Re: a question on incompatibility of properties in a one particle system

From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 10/20/04 

Date: Wed, 20 Oct 2004 04:12:47 -0000

 bernard.chaverondier:
>"Bilge" <dubious@radioactivex.lebesque-al.net> a écrit dans le message de
>news:slrncn9kad.1qe.dubious@radioactivex.lebesque-al.net...
>
>Bilge
>> The uncertainty, \delta A\Delta B >= hbar/2, occurs for any
>> pair of hermitian operators with a commutator equal to i\hbar.
>
>Chaverondier
>Yes and the issue we are discussing about is that the interpretation
>of this result in terms of uncertainties relies on the interpretation of
>quantum measurement uncertainties. The question is to know if
>such measurement induced uncertainties are fundamental or result
>from the lack of knowlege ot the observer about the quantum state
>of the measuring apparatus and that of the environement.

  I think it's fairly straight forward to determine. In order to construct
an experiment, you have to choose in advance what it is you plan to
measure so that you don't try to measure two incommensurate quantities.
This doesn't happen in classical physics and in scattering experiments,
the actual interactions in the detectors is irrelevant. Measuring an
anguar distribution that distinguishes between spin observables almost
never is done by analyzing the spin of the scattered particles. That is
too hard. What is usually done is just a simple measurement of an
asymmetry in the direction of the scattered particles or a difference in
total cross section using a polarized beam or polarized target or possibly
both. A tyipical analyzing power measurement does nothing but count
particles in two detectors which are located symmetrically about the
target. You get counts in the right side and left side detectors and take
the analyzing power to be something like A = (L-R)/(L+R). There's no
mysterious epr correlations involved. You seem to forget that quantum
mechanics gets the most use in situations that require quantum mechanics,
but have nothing at all to do with epr measurements. You still don't
have a classical experiment, since something like a tensor polarized
deuteron beam is not classical.

  What you're doing is attempting to explain a particular experiment
with an unnecessary and elaborate interpretation and completely
ignoring the zillions of other, more mundane examples of commutation
relations and the uncertainty principle appear for exactly the same
reason.

>I believe into this second interpretation which is a deterministic,
>contextual hidden variables, explicitly non local interpretation
>of quantum mechanics and I provide in this post some of the
>reasons why I favor this deterministic interpretation of QM.
 
  You can believe whatever you wish, but unless you can find an
experiment that gives what you believe some additional reality,
all you're doing is adding philosophical baggage that at best
serves no purpose and at worst is ligically incompatible with
what you are trying to explain with it.

>(see also the sub-quantum (deterministic) theory of Micho Durdevich,
>Universidad Nacional Autonoma de Mexico, "Physics Beyond the
>Limits of Uncertainty Relations". A picture of physical reality which
>is based on individual physical systems, completely causal,
>and statistically compatible with quantum mechanics.
>http://www.matem.unam.mx/~micho/subq.html)
 
  OK, what that boils down to is yet another attempt to attribute the
uncertainty principle to something else in order to say some even
more abstract quantity is deterministic (in a weird sort of way),
but for some rather nebulous reason, we can't observe a particle
such that it doesm't appear to behave just like quantum mechanics.
Sorry, I don't buy it without an example of an experiment which can
distinguish between the interpretations. Attributing reality to
something with no real existence is silly.

>Bilge
>> Representation is irrelevant. You don't need to choose
>> a representation in which either p or x is diagonal.
>
>Chaverondier
>Of course. That is not the issue. The issue is about Heisenberg
>uncertainties and the fact that these uncertainties pertains actually
>to the uncertainties showing up in the quantum measurement process
 
  So far, they show up just like the standard theory says they will.
As far as I know, the epr experiment did not require any novel
explanations to construct. It was constructed from standard quantum
theory, in part, because einstein thought what quantum mechanics
predicted was ridiculous on its face.

>Now, the manner you transform a position representation into a
>momentum one stems from the commutation relation.

   That's a rather content-free statement. What you just said is
equivalent to saying the manner in which you perform a canonical
transforms stems from the poisson bracket. Well, that's only true because
a canonical transformation preserves poisson brackets by definition. The
reason canonical transformations are important is because they preserve
possoin brackets. All that means is that the poisson brackets are
important to the theory and the particular choice of variables that
preserve them is irrelevant to any physics, apart from what it happens
to be convenient to measure.
 
>This relation amounts to indicate that the two representations are Fourier
>transforms one of each other.
 
  So what? How you transform between representations is irrelevant.
What's relevant is that the commutator bracket isn't changed in
fundamental way. What's the commutator [p,x] in the number basis,
|n>? It's simple. It's -i\hbar. You can check it by performing a
canonical transformation and obtaining x = a + a(+), p = i(a - a(+)).
That quantizes the harmonic oscillator, which is quantized in whatever
basis you choose.

>The fact that the two representation are Fourier transform of each other
>(ie the commutation relation) is not intrinsically the cause of Heisenberg
>uncertainties.
>Indeed, the fact that two observables cannot be diagonalized
>in the same Hilbert basis wouldn't give rise two the indeterminacy of the
>measurement of one of them just after the other one has been measured
>if the quantum measurement uncertainties were not to show up.
 
  Buy a quantum mechanics book. What you are saying is complete non-sense.

[...]
>Bilge
>> What's impossible about simultaneous measurements?
>
>Chaverondier
>It's impossible to know with certainty the position measurement
>outcome of a quantum particle (for instance) even if a momentum
>measurement has provided a precise representation of its
>quantum state (in momentum representation).
 
  Again, you demonstrate that you don't know what you are talking about.
Even conjugate operators commute on spacelike intervals.

[*snip*]

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