Tom Roberts wrote in message
...
greywolf42 wrote:
Nobody is talking about the 'Newtonian' approximation, Tom. We're
discussing the weak-field limit of GR.

The disconnect here is that you seem to think that there is some sort of
"weak-field limit of GR" that is still GR. In the standard vocabulary of
physics, the phrase "weak-field limit of theory X" is shorthand for "an
APPROXIMATION to theory X in which one considers weak fields, and
neglects higher-order terms in a suitable expansion of theory X".

So the rest of us interpret the phrase "weak-field limit of GR" as an
approximation. What you are trying to say would more properly be
expressed as: GR applied to a weak-field situation.

GR applied to a weak-field situation has a "speed of gravity" equal to
c. Indeed, one need not limit oneself to weak fields....

Tom, thanks for your clarification, in that your use of the "weak field
limit" is actually a numerical approximation to GR, rather than GR itself.

We agree then, that in the 'weak field' situation/limit, the speed of
gravity in GR is 'c.'

greywolf42
ubi dubium ibi libertas

greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Tom Roberts wrote in message
...

This is not true. In order to obtain the Newtonian limit of GR, one
must
have:
a) weak fields
b) velocities small compared to c
c) Newtonian-like coordinates

Nobody is talking about the 'Newtonian' approximation, Tom. We're
discussing the weak-field limit of GR.

Umm, when you neglect *all* terms that go like 1/c they're one and the
same.

Well, yeah. When you neglect all the differences, they're the same.
This
is supposed to be information?

Okay, let me put it another way. I am talking about
*THE*LIMIT*THAT*TOM*DESCRIBED.

In *THAT* limit, GR gives you a 1/r potential *uniquely* hence there was
no "backfit" onto Newton. A "backfit" onto Newton would have invovled
tweaking some arbitrary function of "r" to give you the 1/r. You do not
need to do that in GR.

Is that 100% clear?

No, it is not.

I didn't think it would be.

I'm still trying to understand why you want to use an
approximation to GR to demonstrate a point about how GR was derived.

I'm not. You seem to think that's what happened, but it isn't. Einstein
formulated GR. This theory contained two arbitrary constants c and G.
Now all these constants do is fix the units you're using. And they
are constant, so first he fixed c by demanding agreement with SR, and
then he fixed G by TAKING THE NEWTONIAN LIMIT, or to use his words
deriving "Newton's theory as a first approximation" (Principl of Relativity,
page 157). This is where he fixes the value of G (page 160).
As Tom Robert's pointed out calling this a limit versus an approximation
is a semantic quibble.

The MAIN point is that GR is ALREADY derived by page 157. Indeed the field
equations appear on page 144 and page 149 (for the matter free and matter cases
respectivly). Hence, there was no *BACKFIT* onto Newton (however you think it
was done). The theory is presented PIOR to the discussion of the Newtonian
limit.

Do you dispute that at all?

Let me try one step at a time. The original point under discussion was your
dislike of my claim that Einstein 'backfit' the equations of GR onto
Newton's equation.

See above. If that's not clear, I don't know what will be.

[snip speed of gravity diversion]

[snip the rest, which is a pointless diversion from the main issue]

If those statements were 'pointless diversions,' I'm curious why you
(Matthew and Tom) started them. But it really doesn't matter.

*You* keep wanting to talk about the speed of gravity. And quibble
over the difference between a limit and an approximation (which
for working theorists is non-existent).

--
Matthew Nobes
c/o Physics Dept. Simon Fraser University, 8888 University
Drive Burnaby, B.C., Canada
http://www.sfu.ca/~manobes

greywolf42 wrote:

Steve Carlip wrote in message
...
greywolf42 wrote:

[...]
The weak-field limit is NOT an 'approximation.' There is a fundamental
distinction between a limit and an approximation. A limit is 'really'
reached with all terms. An approximation simply ignores portions of the
theory.

