I've been reading the responses to the problem (Two identical capacitors,
one charged, are then connected, share charge equally, and half the
original stored energy is gone. Why?) I am amazed and impressed at the
length people will go to analyze details, seeing and examining every tree,
and failing to realize the kind of forest these are in. I read about the
effect of the resistance, the length of connecting wires, whether there's
a spark, radiation damping, and whatnot, which doesn't shed light on a
central question here: Why does the result (half the energy goes
elsewhere) *not* depend on these particular details? If the only loss were
radiative, you'd get 1/2 for the energy loss. If the only loss were
resistive, you'd get 1/2. If it is a combination of both, you'd get 1/2.
I chose identical capacitors, which is one reason you get 1/2, but that
was only for convenience of discussion. The principle (if there is one)
could be applied to any pair of unequal capacitors, and the resulting
fractional energy loss would be a different value.
One of the goals of physics is to formulate principles which are
universal, and *don't* (within specified conditions) depend on the details
of a particular situation. The conservation laws, for example. The
equipartition theorem. The fact that any non-equilibrium distribution of
particles of a quasi-ideal gas will approach an equilibrium condition,
given enough time. The 'details' in this last one have to do with the
particular mechanism of particle interaction.
Is there such an over-riding principle at work in the capacitor problem?
If so, what is it?
There seem to be two cultures of physicists (at least) in this group,
judging by responses to recent problems.
One group wants to get down to nitty-gritty details, is impatient with
idealizations and gedanken experiment approaches, and dismisses some
simplifications as unworthy of discussion (forgetting that many historical
advances in physics were the result of first considering over-simplified
cases and gedanken experiments, then returning to the real world to deal
with the messy details and complications).
Another group is impatient with the details, and wants to find whether
there is an overriding principle which is applicable, sparing us the pain
of dealing with complicating details. The members of this camp want to
strip away the complications and get to the heart of the matter, or at
least find out whether there is one.
And of course, others want to judiciously use either approach, whichever
gets the job done.
And many students just want to get to the bottom line, be given an
authoritative answer (whether or not they understand it) and find out
whether that question will be on the exam.
If we had to contend with real world problems exclusively, with all their
complications, exceptions, and experimental difficulties; and if we were
never allowed to simplify, idealize, ignore exceptions, etc., progress in
physics would have been severely retarded, and would be little more than
applied engineering, or something like the medical and social 'sciences'.
We might not have developed thermodynamics, kinetic theory, atomic theory,
relativity, quantum mechanics, etc. All these originated in highly
idealized (and we now realize, incorrect) forms, and then were refined to
more closely relate to the real world, and were also modified and improved
as newer technology allowed new information to be acquired. And all of
them had a far more important role in physics: They suggested, inspired
and pointed the direction for fruitful experiments. Theory drives
experimentation, and vice versa.
-- Donald
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Dr. Donald E. Simanek Office: 717-893-2079
Prof. of Physics Internet: dsimanek@eagle.lhup.edu
Lock Haven University, Lock Haven, PA. 17745 CIS: 73147,2166
Home page: http://www.lhup.edu/~dsimanek FAX: 717-893-2047
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