breuel@h-sc1.UUCP (thomas breuel) (11/06/85)
Ok. A thought experiment that shows that potential or kinetic energy in
a closed system contributes to its restmass:
Take a closed box with ideal mirrors as walls and put into it two
positronium atoms (atoms made out of an electron and a positron). The
box with its contents has a certain mass. Now one of the positronium
atoms decays, and the energy released in the decay excites the other
positronium atom. Now, since nothing has left or entered the box, by
the weak equivalence principle, the mass of the box is unchanged. The
amount of matter that it contains, however, is reduced. Therefore, some
of the mass in the box must be attributed to the exitation of the
remaining positronium atom. In a classical model, we can consider this
mass to consist of a kinetic and a potential part, and as the two
particles revolve around one another, sometimes it is present mostly as
kinetic, and sometimes it is present purely as potential energy.
Two examples:
When you lift a cannon ball in a gravitational field, its restmass
doesn't change. The restmass of the system earth-cannon ball does,
however, change, just by the amount of energy that you put in to lift
the cannon ball.
Similarly, if you have two electrons very close to one another and they
start moving apart due to their mutual repulsion, both the restmass of
the entire system and the restmass of each electron remain constant.
Only if you use up some of the energy stored in their repulsion, the
mass of the whole system decreases. ('use up' means 'remove from the
system').
Thomas.
PS: all these arguments are, of course, assuming the correctness of a
few, relatively well established, physical rules, like the weak
equivalence principle &c.
PPS: in essence, the above examples are nothing but trivial
re-statements (unless there is a flaw in them) of the weak equivalence
principle.