Re: Inertial vs gravitational mass

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

Nathaniel Davis wrote:

> Please forgive my ignorance if
> this query sounds trivial.

This is not trivial.  Really, really really not trivial.

> Why is inertial mass always equal to gravitational mass?

Let me turn the question around.
How sure are you that they are equal?
How do you know?

Hint:  If you want experimental evidence of
equality, look at table V in:
  http://www.mazepath.com/uncleal/eotvos.htm

For additional entertainment:
  http://www.google.com/search?q=test+equivalence-principle

> Students understand a relationship HAS to exist;

Actually a relationship doesn't HAVE to exist...
certainly not necessarily an equality relationship.
A non-null result from one of the experimental
tests would be surprising, but would not cause
the earth to fall out of its orbit.

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.  Strictly speaking, mass
is not "the" only source of "the" gravitational
field.  For example, funny things happen with
rapidly-rotating masses.