A Holographic Principle for Non-Relativistic Quantum Mechanics

TL;DR

This paper presents a five-dimensional holographic framework for non-relativistic quantum mechanics, offering intuitive explanations for quantum phenomena and addressing foundational issues like measurement and entanglement.

Contribution

It introduces a 5D holographic principle that models quantum particles as classical threads, simplifying quantum explanations and eliminating the measurement problem.

Findings

Provides a duality between 5D classical threads and 4D quantum particles.

Offers intuitive explanations for quantum phenomena such as tunnelling and interference.

Discusses advantages and limitations of the 5D holographic approach.

Abstract

The quantum-classical isomorphism for self-consistent field theory, which allows quantum particles in space-time to be represented as classical one-dimensional threads embedded in a five dimensional thermal-space-time, is summarized and used to explain a selection of quantum phenomena. Introduced by Feynman, and used for modern quantum simulations, the isomorphism, when phrased in a field-theoretic way, has been shown to be the same as quantum density functional theory, the theorems of which guarantee equivalent predictions with non-relativistic quantum mechanics. If the Feynman dimension is considered to be real, there is a duality between classical threads in five dimensions and quantum particles in four dimensions. Using the 5D picture, intuitive explanations are given for quantum phenomena including the uncertainty principle, tunnelling, geometric phase, and interference effects. Advantages of the 5D picture are presented, which include fewer postulates, no measurement problem, and the need for only classical concepts in the higher dimensional space. Limitations of the approach such as the interpretation of entanglement and spin are discussed.