Re: The absurdity of nature ... and science

[Bruno Marchal]

> On 26 May 2020, at 16:45, Philip Thrift  wrote:
> 
> 
> 
> https://americanaffairsjournal.org/2020/05/science-without-validation-in-a-world-without-meaning/


Interesting. Of course this makes me happy:

<<
Einstein, who was a kind of pantheist who identified God with the laws of 
nature, went so far as to say, “Science can be created only by those who are 
thoroughly imbued with the aspiration toward truth and understanding. This 
source of feeling, however, springs from the sphere of religion.”18 
We
 may not be able to attain truth in this sense, but there needs to be an 
aspiration toward truth, as defined within a humanly meaningful epistemology. 
This, Einstein argued, is rooted in religion. The salient point is that 
Einstein possessed a drive to know, and that drive came from a sense of the 
sacred deep within.
>>

Eventually, thanks to Gödel, Einstein seemed to have understood that 
mathematics might be the fundamental science, and that mathematics was by 
itself a source of mystery.

With the assumption of Indexical Digital Mechanism (aka computationalisme, or 
simply Mechanism) the point is that there is no more choice in this matter.

Scientific religion might be defined by the scientific studies of what is 
beyond science. Gödel’s incompleteness illustrates the possibility of this, and 
with Mechanism, Gödel-Löb-Solovay two theorems, leading to the mathematical 
theory G and G* provides the precise tool to study the geometry and topology of 
this intrinsic ignorance by all machines. The non emptiness of G* minus G 
explains where the aspiration of truth comes from, for the introspectively sane 
machine. It makes Mechanism refutable, and validated up to now.

Bruno



> 
> @philipthrift 
> 
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Re: Coordinate time vs Proper time

[smitra]

On 27-05-2020 11:07, Alan Grayson wrote:

On Tuesday, May 26, 2020 at 6:24:32 PM UTC-6, Brent wrote:


On 5/26/2020 6:49 AM, Alan Grayson wrote:

On Tuesday, May 26, 2020 at 5:51:50 AM UTC-6, Alan Grayson wrote:

On Sunday, May 24, 2020 at 4:49:48 PM UTC-6, Brent wrote:

On 5/24/2020 11:21 AM, Alan Grayson wrote:

On Sunday, May 24, 2020 at 8:51:35 AM UTC-6, Alan Grayson wrote:

On Saturday, May 23, 2020 at 12:06:33 PM UTC-6, Brent wrote:

On 5/22/2020 11:25 PM, Alan Grayson wrote:

On Friday, May 22, 2020 at 11:03:40 PM UTC-6, Brent wrote:

On 5/22/2020 9:48 PM, Alan Grayson wrote:

On Friday, May 22, 2020 at 9:05:23 PM UTC-6, Brent wrote:

On 5/22/2020 6:26 PM, Alan Grayson wrote:

On Monday, May 18, 2020 at 3:28:40 PM UTC-6, Alan Grayson wrote:
Suppose the universe is a hyper-sphere, not expanding, and an
observer travels on a closed loop and returns to his spatial
starting point. His elapsed or proper time will be finite, but what
is his coordinate time at the end of the journey?  TIA, AG

It's not a dumb question IMO. If you circumnavigate a spherical
non-expanding universe, what happens to coordinate time at the end
of the journey? Does something update the time coordinate? Or does
it somehow miraculously(?) remain fixed? TIA, AG


Are you supposing the universe is a 3-sphere?  In that case It's just
like going around a circle.  The degree marks on the circle are
coordinates, they have no physical meaning except to label points.  So
if you walk around the circle you measure a certain distance (proper
time) but come back to the same point.

Or are you supposing it's a 4-sphere so that all geodesics are closed
time-like curves?  I don't know how that would work.  I don't think
there's any solution of that form to Einstein's equations.

Brent

I'm supposing a 4-sphere and (I think) closed time-like curves. The
traveler returns presumably to his starting position, but is the time
coordinate unchanged? AG

I don't think there's any very sensible answer in that case.  Goedel
showed there can be solutions with closed time-like curves if the
universe is rotating.  But solutions of GR don't have any dynamic
connection to matter and the entropy of matter.  In the same spirit
there could be a solution to quantum field theory that was close
around the time like curve...in which case you'd experience "Groundhog
Day"...including your thoughts.

Brent

What does entropy have to do with this problem? AG

Increasing entropy points the direction of time.

