Are there forces in relativity?

On Aug 8, 6:51*am, Tom Roberts wrote in
sci.physics.relativity:
Darwin123 wrote:
On Aug 7, 1:46 pm, (Daryl McCullough) wrote:
Darwin123 says...
Your examples reinforce my the idea that SR is a
weak field limit.
In the *zero* field limit, GR turns into SR. When the
field is nonzero but small, it is hard to interpret GR
as SR + corrections.

Yes. SR is basically GR applied to a manifold with no mass-energy, and
the topology of R^4.

* * * Okay, here is a problem. The Michaelson Morley experiment was
not performed in a zero field environment. It was not even performed
in a free fall environment. The experiment was performed in a system
that was accelerating toward the center of the earth due to a
combination of gravitational force and contact forces. The
gravitational field was not zero, and the gravitational potential
between the apparatus and the center of the earth was not zero. How
come the Michaelson Morley experiment "explain" the results of the
Michaelson Morley experiment?

Physics is a quantitative science. One can COMPUTE how large an error is
made by applying SR to an experiment like this, rather than the full,
rigorous application of GR (which is VASTLY more difficult and
complicated). The answer is that the errors due to that approximation
are many orders of magnitude smaller than the experimental resolution.
See below.

So this is not really a problem.

* * *The same question can be asked on the Hafele Keating experiment.
The Hefele Keating experiment was not performed in an environment with
zero gravitational field. Yet, Hefele claimed the the time difference
in the Hefele Keating experiment could
*mostly be explained using SR, without recourse to the full general
relativity theory.

Their actual paper discusses the effects of both gravitation and motion.
Both are important; both were used. In the approximation to GR that they
used, there are two terms, one involving velocity relative to the ECI
(though IIRC they did not call it that), and one involving gravitational
potential. They called the two terms "SR effect" and "GR effect", which
is a misnomer, as BOTH are part of that approximation to GR.

However, according to you there would have to be a zero
gravitational field in order for SR to be better than Newton.

You are reading stuff into other posts that simply is not there.

* * *Again, if this is true than the classic SR experiments aren't
valid. They were all done in significant gravitational fields. By
significant, I mean if there was no gravity the devices would not have
followed the paths given.

For tabletop optical experiments on earth, the primary effects of
gravity are canceled by contact (E&M) forces from the table. Yes, the
light rays will fall due to the earth's gravitation. Work it out, and
you'll find the effects of this are significantly smaller than
experimental resolutions. See below.

* * None of the classical SR experiments were performed in free fall.

Yes. But none were invalidated by this, because one can COMPUTE the
effects of gravity on their measurements, and in all cases are found to
be negligible. I repeat: physics is a QUANTITATIVE science.

* * *My question is how to distinguish an experiment that supports SR
alone from an experiment that supports GR.

Basically: is gravity important? For a light ray traveling a few meters
on earth, it is not. In all cases one can COMPUTE how accurate it is to
use the approximation of SR.

The honest answer may be
that there is none. This would imply that SR is not self consistent.

See above. There is no such implication.

* * *So when I analyze the Michaelson Morley experiment, I should
transform to a free falling coordinate system.

Sure. Let's do that.

For simplicity choose the freefalling frame that is at rest relative to
the apparatus when a given phase of the light beams start their travel.
They travel about 10 meters, which takes about 30 ns. During 30 ns that
frame falls (1/2)*g*t^2=0.5*9.8*(3e-8)^2=4e-15 meters, which is
significantly less than one wavelength (which is about 5e-7 meters). And
this fall is perpendicular to the light paths, so the relevant angle is
atan(4e-15/10)=4e-16 and the variation in path length is less than
10*(1-cos(4e-16))=8e-31 -- VASTLY smaller than they could possibly
measure using fringes separated by 2.5e-7 meters.

* * * * This is still true for experiments like Brillet and Hall
* * * * that are roughly a million times more sensitive.

Or else use General
relativity. Or else ignore the results, because they are consistent
with Newtonian mechanics.

No. Just estimate how large the error is in neglecting the falling of
the above frame, and realize that SR is an EXCELLENT approximation for
this experiment.

* * *I am now totally confused as to where on earth SR is valid. It
sounds almost like SR is never valid on the surface of the earth.

SR is valid for experiments in which gravitation is not significant.
This includes most tabletop optical experiments, and virtually all
particle experiments, etc. That includes all of the tests of SR, and
most non-gravitational terrestrial experiments.

Tom Roberts

Honest Roberts is special relativity valid "for an accelerated
observer in a region without any significant gravitation (e.g. in
Minkowski spacetime)":

http://groups.google.ca/group/sci.ph...2a006c7d508022
Pentcho Valev: CAN THE SPEED OF LIGHT EXCEED 300000 km/s IN A
GRAVITATIONAL FIELD? Tom Roberts: Sure, depending on the physical
conditions of the measurement. It can also be less than "300000 km/
s" (by which I assume you really mean the standard value for c). And
this can happen even for an accelerated observer in a region without
any significant gravitation (e.g. in Minkowski spacetime)."

Pentcho Valev