Re: operationally inertial frames

["A. R. Marlow" <marlow@LOYNO.EDU>]

I see what you mean now:  the force would be of the form m*K(t) on a
particle of mass m, where K(t) could be an arbitrary function of time.
Then the acceleration of any given particle would simply be x''(t) = K(t),
and relative accelerations would be x2'' - x1'' = 0, so no deformation.
OK, but then such a force is undetectable, and operationally is equivalent
to no force.  This is exactly the viewpoint that Einstein ended up with in
the final version of general relativity, where gravitation is not a force,
but the spacetime deformation produced by the curvature of spacetime.
This shows up only in the tidal deformations produced on particles
relative to each other.  Everything else can be transformed away by a mere
choice of coordinates, and so is operationally equivalent to zero force.

In general relativity, once you postulate a certain distribution of
matter (the stress-energy tensor), everything else is fixed, the curvature
of spacetime, the metric, the geodesic structure, everything.  The
geodesic structure gives a class of frames (the freefall frames) that are
every bit as privileged in GR as the inertial frames are in Newtonian
theory.  As John Archibald Wheeler tirelessly points out, physics only
looks simple when expressed in terms of such frames.  Once the laws of
physics are stated in terms of such frames, then, of course, you may
transform to any arbitrary frames you wish, and derive what complicated
forms the laws take on in such exotic frames.  This is exactly the same
procedure used in Newtonian physics also: start with the laws stated for
inertial frames.  You may then transform to any arbitrary frame you wish,
and so derive what forms the laws take in those frames.

On Wed, 13 Oct 1999, John Mallinckrodt wrote:

> On Wed, 13 Oct 1999, A. R. Marlow wrote:
>
> > I don't think it's nitpicking to point out that, if the shaking of the
> > earth were at all fast, the structure of the earth would be altered
> > (shape, Etc., crushed? smashed?) from the application of the forces needed
> > to do the job.  I think that would be pretty noticeable, locally and
> > globally.
>
> Not true.  The forces are applied inertially so there is exactly zero
> deformation.
>
> John Mallinckrodt      mailto:ajm@csupomona.edu
> Cal Poly Pomona          http://www.csupomona.edu/~ajm

A. R. Marlow                          E-MAIL:  marlow@loyno.edu
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