Re: Duplication Thought Experiment Involving Complementarity

From: Brent Meeker <meekerdb.domain.name.hidden>
Date: Tue, 10 Sep 2002 18:10:30 -0700

On 10-Sep-02, George Levy wrote:

>> Complementarity is a property of any two quantum operators
>> that are related by the Fourier transform (x <-> id/dx). The
>> proof is well known, and can be found (eg) in Shankar's
>> book.


> Come on! This is circular reasoning. Conventional QM
> complementarity requires 2D Fourier. Therefore 2D Fourier
> must describe complementarity. True for conventional QM. I
> was talking about other MWs within the Plenitude. Could their
> complementarity be described by Hadamar transforms for
> example?

Observables come in complementary pairs (instead of triples or
something else) because the laws of physics are 2nd order
(partial) differential equations. Hence a position has a
canonically conjugate momentum and vice versa. The reason
they are related by a Fourier transform is that the action of
a wave in the Hamilton-Jacobi form of classical mechanics has
the products of the conjugate variables in the exponent. See
Goldstein, section 10-8.

...

Brent Meeker
"Pluralitas non sunt ponenda sine necessitate"
      --- William of Ockham
Received on Tue Sep 10 2002 - 18:23:07 PDT