Re: arbitrary choice of zero of potential

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

At 10:24 AM 10/17/01 -0400, Ludwik Kowalski wrote:
> the following two statements do seem to be contradictory.
>
> "All potential energy must go to zero when the interacting
>   particles are infinitely far apart."  [assertion 1]
>
> " PEgrv = 0 can be chosen arbitrarily at any distance
>    between a particle and the center of our planet."  [assertion 2]
>
> Why is this not a paradox? If PEgrv MUST be zero at
> infinity then we should never allow it to be zero at other
> places, for example, at the sea level or at Mount Everest.

As I said before, the zero of potential can be chosen arbitrarily at ANY
point;  there is no reason why it should be "between" anything.  Indeed
once you have chosen a point (ANY point) you can choose ANY value for the
potential at that point, not necessarily zero.  That is, you could choose a
gauge such that the potential is zero nowhere at all;  the global minimum
could be 1000 units.  Assertion [2] follows as a corollary, but should not
be taken as the preferred general statement.

I'm not 100% sure how to parse assertion [1].  If it means what I think it
means, it's just plain false.  You might choose a gauge such that the
gravitational potential energy of a satellite far, far from the earth is
zero; that's your choice.  But you cannot tell me I "must" choose the same
gauge;  that's my choice, and you cannot take it away from me.

No physically-relevant quantity will depend on the choice of gauge.  The
amount of fuel, time, etc. needed to launch the satellite into position
will be independent of the choice of gauge;  such things will depend only
on point-to-point differences in potential.