With that terminology, the weak field limit *is* an approximation -- it's
obtained by explicitly throwing away terms that are quadratic and
higher in the deviation of the metric from the Minkowski metric. The
Newtonian approximation, on the other hand, is a limit -- see Frittelli
and Ruela, Commun. Math. Phys. 166 (1994) 221.

So, according to Steve, the "approximation" term used by Relativists is
really a "limit." And the "limit" term used by Relativists is really an
"approximation." If true, this would merely be another sloppy set of terms
by relativists.

I've checked a few of the standard texts to see how
they describe (1) weak fields and (2) Newtonian
gravity in general relativity.

Wald's textbook refers to the ``linear approximation''
and the ``Newtonian limit.'' Misner, Thorne, and
Wheeler use ``linearized theory of gravity'' and
``Newtonian limit.'' Weinberg says ``weak-field
approximation'' and ``Newtonian limit.'' Schutz
uses ``linearized theory'' and ``Newtonian limit.''
d'Inverno uses ``linearized approximation'' or
``linearized theory''; he also refers to the ``weak
field limit,'' but by that he means the Newtonian
limit. In his new textbook, Hartle uses ``linearized
theory'' and ``Newtonian limit.'' Carroll's book
isn't out yet, as far as I know, but his lecture notes
refer to ``the linearized field equations'' and ``the
Newtonian limit.'' Ohanian and Ruffini say ``linear
approximation'' and ``Newtonian limit.'' Hughston
and Tod use ``linearized approximation'' and ``slow
motion limit.'' My own book on (2+1)-dimensional
gravity doesn't use a phrase for the weak field
approximation, but writes the equations in a way
that explicitly shows what order is dropped; I say
``Newtonian limit.''

So who, exactly, are you complaining about?

Steve Carlip

Thomas Clarke wrote:
"Tom Roberts" wrote in message

GR applied to a weak-field situation has a "speed of gravity" equal to
c. Indeed, one need not limit oneself to weak fields....


What about strong field solutions like the Alcubierre
"warp drive".
http://www.wikipedia.org/wiki/Alcubierre_drive

The theory known as GR includes a requirement that energy density be
non-negative everywhere. Aclubierre is discussing an EXTENSION to GR.

That requirement is necessary to avoid closed timelike loops,
which would violate our common notions of causality. IOW:
generalizations of GR to permit closed timelike loops are
refuted by ordinary observations, unless such loops are
restricted to unobservable regions. For instance, I
believe that some approaches to quantum gravity permit
closed timelike loops at the Planck scale (which are
therefore unobservable, and useless for warp drives)....


Tom Roberts

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Tom Roberts wrote in message
...

This is not true. In order to obtain the Newtonian limit of GR,
one
must
have:
a) weak fields
b) velocities small compared to c
c) Newtonian-like coordinates

Nobody is talking about the 'Newtonian' approximation, Tom. We're
discussing the weak-field limit of GR.

Umm, when you neglect *all* terms that go like 1/c they're one and
the
same.

Well, yeah. When you neglect all the differences, they're the same.
This
is supposed to be information?

Okay, let me put it another way. I am talking about
*THE*LIMIT*THAT*TOM*DESCRIBED.

In *THAT* limit, GR gives you a 1/r potential *uniquely* hence there
was
no "backfit" onto Newton. A "backfit" onto Newton would have invovled
tweaking some arbitrary function of "r" to give you the 1/r. You do
not
need to do that in GR.

Is that 100% clear?

No, it is not.

I didn't think it would be.

Then you should have written more clearly.

I'm still trying to understand why you want to use an
approximation to GR to demonstrate a point about how GR was derived.

I'm not.

But the issue you seem to want to discuss is whether or not Einstein
'backfit' GR onto Newton's equation in any manner. If this has no relation
to the speed of gravity, why are you insisting on discussing it?

You seem to think that's what happened, but it isn't. Einstein
formulated GR. This theory contained two arbitrary constants c and G.

The 'G' appeared after Einstein backfit his equations to Newton's equation,
yes. The 'c' was an arbitrary (though logical) selection of Einstein for
the finite speed of gravity.

Now all these constants do is fix the units you're using.

