Review of N. David Mermin; There is no quantum measurement problem. Physics Today, 2022
Summary:
The author examines the question of whether or not there is a quantum measurement problem (QMP). As the title suggests, he claims there is none. Mermin first includes a section in which he categorizes quantum physicists in terms of their beliefs regarding the measurement problem as well as discusses whether or not probability is an objective feature of nature, a section that he calls “The quantum measurement problem” and a third section entitled, “Keep the scientist in the science”.
Review:
Mermin classifies quantum physicists into three categories which can be restated as: (1) those who think quantum mechanics has a measurement problem; (2) those who think, as Mermin does, that there is no measurement problem; and (3) those who think the issue is not worth serious thought. One would think in dividing the set of physicists into categories, that the sets defined would represent a partition of the physicists. Yet, consider a physicist in category (3) who thinks the issue is not worth serious thought. A physicist in this category would logically also think there is no measurement problem. Then such a physicist would be in (2) and (3) simultaneously. Hence the categories as defined by Mermin do not represent a true partition of the set of physicists.
A partition can be formed as follows: (1) those who think quantum mechanics has a measurement problem; (2) those who think that there is no measurement problem or that the issue is not worth serious thought. Now, it is reasonable to expect, that physicists only consider something to be a problem if its resolution provides some additional predictive power over the current theory. Therefore, we can further simplify the categories to: (1) those who think that resolution of the quantum measurement problem can provide more predictive power than the current theory, and (2) those who think that resolution can’t. Let us for the remainder of this review utilize this simplified set of categories
After shortly introducing his categorizations, Mermin states, “Quantum mechanics is inherently statistical. There is no deeper underlying theory that gives a fuller description.” However, with our new categorizations, one can see clearly that if you accept Mermin’s statement, this implies that everyone now must be in our Group 2, ipso facto! We agree that “no deeper underlying theory” implies “no measurement problem”. One doesn’t need to read the remainder of the paper to understand Mermin’s position, it becomes crystal clear after only Mermin’s second paragraph of the paper.
Now that we have narrowed the main crux of Mermin’s paper to a single tangible issue that can be addressed, the real question on the table is whether or not resolution of the quantum measurement problem can or cannot have more predictive power than the current quantum theory, assuming the two postulates of quantum theory are correct. In order to examine this further, let us examine the true historical definition of the quantum measurement problem. The modern-day measurement problem arose when Einstein provided a letter to Schrödinger detailing the possibility of a charge of gunpowder being in a superposition of having blown up and not blown up [1]. Later Schrödinger wrote the well-known paper [2] where the Schrödinger-Cat paradox arose, stating:
When two systems of which we know the states by their respective representatives, enter into temporary physical interaction due to known forces between them, and when after a time of mutual influence the systems separate again, then they can no longer be described the same way as before, viz., by endowing each of them with a representative state of its own. I would not call that one but the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought. By the interaction the two representatives (or psi-functions) have become entangled
In the original measurement problem as explained by Schrödinger, it isn’t specified where the measurement occurs nor the mechanism of the measurement. One is only left with the understanding that after interaction, quantum systems become entangled. Now, one can continue this reasoning and obtain the prediction that either a cat will ultimately be in a superposition of being dead and alive simultaneously or more precisely, being in a superposition of the entangled state of (alive with no poison molecules) and (dead with poison molecules). So, as Einstein expected and Schrödinger himself raised, it seems there is a problem with his equation. The measurement problem fundamentally arises because Schrödinger’s equation predicts entanglement and was supplemented by a projection or measurement postulate by von Neumann. The question then emerges as to whether the projection postulate is indicative of a physical process, separate from Schrödinger’s unitary evolution, or not. Initially, Schrödinger considered the entanglement between two interacting systems and illustrated the entanglement that can result after interaction. We have proven in our book [3, Ch. 3] , that the Schrödinger equation’s predicted entanglement continues to exist, regardless of the detector size. Hence an obvious hypothesis to form is that there is another physical process at work that is distinct from Schrödinger’s process, since Schrödinger’s equation could not have accounted for the result using standard scientific methodology. Now, our work in [3, Ch. 3] is not a conjecture, nor hypothesis, it is a rigorous proof and there is no manner in which Mermin or anybody else will ever be able to produce a tangible scientific model using Schrödinger’s equation alone.
