Causality - Complexity - Consistency: Can Space-Time Be Based on Logic and Computation?

TL;DR

This paper explores whether space-time can be derived from logic and computation, proposing an intrinsic measure of randomness based on Kolmogorov complexity, and discusses implications for non-local correlations, thermodynamics, and the emergence of space-time.

Contribution

It introduces a new, intrinsic measure of randomness for bit strings based on Kolmogorov complexity, challenging traditional causal assumptions in physics.

Findings

Proposes an alternative randomness measure related to Kolmogorov complexity.

Connects logical reversibility to thermodynamics and the arrow of time.

Suggests space-time may emerge from data-compressibility relations in bit strings.

Abstract

The difficulty of explaining non-local correlations in a fixed causal structure sheds new light on the old debate on whether space and time are to be seen as fundamental. Refraining from assuming space-time as given a priori has a number of consequences. First, the usual definitions of randomness depend on a causal structure and turn meaningless. So motivated, we propose an intrinsic, physically motivated measure for the randomness of a string of bits: its length minus its normalized work value, a quantity we closely relate to its Kolmogorov complexity (the length of the shortest program making a universal Turing machine output this string). We test this alternative concept of randomness for the example of non-local correlations, and we end up with a reasoning that leads to similar conclusions as in, but is conceptually more direct than, the probabilistic view since only the outcomes of measurements that can actually all be carried out together are put into relation to each other. In the same context-free spirit, we connect the logical reversibility of an evolution to the second law of thermodynamics and the arrow of time. Refining this, we end up with a speculation on the emergence of a space-time structure on bit strings in terms of data-compressibility relations. Finally, we show that logical consistency, by which we replace the abandoned causality, it strictly weaker a constraint than the latter in the multi-party case.