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Re: "quantization"

On non-unique theories, gauge transformations are an interesting point.
Actually, any nonrelativistic theory with a potential energy has a
philosophically similar feature since the zero-point of the potential
energy is arbitrary. That ambiguity could be cured by invoking
relativity except that we don't really know how to calculate the energy
of the vacuum.

As far as the definition of "mathematically equivalent" is concerned, I
would propose the following: If in two theories all of the equations of
the second can be derived using the first, and vice versa, the two
theories are mathematically equivalent for philosophical purposes. If
all the physical results of the two are the same and can be shown by
direct mathematical manipulations to be the same, but the equations are
not identical [as in formulations differing by gauge transformations], I
am not sure whether I would or would not want to regard the two as
equivalent. Perhaps one should call that situation "essentially
equivalent mathematically" and argue about how philosophically important
the situation is case by case. If the physical results are the same by
accident, I personally have to reconsider my world view or assume that
the mathematical argument exists and hasn't been found yet.

JACK L. URETSKY (C) 1996; HEP DIV., ARGONNE NATIONAL LAB, ARGONNE, IL
60439 wrote:

Hi all-
On non-unique theories. Question is, what do you mean by
"mathematically equivalent". Take electrodynamics in two different
gauges.
Are the two formulations "mathematically equivalent"? We know that
they
ar e physically equivalent because they make identical predictions
about
physics.
Another case in point, is Hamiltonian mechanics
"mathematically
equivalent" to Newtonian mechanics? What is your criterion?
Regards,
Jack

--
Maurice Barnhill, mvb@udel.edu
http://www.physics.udel.edu/~barnhill/
Physics Dept., University of Delaware, Newark, DE 19716