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Location and Causality in Quantum Theory

Dickinson, Robert Antony

[Thesis]. Manchester, UK: The University of Manchester; 2013.

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Abstract

An operational development of quantum theory is presented, from general correlations through single-particle theories to elementary quantum field theory, with a focus throughout on causal relations. The objective is to establish the extent to which quantum theories are consistent with the principle of relativistic causality (that no two events separated by a distance greater than their separation in time multiplied by the speed of light may have a causal influence on each other) and to examine the assumptions that this analysis requires. To do this, it is necessary to pay particular attention to the notions of spatial location and measurement. It is found that in a relativistically causal theory, any measurement made in a finite spatial region must have the capacity for particle creation. A number of derivations are presented, including some relativistic single-particle propagators and a Hamiltonian based on the square root of the Klein Gordon equation.

Layman's Abstract

This dissertation explores causal relations - the nature of cause and effect - in quantum theory. To do this with awareness of special relativity, it is also necessary to look carefully at the way spatial location is represented. With this in mind, quantum theory is set out here from first principles with a particular focus on measurement, signalling and location. It is shown that single particle quantum theories are inconsistent with relativistic causality and that, in a quantum field theory, any measurement made in a finite region of space must involve some probability of particle creation.