Robert Twiss schrieb:
> Seems to me a simple dimensional analysis shows the fallacy
> of Koenemann's argument: The dimensions of f/A are [M][L][T^(-2)] /
> [L^2] and of U are [M][L^2][T^(-2)] / [L^3], so the dimensions of
> both quantities are the same: [M]/[L][T^2]. Thus both quantities
> scale the same way with the dimension of the system, and Koenemann's
> conclusion must be incorrect.
The dimensions of a physical term do not tell you which function it follows.
This we find from considering boundary conditions or other constraints; this
discussion is very much about finding out which are the proper constraints.
But if you wish to ignore the divergence theorem and potential theory - well,
at the very least you could let me know why you do so; after all, this argument
is not new to you. Silence is not an answer.
At any given scale you have the choice (a) to consider some given mass with a
given surface, then to consider a part of that surface _at constant mass_; in
this case f/A holds. Or (b) you consider a smaller mass with a smaller surface
which is then the _entire_ surface of the mass; in that case f/A does not hold.
In both cases A is a variable, but only in (b) mass is a variable too. And that
is all the difference that matters.
Falk Koenemann
_____________________________________________________________________
| Dr. Falk H. Koenemann Aachen, Germany |
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| URL: http://home.t-online.de/home/peregrine/hp-fkoe.htm |
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