You are incorrect. The equations stand regardless of the unitary system
that we're using.

And they
are constant, so first he fixed c by demanding agreement with SR,

And this is 'backfitting' to SR.

{#A}

and
then he fixed G by TAKING THE NEWTONIAN LIMIT, or to use his words
deriving "Newton's theory as a first approximation" (Principl of
Relativity,
page 157).

{Note to other readers: The 1952 Dover compendium of seminal works in
Relativity. The paper is Matthew is referring to is 'The Foundation of the
General Theory of Relativity,' Einstein, 1916}

This is where he fixes the value of G (page 160).
As Tom Robert's pointed out calling this a limit versus an approximation
is a semantic quibble.

Thank you for proving my point. (That was a lot of effort for nothing.)
Einstein 'fixed G by taking the Newtonian limit' is a statement equivalent
to Einstein 'backfit his equation to Newton's equation.'

The MAIN point is that GR is ALREADY derived by page 157.

'GR' was not complete on page 157. Some arbitrary mathematics with some
symbols had been created at this point. And the equations had specific
properties that Einstein postulated that the equations 'had to have.' It
was a superb effort in Platonic thought. However, none of the mathematics
could be matched to anything in the physical universe.

Indeed the field
equations appear on page 144 and page 149 (for the matter free and matter
cases
respectivly). Hence, there was no *BACKFIT* onto Newton (however you
think it
was done). The theory is presented PIOR to the discussion of the
Newtonian
limit.

In order to compare his thought construction to reality, Einstein needed to
determine the values of various constants that existed in his equations. He
selected 'c' for the speed of gravity. He selected the Newtonian 'G' for
the gravitational constant. And he selected '0' for the cosmological
constant (at first).

One of the reasons that it took Einstein 'as long as' 1916 to finish GR is
that he insisted that his 'pretty' mathematics and principles match the
observed universe. He made several false starts (with mathematics similar
to, but slightly different from page 157) that he tossed out when he
couldn't make them match observation.

Do you dispute that at all?

Let me try one step at a time. The original point under discussion was
your
dislike of my claim that Einstein 'backfit' the equations of GR onto
Newton's equation.

See above. If that's not clear, I don't know what will be.

[snip speed of gravity diversion]

???? I made no diversion.

[snip the rest, which is a pointless diversion from the main issue]

If those statements were 'pointless diversions,' I'm curious why you
(Matthew and Tom) started them. But it really doesn't matter.

*You* keep wanting to talk about the speed of gravity. And quibble
over the difference between a limit and an approximation (which
for working theorists is non-existent).

But *I* didn't start the quibble. Nor did *I* start the diversion into the
speed of gravity.

We were discussing your dislike of my use of the word 'backfit' for
Einstein's derivation of GR:

greywolf42 (7/31):
"Einstein found a mathematical set of equations that had the properties that
he desired. However, Einstein had to determine the constants of that
mathematics. All the math is is symbols. In order to determine one set of
boundary conditions, Einstein decided (wisely so) to make the weak-field
solution (almost) equal to Newton's gravitational equation. (That's the 8
pi part.) It was a very explicit backfit."

{see note #A, above, where -- except for using the words 'fixes the value of
G' instead of the word 'backfit' -- Matthew substantively agrees with my
original postion.}

Thomas Clarke joined in with some comments, and you replied to him that:
"The *important* thing about GR is that it reduces to an inverse square law
in the weak field limit."

To which I responded on 8/1:
"Plus a constant speed of gravity equal to 'c'.

Note, here, that *you* diverted into a general discussion about the
'importance' of GR and the weak field limit (approximation/solution) to GR.
*I* had left the issue of speed unmentioned {"(almost) equal"} since it was
not directly applicable to the source of "G". *You* then expanded the
discussion about GR in general reducing to an inverse square law. At which
point I felt that I had to correct you. GR differs from the Newtonian in
that GR has an explicit speed-of-gravity -- even for arbitrarily weak
fields.

greywolf42
ubi dubium ibi libertas

On Fri, 08 Aug 2003 12:59:37 -0700, greywolf42 wrote:

Matthew Nobes wrote in message
...

