On 11/17/2003 07:38 PM, Herbert H Gottlieb wrote:
>
> *** Since the string has no mass, it is a virtual string
> and its motion will also be virtual. This can be proven,
> without doubt, by a well thought-out virtual (gedanken)
> experiment.
OK, that's the metaphysical answer.
But the physics answer is different!
As I hinted in another msg a few minutes ago, in
physics there is a good general strategy:
When faced with a pathological case, do the
corresponding non-pathological case. Then,
at the end, pass to the limit (if necessary).
There are tons of examples where this works
beautifully.
a) Obviously "infinite" things can cause
pathologies. Consider "large" things instead.
b) Sometimes zero is also pathological, as
illustrated by this massless string.
Another example: lots of "DC" circuits don't
make sense at zero frequency. You have to
consider the case where some things are
slow compared to other things, and then
(if necessary) pass to the limit.
On 11/17/2003 09:39 PM, Hugh Haskell wrote:
>
> This is an important point for everyone to remember,
Yeah.
=====================
Sometimes this strategy doesn't work.
-- Sometimes the limit doesn't exist. For instance,
what's the entropy of a spin in zero field at zero
temperature? The answer is annoyingly dependent on
the _order_ in which the limits are taken. You need
to know more about the physics before the question is
answerable.