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Do We Have any Viable Solution to the Measurement Problem?

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Abstract

Wallace has recently argued that a number of popular approaches to the measurement problem can’t be fully extended to relativistic quantum mechanics and quantum field theory; Wallace thus contends that as things currently stand, only the unitary-only approaches to the measurement problem are viable. However, the unitary-only approaches face serious epistemic problems which may threaten their viability as solutions, and thus we consider that it remains an urgent outstanding problem to find a viable solution to the measurement problem which can be extended to relativistic quantum mechanics. In this article we seek to understand in general terms what such a thing might look like. We argue that in order to avoid serious epistemic problems, the solution must be a single-world realist approach, and we further argue that any single-world realist approach which is able to reproduce the predictions of relativistic quantum mechanics will most likely have the property that our observable reality does not supervene on dynamical, precisely-defined microscopic beables. Thus we suggest three possible routes for further exploration: observable reality could be approximate and emergent, as in relational quantum mechanics with the addition of cross-perspective links, or observable reality could supervene on beables which are not microscopically defined, as in the consistent histories approach, or observable reality could supervene on beables which are not dynamical, as in Kent’s solution to the Lorentzian classical reality problem. We conclude that once all of these issues are taken into account, the options for a viable solution to the measurement problem are significantly narrowed down.

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Notes

  1. We note that there are a class of ideas sometimes mentioned in connection with the interpretation of quantum mechanics, like retrocausality [5] and superdeterminism [6], which are not in and of themselves solutions to the measurement problem: they don’t say anything in particular about the emergence of our shared observable reality, rather they are simply properties that a solution to the measurement problem may or may not have (for example, the transactional interpretation [7, 8] is a solution to the measurement problem which has the property of being retrocausal). So we will not have much to say about these ideas in this article—not because there is anything wrong with them, but because they are not answers to the questions we are addressing here.

  2. Incidentally, this point illustrates why older versions of the Everett interpretation, which postulate precisely defined worlds or minds in addition to the wavefunction, must inevitably yield to the modern emergence picture [31]: as soon as the Everettians provide a prescription to make their worlds precise, they lose their most crucial advantage.

  3. The postulate of cross-perspective links may sound somewhat ad hoc, but it can to some degree be justified on the grounds that RQM is intended to be a physicalist appraoch and thus Alice’s conscious awareness of seeing a definite value of some variable must supervene on some physical variable of Alice which should be accessible to Bob by the right kind of measurement. Ultimately we might hope to have a more constructive account of the nature of this variable and the way in which Bob accesses it, but the postulate at least serves to indicate what kind of structure must be added to an orthodox interpretation if we are to arrive at a SWR approach.

  4. Thanks to Carlo Rovelli for this suggestion.

  5. Quantum gravity is not the main topic of this article, but it’s worth nothing that if we take this approach one might think the same problem would re-emerge when we move to quantum gravity—many physicists believe that spacetime itself is only approximate and emergent in quantum gravity, so if ‘systems’ are defined in terms of regions of space then systems are still approximate and emergent when we get to quantum gravity. However, perhaps there might be a way to understand a ‘system’ as some subregion of whatever substratum underlies spacetime in quantum gravity (e.g. a single node or set of nodes in a spinfoam) with these subregions becoming regions of spacetime in an appropriate limit.

  6. Or we could insist that spacetime is in fact discrete and hence there is not a continuum of possible bases, in which case it is more plausible that Bob could manage to reliably measure Alice in the exact basis corresponding to the outcome of her measurement. In fact RQM is often linked with loop quantum gravity, which does indeed tell us that spacetime is discrete, so this route could make sense.

  7. A time-evolution formulation of the Einstein equations does exist [64, 65], but the original global formulation remains central to research in the field and there seems no obvious reason to think that the time-evolution formulation must be more fundamental.

  8. Kent also makes allowance for the possibility that there is no end of time—in this case we simply take a limit as \(t \rightarrow \infty\), making some assumptions which ensure that the limit is well-defined.

  9. Although for all practical purposes we can assume that macroscopic measurement outcomes will be recorded in the final state and thus the dependence on the future doesn’t get in the way of applying the framework to real experiments.

  10. The need for two selection steps is admittedly somewhat clunky. It would be preferable to combine these steps in some way, or perhaps we could eliminate the first step altogether by invoking something like Chen’s quantum Wentaculus [77]. This approach prescribes a unique initial state, so the laws of nature single out a unique multiverse. Then just as in the Newtonian case we would have a single selection step, except that this step would be probabilistic rather than arbitrary.

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Acknowledgements

Thanks to Carlo Rovelli and Adrian Kent for some interesting discussions on topics covered in this paper. This publication was made possible through the support of the ID 61466 grant from the John Templeton Foundation, as part of the ”The Quantum Information Structure of Spacetime (QISS)” Project (qiss.fr). The opinions expressed in this publication are those of the author and do not necessarily reflect the views of the John Templeton Foundation.

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Adlam, E. Do We Have any Viable Solution to the Measurement Problem?. Found Phys 53, 44 (2023). https://doi.org/10.1007/s10701-023-00686-x

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