Science > Physics > Quantum Gravity 152.0: The Heisenberg Uncertainty Illusion
| Topic: |
Science > Physics |
| User: |
"OsherD" |
| Date: |
10 Jun 2007 01:41:39 AM |
| Object: |
Quantum Gravity 152.0: The Heisenberg Uncertainty Illusion |
From Osher Doctorow
The equation which I derived in the last few posts:
1) P(A-->B ' ) = [1 - P(A-->B)] + [1 - P(A)]
suggests a way to analyze the Heisenberg Uncertainty Principle (HUP).
HUP asserts that precisely measuring position and momentum are (part
of) conjugate or complementary events or processes, so let's call the
first B and the second is (part of) the complement of B, namely B
' . Causality or Causation is asserted to not apply across B and B '
by HUP, so let's consider a candidate A for a (Probable) Cause for
which the Effect is B or B ' . To prove HUP, we would want to prove:
2) P{(A-->B)(A-->B ' )} = 0 (HUP formulation)
where adjacent parentheses indicate intersection. However, we can
easily prove that:
3) (A-->B)(A-->B ' ) = (A ' U B)(A ' U B ' ) = A '
and therefore (2) is equivalent to:
4) P(A ' ) = 0 (HUP formulation)
which in turn means:
5) P(A) = 1 (since P(A ' ) = 1 - P(A) from probability theory).
So any Cause which is not completely deterministic (in the sense of
having probability 1) violates HUP.
Couldn't HUP "live with" this restriction? No. First of all,
Schrodinger and Condon showed that the HUP is equivalent to a claim
about standard deviations/variances/uncertainties which therefore
means that it refers to probabilities and statistical approximations
to probabilities. So complete determinism is not the scenario of
HUP.
In addition, a recent paper by Graciela Domenech and Hector Freytes of
Argentina, "Contextual logic for quantum systems," arXiv: quant-ph/
0702023 v1 2 Feb 2007, 16 pages, based partly on prior work with the
Belgian de Ronde, argues quite effectively that with proper
formulation in terms of sheaves and other things, even analogs of
material implication and negation and unions and intersections survive
in Quantum Logic, which (probably without their knowledge) agrees with
the early 1970s work of Peter Mittelstaedt of U. Cologne/Koln Germany
and which was part of the anti-Heisenberg and anti-Piron/Jauch
Heisenberg-imitating Quantum Logic school of Switzerland. Note that
de Ronde in another paper seems totally unaware of any relationships
of his and the others' work to HUP and does the usual acceptance of
HUP as "fundamental" a knee-jerk reaction of logicians trying to be
accepted in physics.
Osher Doctorow
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