Brent

Let me pose the question another way: Is coordinate time ever updated?
AG

Or say, in the Twin Paradox, the elapsed or proper time for the
traveling twin is less than for the Earth-bound twin, but when they
meet, do they share the same coordinate time? AG

Yes.  Coordinates are labels for points, so if you're together with
your twin, you both are at the same point in spacetime and that point
only has one label in any given coordinate system.

Brent

Since time is just ONE of the 4 labels for spacetime points, can they
be assigned at random? What specific function do they satisfy? AG

How is the time coordinate chosen such that the Lorentz distance
between spacetime points is meaningful? AG

The proper distance/duration is an invariant, it doesn't depend on the
coordinate system.

Brent

I think the invariance of proper distance/duration a direct result of
the Lorentz transformation, and is one of the results of SR. If that's
the case, is it used in GR to derive EFE's? TIA, AG



The Lorentz transform results from demanding that ds^2 for a flat 
space-time is an invariant. It's easy to derive this, as you know 
rotations and translations leave the ordinary Euclidic metric invariant, 
the relative minus sign between time and space means that instead of 
cos(theta) and sin(theta), you get cosh(theta) and sinh(theta) in 
transforms that mix time and space.


Saibal



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Re: Coordinate time vs Proper time

[Alan Grayson]

On Wednesday, May 27, 2020 at 9:18:40 AM UTC-6, smitra wrote:
>
> On 27-05-2020 11:07, Alan Grayson wrote: 
> > On Tuesday, May 26, 2020 at 6:24:32 PM UTC-6, Brent wrote: 
> > 
> >> On 5/26/2020 6:49 AM, Alan Grayson wrote: 
> >> 
> >> On Tuesday, May 26, 2020 at 5:51:50 AM UTC-6, Alan Grayson wrote: 
> >> 
> >> On Sunday, May 24, 2020 at 4:49:48 PM UTC-6, Brent wrote: 
> >> 
> >> On 5/24/2020 11:21 AM, Alan Grayson wrote: 
> >> 
> >> On Sunday, May 24, 2020 at 8:51:35 AM UTC-6, Alan Grayson wrote: 
> >> 
> >> On Saturday, May 23, 2020 at 12:06:33 PM UTC-6, Brent wrote: 
> >> 
> >> On 5/22/2020 11:25 PM, Alan Grayson wrote: 
> >> 
> >> On Friday, May 22, 2020 at 11:03:40 PM UTC-6, Brent wrote: 
> >> 
> >> On 5/22/2020 9:48 PM, Alan Grayson wrote: 
> >> 
> >> On Friday, May 22, 2020 at 9:05:23 PM UTC-6, Brent wrote: 
> >> 
> >> On 5/22/2020 6:26 PM, Alan Grayson wrote: 
> >> 
> >> On Monday, May 18, 2020 at 3:28:40 PM UTC-6, Alan Grayson wrote: 
> >> Suppose the universe is a hyper-sphere, not expanding, and an 
> >> observer travels on a closed loop and returns to his spatial 
> >> starting point. His elapsed or proper time will be finite, but what 
> >> is his coordinate time at the end of the journey?  TIA, AG 
> >> 
> >> It's not a dumb question IMO. If you circumnavigate a spherical 
> >> non-expanding universe, what happens to coordinate time at the end 
> >> of the journey? Does something update the time coordinate? Or does 
> >> it somehow miraculously(?) remain fixed? TIA, AG 
> > 
> > Are you supposing the universe is a 3-sphere?  In that case It's just 
> > like going around a circle.  The degree marks on the circle are 
> > coordinates, they have no physical meaning except to label points.  So 
> > if you walk around the circle you measure a certain distance (proper 
> > time) but come back to the same point. 
> > 
> > Or are you supposing it's a 4-sphere so that all geodesics are closed 
> > time-like curves?  I don't know how that would work.  I don't think 
> > there's any solution of that form to Einstein's equations. 
> > 
> > Brent 
> > 
> > I'm supposing a 4-sphere and (I think) closed time-like curves. The 
> > traveler returns presumably to his starting position, but is the time 
> > coordinate unchanged? AG 
> > 
> > I don't think there's any very sensible answer in that case.  Goedel 
> > showed there can be solutions with closed time-like curves if the 
> > universe is rotating.  But solutions of GR don't have any dynamic 
> > connection to matter and the entropy of matter.  In the same spirit 
> > there could be a solution to quantum field theory that was close 
> > around the time like curve...in which case you'd experience "Groundhog 
> > Day"...including your thoughts. 
> > 
> > Brent 
> > 
> > What does entropy have to do with this problem? AG 
> > 
> > Increasing entropy points the direction of time. 
> > 
> > Brent 
> > 
> > Let me pose the question another way: Is coordinate time ever updated? 
> > AG 
> > 
> > Or say, in the Twin Paradox, the elapsed or proper time for the 
> > traveling twin is less than for the Earth-bound twin, but when they 
> > meet, do they share the same coordinate time? AG 
> > 
> > Yes.  Coordinates are labels for points, so if you're together with 
> > your twin, you both are at the same point in spacetime and that point 
> > only has one label in any given coordinate system. 
> > 
> > Brent 
> > 
> > Since time is just ONE of the 4 labels for spacetime points, can they 
> > be assigned at random? What specific function do they satisfy? AG 
> > 
> > How is the time coordinate chosen such that the Lorentz distance 
> > between spacetime points is meaningful? AG 
> > 
> > The proper distance/duration is an invariant, it doesn't depend on the 
> > coordinate system. 
> > 
> > Brent 
> > 
> > I think the invariance of proper distance/duration a direct result of 
> > the Lorentz transformation, and is one of the results of SR. If that's 
> > the case, is it used in GR to derive EFE's? TIA, AG 
> > 
>
> The Lorentz transform results from demanding that ds^2 for a flat 
> space-time is an invariant. It's easy to derive this, as you know 
> rotations and translations leave the ordinary Euclidic metric invariant, 
> the relative minus sign between time and space means that instead of 
> cos(theta) and sin(theta), you get cosh(theta) and sinh(theta) in 
> transforms that mix time and space. 
>
> Saibal 
>

