56 PM, meekerdb  wrote:

> The event horizon due to acceleration is just relative to the one
> accelerated.  I doesn't warp space, so there's no reason it should interact
> with anything.
>
> Brent
>
> On 2/13/2014 12:41 PM, LizR wrote:
>
>> Acceleration does cause the formation of an event horizon, I believe,
>> which might be considered to couple it with gravity (in an unexpected way).
>>
>
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RE: How does acceleration curve space? Can anyone provide an answer?

2014-02-13 Thread Chris de Morsella


-Original Message-
From: everything-list@googlegroups.com
[mailto:everything-list@googlegroups.com] On Behalf Of meekerdb
Sent: Thursday, February 13, 2014 1:56 PM
To: everything-list@googlegroups.com
Subject: Re: How does acceleration curve space? Can anyone provide an
answer?

>> The event horizon due to acceleration is just relative to the one
accelerated.  I doesn't warp space, so there's no reason it should interact
with anything.

Then, would it be fair to say that the only thing special about the event
horizon is this "Hotel California" effect?

" Last thing I remember, I was
Running for the door
I had to find the passage back
To the place I was before
"Relax, " said the night man,
"We are programmed to receive.
You can check-out any time you like,
But you can never leave! "
(Eagles)

Cheers,
Chris

Brent

On 2/13/2014 12:41 PM, LizR wrote:
> Acceleration does cause the formation of an event horizon, I believe, 
> which might be considered to couple it with gravity (in an unexpected
way).

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Re: How does acceleration curve space? Can anyone provide an answer?

The event horizon due to acceleration is just relative to the one accelerated.  I doesn't 
warp space, so there's no reason it should interact with anything.


Brent

On 2/13/2014 12:41 PM, LizR wrote:
Acceleration does cause the formation of an event horizon, I believe, which might be 
considered to couple it with gravity (in an unexpected way).


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Re: How does acceleration curve space? Can anyone provide an answer?

On 14 February 2014 10:38, meekerdb  wrote:

>  On 2/13/2014 11:02 AM, Jesse Mazer wrote:
>
> Even though the curvature disappears in the first order terms, it remains
> in the higher order terms, whereas curvature is really zero in all terms
> for an accelerating observer in flat spacetime. So, the answer to your
> question is that acceleration does not in itself cause spacetime curvature,
> SR can handle acceleration just fine as discussed at
> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html ,
> but this isn't a violation of the equivalence principle since the
> mathematical formulation of the principle deals only with first-order terms.
>
>
> As an example SR is used to calculate the size of proton bunches in the
> LHC even though they are at % of the speed of light and subject to
> enormous acceleration at the turning magnets.
>

Wow, and there I was thinking we'd never achieve FTL travel!

:-)

(Sorry)

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Re: How does acceleration curve space? Can anyone provide an answer?


On 2/13/2014 11:02 AM, Jesse Mazer wrote:
Even though the curvature disappears in the first order terms, it remains in the higher 
order terms, whereas curvature is really zero in all terms for an accelerating observer 
in flat spacetime. So, the answer to your question is that acceleration does not in 
itself cause spacetime curvature, SR can handle acceleration just fine as discussed at 
http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html , but this isn't a 
violation of the equivalence principle since the mathematical formulation of the 
principle deals only with first-order terms.


As an example SR is used to calculate the size of proton bunches in the LHC even though 
they are at % of the speed of light and subject to enormous acceleration at the 
turning magnets.


Brent

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Re: How does acceleration curve space? Can anyone provide an answer?

