I am reacting to all three messages of this tread (posted on 3/31/97).
Yes there are fuzzy situations but cause and effect relations are often
defined very clearly. This hoppens when an event A, influencing, B takes
place, or exists, before B. For example:
A=not studying, B=poor grades
A=buying this stock, B=getting rich
A=a sex relation, B=pregnancy
A=force field, B=accelerating stone
A=poor contact, B=no current
We know that gravitational attraction caused a solar exclipse during an
ancient battle and that it will cause high tides tomorrow at this beach.
And now fuzzy situations. How do we teach electrostatics? We say that a
charge distribution is given and we show how to calculate E by applying
the principle of superposition, or Gauss's law. Suppose it is a uniform
distribution of Q over a disk (two large flat surfaces connected along
the rim). We ignore the rim, a very small fraction of the total area;
and we ignore the instanteneous feedback that the field will have on
the distribution of Q.
This is OK for an artificial problem but in reality the feedback exists.
An initial distribution of Q will create a transient field, that field
will change the distribution, the new field will be established, causing
a new distribution, a new field, etc., until an equilibrium is established.
In a student problem we say "the distribution remains uniform", no matter
what.
A particular chicken came from the egg his mother produced x weeks ago.
A field we observe is caused by this particular distribution of charges.
Many generations of chicken and egs? Yes. Many disagreements about the
beginning? Yes. But I am comfortable with thinking that cause and effect
relations are at the base of everything.
Sorry for this triva; I just wanted to share it. And there is a clear
link between this philosophy and the elementary calculation I am trying to
finish. It shows that the final distribution of Q over a metallic disk can
not possibly remain uniform. Why? Because I found a distribution for which
potential energy (the sum of all the k*dQ*dq/r components) is smaller than
for the uniform one. I will be more specific during the weekend.
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: Gedanken-ing is not enough; physics is an experimental science! :
: Inspired by thinking about phys-L messages on capacitors :
: Ludwik Kowalski :
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kowalskiL@alpha.montclair.edu http://www.csam.montclair.edu/~kowalski
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