From: Sidney Keith (sidkeith@hotmail.com)
Date: Fri Nov 17 2000 - 09:13:37 PST
From: "Sidney Keith" <sidkeith@hotmail.com> Subject: Conservation of Momentum Date: Fri, 17 Nov 2000 17:13:37 GMT Message-ID: <F234v5iJarnJ3kEPF3c00000c31@hotmail.com>
Nathania, I think your student is right to wonder about the conservation of
momentum; it's not a corollary of the conservation of energy but a
completely different phenomenon with an independent basis. This brings up
one of my favorite pieces of science, Noethe's theorem. It proves
mathematically that the conservation of energy is a result of the fact that
all times are the same; an experiment done on Tuesday will have the same
result as one done on Wednesday everything else being equal. If there were
no conservation of energy, everything done on Tuesday would have a different
outcome from the same thing done on Wednesday, because the total energy
available would have changed, and it would be possible to "mark" Tuesday as
a special time when the level of energy available was so-and-so. Since we
know we can't do this, energy must be conserved.
Similarly, according to Emily Noethe (one of the great female scientists,
who was not allowed a position in Gottingen despite her obvious brilliance
because she was a woman, and then had to flee the Nazis because she was
Jewish), the conservation of momentum is the result of the identity of all
places to each other, and the conservation of angular momentum to the
identity of all directions in space. The reasoning is similar. Traveling
over a given amount of space takes the same amount of energy for two
identical masses; if it didn't, we could distinguish between parts of space,
which we know we can't.
My favorite is the conservation of angular momentum; the universe doesn't
know or care whether it is facing north or south, east or west. These are
arbitrary earth-bound distinctions we have grown up with; they have no
physical reality. So a top will just keep on spinning forever (without
friction); it doesn't know it is moving at all!
To me that's a marvelously simple but powerful way to dwelve into the
deepest secrets of the universe. The identity of all times, places, and
directions is a truth so simple we never think about it, but it turns out to
have the profoundest of implications. The unity of utter simplicity and
deep insight, what a pleasure! Your student might enjoy this explanation of
the conservation of momentum as compared to that of energy.
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