[...]

You seem to think that's what happened, but it isn't. Einstein
formulated GR. This theory contained two arbitrary constants c and G.

The 'G' appeared after Einstein backfit his equations to Newton's equation,
yes...

[...]

Wrong. Plainly and simply wrong. I don't know another way of saying this.
Either it is an intentional lie on your behalf, or you simply do not know
how the field equations were derived. Either way, it doesn't change the
fact that the above statement is simply one of the most blatant falsehoods
I have ever seen you utter.

Jeff

greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
Is that 100% clear?

No, it is not.

I didn't think it would be.

Then you should have written more clearly.

It's difficult, because you pretend to speak the langauge of physics,
yet see to desire engaging in semantic quibbles about what is a limit
versus an approximation.

I'm still trying to understand why you want to use an
approximation to GR to demonstrate a point about how GR was derived.

I'm not.

But the issue you seem to want to discuss is whether or not Einstein
'backfit' GR onto Newton's equation in any manner. If this has no relation
to the speed of gravity, why are you insisting on discussing it?

I'm not. You keep saying it, not me.

You seem to think that's what happened, but it isn't. Einstein
formulated GR. This theory contained two arbitrary constants c and G.

The 'G' appeared after Einstein backfit his equations to Newton's equation,
yes. The 'c' was an arbitrary (though logical) selection of Einstein for
the finite speed of gravity.

Both untrue. The G is there (kappa, in equation 53, page 149). The only thing
the Newtonian limit is used for is fixing a numerical value of G. Equation 53, BY ITSELF,
leads to equation 68, which is Newton's law of gravitation, dervied from GR. C is not
arbitrary, for if it were different than the speed of light the metric (4) (page 120) would
not be reproduced, hence SR would not be recovered.

It is worth stressing that *ANY* experiment could be used to fix the value of G. For example,
one could take equation 53 and derive the orbital decay formula for binary plusars, then
fit G to that. There is *no* logical need to use a Newtonian limit experiment. (This is
analogous to every other theory in physics, for example, in quantum electrodynamics there
are many different methods used to determine the charge of the electron).

Now all these constants do is fix the units you're using.

You are incorrect.

Well, no, I'm not. All the constants do is fix the units.

The equations stand regardless of the unitary system
that we're using.

Yes, and the 1/r NEWTONIAN potential comes out of equation 53 the FULL FIELD EQUATON, sans backfit.

And they
are constant, so first he fixed c by demanding agreement with SR,

And this is 'backfitting' to SR.

{#A}

and
then he fixed G by TAKING THE NEWTONIAN LIMIT, or to use his words
deriving "Newton's theory as a first approximation" (Principl of
Relativity,
page 157).

{Note to other readers: The 1952 Dover compendium of seminal works in
Relativity. The paper is Matthew is referring to is 'The Foundation of the
General Theory of Relativity,' Einstein, 1916}

This is where he fixes the value of G (page 160).
As Tom Robert's pointed out calling this a limit versus an approximation
is a semantic quibble.

Thank you for proving my point. (That was a lot of effort for nothing.)
Einstein 'fixed G by taking the Newtonian limit' is a statement equivalent
to Einstein 'backfit his equation to Newton's equation.'

This is what I dispute. It's not a backfit, it's simply fixing an unknown
constant. This has nothing to do with the derivation of GR.

The MAIN point is that GR is ALREADY derived by page 157.

'GR' was not complete on page 157.

This is untrue, the full field equations are there, no more needs doing.

Some arbitrary mathematics with some
symbols had been created at this point.

Untrue, all physical preditions of GR can be made starting with the equations
presented on page 157.

And the equations had specific
properties that Einstein postulated that the equations 'had to have.' It
was a superb effort in Platonic thought. However, none of the mathematics
could be matched to anything in the physical universe.

Untrue, yet again. I can take those equations, and derive all the physics of
GR from them. See the latter half of Misner Thorne and Wheeler for repeated
applications of this.

