Any realistic model of a physical system must be computationally realistic

TL;DR

The paper argues that for a physical model to be considered realistic, it must be computationally feasible, showing that microscopic quantum systems can be realistically modeled but macroscopic systems cannot due to computational complexity.

Contribution

It introduces the concept of computational realism in physical theories and analyzes the computational feasibility of quantum models for microscopic versus macroscopic systems.

Findings

Microscopic quantum models are computationally realistic due to small degrees of freedom.

Macroscopic quantum models are non-realistic because of computational intractability.

Computational complexity constrains the realism of physical models.

Abstract

It is argued that any possible definition of a realistic physics theory -- i.e., a mathematical model representing the real world -- cannot be considered comprehensive unless it is supplemented with requirement of being computationally realistic. That is, the mathematical structure of a realistic model of a physical system must allow the collection of all the system's physical quantities to compute all possible measurement outcomes on some computational device not only in an unambiguous way but also in a reasonable amount of time. In the paper, it is shown that a deterministic quantum model of a microscopic system evolving in isolation should be regarded as realistic since the NP-hard problem of finding the exact solution to the Schrodinger equation for an arbitrary physical system can be surely solved in a reasonable amount of time in the case, in which the system has just a small number of degrees of freedom. In contrast to this, the deterministic quantum model of a truly macroscopic object ought to be considered as non-realistic since in a world of limited computational resources the intractable problem possessing that enormous amount of degrees of freedom would be the same as mere unsolvable.