Hidden variables
• From the point of vue of wave packet reduction within hidden
variables approach, as considered by L. De Broglie, it may be asked
what happens in the case where the studied variable is the momentum,
and that it is measured by means of a position measure.
Let us consider a source of photons with spherical symmetry and a
detector used to measure the py
component of the momentum, by means of the y coordinate of the impact
point. One may then say that, the more far from the source is the
detector, the more precise (for a constant precision on the y
coordinate) is the measure of py (connected to the path from
the source to the detector). On the opposite the 
perturbation caused by this measure does not decrease
since it depends only on the 
precision. The act
of y measurement has disturbed the py value after the measurement, but
the photon arrived at well defined y, and with well defined py
(by the motion it has before).
It is thus possible to interpret this by assuming that parcicles do
exist,
that the y and py variables associated with them are defined
at the same time, but that the values of these variables are accessible
only by interactions, the symmetries of which (carried by the wave) are
on the other hand subject to the rule > h.
This rejoins L. De Broglie's ideas about hidden variables, with this
peculiarity that the relativistic instantaneousness and localeousness
break the argument studied experimentally by A. Aspect [1, 2] : it would concern in
this case “non local” hidden variables (with the classical meaning of
this expression), the understanding of which would first require a
re-foundation of our interpretation of space-time.
__________________
References :
1. see as example :
A. Aspect, J. Dalibard and G. Roger,
“Expérimental test of
Bell's inequalities using time-varying analysers”, Phys. Rev. Letters,
Vol. 49, n°
25, p. 1804 (1982) ;
O. Freire, “La bizarrerie quantique
révélée par trois expériences”, La
Recherche n° 400, september 2006.
2. A. Aspect and P. Grangier, “Des intuitions d'Einstein aux bits
quantiques”, Pour la Science n° 326, december 2004 (article
about which, elsewhere, I fear alas that the importance of the
decoherence is such that it practically forbids any utilization of a
large number of intricated components).
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