But why would you want ds^2 to be invariant? The answer IMO, is that
the LT leaves the SoL invariant as we change coordinate systems, and
using this requirement is sufficient for deriving the LT. AG 

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Re: The size of the universe

[Lawrence Crowell]

There is a tendency in science fiction to see alien life as similar to 
Earth life. Intelligent life is again similar to us. The problem is that 
alien life may be profoundly different on just a molecular level. On Earth 
there are three major branches of multicellular life, animals, plants and 
fungi, with slime molds a minor branch. If there is complex life on some 
other planet chances are good it will have few resemblances to any of 
these. There might be photosynthetic life forms, but even here on Earth 
there are bacteria with photo active pigments that are orange or violet. 
So, the planet might not have a green color, but orange or violet. There 
might be life forms that have motor abilities, but this might be very 
different from actin-myosin process in muscles. There might be processing 
networks, but most likely they would not be what we call brains. 

The diversity of possible forms is enormous. There might be some life form 
that has the ability to manipulate matter and energy, or what we might call 
technology. If they develop the ability to transmit signals by 
electromagnetic fields then in some ways it is a fair conjecture that they 
process information according to mathematical rules. Physics is physics, no 
matter what, or maybe we might ask who, the ET life form happens to be. 
However, the difference in processing such ET life forms have might map 
this into something similar to what an encryption code does. In other 
words, they might be doing and thinking, if thinking is even the right 
term, the same as we do, but it is expressed in ways that are almost 
undecipherable. 

It is also possible there are self-organizing systems that are entirely 
different from what we call biology. These might exist on planets or they 
might exist elsewhere, whether in vacuum or on something such as a white 
dwarf star. 