Indeed the field
equations appear on page 144 and page 149 (for the matter free and matter
cases
respectivly). Hence, there was no *BACKFIT* onto Newton (however you
think it
was done). The theory is presented PIOR to the discussion of the
Newtonian
limit.

In order to compare his thought construction to reality, Einstein needed to
determine the values of various constants that existed in his equations. He
selected 'c' for the speed of gravity. He selected the Newtonian 'G' for
the gravitational constant.

He didn't SELECT THEM. He matched them onto experiment. Just like you do
in electrodynamics, you devise an experiment to measure "e". Or in quantum
mechanics, with h. The THEORY is done as of the presentation of the field
equations.

And he selected '0' for the cosmological
constant (at first).

One of the reasons that it took Einstein 'as long as' 1916 to finish GR is
that he insisted that his 'pretty' mathematics and principles match the
observed universe. He made several false starts (with mathematics similar
to, but slightly different from page 157) that he tossed out when he
couldn't make them match observation.

Do you dispute that at all?

Let me try one step at a time. The original point under discussion was
your
dislike of my claim that Einstein 'backfit' the equations of GR onto
Newton's equation.

See above. If that's not clear, I don't know what will be.

[snip speed of gravity diversion]

???? I made no diversion.

[snip the rest, which is a pointless diversion from the main issue]

If those statements were 'pointless diversions,' I'm curious why you
(Matthew and Tom) started them. But it really doesn't matter.

*You* keep wanting to talk about the speed of gravity. And quibble
over the difference between a limit and an approximation (which
for working theorists is non-existent).

But *I* didn't start the quibble. Nor did *I* start the diversion into the
speed of gravity.

We were discussing your dislike of my use of the word 'backfit' for
Einstein's derivation of GR:

greywolf42 (7/31):
"Einstein found a mathematical set of equations that had the properties that
he desired. However, Einstein had to determine the constants of that
mathematics. All the math is is symbols. In order to determine one set of
boundary conditions, Einstein decided (wisely so) to make the weak-field
solution (almost) equal to Newton's gravitational equation. (That's the 8
pi part.) It was a very explicit backfit."

{see note #A, above, where -- except for using the words 'fixes the value of
G' instead of the word 'backfit' -- Matthew substantively agrees with my
original postion.}

Thomas Clarke joined in with some comments, and you replied to him that:
"The *important* thing about GR is that it reduces to an inverse square law
in the weak field limit."

To which I responded on 8/1:
"Plus a constant speed of gravity equal to 'c'.

Note, here, that *you* diverted into a general discussion about the
'importance' of GR and the weak field limit (approximation/solution) to GR.
*I* had left the issue of speed unmentioned {"(almost) equal"} since it was
not directly applicable to the source of "G". *You* then expanded the
discussion about GR in general reducing to an inverse square law. At which
point I felt that I had to correct you. GR differs from the Newtonian in
that GR has an explicit speed-of-gravity -- even for arbitrarily weak
fields.

The point is your "correction" is not germane to the issue at hand. It's a
totally irrelvent point. My only point is that GR is fully formulated by
the time one gets to the field equations. You DO NOT need to take the
Newtonian limit, it's just ONE way of fixing the constants, not the only
way. Hence to say GR was "backfit" onto Newton seems like, at best, a
bizzare way of putting it, or (more to the way I suspect you mean it) a
dishonest way of putting it, since it seems to imply that you somehow
need Newtonian mechanics to get to GR.

--
Matthew Nobes
c/o Physics Dept. Simon Fraser University, 8888 University
Drive Burnaby, B.C., Canada
http://www.sfu.ca/~manobes

Steve Carlip wrote in message ...
Old Physics wrote:

If a massive shell of matter has the same gravity as a solid
sphere with the same number of atoms, would the collapse of the shell
result in an increase in mass,

Not according to general relativity. The gravitational field at a fixed
distance will remain he same, as long as you're looking at a point that
was always outside the shell and the collapse is spherically symmetric.

ie. the original mass plus the IR
radiation that results from the conversion of kenetic energy to heat?

