arXiv subjects

Edward J. Gillis

Publications and source records attributed to Edward J. Gillis.

11 recordsLinked to original sources

arXiv2026

Wave Function Collapse, Lorentz Invariance, and the Third Postulate of Relativity

The changes that quantum states undergo during measurement are both probabilistic and nonlocal. These two characteristics complement one another to insure compatibility with relativity and maintain conservation laws. The probabilistic nature of nonlocal effects prevents the superluminal transmission of information, while nonlocal entanglement relations provide a means to enforce conservation laws in a probabilistic theory. In order to explain measurement-induced changes in terms of fundamental physical processes it is important to take these two key characteristics into account. One way to do this is to modify the Schroedinger equation by adding stochastic, nonlinear terms. A number of such proposals have been made over the past few decades. A recently proposed equation based on the assumption that wave function collapse is induced by a sequence of correlating interactions of the kind that constitute measurements has been shown to maintain strict adherence to conservation laws in individual instances, and has also eliminated the need to introduce any new, ad hoc physical constants. In this work it is shone that the proposed stochastic modification to the Schroedinger equation is also Lorentz invariant, even though it is formulated in a preferred reference frame. It is further argued that the additional spacetime structure that the proposed modification requires provides a way to implement the assumption that spacelike-separated operators (and measurements) commute, and that this assumption of local commutativity should be regarded as a third postulate of relativity.

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arXiv2022

Objective Collapse Equation Maintains Conservation Laws With No New Constants

Modified versions of the Schrödinger equation have been proposed in order to incorporate the description of measurement processes into the mathematical structure of quantum theory. Typically, these proposals introduce new physical constants, and imply small violations of momentum and energy conservation. These problematic features can be eliminated by assuming that wave function collapse is induced by the individual interactions that establish correlations between systems. The generation of a sufficient number of small, random shifts of amplitude between interacting and noninteracting branches of the wave function can bring about collapse on a scale consistent with our macroscopic experience. Two-particle interaction potential energies can be used as the basis for a collapse term added to the Schrödinger equation. The range of the interactions sets the distance scale of the collapse effects; the ratio of potential energies to the total relativistic energies of the particles determines the magnitude of the amplitude shifts, and the rate at which the interactions proceed fixes the timing parameters. Consistency with conservation laws in individual experiments is maintained because the collapse operator automatically takes into account the small, residual entanglement between the measured system and systems with which it has previously exchanged conserved quantities during interactions. Conservation is exact for momentum and orbital angular momentum, and it holds for energy within the accuracy allowed by the limited forms of energy describable in nonrelativistic theory.

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arXiv2022

Is the relativistic Structure of Spacetime Ontic or Epistemic?

As repeatedly emphasized by Einstein our knowledge of the structure of space and time is based entirely on inferences from observations of physical objects and processes. At the most fundamental level these objects and processes are described by quantum theory. However, the ontological status of the theoretical entities employed by quantum theory is a matter of considerable debate. Furthermore, the nonlocal correlations identified by Bell cannot readily be explained within the standard relativistic framework. This suggests that we should re-examine our understanding of spacetime.

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arXiv2022

Wave Function Collapse, Correlating Interactions, and Conservation Laws

The assumption that wave function collapse is induced by correlating interactions of the kind that constitute measurements leads to a stochastic collapse equation that does not require the introduction of any new physical constants and that is consistent with conservation laws. The collapse operator is based on the interaction (potential) energy, with a variable timing parameter related to the rate at which individual interactions generate the correlations. The approximate localization of physical systems follows from the distance-dependent nature of the interaction potentials. The equation is consistent with strict conservation of momentum and orbital angular momentum, and it is also consistent with energy conservation within the accuracy allowed by the limited forms of energy that can be described within nonrelativistic theory. The possibility of extending the proposal to a fully relativistic version is discussed.

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arXiv2021

Conserved Quantities and Measurements

When a measurement is made on a system that is not in an eigenstate of the measured observable, it is often assumed that some conservation law has been violated. Discussions of the effect of measurements on conserved quantities often overlook the possibility of entanglement between the measured system and the preparation apparatus. The preparation of a system in any particular state necessarily involves interaction between the apparatus and the system. Since entanglement is a generic result of interaction, as shown by Gemmer and Mahler[1], and by Durt[2,3] one would expect some nonzero entanglement between apparatus and measured system, even though the amount of such entanglement is extremely small. Because the apparatus has an enormous number of degrees of freedom relative to the measured system, even a very tiny difference between the apparatus states that are correlated with the orthogonal states of the measured system can be sufficient to account for the perceived deviation from strict conservation of the quantity in question. Hence measurements need not violate conservation laws.

