| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
01 Jun 2005 07:02:51 PM |
| Object: |
Phase Paradox: Heisenberg vs Einstein |
From Osher Doctorow
COPYRIGHT NOTICE
Phase Paradox: Heisenberg vs Einstein
Copyright By Owner Osher Doctorow Ph.D.
First Published 2005
The Heisenberg Uncertainty Principle (HUP) and Einstein's Special
Relativity (SR) and the latter's Light Cone (LC) interpretation contain
some rather curious implicit rather than explicit choices regarding
phases (phase in the sense of basic type of physical state like gas,
liquid, solid, plasma, Bose-Einstein condensate, superfluid (may
overlap), superconductor, and even black hole).
HUP is interpreted usually as not indicating phase differences between
position and momentum but rather some deep fundamental characteristic
of microscopic (quantum) scenarios, and SR and LC vary in their
interpretations with most physicists thinking that only subluminal or
luminal signals are possible although superluminal phase or group
velocities are possible, while some including Sir Arthur Stanley
Eddington have pointed out that superluminal velocities/speeds are
theoretically possible but that (in his opinion) we can't communicate
with the superluminal regime (which Professor Nimtz of U. Cologne/Koln
thinks that we can in the sense that superluminal signals are
possible).
I'll try to continue shortly.
Osher Doctorow
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| User: "OsherD" |
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| Title: Re: Phase Paradox: Heisenberg vs Einstein |
01 Jun 2005 07:21:34 PM |
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From Osher Doctorow
I think that most theoretical and mathematical physicists will agree
that there are at least theoretically subluminal, luminal, and
superluminal phases, even if only group/phase velocities "populate" the
superluminal phase under certain conditions.
The biggest difficulty comes with the Heisenberg Uncertainty Principle
(HUP), and that brings me to Hilbert Space. The main type of Hilbert
Space is L2, which is the square integrable functions f:
1) I /f/^2 du < infinity
where u is some Lebesgue type of measure and I...du is Lebesgue
integral.
Schrodinger and some others have proven HUP with the assumption that
the self-adjoint operator formalism holds on Hilbert Space, but
remember that we are talking formal vs actual in terms of physical
reality.
Readers presumably know the counter-arguments to Heisenberg of Max
Jammer of Bar-Ilan and CUNY Universities in his Philosophy of Quantum
Mechanics, Wiley: N.Y. 1974 which I've often cited, but there's also an
additional difficulty. If the Uncertainty taken as a variance or
standard deviation (in Schrodinger's proof) of position decreases
essentially (or in terms of bounds) as the uncertainty of momentum
increases, then since variance is an L2 quantity, what happens to the
finite variance requirement?
I'll try to continue shortly.
Osher Doctorow
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