From: scerir (scerir@libero.it)
Date: Sun Jan 13 2002 - 13:22:21 MST

'I've said it before, I'll say it again:
Can a dog collapse a state vector?
Dogs don't use state vectors.
I myself didn't collapse a state vector
until I was 20 years old.'
- Christopher A. Fuchs (2001)

Heh. It's not so simple, dr. Fuchs, and you know this very well.

Einstein, at the Solvay Conference of 1927, talking about the
electron wave packet, the diffraction, and the resulting
registration on a screen, said: 'If |psi|^2 were simply
considered as the probability for a particle to be at a place
at that definite instant, it might happen that one and the same
elementary process would cause an action at two or more places
on the screen.' [A. Einstein, in "Electrons et Photons - Rapports
et Discussions du Cinquieme Conseil de Physique Tenu a Bruxelles
du 24 au 29 Octobre 1927", Institut International de Physique
Solvay, Gauthier-Villars, Paris,1928, pages 253-256].

At that time Bohr has already developed his 'complementarity'
principle (Sept. 16, 1927, 'The Quantum Postulate and the
Recent Develpoment of Atomic Theory', in 'Atti del Congresso
Internazionale dei Fisici' (at Como), Zanichelli, 1928).
Actually this principle states that if one analyzes any
situations where it is possible to know, fully, the path
the particle took, the interference pattern cannot be observed.
Likewise if one observes the interference pattern, no information
about path is available.

Heisenberg (and perhaps also Bohr) thought that the 'general'
complementarity principle and his 'special' uncertainty
principle had something to do with the concept of 'information'.
And now we know they have something to do with the '_finiteness_'
of available information.

Against Einstein's objection, Heisenberg and Dirac and Pauli
emphasized that the 'wave function' did not represent a course
of events in space and time, but it did rather express just our
'knowledge' of the events. Einstein did not agree. He developed
new objections. In example he represented a photon by a 'wave
packet' built up out of _Maxwell_ waves, with some extension and
frequency. By means of a semi-transparent mirror it is possible
to decompose that packet in a reflected one and in a transmitted
one. These two packets, after a little time, are well separated.
Thus the probability = 1 of finding the photon in a region implies
the probability = 0 of finding the photon in the other space-like
separated region. Thus the famous 'spooky' action at-a-distance,
'spukhafte Fernwirkungen', had his birth well before 1935 (the
EPR argument). Einstein wrote about this issue also in "Louis de
Broglie, Physicien et Penseur", A. George (ed.), Albin-Michel,
Paris, 1953, page 9. The argument, polished a bit, now is called
the 'de Broglie paradox' (Louis de Broglie, J. Phys. Radium, (1959),
20, 963).

But that is not the end of my story. It's interesting to note
that Heisenberg (but not Bohr) believed that the 'collapse' of
the 'wave packet' (thus also those 'spooky' actions) was _indeed_
a physical action, triggered by the 'indivisibility' of the particle
(The Physical Principles of the Quantum Theory, Un. Chicago P.,
page 39). Was he right ? It seems so.

Raymond Chiao and Paul Kwiat (among the very best in the field)
performed experiments with a couple of entangled photons (PDC
generated). One member of the pair (the idler) is sent to a filter
and to a photomultipier. The other member (the signal) is sent to
an interferometer (Michelson type). Now, in order to conserve
total energy and to fullfill the uncertainty (time, energy) relations,
they find that the visibility of the signal photon fringes depends
on the bandwith of the filter through which just the idler photon
goes. Thus the width of the collapsing signal photon wave packet
depends on that (remote, and well separated) filter.

That's not completely new, because others experiments (about the
ghost effect, about Popper's suggestion, etc.) already showed
that the 'collapse' of a (splitted) 'wave packet' (just one
particle, or two particles entangled in a singlet state) follows
the non-separability rule. That is to say: quantum correlations
at a distance are real, nonlocal, instantaneous. But also uncaused
(thus special relativity is safe).


'Like an ultimate fact without any cause,
the individual outcome of a measurement
is, however, in general not comprehended
by laws.'
- Wolfgang Pauli

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