Yet, tangible models are the cornerstone of engineering and science. If a civil engineer builds a structure, a mechanical engineer creates a device, or an electrical engineer designs a circuit, they all use known methods based on physics. Additionally, they can simulate the device and see how it will perform in a variety of conditions. In science one typically finds experimental observations of new or novel phenomenon compared side-by-side with theoretically expected results. That is, the main use of theory is to make predictions necessary to design, evaluate, improve across broad disciplines of engineering and science.
On the other hand, if one believes Schrödinger’s equation is universally correct and accounts for measurement, then, as this is an equation and equations are found in nearly every branch of engineering and science, one can surely show us at least an approximate model based on such an equation that predicts measurement. Hence, we would expect Mermin to propose a quantum model of system plus detector with a joint Hamiltonian as is done in nearly every paper in theoretical quantum mechanics, and work through it to show that Schrödinger’s equation does provide the product state results required of the measurement postulate. However, Mermin does not do this. Why? We expect it is because he is well-aware that he can’t without resorting to superdeterministic theories! That is, this is indeed a major problem that cannot be resolved by Schrödinger’s equation alone. Yet, Mermin makes no effort to present this fact in Physics Today, which is quite remarkable and appears to us a failure of the American Institute of Physics to present a balanced scientific viewpoint on this subject. Rather than attempt to propose such a model, Mermin does not mention this extraordinary shortcoming, but instead puts forward the narrative that whether or not a separate process exists for measurement, the issue is still a mute scientific issue. How does he do this? Mermin states in the 2nd section of the paper:
The measurement problem stems from the two ways of viewing a measurement: the system alone or the system + apparatus. If the system alone is measured, its state collapses. But the state of the composite system + apparatus does not collapse until the apparatus is examined. Which description is correct?
This definition that Mermin makes of the QMP is clearly not a description of the original problem as proposed by Schrödinger, but rather a proposed characterization of the QMP. The word “entanglement” which Schrödinger was clearly concerned about is nowhere to be found in Mermin’s article. How is that possible? Mermin in this regard has already stated as fact in his 2nd paragraph that “There is no deeper underlying theory that gives a fuller description”. In other words, Mermin is claiming here that nobody can hope to resolve the measurement problem in any meaningful scientific manner, i.e. that the best one can hope for are philosophical interpretations. The rationale is given earlier in the paper where Mermin states:
So as far as probabilities are concerned, it makes no difference whether one applies quantum mechanics to the original system alone or to the composite original system + apparatus.
The only argument that we can see being made by Mermin to justify his general claim that there is no measurement problem is that it makes no difference where the collapse postulate is applied and hence the problem cannot be hoped to be resolved. This argument was originated by von Neumann in his well-known von Neumann chain argument.
The question we will now address is whether von Neumann’s chain argument is necessary and sufficient to establish that the two postulates he proposed are complete in the sense that it can form the basis of a new theory that encompasses the theory of measurement that resolves the measurement problem, and offers more predictability than the current theory. Interestingly, von Neumann was aware there could be self-contradiction between the two postulates. He states in [4, p. 420],
The dual form is therefore justified. However, the danger lies in the fact that the principle of the psycho-physical parallelism is violated, so long as it is not shown that the boundary between the observed system and the observer can be displaced arbitrarily.
It might be confusing to understand von Neumann’s statement because of the sentence structure and as well as the use of the term psycho-physical parallelism. What is meant by this is that the two postulates are self-consistent as long if it can be shown that the statistics of the observation are the same, independent of where the projection postulate is applied in the chain of interactions. The chain being the system, the system plus apparatus, and eventually the system, plus apparatus plus local environment, continuing on-and-on ultimately leading to the system through the level where an observer becomes conscious of the measurement result.
