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Re: arbitrary choice of zero of potential



That aspect of special relativity escaped me and I am
glad that JohnM elaborated on it. Would it then be
appropriate to conclude that in classical physics
PEgrv can be chosen as zero everywhere? I suppose it
was a blunder to say that "what is necessary in a
more general model is necessary in a simpler model."

The broader question is "when and how should traditional
textbooks be modified to be in line with what we learn
about the true nature of reality in more advanced courses?"
In other words, is it okay to say "accept this or that
because more advanced models call for it?" I do not
think so. In this particular situation I see no harm
to continue saying that PEgrv=0 can be chosen anywhere
and wait for a more advanced model to take away this
freedom of choice. What is wrong with this?
Ludwik Kowalski

John Mallinckrodt wrote:

"All potential energy must go to zero when the interacting
particles are infinitely far apart." [assertion 1]

I'm not 100% sure how to parse assertion [1]. If it means
what I think it means ...

I suspect that it doesn't. This assertion entered the discussion
because of a point that Bruce Sherwood and Ruth Chabay made at the
most recent AAPT meeting. Their point is, I believe, unarguable
(although, almost any point seems to become arguable around
here!), but it also does *not* mean that it is "never O.K." to
choose the zero point of potential energy arbitrarily.

I quote the abstract for their paper which I think explains the
meaning of assertion 1 and demonstrates its "unarguable" nature:

"It is customary to emphasize that only differences in potential
energy are physically meaningful, and therefore the zero of
potential energy is arbitrary. After 1905 we should have changed
our tune. When particles are at rest and very far apart, their
total energy must be equal to the sum of their rest energies,
which means that the potential energy of interacting particles
must go to zero at large separations. If an arbitrary constant is
added, energy and momentum will not transform correctly between
different reference frames. Recognizing the absolute nature of
potential energy has far-reaching pedagogical consequences, and we
have addressed the issues in a calculus-based introductory
textbook to appear this summer."

John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm