Re: arbitrary choice of zero of potential

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

At 10:49 PM 10/17/01 -0700, John Mallinckrodt wrote:

> I think I hear you saying that the invariant mass
> of a system is independent of any interactions between its parts.
> Is that right?  If not, please correct. If so, are you saying, for
> instance, that the invariant mass of an "atom" of positronium is
> precisely twice that of a single electron?

Nope.  Good question, though.

In reality, the positronium consists of electron + positron + fields.  The
fields contribute to the mass of the combined system, no problem.

In contrast, if we have a field-free region at one potential or another,
the potential _per se_ does not contribute to the laws of motion.

Note that the fields are derivatives of the potential.

I have the following picture in mind:  Imagine a bunch of model cars
running around a model track.
 -- I have one setup on a high shelf and one setup on a low shelf.  They
have the same dynamics.  The different gravitational potential is
irrelevant.  (Assume the local g field is uniform.)
 -- I have a third setup on a tilted shelf;  that greatly affects the
dynamics.

==========================

Nitpickers note:  Adding a constant to electrostatic potential (or the
analogous static piece of the gravitational potential) is a _subset_ of the
possible gauge transformations.  This is the part that was asked about, so
it's all that needs to be discussed here, but keep in mind that fancier
gauge transformations exist.  See e.g. Jackson _Electrodynamics_ page 220
for the next level of detail.