That is, so long as the statistics of the observer are independent of whether the projection occurs directly on the system, to the apparatus, or only at the level of the conscious observer, then the two postulates are self-consistent. If this is true, von Neumann believed the issue would be mute, so that there would be no measurement problem. So let us examine what von Neumann went on to prove.
It was proven by von Neumann in [4, pp. 439–445] that if one considers a macroscopic detector or apparatus that couples with the quantum system via a measurement model that von Neumann proposed using Schrödinger’s equation followed by projection, there is no observable consequence if one projects anywhere between the system and where an observer becomes aware of the results. This shows for the measurement model that von Neumann considered, the position where measurement occurs can be shifted anywhere between the apparatus and the consciousness of the observer, without any changes in the statistics that the observer finds.
Conclusions
It is impossible to obtain, in a scientifically acceptable manner using Schrödinger’s equation, the product states found when measurement occurs. All newly discovered physical processes that we are aware of historically are capable of being either directly or indirectly verified and further investigated both theoretically or experimentally. For example, the manner in which gravity acts on two different masses to accelerate at the same time was shown in an experiment in the late 1500s by Galileo and formalized theoretically by Newton’s theory. Consider Kepler’s laws of planetary motion, Newton’s laws of motion, Maxwell’s equations of electromagnetism, the photoelectric effect, Einstein’s special relativity and general relativity, and this list is only the beginning. In fact, all successful new theories that we are aware of throughout the history of mankind generally have been experimentally verified. The claim that Mermin makes is rather extraordinary in this sense that if it were true, it would imply an exception to all scientific discoveries of the past.
Historical precedents dictate the primary hypothesis that there exists a physical process, distinct from the unitary process of Schrödinger’s equation, that governs the measurement process. Rather than provide a model for a physical process that can explain measurement using Schrödinger’s equation (which he can’t), it is claimed by Mermin that the measurement process cannot be formally or experimentally completed beyond the current two postulates. Yet the two postulates certainly do not appear to be complete in that they simply assume that measurement has occurred and furthermore assume measurement occurs in a particular basis for which no methodology is provided to determine the basis. There are clear major unresolved issues that remain such as the specific prediction of the conditions under which measurement occurs and the measurement basis that occurs. These issues need to be resolved before quantum theory can be claimed in any manner to be complete. On the other hand, if there is something preventing the scientific community from completing the theory and Mermin’s claim is indeed true, it would represent a radical departure of all prior major historical scientific discoveries. History is not on Mermin’s side.
A major issue in Mermin’s arguments appears to be directly related to the issue of whether or not von Neumann’s proof of the arbitrariness of the shift implies that the two postulates of von Neumann cannot be further investigated both experimentally or theoretically to provide more predictive power than the current conventional theory. In order to answer this question requires analyzing the issue in more detail and this will be presented in an upcoming paper [5] on the implications of von Neumann’s chain theorem. It will be seen that von Neumann’s chain theorem cannot be used to bolster Mermin’s position and Mermin’s arguments regarding the non-existence of a measurement problem are utter nonsense.
There is a quantum measurement problem, of that there is no doubt!
References
[1] A. Fine, The Shaky Game: Einstein, Realism and the Quantum Theory. Chicago,: University of Chicago Press, 1986.
[2] E. Schrödinger, “The present situation in quantum mechanics,” Naturwissenshaften (English translation in Proceedings of the American Philosophical Society vol 124), vol. 23, pp. 802–812, 1935.
[3] M. Steiner and R. Rendell, The Quantum Measurement Problem. Inspire Institute, 2018.
[4] J. von Neumann, Mathematical Foundations of Quantum Mechanics. Princeton, NJ: Princeton University Press, 1955.
[5] M. Steiner and R. Rendell, “Discrimination of Unitary Evolution and the Measurement Process: Theory and Implications,” (submitted for publication, 2026).