Review of J. R. Hance and S. Hossenfelder, What does it take to solve the measurement problem?, J. Phys. Commun. 6 102001 (2022)

Summary:

The question is considered of whether or not the measurement problem is strictly a philosophical problem resolved by an interpretation, or a real problem requiring further scientific investigation.  This question is still being debated in the literature and a recent paper [1] is cited by Mermin published in Physics Today that claims there is no measurement problem. The authors conclude that the problem is a real problem and not resolvable by an interpretation. They go on to propose requirements that a solution would need to fulfill in order to consider the measurement problem resolved. 

In Section 1 a short introduction is given. Basic axioms of quantum mechanics are given in Section 2 such as the invocation of Schrödinger’s equation unless a measurement occurs for which Born’s rule is utilized. In Section 3 problems are presented that are associated with the incompleteness of the basic axioms. In particular, the lack of a definition of what physically constitutes a measurement device. This definition of a device should give some ability to describe where the Heisenberg cut is placed.  The authors discuss the problem with Schrödinger’s equation providing an explanation of classical bodies.  The entanglement of Schrödinger’s equation does not appear to persist and the h→0 limit of quantum mechanics is claimed not to reproduce classical mechanics such as for chaotic systems. Issues with locality, causality, conservation laws, and gravity are considered.  In Section 4, five requirements are presented that a proposed solution to the measurement problem should meet: 1) agree with all existing data, 2) reproduce current quantum theory in a well-defined limit, 3) explain what constitutes a measurement device, 4) reproduce classical physics in a well-defined limit, 5) resolve the inconsistency between the non-local measurement collapse and local stress-energy conservation. This last issue is related to the so far inability to produce a theory of quantum gravity.  The authors discuss the properties that a solution has. They propose in one possibility that the wavefunction evolves via Schrödinger’s equation and is updated via Born’s rule but is an incomplete description in the sense that there is an additional component or hidden variables needed to specify the physical state that evolves locally. The second possibility is that the wavefunction is a complete description but evolves via a local non-deterministic law. A third possibility is proposed as some combination of the first and second possibilities. Various prior solution attempts are discussed in Section 6 such as decoherence theory and many worlds theory. In Section 6 issues of statistical independence of hidden variables is discussed and in Section 7 the authors briefly address the issue of what could a solution to the quantum measurement problem be useful for.

Strengths:

1. The authors are one of the few that we have seen that have an excellent understanding of the measurement problem.  
2. An axiom is proposed that a system evolves according to Schrödinger’s equation until measurement occurs for which the evolution occurs according to Born’s rule.  This is actually different than von Neumann’s theory and if true would be a significant advancement.
3. Proposed requirements are given that a theory must meet to be considered a solution to the measurement problem, chiefly among them that the theory provide an explanation as to what constitutes a measurement device.
4. The authors examine what uses a solution to the quantum measurement problem potentially have.  This is novel and interesting and the authors predict that a solution would:
   • Improve understanding in which cases a measurement process occurs
   • Would almost certainly improve our ability to control quantum states
   • Possibly have technological applications.

Weaknesses:

1. The wording “classical limit” is utilized but not defined.  What precisely is meant by classical?  Are all deterministic equations classical? If so, isn’t Schrodinger’s equation classical? We expect in the manner that the authors use the term classical, that deterministic equations that were found prior to Maxwell’s equations such as Newton’s, Bernoulli’s, etc. equations that apply to macroscopic systems are classical. Note that defining classical in this manner is hardly a good definition of “classicality”. Are all macroscopic systems classical? If so, do we currently know if consciousness that may consist of a large number of particles, is a classical system? By many accounts consciousness is rather non-classical. A definition of “classical” appears to us to be necessary in order to follow the authors arguments in a rigorous manner.  At present, it isn’t clear to us what conclusions can be truly drawn when the authors use the term classical and it is left undefined. This is a minor weakness.
2. Requirement 1, 2, and 4 are all related to reproduce the results of what is currently expected in theoretical and experimental physics.  It seems to us these three requirements could have been compressed with some additional effort into a new single requirement which would have made the solution requirements simpler.
3. Requirement 5 requires that the inconsistency between the non-local measurement collapse and local stress-energy conservation be resolved.  While this is an admirable additional task to assign to those slaving away at a solution, if a theory were successful in meeting Requirements 1-4, we would say hat’s off and the measurement problem is solved. In such a case, we would argue that Requirement 5 becomes a secondary requirement to be met. That is, Requirement 5 is not a primary impediment to the measurement problem’s solution but rather a secondary requirement to be considered after Requirement 1-4 are satisfied. Even now, there are problems with QED such as infinite self-energies and issues when there are interactions, but these are secondary issues and QED has been utilized successfully to make a huge number of predictions.  Certainly, if one can propose a solution that meets all Requirements 1-5 at the same time, yippee ki yay. But don’t expect that to happen.  On the other hand, one could argue that this is nitpicking on our part, which we would agree, and so is a minor weakness of the paper.

Relationship to other work:

1. The authors do not fully justify their claim that unitary theory alone does not suffice to explain the result of measurements.  We feel further justification of this point would have improved the presentation. In our book [2], Chapter 3, we show that unitary theory combined with the known results of measurements shows a contradiction for which unitary predicted entanglement can be unitary distinguished from measurement. Furthermore, the problem does not go away in the limit as the number of particles increases.  On the other hand, this is a minor weakness as we believe the authors’ conclusions are correct in that this implies that there is a real measurement problem that is not resolvable by strictly an interpretation. 
2. In our book, we also proposed requirements that a solution to the quantum measurement problem must meet.  Our requirements are different in several details than proposed in this work and we are in the process of extending that work. However, both have in common the most important aspect that has been largely overlooked by the physics community which is that a solution to the measurement problem must show what constitutes a measurement device.

Conclusions:

In recent years, theory on the measurement problem has often been constrained to publications in philosophy.  Many mainstream physics publications had avoided the measurement problem because of a lack of understanding of whether or not the problem is simply a philosophical problem requiring an interpretation or a real problem requiring new physics and experiments.  The overall majority of philosophical papers that we have seen have focused strictly on interpretations and it appears to us that an overwhelming majority but not all philosophers who are engaged in this issue have provided specious arguments and convinced themselves that the problem only requires an interpretation for its resolution. This is without a doubt, wrong.  Because of this, progress on the measurement problem has severely lingered because of the lack of understanding of the detailed physics of the quantum measurement problem by many philosophers and even some well-known physicists such as Mermin [1].

The authors have an excellent understanding of the fine details of the quantum measurement problem. Based on their understanding, they have published in a journal for the first time a set of physics requirements that a theory must meet to be considered a solution to the measurement problem (though a set of requirements have previously appeared in book form [2]).  These important requirements are bringing people to the understanding that the measurement problem requires a serious physics investigation. The requirements, when met will be expected to be relevant to the understanding of new fundamental physics. Additionally, such new understanding of the physics of quantum measurement can be expected to open new doors in other areas and perhaps provide major technological advancements, similar to that achieved through quantum mechanics and quantum information.

[1]         N. D. Mermin, “There is no quantum measurement problem,” Phys Today, vol. 75, no. 6, pp. 62–63, Jun. 2022, doi: 10.1063/PT.3.5027.

[2]         M. Steiner and R. Rendell, The Quantum Measurement Problem. Inspire Institute, 2018.