Introduction to Q-Epsilon: A Reduction to Quantum Mechanics

Our Q-Epsilon framework builds upon established quantum field theory principles developed byWeinberg [1] and Peskin & Schroeder [2]. Weinberg's comprehensive treatment of field theoryprovides essential mathematical tools for handling field propagation across dimensions, which weextend by adding the modulation dimension ε. While Weinberg focuses on standard spacetime, ourapproach introduces a third dynamic axis (modulation), but utilizes similar differential equationstructures. The algebraic methods from Peskin & Schroeder's work—particularly their treatment offield oscillators and propagators—provide technical foundations that we adapt to handle modulationpropagation.The deterministic underpinnings of our approach connect to Bohm's hidden variables theory [3],though with crucial differences. Where Bohm introduces a separate "pilot wave" to guide particles,our theory identifies modulation itself as the guiding principle, with no separate hidden variablesneeded. Similarly, while 't Hooft's cellular automaton interpretation [4] shares our deterministicgoals, his discrete computational model contrasts with our continuous field-based approach. Boththeories aim to restore determinism to quantum mechanics, but through fundamentally differentmechanisms.Carroll's recent work [5] on how classical reality emerges from quantum fields provides a valuablecontemporary perspective that parallels our own. Carroll argues that quantum field theory underlieseveryday reality, but focuses primarily on decoherence as the emergence mechanism. In contrast,our theory identifies modulation coherence as the key organizing principle, offering a morefundamental explanation for emergence that could potentially address limitations in Carroll'sdecoherence-based approach.