2014-02-13 Thread John Mikes

Congrats! Illustrates how 3-4 wrongs (unknowns?) make a right.(explained).
Event horizon - nice. Even if you "couple it".
Gravity: a toughy one. I have an explanation so good that nobody repeats
it. An 'unexpected way' is unexpected.  JM


On Thu, Feb 13, 2014 at 3:41 PM, LizR  wrote:

> Acceleration does cause the formation of an event horizon, I believe,
> which might be considered to couple it with gravity (in an unexpected way).
>
>
> On 14 February 2014 09:33, Jesse Mazer  wrote:
>
>>
>> On Thu, Feb 13, 2014 at 2:32 PM, Edgar L. Owen  wrote:
>>
>>> Jesse,
>>>
>>> Let me think about this, but it is NOT the observer in "free fall in a
>>> gravitational field" that is equivalent to acceleration. It is an observer
>>> RESISTING free fall (e.g. standing on the surface of the earth) that is
>>> equivalent to acceleration.
>>>
>>
>> Suppose the observer who's not moving on a geodesic path (call her Alice)
>> passes through the small spacetime neighborhood where the observer who IS
>> moving on a geodesic path (call him Bob) is defining his  "local inertial
>> frame" (Bob's geodesic path can either by a free-fall path through curved
>> spacetime, or inertial motion in flat spacetime, since both qualify as
>> geodesics in their respective spacetimes). As Alice passes through this
>> region, she performs some experiment and notes the physical result.
>> Whatever physical elements are involved in this experiment, Bob can analyze
>> them too, and he should predict the SAME result even if his analysis is a
>> bit different--for example, if Alice is standing on a platform and lets go
>> of a ball, the ball will hit the platform, from Alice's point of view this
>> is due to a gravitational force and from Bob's point of view this is due to
>> the platform accelerating up towards the ball, but either way the actual
>> prediction is the same. So, to say that Bob should observe the same results
>> of any local experiment (provided he is approximating everything to first
>> order) regardless of whether he's moving inertially in flat spacetime or
>> free-falling in gravity is physically equivalent to saying Alice should
>> observe the same results of any local experiment (again ignoring
>> second-order and higher effects) regardless of whether she's accelerating
>> through Bob's region in flat spacetime, or passing through his region
>> because he's in free-fall while she is not (say, she's standing on a
>> platform resting on a pole embedded in the Earth below, while Bob falls
>> past her).
>>
>> Jesse
>>
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>
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Re: How does acceleration curve space? Can anyone provide an answer?

Acceleration does cause the formation of an event horizon, I believe, which
might be considered to couple it with gravity (in an unexpected way).


On 14 February 2014 09:33, Jesse Mazer  wrote:

>
> On Thu, Feb 13, 2014 at 2:32 PM, Edgar L. Owen  wrote:
>
>> Jesse,
>>
>> Let me think about this, but it is NOT the observer in "free fall in a
>> gravitational field" that is equivalent to acceleration. It is an observer
>> RESISTING free fall (e.g. standing on the surface of the earth) that is
>> equivalent to acceleration.
>>
>
> Suppose the observer who's not moving on a geodesic path (call her Alice)
> passes through the small spacetime neighborhood where the observer who IS
> moving on a geodesic path (call him Bob) is defining his  "local inertial
> frame" (Bob's geodesic path can either by a free-fall path through curved
> spacetime, or inertial motion in flat spacetime, since both qualify as
> geodesics in their respective spacetimes). As Alice passes through this
> region, she performs some experiment and notes the physical result.
> Whatever physical elements are involved in this experiment, Bob can analyze
> them too, and he should predict the SAME result even if his analysis is a
> bit different--for example, if Alice is standing on a platform and lets go
> of a ball, the ball will hit the platform, from Alice's point of view this
> is due to a gravitational force and from Bob's point of view this is due to
> the platform accelerating up towards the ball, but either way the actual
> prediction is the same. So, to say that Bob should observe the same results
> of any local experiment (provided he is approximating everything to first
> order) regardless of whether he's moving inertially in flat spacetime or
> free-falling in gravity is physically equivalent to saying Alice should
> observe the same results of any local experiment (again ignoring
> second-order and higher effects) regardless of whether she's accelerating
> through Bob's region in flat spacetime, or passing through his region
> because he's in free-fall while she is not (say, she's standing on a
> platform resting on a pole embedded in the Earth below, while Bob falls
> past her).
>
> Jesse
>
> --
> 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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> Visit this group at http://groups.google.com/group/everything-list.
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Re: How does acceleration curve space? Can anyone provide an answer?