LC

On Wednesday, May 27, 2020 at 4:27:40 PM UTC-5, Brent wrote:
>
>
>
> On 5/26/2020 10:51 PM, Jason Resch wrote:
>
>
>
> On Tue, May 26, 2020 at 11:16 PM 'Brent Meeker' via Everything List <
> everyth...@googlegroups.com > wrote:
>
>>
>>
>> On 5/26/2020 3:33 PM, Jason Resch wrote:
>>
>>
>>
>> On Wed, May 20, 2020 at 5:14 PM 'Brent Meeker' via Everything List <
>> everyth...@googlegroups.com > wrote:
>>
>>>
>>>
>>> On 5/20/2020 6:39 AM, Bruno Marchal wrote:
>>> > Hi Jason,
>>> >
>>> > When you say that Reality is infinite, are you alluding to the 
>>> > (phenomenological) physical reality? Or the absolute reality?
>>> >
>>> > With mechanism, it is very plausible that the physical reality is 
>>> > infinite, as it is a sort of broder of the universal mind (the mind of 
>>> > the “virgin” universal machine).
>>> >
>>> > But even with an infinite physical reality, it is unclear if we are 
>>> > alone or not, in the physical reality. We are numerous in the 
>>> > arithmetical reality (which can be taken as the absolute one, modulo a 
>>> > change of universal machinery). But to have alien fellows in the 
>>> > physical reality, you need some homogeneity in that reality, which is 
>>> > not obvious at first sight.
>>> >
>>> > In fact, I get the impression that we might be rare, if not alone. The 
>>> > probability for life might be as close to zero as von Neumann thought, 
>>> > but even the possibility of its evolution requires many conditions, so 
>>> > many that we might be alone in the cosmos (not in the multiverse, as 
>>> > there we have even doppelangers).
>>>
>>> I think the evidence suggests that there is a lot of life in the visible 
>>> universe and even a lot of technological civilizations...but they are so 
>>> sparse that we are effectively alone.
>>>
>>>
>> Hi Brent,
>>
>> As promised I've just finished writing about the existence of life and 
>> intelligent life in the universe. I'd appreciate your thoughts.
>>
>> Though life could be very rare I describe another possibility, which is 
>> that it miniaturizes and becomes so unlike and alient to the biological 
>> life we're familiar with and looking for that we don't notice it.
>>
>>
>> But we do know that even the most microscopic "life", even viruses grow 
>> and reproduce using the same mechanism at the molecular level as we do: 
>> DNA, RNA, mRNA, proteins, ATP=>ADp,...  That's really the basis for 
>> thinking that all life on Earth had a single origin.  Even archea and 
>> bacteria use the same metabolic pathways.
>>
>>
> I agree life will likely start in more or less recognizable ways, but I 
> believe that after a few thousand or million years of being a technological 
> civilization, it will reach stages that are unrecognizable to us. They will 
> most likely be non-biological, and non-corporeal, living in virtual 
> realities. Computers are substrate independent and can take many different 
> forms. Moreover they can be arbitrarily efficient so long as they are 
> logically reversible. There need not be any significant heat signature.
>
>
> That's why I said you needed to say what your definition of "life" was 

Re: The size of the universe

['Brent Meeker' via Everything List]

On 5/26/2020 10:51 PM, Jason Resch wrote:



On Tue, May 26, 2020 at 11:16 PM 'Brent Meeker' via Everything List 
> wrote:




On 5/26/2020 3:33 PM, Jason Resch wrote:



On Wed, May 20, 2020 at 5:14 PM 'Brent Meeker' via Everything
List mailto:everything-list@googlegroups.com>> wrote:



On 5/20/2020 6:39 AM, Bruno Marchal wrote:
> Hi Jason,
>
> When you say that Reality is infinite, are you alluding to the
> (phenomenological) physical reality? Or the absolute reality?
>
> With mechanism, it is very plausible that the physical
reality is
> infinite, as it is a sort of broder of the universal mind
(the mind of
> the “virgin” universal machine).
>
> But even with an infinite physical reality, it is unclear
if we are
> alone or not, in the physical reality. We are numerous in the
> arithmetical reality (which can be taken as the absolute
one, modulo a
> change of universal machinery). But to have alien fellows
in the
> physical reality, you need some homogeneity in that
reality, which is
> not obvious at first sight.
>
> In fact, I get the impression that we might be rare, if not
alone. The
> probability for life might be as close to zero as von
Neumann thought,
> but even the possibility of its evolution requires many
conditions, so
> many that we might be alone in the cosmos (not in the
multiverse, as
> there we have even doppelangers).

I think the evidence suggests that there is a lot of life in
the visible
universe and even a lot of technological civilizations...but
they are so
sparse that we are effectively alone.


Hi Brent,

As promised I've just finished writing about the existence of
life and intelligent life in the universe. I'd appreciate your
thoughts.

Though life could be very rare I describe another possibility,
which is that it miniaturizes and becomes so unlike and alient to
the biological life we're familiar with and looking for that we
don't notice it.


But we do know that even the most microscopic "life", even viruses
grow and reproduce using the same mechanism at the molecular level
as we do: DNA, RNA, mRNA, proteins, ATP=>ADp,...  That's really
the basis for thinking that all life on Earth had a single
origin.  Even archea and bacteria use the same metabolic pathways.


