Matthew Nobes wrote in message
...
greywolf42 wrote:

Tom Roberts wrote in message
...
greywolf42 wrote:
If the speed of gravity = c in GR (and 'that's it'), then the speed
of gravity is 'c' in the weak limit. NOT infinity.

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?

That's the case *I* was talking about when disputing your claim that GR
was "backfit". I'll try to be really clear here,

I'm not sure what your point was, then. Why would you use an approximation
to GR to demonstrate a point about how GR was derived?

*If* you *neglect* *all* terms that go like 1/c then GR reduces to a
*1/r* potential. Hence there is no "backfit" onto Newtonian gravity.

But GR includes terms that 'go like' 1/c in the weak-field limit.

And the two sentences appear to be a non-sequiteur. How does the first
sentence have anything to do with the second sentence?


[snip]
Precisely my point. No one was talking about an approximation to GR.
We
were discussing the weak-field limit (which is not an approximation).

Yes it is.

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.

You keep terms up to some power of 1/c and throw the rest
away. If you neglect *all* terms of order 1/c and higher you get
Newtonian gravity, hence there was no "backfit".

And, again, the last two phrases appear to be a non-sequiteur. How does the
first phrase have anything to do with the second phrase?

greywolf42
ubi dubium ibi libertas

greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Tom Roberts wrote in message
...
greywolf42 wrote:
If the speed of gravity = c in GR (and 'that's it'), then the speed
of gravity is 'c' in the weak limit. NOT infinity.

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? Do you dispute that at all?

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

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

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.

Steve Carlip

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.

Steve Carlip

Esteemed Dr. Carlip,

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

Respectfully,
stephen kearney

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

Matthew Nobes wrote in message
...
greywolf42 wrote:

Matthew Nobes wrote in message
...
greywolf42 wrote:

Tom Roberts wrote in message
...
greywolf42 wrote:
If the speed of gravity = c in GR (and 'that's it'), then the
speed
of gravity is 'c' in the weak limit. NOT infinity.

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

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.

Your current line of reasoning started when you proffered the statement that
"The point is in GR the speed of gravity is c and that's it." I happen to
agree that the base speed of gravity in GR is 'c.' (We've found that we
disagree on what happens in the strong limit of GR -- but I believe that is
irrelevant to the subject under discussion.)

So, the base theory of GR -- as Einstein described it in "The Foundation of
the General Theory of Relativity", 1916 -- includes a speed of 'c' for the
speed of gravity.

Are we together on this first step?

[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.

greywolf42
ubi dubium ibi libertas

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. (Like "defining" the speed of gravity to be '1' unit ...
and then dropping the physical term from the equations.)

But 'approximation' and 'limit' are still not the same thing. I suspect
there is actually a misunderstanding on what constitutes 'GR,' versus what
constitutes a 'deviation' from GR. Or what constitutes a mathematical
procedure for approximating GR.

But next time I'm at the library, I'll see what the mathematical priests
have come up with this time.

greywolf42
ubi dubium ibi libertas

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.

Steve Carlip

Esteemed Dr. Carlip,

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

Respectfully,
stephen kearney

My question maybe off thread, but it is not off topic. sk

"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

This seems like a situation governed by GR in
which there is a "wave" traveling faster than light.

Of course it requires "exotic matter" which may not exist,
or have a substitute,
so such faster than light "waves" may not exist.

Tom Clarke





--
Posted via Mailgate.ORG Server - http://www.Mailgate.ORG

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 Roberts