A Class of Deductive Theories that cannot be Deterministic: Classical and Quantum Physics are not deterministic

TL;DR

This paper explores the inherent non-determinism in classical and quantum physics, introducing the Memory Paradox, which challenges traditional views and shows non-determinism arises naturally without extra assumptions.

Contribution

It identifies and discusses the Memory Paradox, revealing that both classical and quantum physics are fundamentally non-deterministic, extending previous theoretical work.

Findings

Classical physics is non-deterministic due to the Memory Paradox.

Quantum physics's non-determinism follows naturally from the paradox.

The work extends prior theoretical analysis on determinism in physics.

Abstract

The problem of the determinism of Quantum Mechanics has been a main one during the 20th century. At the same time, in the context of Logic and Set Theory, the importance of ancient paradoxes as well as the appearance of many new ones, has shed light on and deeply influenced the foundations of Mathematics and somehow of Physics. But, strangely, concerning Physics, a paradox which we call the Memory Paradox has remained yet undiscovered, despite its simplicity and remarkable consequences, mostly in Physics and surprisingly in classical Physics that appear to be non deterministic, contrary to the general belief since Newton, Laplace, etc.. The non determinism of Quantum Physics follows without any supplementary hypothesis. This paper extends a previous one (arXiv: 1203.2945v1 [physics.gen-ph] 13 Mar 2012).