If you want to think of it in these terms, the relevant energy you need
to look at is ``quasilocal energy,'' which includes a contribution
analogous to Newtonian gravitational potential energy. The change
in this potential energy piece balances the other energy changes;
the total quasilocal energy remains constant.

(Of course, some of the IR radiation you speak of will eventually
radiate out past the point at which you're measuring the
gravitational field. As that happens, the field at that point will
decrease.)

Steve Carlip

So when I lift my coffee cup from the table it has more mass, more
quasilocal energy, but is less time dilated?
BTW, a foil sphere a trillion LYrs in radius and about one gram
per square foot would have a mass of some 10^58 gms or about 10^25
times greater than the sun. It would constitute a black hole with an
event horizen of the same radius. Of course thats some sixty times
the present size of the universe thus far.
As a thought experiment, suppose you could gradually enlarge a
sphere made of Gailien chains (the massless variety). What geometric
changes would it undergo as it neared the size of the universe, would
its topology change?
I think this is a question that many in this group would like to
see answered by an expert in the field, like yourself.

Extreme thanks for your post, and for bringing it to my attention.
Stephen Kearney

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
Is that 100% clear?

No, it is not.

I didn't think it would be.

Then you should have written more clearly.

It's difficult, because you pretend to speak the langauge of physics,
yet see to desire engaging in semantic quibbles about what is a limit
versus an approximation.

That's why you snipped your own turbid statement.

I'm still trying to understand why you want to use an
approximation to GR to demonstrate a point about how GR was derived.

I'm not.

But the issue you seem to want to discuss is whether or not Einstein
'backfit' GR onto Newton's equation in any manner. If this has no
relation
to the speed of gravity, why are you insisting on discussing it?

I'm not. You keep saying it, not me.





You seem to think that's what happened, but it isn't. Einstein
formulated GR. This theory contained two arbitrary constants c and G.

The 'G' appeared after Einstein backfit his equations to Newton's
equation,
yes. The 'c' was an arbitrary (though logical) selection of Einstein
for
the finite speed of gravity.

Both untrue. The G is there (kappa, in equation 53, page 149). The only
thing
the Newtonian limit is used for is fixing a numerical value of G.

LOL! "G" is simply an unknown constant prior to the numerical value being
determined by backfitting to Newton's equation.

Equation 53, BY ITSELF,
leads to equation 68, which is Newton's law of gravitation, dervied from
GR. C is not
arbitrary, for if it were different than the speed of light the metric (4)
(page 120) would
not be reproduced, hence SR would not be recovered.

Precisely my point. The speed of light is assumed to be the speed of
gravity. This is a backfit to SR. (Einstein assumes that GR will approach
SR.)

It is worth stressing that *ANY* experiment could be used to fix the value
of G. For example,
one could take equation 53 and derive the orbital decay formula for binary
plusars, then
fit G to that.

Well, one *could* do that. But we are discussing what Einstein actually
*did.* Which was to make sure that GR reduced to the Newtonian static case
in a static situation.

There is *no* logical need to use a Newtonian limit experiment.

This is a self-contradictory statement. The Newtonian limit is not an
experiment.

(This is
analogous to every other theory in physics, for example, in quantum
electrodynamics there
are many different methods used to determine the charge of the electron).

Irrelevant. Though QED assumes the charge of the electron from outside the
theory. (Per renormalization)

Now all these constants do is fix the units you're using.

You are incorrect.

Well, no, I'm not. All the constants do is fix the units.

We can use any units we like. The physical speed is unchanged. But one
needs to tie that pretty math into the real world. And the physical *value*
of G is not dependent on the units we select to measure same. Unless you're
back to the Mars lander team.

The equations stand regardless of the unitary system
that we're using.

Yes, and the 1/r NEWTONIAN potential comes out of equation 53 the FULL
FIELD EQUATON, sans backfit.

I'm not discussing just the mathematical form of the potential. I'm
discussing both the mathematical form (which Einstein required to match the
Newtonian form) and the determination of physical constants. Had Einstein
not recovered the Newtonian form in the weak field condition, he would have
tossed out his pretty equations (as he did many times prior to 1916) and
started over.

