Mehran- Thanks for this explanation. This is fundamentally the point
that Galileo himself made. It's the most compelling argument for why
different sizes of objects made of the same stuff should fall together.
We failed to make clear that our less compelling argument addressed
a tougher question- why would objects made of all sorts of different
stuff fall at the same rate. The argument that nature doesn't care
which batch of things you lump together to call a falling object
doesn't deal with that more general question.
it's great to see that you're reading this with such care.
These theories are tied very closely to observations, and the
equivalence of gravitational mass and inertial mass is not something
you can deduce from pure logic, because different things are made up of
different kinds of matter. For example, the relationship between the m
in F=GMm/r^2 and F=ma may be different for protons and neutrons. Why
not, as they have different electric charges, perhaps they have
different gravitational "charges" too. The experiments of Eotvos on
different materials, repeated much later and with much higher precision
by Dicke (and my book, Misner, Thorne and Wheeler's fine book
"Gravitation" was written in the early 1970's and so later experiments
are not covered) shows that different materials do in fact feel gravity
the same way as each other, bolstering Einstein's equivalence
principle. But we'd have to throw that principle out if we found
evidence conflicting with it.
Such evidence was claimed to be had in the late 1980's when a group
of physicists (Fishbach et al) reanalyzed the old Eotvos data and
claimed to find correlations with gravitational interactions and
properties of the materials Eotvos used. This investigation was roundly
criticized -- after all, experiments can and should be repeated with
better equipment and better control over the material samples (I seem
to remember Eotvos used "porphyry" and "wormwood", the exact
compositions of the particular samples used are to this day still
uncertain). The claim wasn't that Einstein's GR was wrong, but rather
that there was a "fifth force". Subsequent precision measurements ruled
out a fifth force of this type.
This whole episode just underscores the need to confront
theoretical ideas with observations in order to advance our
(republished on 07/12/06)