Re: Super Copenhagen Interpretation (Consistent Histories)
- From: markwh04@xxxxxxxxx
- Date: Thu, 27 Apr 2006 21:19:43 +0000 (UTC)
Fizyk wrote:
The need for interpretation arises when you want to perform a measurement on
a quantum system. When does the wavefunction collapse? Never?
In the Heisenberg picture, the question doesn't exist since the
collapse rule (i.e. Lueder's rule) merges with the evolution rule (the
Schroedinger equation) into a single rule:
P(A1(x1) = a1, A2(x2) = a2, ..., An(xn) = an | state W)
= W[ T[P1...Pn] T'[P1...Pn] ],
where T[] is the time-ordered product operator, and T'[] the 'reverse'
time-ordered product operator; W[] the linear functional associated
with state W; Pi being the projector of the eigenspace of Ai(xi) at
eigenvalue ai; xi a spacetime point. This attaches a probability
metric, conditioned on W, to the event space
E = spec(A1(x1)) x spec(A2(x2)) x ... x spec(An(xn)).
There is no "when" here, since states in the Heisenberg picture aren't
changing; and no "wavefunction" to collapse, since it's the operators
that have all the dynamics, not states. Nor it is just about
"wavefunctions", since W can be a mixed state ... mixed states are more
general than wave functions.
Nor, for that matter, is it even restricted to Quantum Theory at all!
The same rule above applies to Classical Physics, and the various
instances of Classico-Quantum physics that comprise the quantum
theories with superselection!
Indeed, it's hard to read "collapse" anywhere into the expression above
when it applies over the entire classico-quantum continuum from pure
quantum, to pure classical, to all the classico-quantum theories in
between. But it's equivalent to Lueder + Schroedinger, at the pure
quantum end of the continuum. Therefore, if Lueder means "collapse",
then the above correspondence drags it down the slippery slope of the
theory-continuum all the way to Classical Physics. Therefore, either
Classical Physics has collapse, or the Lueder rule's purported reading
as "collapse" is in fact a misreading totally absent from the
re-written form above.
Eat your heart out, Goedel.
.
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