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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
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*>> book.
*

*> Come on! This is circular reasoning. Conventional QM
*

*> complementarity requires 2D Fourier. Therefore 2D Fourier
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*> 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

Date: Tue, 10 Sep 2002 18:10:30 -0700

On 10-Sep-02, George Levy wrote:

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

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