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Relativistic formulation of quantum state diffusion

Lajos Diósi

Published Jan 1, 1998• 4 citations
OpenAlex

Abstract

The recently reported relativistic formulation of the well-known non-relativistic quantum state diffusion is seriously mistaken. It predicts, for instance, inconsistent measurement outcomes for the same system when seen by two different inertial observers.

Related papers

Relativistic formulation of quantum state diffusion?

Lajos Diósi

The recently reported relativistic formulation of the well known non-relativistic quantum state diffusion is mistaken. It predicts, for instance, inconsistent measurement outcomes for the same system when seen by two different inertial observers.

arXiv:quant-ph/9803039•Journal of Physics A Mathematical and General•Nov 27, 1998•3 citations

Reply to `Relativistic formulation of quantum state diffusion?'

Heinz‐Peter Breuer, Francesco Petruccione

It has been demonstrated recently by the authors that the non-relativistic quantum state diffusion model can be generalized to yield a consistent, relativistically covariant theory. It is shown here that the `counterexample' constructed by Diósi can easily be disproven.

Journal of Physics A Mathematical and General•Nov 27, 1998•2 citations

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The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincaré subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schrödinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.

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Recent work has argued that the concepts of entanglement and nonlocality must be taken seriously even in systems consisting of only a single particle. These treatments, however, are nonrelativistic, and, if single-particle entanglement is fundamental, it should also persist in a relativistic description. Here, we consider a spin-1/2 particle in a superposition of two different velocities as viewed by an observer in a relativistically boosted inertial frame and show that the entanglement between the two velocity modes survives right up to the speed of light. We also discuss how quantum gates could be implemented in this way and apply our results to the case of a superconductor. In particular, we show that an $s$-wave superconductor would have $p$-wave components for a boosted observer.

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RELATIVISTIC QUANTUM MECHANICS

Vishnu S. Mathur, Surendra Singh

We have seen in earlier chapters that non-relativistic quantum mechanics does provide a consistent scheme to explain numerous phenomena in atomic, molecular and nuclear physics, but it does not conform to the equivalence of space and time as envisaged in the theory of relativity.

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The philosophical problems of implementing superselection rules

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Some physicists believe that superselection rules should be implemented to get rid of inconsistencies when a theory is framed in terms of a new mathematical formulation, whilst others think that this new formulation should be modified instead of implementing those rules, at the expense of introducing additional mathematical structure. The outcome, however, is that we are still uncertain whether these rules should be implemented and how they should be interpreted and assessed from the philosophical point of view. Based on a detailed examination of the group-theoretic reformulation of (relativistic and non-relativistic) quantum mechanics that prompts physicists to impose superselection rules, I shall argue that the implementation of these rules involves serious heuristic and epistemological concerns. Considering this argument, I shall conclude that there are suitable philosophical reasons to claim that the implementation of superselection rules should be rejected and that there are certain circumstances when the formulation of a theory should be modified.

arXiv:2310.03014•Oct 4, 2023•0 citations
The measurement processes that are traditionally described within the realm of non-relativistic quantum mechanics are transcribed into the covariant framework of Cartan's space, the four-valued representation space of the restricted conformal group for special relativity. It is assumed at the outset that the non-relativistic quantum measurement mechanisms of state reductions as well as the definition of Born probabilities should remain unaltered when the passage to the covariant framework is worked out. The correlations between observations registered in different spacetime frames, concerning intermediate steps and outcomes of microscopic measurements, are attained through the implementation of the orthochronous proper Poincaré subgroup of an appropriate realization of SU(2,2). It will be seen that the settlement of such correlations strongly supports the view whereby the physical inner structure of the Schrödinger quantum mechanical picture may be described consistently within special relativity. The overall work likewise affords a fundamental background to the construction of covariant quantum computational gates whilst making it feasible to elaborate upon the predicted and observed formation of entangled states in processes of creation-annihilation pairs. In addition, it is suggested that the usually accepted non-locality feature of the old quantum mechanics should be reconsidered inside an actual relativistic formulation. The important question as to whether quantum computation should bear an invariant character is then raised.
Recent work has argued that the concepts of entanglement and nonlocality must be taken seriously even in systems consisting of only a single particle. These treatments, however, are nonrelativistic, and, if single-particle entanglement is fundamental, it should also persist in a relativistic description. Here, we consider a spin-1/2 particle in a superposition of two different velocities as viewed by an observer in a relativistically boosted inertial frame and show that the entanglement between the two velocity modes survives right up to the speed of light. We also discuss how quantum gates could be implemented in this way and apply our results to the case of a superconductor. In particular, we show that an sss-wave superconductor would have ppp-wave components for a boosted observer.
Some physicists believe that superselection rules should be implemented to get rid of inconsistencies when a theory is framed in terms of a new mathematical formulation, whilst others think that this new formulation should be modified instead of implementing those rules, at the expense of introducing additional mathematical structure. The outcome, however, is that we are still uncertain whether these rules should be implemented and how they should be interpreted and assessed from the philosophical point of view. Based on a detailed examination of the group-theoretic reformulation of (relativistic and non-relativistic) quantum mechanics that prompts physicists to impose superselection rules, I shall argue that the implementation of these rules involves serious heuristic and epistemological concerns. Considering this argument, I shall conclude that there are suitable philosophical reasons to claim that the implementation of superselection rules should be rejected and that there are certain circumstances when the formulation of a theory should be modified.