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A new wave-packet approach to coherent superpositions of macroscopically distinct states and the quantum-to-classical transition in closed systems | | N L Chuprikov
; | | Date: |
16 Nov 2009 | | Abstract: | A new wave-packet approach to a 1D completed scattering (with a symmetrical
barrier) and double slit diffraction (with identical slits) is presented. In
either case, a coherent superposition of macroscopically distinct states
(CSMDS) appears, for which Born’s averaging rule fails in giving the {it
expectation} values of one-particle observables. This approach treats either
process as a complex one to consist from two coherently evolved, interconnected
one-particle sub-processes. Supporting the quantum-to-classical transition for
a closed system in a CSMDS, it proves and simultaneously disproves the next two
statements to point to a deep gap to exist at present between classical and
quantum theories: (i) "No unitary treatment of the time dependence can explain
why only one of $...$ components [to enter a CSMDS] is experienced" (Joos and
Zeh); (ii) "Probability theory must go beyond the classical (Kolmogorov) model"
(Accardi). It proves the first statement, as the time evolution of the
sub-processes is {it piecewise} unitary. But it simultaneously disproves it,
as this non-unitary evolution arises in the framework of the Schr"odinger
equation. It partially disproves the second statement, as the probability space
to describe the double slit diffraction is reduced to the sum of two
Kolmogorovian ones to describe incompatible interconnected sub-processes (a
particle passes only through one of two open slits); a similar decomposition is
presented for all stages of the 1D completed scattering of {it narrow} in
$k$-space wave packets, as well as for the scattering of {it wide} wave
packets, excepting the very stage of the scattering event. This exception
proves the second statement - in the general case, quantum probability spaces
associated with CSMDSs are irreducible to classical ones. | | Source: | arXiv, 0911.2980 | | Services: | Forum | Review | PDF | Favorites | |
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