Nice summary of the issues that I didn't snip, see below.
Are you familiar with the AJP article:
Nonequivalence of a uniformly accelerating reference frame and a frame
at rest in a uniform gravitational field
Edward A. Desloge
Physics Department, Florida State University, Tallahassee, Florida
32306
(Received 21 October 1988; accepted 21 February 1989)
A general expression is obtained for the space-time interval between
neighboring events in a one-dimensional space in which it is possible to
set up a rigid reference frame. Particular expressions are then obtained
for the interval for the special cases of a rigid frame at rest in a
uniform gravitational field and a rigid frame uniformly accelerating in
field-free space. The two expressions are not equivalent and are used to
show why, how, and to what extent observations made in a rigid enclosure
at rest in a gravitational field are not equivalent to observations made
in a rigid enclosure that is uniformly accelerating in field-free space.
Two facts of particular interest that are demonstrated in the course of
the analysis are the following: (i) Two spatially separated particles
that are simultaneously released from rest and allowed to fall freely in
a uniform gravitational field will not remain at rest with respect to
one another. (ii) Uniformly accelerating reference frames and inertial
frames are the only possible one-dimensional rigid frames in flat
space-time. (c)1989 American Association of Physics Teachers
<snip>
|
| For one: Any accelerating system (rectilinear accel or
| rotational motion) is flat. This is a point that save for
| one obscure text, never seems to be covered in GR
| texts/courses. I think the reason is that most physicists
| are confused by it and don't understand the differences
| between grav and accel. I have even seen a popular level
| book written by a physicist that says accelerating frames are curved.
|
| The basic principle is this. If the Riemann curvature tensor
| for a given space is zero in one coordinate system, it is
| zero in all coordinate systems.
| Accelerating frames are transformations of coordinates in 4D
| from an inertial
| (flat) coordinate system to a non-inertial (accelerating) 4D
| coord system.
| Thus, the curvature tensor is zero in the new coords.
|
| the equivalence principle is only true locally (at a point.)
| No acclerating system is everywhere equiv to a gravitational
| system, and vice versa. The key here is that there is no
| transformation that can take us from an inertial system to a
| gravitational system (but there are transformations from
| inertial to accelerating.) Both accel and grav systems are
| non-inertial, but only grav systems are curved. Both accel
| and grav systems can have time dilation effects. It is not
| time dilation per se (or for that matter length
| contraction) that gives rise to curvature. Consider a flat
| piece of rubber. Stretch
| it. It is still flat, even though coordinate length
| measurements may have changed.
| <snip>
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