On 11/14/2003 07:38 PM, Nathaniel Davis wrote:
>
> I remember my college professors constantly alluding the fact that
> inertial mass is always equal to gravitational mass. But why is this
> true?
There are several good answers to that.
1) We don't know 100% for sure that it is true.
From time to time respectable, clever people have
found it worthwhile to do the experiment, comparing
gravitational mass to inertial mass. If the
equivalence were 100% obvious and axiomatic,
nobody would bother doing such experiments.
2) Based on the experimental track record alone,
it would be a surprise to find a non-equivalence.
But experiments have turned up surprising things
in other areas in the past.
In any case it's safe to say that any such non-equivalence
must be small under ordinary conditions.
3) Based on theory, it would be a surprise to find
a non-equivalence. General relativity has great
power and elegance, and makes lots of predictions
that are well supported by observations.
One of the central predictions is that the gravitational
field (if you define that carefully enough) is an
acceleration field. That is, at any given point, the
effect of gravity is indistinguishable from the effect
of working in an accelerated reference frame.
If you buy this theory, then it immediately follows
that gravitational mass must be equivalent to inertial
mass.
To say it the other way, if you think there is a
non-equivalence, you've got at tremendous amount of
work to do, because you'll have to invent a theory
to replace GR.
4) If you want to get fussy about it, it is actually
possible to set up a "gravitational" field where one
mass does not respond the same as another mass.
In particular, mass is definitely not the only source
term for the gravitational field. If you have a
rapidly spinning object, it creates a funny additional
field, called the gravimagnetic field, in analogy
with the way a spinning charged object creates a
magnetic field in addition to the prosaic electric
field. The gravimagnetic field couples to a spinning
test particle differently than a nonspinning test
particle of the same mass.
The equivalence principle is still valid and important
... you just have to state it carefully to exclude
funny business such as this.