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arXiv:quant-ph/0209051

A spontaneous collapse model on a lattice

Fay Dowker B, Joe Henson C

Published Sep 6, 2002• 12 citations
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Abstract

We present a spontaneous collapse model of a field theory on a 1+1 null lattice, in which the causal structure of the lattice plays a central role. Issues such as ``locality,'' ``non-locality'' and superluminal signaling are addressed in the context of the model which has the virtue of extreme simplicity. The formalism of the model is related to that of the consistent histories approach to quantum mechanics.

DOI
10.48550/arxiv.quant-ph/0209051

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We present a spontaneous collapse model of a field theory on a 1+1 null lattice, in which the causal structure of the lattice plays a central role. Issues such as locality,'' non-locality'' and superluminal signaling are addressed in the context of the model which has the virtue of extreme simplicity. The formalism of the model is related to that of the consistent histories approach to quantum mechanics.
We present simulations of causal dynamical wavefunction collapse models of field theories on a 1 + 1 null lattice. We use our simulations to compare and contrast two possible interpretations of the models, one in which the field values are real and the other in which the state vector is real. We suggest that a procedure of coarse graining and renormalizing the fundamental field can overcome its noisiness and argue that this coarse grained renormalized field will show interesting structure if the state vector does on the coarse grained scale. We speculate on the implications for quantum gravity.
We provide a precise definition and analysis of quantum causal histories (QCHs). A QCH consists of a discrete, locally finite, causal pre-spacetime with matrix algebras encoding the quantum structure at each event. The evolution of quantum states and observables is described by completely positive maps between the algebras at causally related events. We show that this local description of evolution is sufficient and that unitary evolution can be recovered wherever it should actually be expected. This formalism may describe a quantum cosmology without an assumption of global hyperbolicity; it is thus more general than the Wheeler–De Witt approach. The structure of a QCH is also closely related to quantum information theory and algebraic quantum field theory on a causal set.
A local, deterministic toy model for quantum mechanics is introduced and discussed. It is demonstrated that the model makes the same predictions as quantum mechanics when averaged over the hidden variables. In this model the dynamics depends on the settings of the measurement device at the time of detection but not on how those settings were chosen. As a consequence, the model has a future input dependence and violates statistical independence but is local. We further show that the model is neither fine tuned nor allows for superluminal signaling and discuss the causality relations.
Quantum trajectory theory, developed largely in the quantum optics community to describe open quantum systems subjected to continuous monitoring, has applications in many areas of quantum physics. In this paper I present a simple model, using two-level quantum systems (q-bits), to illustrate the essential physics of quantum trajectories and how different monitoring schemes correspond to different ``unravelings'' of a mixed state master equation. I also comment briefly on the relationship of the theory to the Consistent Histories formalism and to spontaneous collapse models.