And they
are constant, so first he fixed c by demanding agreement with SR,

And this is 'backfitting' to SR.

{#A}

and
then he fixed G by TAKING THE NEWTONIAN LIMIT, or to use his words
deriving "Newton's theory as a first approximation" (Principl of
Relativity,
page 157).

{Note to other readers: The 1952 Dover compendium of seminal works in
Relativity. The paper is Matthew is referring to is 'The Foundation of
the
General Theory of Relativity,' Einstein, 1916}

This is where he fixes the value of G (page 160).
As Tom Robert's pointed out calling this a limit versus an
approximation
is a semantic quibble.

Thank you for proving my point. (That was a lot of effort for nothing.)
Einstein 'fixed G by taking the Newtonian limit' is a statement
equivalent
to Einstein 'backfit his equation to Newton's equation.'

This is what I dispute. It's not a backfit, it's simply fixing an unknown
constant. This has nothing to do with the derivation of GR.

I say 'backfit', you say 'fixing an unknown constant'. We disagree on
terms. However, the determination of 'unknown constants' is very definitely
part of the derivation of 'GR'.

The MAIN point is that GR is ALREADY derived by page 157.

'GR' was not complete on page 157.

This is untrue, the full field equations are there, no more needs doing.

Except for 'fixing the unknown constants.'


Some arbitrary mathematics with some
symbols had been created at this point.

Untrue, all physical preditions of GR can be made starting with the
equations
presented on page 157.

Except for actual values.


And the equations had specific
properties that Einstein postulated that the equations 'had to have.'
It
was a superb effort in Platonic thought. However, none of the
mathematics
could be matched to anything in the physical universe.

Untrue, yet again. I can take those equations, and derive all the physics
of
GR from them. See the latter half of Misner Thorne and Wheeler for
repeated
applications of this.

MTW uses those constants that Einstein had to 'fix.'

Indeed the field
equations appear on page 144 and page 149 (for the matter free and
matter
cases
respectivly). Hence, there was no *BACKFIT* onto Newton (however you
think it
was done). The theory is presented PIOR to the discussion of the
Newtonian
limit.

In order to compare his thought construction to reality, Einstein needed
to
determine the values of various constants that existed in his equations.
He
selected 'c' for the speed of gravity. He selected the Newtonian 'G'
for
the gravitational constant.

He didn't SELECT THEM. He matched them onto experiment.

You contradict your own quote and sources, above, at #A. Einstein backfit
to the Newtonian equation. He did not backfit to experiment. NEWTON
derived his equation based on Kepler's 'laws' and his own equations of
motion. KEPLER determined *his* 'laws' based on experiment. Einstein
didn't.

This is not a 'hit' against Einstein!

Just like you do
in electrodynamics, you devise an experiment to measure "e". Or in
quantum
mechanics, with h. The THEORY is done as of the presentation of the field
equations.

"e" was measured long before there were field equations. But Einstein
didn't compare to experiment, here. There's nothing wrong with that.

And he selected '0' for the cosmological
constant (at first).

One of the reasons that it took Einstein 'as long as' 1916 to finish GR
is
that he insisted that his 'pretty' mathematics and principles match the
observed universe. He made several false starts (with mathematics
similar
to, but slightly different from page 157) that he tossed out when he
couldn't make them match observation.

Do you dispute that at all?

Let me try one step at a time. The original point under discussion
was
your
dislike of my claim that Einstein 'backfit' the equations of GR onto
Newton's equation.

See above. If that's not clear, I don't know what will be.

[snip speed of gravity diversion]

???? I made no diversion.

[snip the rest, which is a pointless diversion from the main issue]

If those statements were 'pointless diversions,' I'm curious why you
(Matthew and Tom) started them. But it really doesn't matter.

*You* keep wanting to talk about the speed of gravity. And quibble
over the difference between a limit and an approximation (which
for working theorists is non-existent).