I agree life will likely start in more or less recognizable ways, but 
I believe that after a few thousand or million years of being a 
technological civilization, it will reach stages that are 
unrecognizable to us. They will most likely be non-biological, and 
non-corporeal, living in virtual realities. Computers are substrate 
independent and can take many different forms. Moreover they can be 
arbitrarily efficient so long as they are logically reversible. There 
need not be any significant heat signature.


That's why I said you needed to say what your definition of "life" was 
at the beginning.  Computers can't be logically reversible and still act 
within the universe...so most people would say that can't be life.  I'm 
not sure a computer can even have thoughts if exists only in a 
reversible superposition of states.




https://alwaysasking.com/are-we-alone/


Not just matter, energy, and time.  Life needs an entropy
gradient.  Your whole section on "Energy" reads as though energy
is consumed.  But energy is conserved.




Good point. I meant energy in the colloquial sense (energy 
available for useful work). Is there a another word I could use for 
this concept that isn't as technical/scary sounding as entropy gradient?


It is low entropy (mostly of sunlight) that is "consumed" by
turning it into higher entropy infrared radiation.  The best
theories of the origin of life postulate alkaline vents as the
locus (which are not so hot as hydrothermal vents).  Have you read
Nick Lane's "The Vital Question"?


I haven't. Thanks for the suggestions, I will have to read more about 
alkaline vents.



I think you make a mistake in jumping right into "what life
needs".  You should first define what you mean by life.  Life as
we know it: carbon, hydrogen based? Anything that reproduces. 
Anything that metabolizes?...what?


You're right, that is an oversight. I will add a definition. Something 
like: self-maintaining processes that convey information across 
generations.



It took a billion to two billion years for/*eukaryotes*/ to
evolve...not multicellular life.  Multicellular life only arose
0.6 billion ya.


Thank you, I will correct this.


Tardigrades are not going to survive on the Moon...that's
fantasy.  They don't eat rocks. Surface 

Re: The size of the universe

[Bruno Marchal]

> On 24 May 2020, at 13:33, Philip Thrift  wrote:
> 
> 
> 
> On Sunday, May 24, 2020 at 5:59:42 AM UTC-5, Bruno Marchal wrote:
> 
>> On 23 May 2020, at 21:05, 'Brent Meeker' via Everything List 
>> > wrote:
>> 
>> 
>> Recently you have said that your theory is consistent with finitism,
> 
> 
> It has always been a finitism. Judson Webb wrote a book explaining exactly 
> this. 
> 
> 
> 
> Worth checking out:
> 
> http://www.bu.edu/philo/profile/judson-c-webb/ :
> 
> Mechanism, Mentalism, and Metamathematics: An Essay on Finitism (by Judson 
> Webb, Reidel 1980), a full length study of the bearing of incompleteness and 
> undecidability theorems of Gödel and Church on the Turing thesis and 
> artificial intelligence, as well as on Hilbert’s Program.


It is the best introduction to my work, especially to the mathematical part, 
with perhaps the book edited by Hoftstadter and Dennett “Mind’s I” for some 
training in the relevant thought experiments to make the link with the 
Mechanist philosophy of mind.. 

Judson Webb shows that incompleteness acts as a sort of guardian angel of the 
Church thesis, by showing that without Gödel’s incompleteness, the 
Church-Turing thesis (usually called “Church’s thesis, and it is due to Kleene) 
would be wrong. That is why I called G* the guardian angel of the machine, 
sometimes ago on this forum.

Kleene himself wrote an excellent paper on this, praising the book of Webb: 
“Reflections on Church’s Thesis”, Notre Dame Journal of Formal Logic, Vol 28, 
N° 4, 1987.

Bruno



> 
> 
> sample @
> https://play.google.com/store/books/details/J_Webb_Mechanism_Mentalism_and_Metamathematics?id=eWl-BgAAQBAJ
> 
> 
> @philipthrift 
> 
> -- 
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> "Everything List" group.
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> .
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>  
> .