On Thu, Feb 13, 2014 at 2:32 PM, Edgar L. Owen  wrote:

> Jesse,
>
> Let me think about this, but it is NOT the observer in "free fall in a
> gravitational field" that is equivalent to acceleration. It is an observer
> RESISTING free fall (e.g. standing on the surface of the earth) that is
> equivalent to acceleration.
>

Suppose the observer who's not moving on a geodesic path (call her Alice)
passes through the small spacetime neighborhood where the observer who IS
moving on a geodesic path (call him Bob) is defining his  "local inertial
frame" (Bob's geodesic path can either by a free-fall path through curved
spacetime, or inertial motion in flat spacetime, since both qualify as
geodesics in their respective spacetimes). As Alice passes through this
region, she performs some experiment and notes the physical result.
Whatever physical elements are involved in this experiment, Bob can analyze
them too, and he should predict the SAME result even if his analysis is a
bit different--for example, if Alice is standing on a platform and lets go
of a ball, the ball will hit the platform, from Alice's point of view this
is due to a gravitational force and from Bob's point of view this is due to
the platform accelerating up towards the ball, but either way the actual
prediction is the same. So, to say that Bob should observe the same results
of any local experiment (provided he is approximating everything to first
order) regardless of whether he's moving inertially in flat spacetime or
free-falling in gravity is physically equivalent to saying Alice should
observe the same results of any local experiment (again ignoring
second-order and higher effects) regardless of whether she's accelerating
through Bob's region in flat spacetime, or passing through his region
because he's in free-fall while she is not (say, she's standing on a
platform resting on a pole embedded in the Earth below, while Bob falls
past her).

Jesse

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Re: How does acceleration curve space? Can anyone provide an answer?

Jesse,

Let me think about this, but it is NOT the observer in "free fall in a 
gravitational field" that is equivalent to acceleration. It is an observer 
RESISTING free fall (e.g. standing on the surface of the earth) that is 
equivalent to acceleration.

So please take this into consideration and respond.

Edgar



On Thursday, February 13, 2014 2:02:15 PM UTC-5, jessem wrote:
>
>
>
> On Thu, Feb 13, 2014 at 12:22 PM, Edgar L. Owen 
> > wrote:
>
>> All,
>>
>> By the Principle of Equivalence acceleration is equivalent to gravitation.
>>
>
> Too vague. A more precise statement is that in an observer in free-fall in 
> a gravitational field can define a "local inertial frame" in an 
> infinitesimally small neighborhood of spacetime around them, and that if 
> the laws of physics are expressed in the coordinates of this frame, they 
> will look just like the corresponding equations in flat SR spacetime, 
> though only in the first-order approximation to the equations (i.e. 
> eliminating all derivatives beyond the first derivatives). See for example: 
> http://books.google.com/books?id=ZfMWbQB2dLIC&lpg=PP1&pg=PA52 and 
> http://books.google.com/books?id=95Frgz-grhgC&lpg=PP1&pg=PA481 and 
> http://books.google.com/books?id=jjBMw0KFtZgC&lpg=PP1&pg=PA5
>
> Even though the curvature disappears in the first order terms, it remains 
> in the higher order terms, whereas curvature is really zero in all terms 
> for an accelerating observer in flat spacetime. So, the answer to your 
> question is that acceleration does not in itself cause spacetime curvature, 
> SR can handle acceleration just fine as discussed at 
> http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html , 
> but this isn't a violation of the equivalence principle since the 
> mathematical formulation of the principle deals only with first-order terms.
>
> Jesse
>
>
>

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Re: How does acceleration curve space? Can anyone provide an answer?