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arXiv:1003.5008

Why Physics Needs Quantum Foundations

Lucién Hardy, Robert W. Spekkens

Published Mar 25, 2010• 49 citations
arXivHTMLPDF

Abstract

We discuss the motivation for pursuing research on the foundations of quantum theory.
DOI
10.48550/arxiv.1003.5008

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This paper is devoted to foundations of probability theory. We discuss interpretations of probability, corresponding mathematical formalisms, and applications to quantum physics. One of the aims of this paper is to show that the probability model based on Kolmogorov's axiomatics cannot describe all stochastic phenomena, i.e., that quantum physics induces natural restrictions of the use of Kolmogorov's theory and that we need to develop non-Kolmogorov models for describing some quantum phenomena. The physical motivations are presented in a clear and brief manner. Thus the reader does not need to have preliminary knowledgeof quantum physics. Our main idea is that we cannot develop non-Kolmogorov models by the formal change of Kolmogorov's axiomatics. We begin with interpretations (classical, frequency, and proportional). Then we present a class of non-Kolmogorov models described by so-called p-adic numbers. Here, in particular, we obtain a quite natural realization of negative probabilities. These negative probability distributions might provide a solution of some quantum paradoxes.
Abstract Albert Einstein thought of physics as the search for the order and harmony of the world—a harmony he spoke of in quasi-religious terms. In his theories of relativity, he succeeded brilliantly in discerning a hidden unity in nature. But by pursuing his unfinished quest for a unified field theory, he abandoned the mainstream of research that was increasingly dominated by the quantum theory he had helped to found, but whose foundations he continued to question. That research has now produced a (partially) unified physics based on quantum field theory. But the ontology of quantum field theory remains opaque. This essay will explore, but reject, the radical proposal that quantum field theory describes a single, non-composite object—the World, and that everything else (elementary particles, chairs, people, planets, space-time) arises as an aspect of the World’s enormously rich structure.
The work leading to this thesis focuses on assessing and extending quantum theories in order to explore and test their implications across various regimes -- including thermodynamics, semiclassical and quantum gravity scenarios, and the in principle detectable predictions of such theories. The general motivation stems from a basic desire to understand the world form its very foundations. For instance, how can we bridge the gap between what we observe or `perceive' and the fundamental quantum nature in our theories. In particular, this work originated from the search to a better understanding of the nature of time according to our physical theories and the common perception that it invariably `flows' to the future, or, in other words, why do we observe distinct natural processes evolving asymmetrically in time? These motivations led to three distinct, yet interconnected and successful, lines of research, presented here in three separate parts: I. On Possible Detections within Physical Theories; II. On Explaining the Approach to Thermodynamic Equilibrium; and III. Relativistic Collapse Theories and a Self-Consistent Model of Semiclassical Gravity.