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Derivation of the Born rule from the unitarity of quantum evolution | | G.B. Lesovik
; | | Date: |
25 Nov 2014 | | Abstract: | In order to make the quantum mechanics a closed theory one has to derive the
Born rule from the first principles, like the Schroedinger equation, rather
than postulate it. The Born rule was in certain sense derived in several
articles, e.g. in [D. Deutsch, Proc. R. Soc. Lond. A455, 3129 (1999)] and [W.
H. Zurek, Phys. Rev. Lett. 90 , 120404 (2003)]. In this work some arguments of
previous authors are simplified and made more "physical". It is shown how to
derive the Born rule using the conservation of quantum state norm
$langlePsi|Psi
angle$ that is the unitary evolution property determined by
the Schroedinger equation. It is this property that makes the probability equal
to the square of the amplitude modulus. Possible modification of the Born rule
is briefly discussed in the case when the evolution of the system is described
by a nonlinear Schroedinger equation. We also present arguments in the spirit
of the Many-World Interpretation to explain the origin of probabilistic
behavior. Simply speaking, the randomness appears as a result of representing
the wave function by using a detector of discrete nature that is found only in
one state at a time, out of two or more possible states. | | Source: | arXiv, 1411.6992 | | Services: | Forum | Review | PDF | Favorites | |
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