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Re: Coordinate time vs Proper time

[Alan Grayson]

On Tuesday, May 26, 2020 at 6:24:32 PM UTC-6, Brent wrote:
>
>
>
> On 5/26/2020 6:49 AM, Alan Grayson wrote:
>
>
>
> On Tuesday, May 26, 2020 at 5:51:50 AM UTC-6, Alan Grayson wrote: 
>>
>>
>>
>> On Sunday, May 24, 2020 at 4:49:48 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 5/24/2020 11:21 AM, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Sunday, May 24, 2020 at 8:51:35 AM UTC-6, Alan Grayson wrote: 



 On Saturday, May 23, 2020 at 12:06:33 PM UTC-6, Brent wrote: 
>
>
>
> On 5/22/2020 11:25 PM, Alan Grayson wrote:
>
>
>
> On Friday, May 22, 2020 at 11:03:40 PM UTC-6, Brent wrote: 
>>
>>
>>
>> On 5/22/2020 9:48 PM, Alan Grayson wrote:
>>
>>
>>
>> On Friday, May 22, 2020 at 9:05:23 PM UTC-6, Brent wrote: 
>>>
>>>
>>>
>>> On 5/22/2020 6:26 PM, Alan Grayson wrote:
>>>
>>>
>>>
>>> On Monday, May 18, 2020 at 3:28:40 PM UTC-6, Alan Grayson wrote: 

 Suppose the universe is a hyper-sphere, not expanding, and an 
 observer travels on a closed loop and returns to his spatial starting 
 point. His elapsed or proper time will be finite, but what is his 
 coordinate time at the end of the journey?  TIA, AG

>>>
>>> It's not a dumb question IMO. If you circumnavigate a spherical 
>>> non-expanding universe, what happens to coordinate time at the end of 
>>> the 
>>> journey? Does something update the time coordinate? Or does it somehow 
>>> miraculously(?) remain fixed? TIA, AG
>>>
>>>
>>> Are you supposing the universe is a 3-sphere?  In that case It's 
>>> just like going around a circle.  The degree marks on the circle are 
>>> coordinates, they have no physical meaning except to label points.  So 
>>> if 
>>> you walk around the circle you measure a certain distance (proper time) 
>>> but 
>>> come back to the same point.
>>>
>>> Or are you supposing it's a 4-sphere so that all geodesics are 
>>> closed time-like curves?  I don't know how that would work.  I don't 
>>> think 
>>> there's any solution of that form to Einstein's equations.
>>>
>>> Brent
>>>
>>
>> I'm supposing a 4-sphere and (I think) closed time-like curves. The 
>> traveler returns presumably to his starting position, but is the time 
>> coordinate unchanged? AG 
>>
>>
>> I don't think there's any very sensible answer in that case.  Goedel 
>> showed there can be solutions with closed time-like curves if the 
>> universe 
>> is rotating.  But solutions of GR don't have any dynamic connection to 
>> matter and the entropy of matter.  In the same spirit there could be a 
>> solution to quantum field theory that was close around the time like 
>> curve...in which case you'd experience "Groundhog Day"...including your 
>> thoughts.
>>
>> Brent
>>
>
> What does entropy have to do with this problem? AG 
>
>
> Increasing entropy points the direction of time.
>
> Brent
>

 Let me pose the question another way: Is coordinate time ever updated? 
 AG 

>>>
>>> Or say, in the Twin Paradox, the elapsed or proper time for the 
>>> traveling twin is less than for the Earth-bound twin, but when they meet, 
>>> do they share the same coordinate time? AG 
>>>
>>>
>>> Yes.  Coordinates are labels for points, so if you're together with your 
>>> twin, you both are at the same point in spacetime and that point only has 
>>> one label in any given coordinate system.
>>>
>>> Brent
>>>
>>
>> Since time is just ONE of the 4 labels for spacetime points, can they be 
>> assigned at random? What specific function do they satisfy? AG 
>>
>
> How is the time coordinate chosen such that the Lorentz distance between 
> spacetime points is meaningful? AG 
>
>
> The proper distance/duration is an invariant, it doesn't depend on the 
> coordinate system.
>
> Brent
>

I think the invariance of proper distance/duration a direct result of the 
Lorentz transformation, and is one of the results of SR. If that's the 
case, is it used in GR to derive EFE's? TIA, AG

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Maxwell's Equations and Black Body radiation

[Alan Grayson]

When one solves ME's, one gets continuous wave solutions. But somehow they 
give the wrong prediction for BB radiation. The correct solution requires 
quantizing the energy packets into discrete packets of energy. But prior to 
the advent of QED, in 1900, how did Planck incorporate this discreteness 
into a continuous theory to yield the correction solution of the BB 
problem? TIA, AG

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