Quantum Computation and Arrows of Time.

Nathan Argaman

doi:10.3390/e23010049

Abstract

Quantum physics is surprising in many ways. One surprise is the threat to locality implied by Bell’s Theorem. Another surprise is the capacity of quantum computation, which poses a threat to the complexity-theoretic Church-Turing thesis. In both cases, the surprise may be due to taking for granted a strict arrow-of-time assumption whose applicability may be limited to the classical domain. This possibility has been noted repeatedly in the context of Bell’s Theorem. The argument concerning quantum computation is described here. Further development of models which violate this strong arrow-of-time assumption, replacing it by a weaker arrow which is yet to be identified, is called for.

Highlights

Feynman suggested that developing reformulations of existing theories can serve to improve our understanding, even if no novel predictions are involved
The upshot of the previous sections is that quantum computation adds to our motivation to develop reformulations of Quantum Mechanics (QM) which do not conform to the standard arrow of time
Standard QM in particular, conform to the Signal-Causality rule—they describe signaling to the future, but not to the past

Summary

Introduction

It is suggested that the algorithmic complexity achievable with quantum computation provides motivation for rejecting the standard arrow of time (Reference [28] and Reference [29] suggest different approaches connecting the flow of time with quantum computation) Here too it appears that a physical principle remains to be identified, one that would limit the freedom obtained with such a rejection. Which operate according to local rules subject to “the” arrow of time, all that can be achieved algorithmically is similar to a standard algorithm with N steps, taking N to appropriately represent the finiteness and the resolution pertaining to these “machines.” This is just the strong (or extended, or physical) Church-Turing thesis. Performing this for N nodes is necessarily an O( N ) task

Models with No Arrow of Time

Discussion

Conclusions