Re: About absolute reference frame......

"Tom Roberts" <tjroberts@xxxxxxxxxx> wrote in message
news:kD80g.1990$Lm5.1822@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx

The same arguement goes with how GR can instantaneously manifest a
curvature in spaceTIME ajacent to a central mass. GR is no better
than Newton on this account.

This is not true. GR is a _field_theory_, and the curvature at point A
depends only on field values in an infinitesimal neighborhood of A;
indeed this holds not just for curvature but for all fields. This can
also be stated: the field values at A can be completely determined from
the field values on a spacelike Cauchy surface inside the past lightcone
of A. This latter observation is the statement of causality in GR.

In particular, in GR curvature does _NOT_ "propagate" from sources. In
Newtonian gravitation, gravitational force does indeed propagate
_instantaneously_ from distant sources (just look at the Green's
function). This latter is the inconsistency I mentioned.


The following three points can also apply to Newtonian mechanics.

** Newtonian law of gravity is also a field theory.

** The gravitational potential at point A only depends on field values
in an infinitesimal neighborhood of A as well.

** When Newton published his law of gravity, he did not know even the
speed of light has a limit. So, if you apply a speed limit to
Newtonian gravitational potential, you basically would achieve the same
causality and consistency in Newtonian mechanics.

So, I still don't see any advancement in concept of GR over Newtonian
mechanics.

What is the difference between "phase space" and "geodesics"?

If you have to ask that, it's no wonder you are confused. Study. Learn.
These are very basic concepts in all of physics, from classical
mechanics to GR to QFT. <shrug>

OK, if you want to skip over this one, that is fine with me.

Given spacetime in general, if space is not curved, would it cause
gravitation?
That depends on the meanings of your words. [...]

You have the tendancy to go off on a tangent when confronted with
logical arguments against your believes imposed from your academic
days. You need to go back to answer my question please.

You are transferring your confusions to me. I _cannot_ answer your
question, because it is not well formed, as I said. The words you used
simply do not fit together in a sensible way, within the context of GR.

No, that is what my experience indicates. If you don't have an answer,
please just say so. Believe me. I would not hold my breath waiting
for your answer.

"if space is not curved" is a coordinate-dependent question
and no general response is possible. Your use of "cause" is
completely inappropriate and meaningless. "gravitation" has
several different possible meanings in GR (metric, connection,
or curvature).

As I have interpreted your arguments above, your argument also
indicates the curvature of spacetime not making any sense because it is
coordinate-dependent. Thus, the whole concept of GR does not make any
sense. In doing so, you are the one transferring your confusions to
me. I was not confused before. Now, I am totally confused.

I have yet to see a "logical argument" from you; all you do is dance....
And I am not discussing "beliefs from academic days", I am discussing my
current understanding of GR. Worry about your own shortcomings, and
don't attempt to ascribe them to me. <shrug>

Extending to the curvature of spacetime, it is coordinate-dependent.
So, talking about the curvature of spacetime does not make any sense.
In doing so, you are rocking the very foundation of GR. Your attempt
to side-step my question produces contradictions to the very core
believes of GR. Why do you blame me for it?

When you jump off a 10-story building, if you are not experiencing a
force pulling you to the ground, what are you experiencing?

Freefall (neglecting air). You will feel no "force" at all, just like
astronauts in an orbiting space station who are also in freefall. Unlike
them, the geodesic path you follow leads to a catastrophic intersection
with the ground. <shrug>

Yes, I agree.

Locally there is no "force", and if while in freefall you
drop a small marble, it will "hang in space" with you,
_proving_ there is no "gravitational force" in your local
freefalling frame. An external observer on the ground will
say that the marble is falling right with you. That ground
observer will indeed claim there is a "gravitational force"
(or equivalent), but that is really due to his being
accelerated upward by the ground. You are confusing that
observer's point of view with "reality", but in fact it is
a parochial viewpoint of no general validity.

What you are saying is very valid, but this is not GR. What you are
talking above is pre-GR, "entwurf", which did not get anywhere. GR is
about how one observes the geodesics of another test object.

Your
zealous belief of the false interpretation to GR is making you making
irrational comments like above.

Again you are transferring your confusions to me. This is most
definitely _not_ "irrational", it's just that you refuse to _learn_ the
context of GR. <shrug>

Properly interpreted, GR is just like
any others which acknowledge gravitation as a force.

This is simply not true. GR requires more degrees of freedom at each
point in the manifold than any "force" can ever express.

As I have pointed out, interpreting gravity (using the principle of
least time) as a force is still very valid in GR despite all the
freedoms you can give to each point in spaceTIME.

.

Relevant Pages

  • Re: About absolute reference frame......
    ... and the curvature at point A depends only on field values in an infinitesimal neighborhood of A; indeed this holds not just for curvature but for all fields. ... In Newtonian gravitation, gravitational force does indeed propagate _instantaneously_ from distant sources. ...
    (sci.physics.relativity)
  • Re: Does the Curvature of Spacetime cause gravity?
    ... Tom Roberts wrote: ... We measure the curvature of spacetime all the time. ... > and obtain Newtonian gravitation. ...
    (sci.physics.relativity)
  • Re: Does the Curvature of Spacetime cause gravity?
    ... We measure the curvature of spacetime all the time. ... the same guy of classical textbook on gravitation by ... As is well-known the textbook derivation is incorrect. ...
    (sci.physics.relativity)
  • Re: Does the Curvature of Spacetime cause gravity?
    ... If you claim that gravity IS spacetime curvature then ... of FTG) holds in the Newtonian limit. ...
    (sci.physics.relativity)
  • Re: Anyone good with Tensors?
    ... The cosmological constant ... Does this new metric indicate a curvature in space? ... Because the underlying manifold is spacetime, ... And I don't claim that gravitation can _only_ be modeled by curvature in spacetime. ...
    (sci.physics.relativity)
Quantcast