The Computational Limit to Quantum Determinism and the Black Hole Information Loss Paradox

TL;DR

This paper argues that under the strong exponential time hypothesis, quantum determinism cannot be universally applied, especially in black hole evaporation, linking computational complexity to fundamental physics and the information loss paradox.

Contribution

It establishes a connection between computational complexity assumptions and the breakdown of quantum determinism in black hole processes.

Findings

Quantum determinism is limited by SETH in predicting macroscopic systems.

Black hole evaporation may serve as physical evidence for computational complexity constraints.

The paper links the information loss paradox to the computational hardness of predicting quantum states.

Abstract

The present paper scrutinizes the principle of quantum determinism, which maintains that the complete information about the initial quantum state of a physical system should determine the system's quantum state at any other time. As it shown in the paper, assuming the strong exponential time hypothesis, SETH, which conjectures that known algorithms for solving computational NP-complete problems (often brute-force algorithms) are optimal, the quantum deterministic principle cannot be used generally, i.e., for randomly selected physical systems, particularly macroscopic systems. In other words, even if the initial quantum state of an arbitrary system were precisely known, as long as SETH is true it might be impossible in the real world to predict the system's exact final quantum state. The paper suggests that the breakdown of quantum determinism in a process, in which a black hole forms and then completely evaporates, might actually be physical evidence supporting SETH.