Re: Inertial vs gravitational mass

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

cliff parker wrote:

> The pendulums with which I am familiar do not change period when the
> bob mass is changed but rather when the pendulum length is changed.

Let's analyze this assertion.

At this juncture two questions must be asked:
 1) How sure are you of this?
 2) How do you know this?

 Before we continue, in case anybody missed the
 point, the pendulum assertion is an instance of
 the equivalence principle:  The pendulum is an
 oscillator like a mass on a spring;  its
 inertia is due to its inertial mass, and its
 restoring force is due to its graviational
 interactions.

 If the period is to remain unchanged, the
 restoring force must be proportional to the
 inertia.

But the questions remain:
 1) How sure are you that this is true?
 2) How do you know this?

As part of item (2), it is important to be clear
about the following:
 2a) Maybe this is an experimentally-based
assertion, being used to support the equivalence
principle, to some moderate level of accuracy, or
 2b) Maybe you think the equivalence principle is
_independently_ well-established, in which case
this assertion is a theoretical prediction.  But
then we're back where this thread started, because
you have to ask why you think the equivalence
principle is well-established.  You can't use the
theoretical properties of the pendulum to
establish the theory!  Or ...
 2c) Something in between.


In case you're wondering, option (2c) is actually
where the action is.  I consider the equivalence
principle to be supported by a whole bunch of
experimental data, of which the pendulum data is
one small part.  It is an amusing part, because
it is elementary and widely known, and because
it dates back to Newton and Galilei if not earlier.
But I consider all the data on an equal footing;
it all linked together by the laws of logic in
the data-analysis step.  The pendulum data constrains
the Eötvös data _and vice versa_.  If there were
an inconsistency between the two, we would have
a big job on our hands to figure out whether one
of the experiments was wrong, and/or whether the
theory that links them needs refinement.