Chapter 1. What is the Quantum Relations Principle?

W. M. Stuckey, Michael Silberstein, Timothy J. McDevitt

Abstract Chapter 1 points out that the mystery of entanglement has led Physics Nobel Laureates to claim “nobody understands quantum mechanics.” The Chapter goes on to introduce: the EPR and EPR–Bell paradoxes, various attempts to resolve them, our proposed resolution whereby the relativity principle (no preferred reference frame, NPRF) justifies the Planck postulate (NPRF + h) exactly like the relativity principle justifies the light postulate (NPRF + c), the Planck postulate as a result of Information Invariance & Continuity from quantum information theory, the importance of the relativity principle, subjective versus objective spacetime models of reality, spacelike and timelike relations in spacetime, and four experiments leading to our Poincaré symmetric ontology.

Jessey Wright

Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.

N. J. B. Green

This chapter discusses some of the fundamental principles in quantum mechanics. Towards the end of the nineteenth century, it had been thought that all the fundamental laws of nature were well-understood. However, the next 20 years saw the development of both quantum mechanics and relativity. The chapter then looks at the representation of a particle by a wavefunction. It also considers operators, observables, eigenfunctions, and eigenvalues, as well as commutation and uncertainty. Since it is not possible for a wavefunction to have characteristic values of two observables with non-commuting operators, it is not possible to specify exact simultaneous values for these observables. It should be noted that the uncertainty principle is rather deeper than the usual physical explanation might imply, it is actually inherent in the description of matter in terms of wavefunctions. Finally, the chapter explains expansion in eigenfunctions; the variational principle; and transition probabilities.