TY - JOUR

T1 - Complex-Valued Classical Behavior from the Correspondence Limit of Quantum Mechanics with Two Boundary Conditions

AU - Aharonov, Yakir

AU - Shushi, Tomer

N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - The two-state-vector formalism presents a time-symmetric approach to the standard quantum mechanics, with particular importance in the description of experiments having pre- and post-selected ensembles. In this paper, using the correspondence limit of the quantum harmonic oscillator in the two-state-vector formalism, we produce harmonic oscillators that possess a classical behavior while having a complex-valued position and momentum. This allows us to discover novel effects that cannot be achieved otherwise. The proposed classical behavior does not describe the classical physics in the usual sense since this behavior is subjected to the feature that only after the final measurement is performed, as a boundary condition, the complex-valued classical effects occur between the initial and the final boundary conditions. This classical behavior breaks down if one does not follow the decided boundary conditions during the experiment, since otherwise, one will contradict the impossibility of retrocausality.

AB - The two-state-vector formalism presents a time-symmetric approach to the standard quantum mechanics, with particular importance in the description of experiments having pre- and post-selected ensembles. In this paper, using the correspondence limit of the quantum harmonic oscillator in the two-state-vector formalism, we produce harmonic oscillators that possess a classical behavior while having a complex-valued position and momentum. This allows us to discover novel effects that cannot be achieved otherwise. The proposed classical behavior does not describe the classical physics in the usual sense since this behavior is subjected to the feature that only after the final measurement is performed, as a boundary condition, the complex-valued classical effects occur between the initial and the final boundary conditions. This classical behavior breaks down if one does not follow the decided boundary conditions during the experiment, since otherwise, one will contradict the impossibility of retrocausality.

KW - Classical systems

KW - Complex-valued trajectories

KW - Harmonic oscillator

KW - Two-state-vector-formalism

UR - http://www.scopus.com/inward/record.url?scp=85130356708&partnerID=8YFLogxK

U2 - 10.1007/s10701-022-00576-8

DO - 10.1007/s10701-022-00576-8

M3 - Article

AN - SCOPUS:85130356708

SN - 0015-9018

VL - 52

JO - Foundations of Physics

JF - Foundations of Physics

IS - 3

M1 - 56

ER -