Solving the Mysteries of Quantum Mechanics: Why Nature Abhors a Continuum

TL;DR

This paper introduces Rational Quantum Mechanics (RaQM), a discretised Hilbert Space theory that explains quantum mysteries through number theory and holism, challenging the continuum-based assumptions of traditional quantum physics.

Contribution

It develops a gravitationally discretised Hilbert Space framework for quantum mechanics, revealing a number-theoretic basis for quantum indivisibility and holistic laws of physics.

Findings

Discretising Hilbert Space resolves quantum mysteries.

Number theory explains quantum indivisibility.

Holism replaces nonlocality in explaining quantum phenomena.

Abstract

Feynman famously asserted that interference is the only real mystery in quantum mechanics (QM). It is concluded that the reason for this mystery, and thereby the related mysteries of complementarity, non-commutativity of observables, the uncertainty principle and violation of Bell's equality, is that the axioms of QM depend vitally on the continuum nature of Hilbert Space, deemed unphysical. We develop a theory of quantum physics - Rational Quantum Mechanics (RaQM) - in which Hilbert Space is gravitationally discretised. The key to solving the mysteries of QM in RaQM is a number-theoretic property of the cosine function, concealed in QM when angles range over the continuum. This number-theoretic property describes mathematically the utter indivisibility of the quantum world and implies that the laws of physics are profoundly holistic. We contrast holism with nonlocality. In theories which embrace the continuum, the violation of Bell's inequality requires the laws of physics to be either nonlocal or not realistic; both incomprehensible concepts. By contrast, holism, as embodied in Mach's Principle or in the fractal geometry of a chaotic attractor, is neither incomprehensible nor unphysical. As part of this, we solve the deepest mystery of all; why nature makes use of complex numbers.