In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born's rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $ \Sigma $, then the observed particle configuration on $ Sigma $ is a random variable with distribution density $ |\Psi_\Sigma|^2 $, suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.

Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces / S. Lill, R. Tumulka. - In: ANNALES HENRI POINCARE'. - ISSN 1424-0637. - 23:4(2021), pp. 1489-1524. [10.1007/s00023-021-01130-4]

Another Proof of Born’s Rule on Arbitrary Cauchy Surfaces

S. Lill
Primo
;
2021

Abstract

In 2017, Lienert and Tumulka proved Born's rule on arbitrary Cauchy surfaces in Minkowski space-time assuming Born's rule and a corresponding collapse rule on horizontal surfaces relative to a fixed Lorentz frame, as well as a given unitary time evolution between any two Cauchy surfaces, satisfying that there is no interaction faster than light and no propagation faster than light. Here, we prove Born's rule on arbitrary Cauchy surfaces from a different, but equally reasonable, set of assumptions. The conclusion is that if detectors are placed along any Cauchy surface $ \Sigma $, then the observed particle configuration on $ Sigma $ is a random variable with distribution density $ |\Psi_\Sigma|^2 $, suitably understood. The main different assumption is that the Born and collapse rules hold on any spacelike hyperplane, i.e., at any time coordinate in any Lorentz frame. Heuristically, this follows if the dynamics of the detectors is Lorentz invariant.
detection probability; particle detector; Tomonaga-Schwinger equation; interaction locality; multi-time wave function; spacelike hypersurface
Settore MATH-04/A - Fisica matematica
2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/1101023
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