Re: equivalence principle for almost homogeneous fields

["John S. Denker" <jsd@MONMOUTH.COM>]

At 06:23 PM 1/26/01 -0500, Michael Edmiston wrote:
> if I am taken to a lab where the
> gravitational field is not homogenous, I should be able to discern the
> accelerations I measure are caused by gravity rather than any uniform
> acceleration of the lab.

Right.

> I don't see why that invalidates anything

Indeed it doesn't.

> Is the problem some people have with what I am saying simply the fact that
> we do not know of any homogeneous gravitational fields?  If so, is it valid
> to claim (2) is not true.  Or is it valid to say that F=mg and F=ma are
> always distinguishable?

There's no major problem;  we just need to formulate the equivalence
principle in a nitpick-resistant form.  So here goes....

Basically it's one of those deals where you give me an epsilon and I'll
give you a delta.  Specifically, if you give me a gravitational field in a
certain region, and a precision epsilon (greater than zero) I'll give you a
size-scale delta (greater than zero) such that within sub-regions of size
delta, the gravitational field will be indistinguishable from an
acceleration of the reference frame, to within the required precision.

If we say it that way, we don't need to require supernaturally perfect
homogenous fields, and we don't need to require supernatural point-like
measuring apparatus.

Advanced nitpickers will note that the foregoing formulation is not
reliable in regions containing a gravitational singularity (e.g. black
holes), nor does it account for quantum gravity effects.

> I think the heart of the matter I am trying to get at is: If there is any
> difference between a homogeneous gravitational field and a reference frame
> in uniform acceleration, what is this difference?

None.

> If there isn't any, then
> there also isn't any difference between F=mg and F=ma.

Agreed.

> If this is true then why can't we call "g" an acceleration and
> why can't we call "a" a gravity field?

Certainly g is an acceleration.  But the converse is tricky:  not every
acceleration is gravity-like;  only acceleration of the reference frame.

> It seems another way to say this is to ask gravitational mass versus
> inertial mass questions.

The equality of gravitational mass and inertial mass is tacitly assumed in
so many places in standard physics that it takes a huge amount of work to
unwind all the assumptions.  There have been some half-hearted attempts to
raise this issue on this list recently.  A serious discussion of this issue
would require a great deal of formalism and a great deal of meticulous
thinking.