Implications of Einstein-Weyl Causality on Quantum Mechanics

TL;DR

This paper explores how Einstein-Weyl causality influences the structure of space-time and its implications for quantum mechanics, proposing a constructible foundation that results in a dense, denumerable space-time with connections to quantum theory.

Contribution

It introduces a constructible foundation for space-time consistent with Einstein-Weyl causality, linking it to quantum mechanics and addressing philosophical paradoxes.

Findings

Dense, denumerable space-time model developed

Connection established between causality and quantum mechanics

Addresses philosophical paradoxes of the real line E

Abstract

A fundamental physical principle that has consequences for the topology of space-time is the principle of Einstein-Weyl causality. We show here that this may have implications on quantum mechanics, as well. Borchers and Sen have rigorously investigated the mathematical implications of Einstein-Weyl causality and shown the denumerable space-time Q^2 would be implied. They then imbedded this space in a non-denumerable space but were left with important philosophical paradoxes regarding the nature of the physical real line E, e.g., whether E = R, the real line of mathematics. Alternatively, their initial result could suggest a constructible foundation. We have pursued such a program and find it indeed provides a dense, denumerable space-time and, moreover, an interesting connection with quantum mechanics.