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Stochastic field dynamics in models of spontaneous unitarity violation
by Lotte Mertens, Matthijs Wesseling, Jasper van Wezel
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Submission summary
| Authors (as registered SciPost users): | Jasper van Wezel |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202312_00001v2 (pdf) |
| Date submitted: | 2024-02-22 16:16 |
| Submitted by: | van Wezel, Jasper |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrodinger’s equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born’s rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born’s rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.
Author comments upon resubmission
We are grateful to the referee for their positive evaluation of our manuscript, and for their constructive remarks.
Below, we reply to the individual points raised in the referee report:
1) We thank the referee for the suggestion and are happy to add additional discussion of this point in the revised manuscript. 2) In the revised manuscript, we added the brief explanation proposed by the referee. 3) We thank the referee for pointing out the lack of clarity here, and add a more detailed discussion of the role of Born's rule to the revised manuscript. 4) As suggested, we add an explanation of how violations of Born's rule allow for faster than light communication. 5) We thank the referee for the suggestion, but think this is a matter of taste. Since BJN and JN are the actual energy scales defining the time evolution operator, we prefer to use these. 6) We agree with the referee that equations 9 and 10 are equivalent to equations 2 and 3 after implementation of consistency constraints on the parameters lambda and a. We emphasize this in the revised manuscript. 7) We thank the referee for the question. "Weak" in this case has the same meaning as in the usual theory of spontaneous symmetry breaking: it refers to anything beyond the limit of practical control. We add a brief explanation of this point in the revised manuscript. 8) We thank the referee for their kind words. 9) We checked the revised manuscript for spelling errors.
Once again, we thank the referee for their helpful input and positive evaluation.
List of changes
See above