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Re: arbitrary choice of zero potential



Promod Pratap <prpratap@uncg.edu>, now on sabbatical in Germany
asked me to post this message because he forgot how post messages
on Phys-L. It is really easy, just press the REPLY or REPLY ALL
button of your brawser while reading a message. The blank window
appears. Compose the message and click SEND. That is what I do
in Netscape.
**********************************************************
Hi,

I am a lurker on the list, and I have not been following this thread
very closely. However, your message below struck me, and I had the
following thoughts. I am not sure how to post it to the list (I just
get a daily digest of messges..). In all the arguments below, I refer
to conservative forces.

The two statements within quotes below appear in different parts of a
discussion on potential energy. Since potential energy is defined as
(-Integral of F.ds), this involves an arbitrary constant of
integration. If we place the limits of integration as the starting and
ending points of s, we are calculating the difference in potential
energy, and the thought is that this is the physically relevant
quantity. This is because we can measure how much work we do, so we
can calculate by how much the potential energy of an object has changed.

Now, we say that the potential energy of an object at infinity is zero
as one of the infinite choices of the constant of integration. So, we
cannot make the two quoted statements simultaneously -- the first
statement is a particular case of the second. We say that two
particles infinitely apart do not interact, so their potential energy
is 0 because it makes intuitive sense. Physically, if we say that the
potential energy at the earth's surface is 0, we are making a choice
(different from the 0 being at infinity), and then the potential energy
at infinite separation is not 0.

Does this make sense? Is it a valid contribution to the discussion?

Promod Pratap

My reply was yes. Then Promod asked me to post the above message.

-------------------------------------------------------------
Date: Wed, 17 Oct 2001 10:24:55 -0400
From: Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>
Subject: Re: arbitrary choice of zero of potential

"John S. Denker" wrote:

> Neither blunder nor paradox. It's just another example
> of gauge invariance.

But to an unsophisticated teacher the following two
statements do seem to be contradictory.

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

" PEgrv = 0 can be chosen arbitrarily at any distance
between a particle and the center of our planet."

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.
Ludwik Kowalski

-------------------------------
Promod Pratap
Univ. of North Carolina
Dept. of Physics and Astronomy
PO Box 26170
Greensboro, NC 27402-6170
Phone: (336)334-3214 (Office)
(336)334-4279 (Lab)