Physical Science International Journal, ISSN: 2348-0130,Vol.: 4, Issue.: 8 (October)
Computational Solution to Quantum Foundational Problems
1Ben-Gurion University of the Negev, Beersheba, Israel.
(1) Abbas Mohammed, Blekinge Institute of Technology, Sweden.
(1) Stanislav Fisenko, Moscow State Linguistic University, Russia.
(4) Lalit A. Patel, USA.
Complete Peer review History:http://www.sciencedomain.org/review-history/5055
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory referred to as the “measurement problem”, actually has a computational character: It implies that there is a generic algorithm, which guarantees exact solutions to the Schr¨odinger equation for every physical system in a reasonable amount of time regardless of how many constituent microscopic particles it comprises. From the point of view of computational complexity theory, this requirement is equivalent to the assumption that the computational complexity classes P and NP are equal, which is widely believed to be very unlikely. As demonstrated in the paper, accepting the different computational assumption called the Exponential Time Hypothesis (that involves P≠NP) would justify the separation between a microscopic quantum system and a macroscopic apparatus (usually called the Heisenberg cut) since this hypothesis, if true, would imply that deterministic quantum and classical descriptions are impossible to overlap in order to obtain a rigorous derivation of complete properties of macroscopic objects from their microstates.
Schr¨odinger equation; Quantum linearity; Reduction postulate; Born rule; Computational complexity; P versus NP question; Exponential Time Hypothesis.
Full Article - PDF Page 1145-1157
DOI : 10.9734/PSIJ/2014/11144Review History Comments