Re: Inertial vs gravitational mass

[David Bowman <dbowman@TIGER.GEORGETOWNCOLLEGE.EDU>]

Regarding Hugh H.'s comment:

> ...   There may be some insights into this buried in general
> relativity, but since GR is based on the postulate that gravitational
> and inertial mass are the same thing, any insights might well end up
> being tautological. David Bowman will probably have something
> relevant to say about this.

Well, it seems other have pretty much already said what I would have
said on this subject.  I would only add a possible clarification to a
point made by John M. and by John D.

Regarding John Mallinckrodt's rendition of the Equivalence Principle
(PoE):

> The PoE says that there is no way to distinguish the effects of a
> local gravitational field from the effects of being in an absolutely
> accelerating reference frame.

I suspect that John's adjective 'local' referring to a 'gravitational
field' may have been intended to cover the point I want to make here,
but I will make it anyway.  That point is that it is the
indistinguishability *itself* that is local.  IOW, there is no
experiment involving only locally acquired data that can distinguish
the effect of a gravitational field from that of an accelerated
coordinate system *in a sufficiently small local neighborhood* of
spacetime.  The effects of gravitation and of an accelerating
coordinate system are only *locally* equivalent in a sufficiently
small lab (such as an Einstein elevator).  Here sufficiently small
means that the size of the region of spacetime that is probed is
so much smaller than any possible curvature scale of spacetime in
that region that the effects of that possible curvature can not be
observed in that region with the equipment available.  Notice that
this makes the effective size of the equivalence region somewhat
dependent on the precision/accuracy of the available equipment.

And regarding where John Denker wrote:
> ...
> To first order, general relativity theory
> predicts equivalence between gravitational
> mass and inertial mass, but
>  a) GR might be wrong, and
>  b) even within GR, you have to be a bit fussy
> about how you state the equivalence principle,
> or you'll get a "principle" that isn't even
> theoretically true.  ...

I would only add that the Equivalence Principle is not the *sole*
domain of GR.  *Other* gravitational theories (Brans-Dicke, Ni,
some 4th order theories, etc.) that are not equivalent to GR are also
constructed to be obedient to the Equivalence Principle, and they
*also* predict the equality of inertial and (passive) gravitational
mass.  In fact all metric theories of gravitation obey the
Equivalence Principle (or at least all the torsion-free ones do--
Cartan's theory which includes nonzero torsion is an exception) and
they all require that inertial mass be equivalent to (passive)
gravitational mass.

David Bowman