But *I* didn't start the quibble. Nor did *I* start the diversion into
the
speed of gravity.

We were discussing your dislike of my use of the word 'backfit' for
Einstein's derivation of GR:

greywolf42 (7/31):
"Einstein found a mathematical set of equations that had the properties
that
he desired. However, Einstein had to determine the constants of that
mathematics. All the math is is symbols. In order to determine one set
of
boundary conditions, Einstein decided (wisely so) to make the weak-field
solution (almost) equal to Newton's gravitational equation. (That's the
8
pi part.) It was a very explicit backfit."

{see note #A, above, where -- except for using the words 'fixes the
value of
G' instead of the word 'backfit' -- Matthew substantively agrees with my
original postion.}

Thomas Clarke joined in with some comments, and you replied to him that:
"The *important* thing about GR is that it reduces to an inverse square
law
in the weak field limit."

To which I responded on 8/1:
"Plus a constant speed of gravity equal to 'c'.

Note, here, that *you* diverted into a general discussion about the
'importance' of GR and the weak field limit (approximation/solution) to
GR.
*I* had left the issue of speed unmentioned {"(almost) equal"} since it
was
not directly applicable to the source of "G". *You* then expanded the
discussion about GR in general reducing to an inverse square law. At
which
point I felt that I had to correct you. GR differs from the Newtonian
in
that GR has an explicit speed-of-gravity -- even for arbitrarily weak
fields.

The point is your "correction" is not germane to the issue at hand. It's
a
totally irrelvent point. My only point is that GR is fully formulated by
the time one gets to the field equations.

And your 'only point' is silly. GR is not fully formed until the constants
are determined.

You DO NOT need to take the
Newtonian limit, it's just ONE way of fixing the constants, not the only
way.

But it is *the* way that Einstein used.

Hence to say GR was "backfit" onto Newton seems like, at best, a
bizzare way of putting it, or (more to the way I suspect you mean it) a
dishonest way of putting it, since it seems to imply that you somehow
need Newtonian mechanics to get to GR.

Well, yes, Newtonian mechanics are needed to get to GR (conservation of
energy and momentum). It in no way demeans Einstein's work to note that he
built on the foundations that others had laid. Without Tycho, no Kepler.
Without Kepler, no Newton. Without Newton, no Einstein. Welcome to science
and the advancement of knowledge.

greywolf42
ubi dubium ibi libertas

(Old Physics) wrote in message om...
Steve Carlip wrote in message ...
Old Physics wrote:

If a massive shell of matter has the same gravity as a solid
sphere with the same number of atoms, would the collapse of the shell
result in an increase in mass,

Not according to general relativity. The gravitational field at a fixed
distance will remain he same, as long as you're looking at a point that
was always outside the shell and the collapse is spherically symmetric.

ie. the original mass plus the IR
radiation that results from the conversion of kenetic energy to heat?

If you want to think of it in these terms, the relevant energy you need
to look at is ``quasilocal energy,'' which includes a contribution
analogous to Newtonian gravitational potential energy. The change
in this potential energy piece balances the other energy changes;
the total quasilocal energy remains constant.

(Of course, some of the IR radiation you speak of will eventually
radiate out past the point at which you're measuring the
gravitational field. As that happens, the field at that point will
decrease.)

Steve Carlip

So when I lift my coffee cup from the table it has more mass, more
quasilocal energy, but is less time dilated?
BTW, a foil sphere a trillion LYrs in radius and about one gram
per square foot would have a mass of some 10^58 gms or about 10^25
times greater than the sun. It would constitute a black hole with an
event horizen of the same radius. Of course thats some sixty times
the present size of the universe thus far.
As a thought experiment, suppose you could gradually enlarge a
sphere made of Gailien chains (the massless variety). What geometric
changes would it undergo as it neared the size of the universe, would
its topology change?
I think this is a question that many in this group would like to
see answered by an expert in the field, like yourself.

Extreme thanks for your post, and for bringing it to my attention.
Stephen Kearney

Does anyone else want to "weigh in"? sk