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From: tan@ihlpg.UUCP (Bill Tanenbaum)
Newsgroups: net.physics
Subject: Re: Potential Energy (could someone expand on the 'yes' answer?)
Message-ID: <1433@ihlpg.UUCP>
Date: Mon, 11-Nov-85 19:44:06 EST
Article-I.D.: ihlpg.1433
Posted: Mon Nov 11 19:44:06 1985
Date-Received: Tue, 12-Nov-85 06:20:33 EST
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Organization: AT&T Bell Laboratories
Lines: 37

> > >Is this true?  Does the potential energy stored in a spring
> > >contribute to its rest mass?  How about a battery, a capacitor, etc?
> > >->	    Jim Galbiati,  GenRad Inc,  Production Test Division	    <-
> > 
> > Yes.
> 
> [Jeff Sonntag]
>      Wow, what an informative answer!  
>      Lets consider a very simple system as a specific example.  Suppose we
> have two electrons rather close together and very far from any other influence
> at T=0.  They have some potential energy stored by virtue of their mutual
> repulsion.  If we let them go, that potential energy is gradually converted 
> to kinetic energy as they speed apart.  
>      If we could measure the mass of these electrons, would we find that
> the two-electron system has more than two electron rest masses?  Would we
> find that each electron has more than one electron rest mass?  If we were
> measuring the electron masses from the reference frame stationary w.r.t. the
> electrons at T=0, would the extra mass measured as T => infinity be the
> same as the extra mass measured due to relativistic effects, or would we
> have to treat that apparent mass change seperately?
--------------------
1) Yes, the 2 electron system has more than two electron rest masses.
2) I'm not sure how you intend to measure the mass of each electron separately
in the above system, so I can't answer the second question.
3) The extra mass of the 2 electron system at T=0 is the same as the relativistic
mass gain at T=>infinity.  (This ignores the possibility that the accelerated
electrons might radiate away some of their energy.)

A better example:  The rest mass of a deuteron (neutron-proton bound state) is
about 2 Mev less than the sum of the separate rest masses of the proton and
neutron.  The 2 Mev deficit is just the binding energy of the attractive
nuclear force.   To ask whether the separate rest masses of the proton and
the neutron bound in the deuteron are less than that of free protons and neutrons
is to ask a meaningless question, unless you have some way of defining and
measuring what you mean by it.  I don't.
-- 
Bill Tanenbaum - AT&T Bell Labs - Naperville IL  ihnp4!ihlpg!tan