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arXiv2020

Interaction-Induced Wave Function Collapse Respects Conservation Laws

Because quantum measurements have probabilistic outcomes they can seem to violate conservation laws in individual experiments. Despite these appearances, strict conservation of momentum, orbital angular momentum, and energy can be shown to be consistent with the assumption that the entangling interactions that constitute measurements induce a real collapse of the wave function. The essential idea is that measured systems always have some pre-existing entanglement relations with (usually larger) systems, and that apparent changes in conserved quantities in the measured system are correlated with compensating changes in these larger systems. Since wave function collapse is mediated by entanglement relations a full accounting of the relevant quantities requires a computation over all interacting, entangled systems. The demonstrations by Gemmer and Mahler[1], and by Durt[2,3], that entanglement is a generic result of interaction are central to the argument. A stochastic collapse equation based on interaction potentials is described and shown to guarantee conservation of the relevant quantities at all stages of evolution.

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arXiv2019

Wave Function Collapse and the No-Superluminal-Signaling Principle

The assumption that wave function collapse is a real occurrence has very interesting consequences - both experimental and theoretical. Besides predicting observable deviations from linear evolution, it implies that these deviations must originate in nondeterministic effects at the elementary level in order to prevent superluminal signaling, as demonstrated by Gisin. This lack of determinism implies that information cannot be instantiated in a reproducible form in isolated microsystems (as illustrated by the No-cloning theorem). By stipulating that information is a reproducible and referential property of physical systems, one can formulate the no-signaling principle in strictly physical terms as a prohibition of the acquisition of information about spacelike-separated occurrences. This formulation provides a new perspective on the relationship between relativity and spacetime structure, and it imposes tight constraints on the way in which collapse effects are induced. These constraints indicate that wave function collapse results from (presumably small) nondeterministic deviations from linear evolution associated with nonlocally entangling interactions. This hypothesis can be formalized in a stochastic collapse equation and used to assess the feasibility of testing for collapse effects.

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arXiv2016

Response to Wiseman, Rieffel, and Cavalcanti on Bell's 1964 Paper

Wiseman has claimed that Bell was wrong in stating that determinism was inferred rather than assumed in the summary of the EPR argument in his 1964 paper. The reply of Wiseman and his co-authors to my comment misstates my reasons for disputing this point, and fails to address the central criticism that their claim is based on a seriously flawed formalization of Bell's argument deriving from an unreasonably strong interpretation of the the terms, 'influence', 'affect', and 'depend on'.

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arXiv2015

On the Analysis of Bell's 1964 Paper by Wiseman, Cavalcanti, and Rieffel

In a recent series of papers Wiseman, Cavalcanti, and Rieffel have outlined and contrasted two different views about what we now call Bell's theorem. They also assert that Bell presented these two different versions at different times. This view is clearly at odds with the detailed explanation that Bell himself gave in his later writings. A careful examination of the historic 1964 paper in context shows clearly that Bell's own later interpretation is the correct one.

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arXiv2012

Relativity Is Not About Spacetime

Quantum measurement predictions are consistent with relativity for macroscopic observations, but there is no consensus on how to explain this consistency in fundamental terms. The prevailing assumption is that the relativistic structure of spacetime should provide the framework for any microphysical account. This bias is due, in large part, to our intuitions about local causality, the idea that all physical processes propagate through space in a continuous manner. I argue that relativity is not a guarantor of local causality, and is not about ontological features of spacetime. It is, rather, an expression of the observational equivalence of spacetime descriptions of physical processes. This observational equivalence is due to the essentially probabilistic nature of quantum theory.

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arXiv2011

Causality, Measurement, and Elementary Interactions

Signal causality, the prohibition of superluminal information transmission, is the fundamental property shared by quantum measurement theory and relativity, and it is the key to understanding the connection between nonlocal measurement effects and elementary interactions. To prevent those effects from transmitting information between the generating and observing process, they must be induced by the kinds of entangling interactions that constitute measurements, as implied in the Projection Postulate. They must also be nondeterministic as reflected in the Born Probability Rule. The nondeterminism of entanglement-generating processes explains why the relevant types of information cannot be instantiated in elementary systems, and why the sequencing of nonlocal effects is, in principle, unobservable. This perspective suggests a simple hypothesis about nonlocal transfers of amplitude during entangling interactions, which yields straightforward experimental consequences.

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