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Review of Franklin, Alexander, and Seifert, Vanessa. “The Problem of Molecular Structure Just Is the Measurement Problem.” The British Journal for the Philosophy of Science, volume 75, number 1, March 2024 doi: 10.1086/715148.

Summary

The authors consider three unresolved issues in deriving molecular structure using quantum mechanics.  They claim that these problems are directly related to the resolution of the quantum measurement problem. The Hund problem of chirality is that molecules of a particular chirality are typically observed rather than superpositions of molecules with a definite chirality.   The second problem concerns isomers which are molecules that have the same atoms, but bonded in different configurations.  If one considers the general Coulombic Hamiltonian of an isolated molecule, which the authors refer to as the resultant Hamiltonian, it is noted that the ground state would be a superposition of the various possible isomers.  On the other hand, it is claimed that no superpositions of isomers are observed in reality. Moreover, there is no clear path to start with the resultant Hamiltonian to derive using standard quantum mechanics the particular configurations that represent isomers.  The third problem identified is that of symmetry breaking.  Here it is said that molecules are found in particular configurations such as ammonia with the nitrogen either found on top of the hydrogen’s or at the bottom of the hydrogen’s but are not found in a superposition.  In Sec. 3 the authors claim that the problems of molecular structure are just special cases of the quantum measurement problem (QMP) as defined by Maudlin in  [1], “the problem of outcomes.”  In Sec. 4 the authors examine various quantum interpretations, such as Everett’s many worlds theory and Bohm’s theory in the expectation that one or more of these will explain where molecular structure comes about.

Strengths

  1. The authors bring attention to the possibility several problems in molecular structure that have not been resolved within standard quantum theory.  These are the problem of chirality, existence of specific isomers, and symmetry breaking. 
  2. The authors bring attention to the possibility that these three problems in molecular structure are related to the QMP.  If one considers that a resolution to the QMP should explain how a large quantum superposition is further reduced to one of the many terms in the superposition, then it is reasonable to investigate whether resolution of the QMP has application to the three problems of molecular structure. 
    • That is, the problem of chirality is that a superposition of left and right chirality is not typically seen; resolution of the QMP is proposed as a solution since a measurement projection process might project a superposition of chirality to a definite chirality of right or left. 
    • Similarly, when one considers the resultant Hamiltonian of a number of atoms, there is no clear path to yield particular specific isomers.  The ground state wavefunction of the resultant Hamiltonian is claimed, “corresponds to a superposition of all the different isomers.”  If this is the case, then the resolution of the QMP could provide a measurement projection process that projects the superposition of the different isomers to a single isomer.
    • When one considers that many molecules are typically observed in a particular configuration such as the ammonia molecule with the nitrogen either at the top or bottom of the hydrogens, the question of why this is so, if the eigenstates of the Hamiltonian are typically superpositions of the molecule.  If a quantum measurement process exists, this could potentially project the molecules to one of the two configurations, breaking the symmetry of the eigenstates of the configurational Hamiltonian.

Weaknesses

  1. Our main concern of this paper is how conclusions are being drawn in this paper. As we take a critical look at the reasoning that is being used to draw conclusions, we believe sufficiently rigor is not always given to be drawing scientific conclusions.  Perhaps it is sufficiently rigorous to be drawing philosophical conclusions.  There seems to be nothing wrong with philosophical reasoning when one argues about ontology or the many various concepts that philosophers deal with. And if the measurement problem was mainly a philosophical problem in that only interpretations are needed to resolve the problem, then we would not be writing this review.  In our view, the measurement problem is primarily a scientific problem whereby its resolution we expect to result in a new quantum theory that is a significant extension of its current form.  Therefore, we believe that the QMP requires a rigorous scientific approach to advance the theory toward resolution. 
  2. Eqn. (1) is incorrect, |+>=(|L>+|L>)/Sqrt(2) should be |+>=(|L>+|R>)/Sqrt(2)
  3. The statement is made, “The paradox stems from the fact that a chiral molecule is always observed as either right-handed or left-handed.” However, no scientific proof of this statement is given. How about “The paradox stems from the fact that chiral molecules have been reported in the literature as either right-handed or left-handed, and we know of no experiments to-date that have reported a superposition of chirality.”
  4. The statement is made, “One way to understand this observation is that the ground state wavefunction of the resultant Hamiltonian corresponds to a superposition of all the different isomers.”  While this might be true, a derivation of this or at least a reference where it is derived would seem to be needed to establish this scientifically.
  5. The statement is made, “Yet, only individual isomers are directly observed.”. How do we know this is always the case? How about, “Yet that we are aware of, only individual isomers have been experimentally observed to-date.” Now, perhaps there are those that feel we are splitting hairs.  However, suppose in the future a Nature paper comes out with the title, “A superposition of two isomers observed.” In the abstract it says, “For the first time, we report on our finding of outstanding scientific importance, of the creation of two isomers in a superposition.  It is found theoretically and confirmed experimentally that the superposition can exist below a critical temperature for which environmental decoherence does not break apart the superposition”. Then, the statement “Yet, only individual isomers are directly observed” would have been demonstrated experimentally to be wrong.  The point is, the statement, “Yet, only individual isomers are directly observed” is in a logical sense, potentially falsifiable.
  6. The statement is made, “A notable feature of this case is that the prediction and observation of tunnelling between the two orientations requires that we take the symmetric superposition state seriously as a representative of the quantum system. However, any particular observation is always of an asymmetric system with a particular orientation.” This is not at all obvious to us.  Although we are not experts on maser design, it has been noted that Ammonia masers operate using eigenstates of the Hamiltonian.  In the on-line notes  it is stated “The principle of an ammonia maser is to isolate the molecules that are in the first excited state, and then to harvest the radiation that is emitted as the molecules decay to the ground state.” So, it appears to us that such superposition states are utilized in maser transitions and we don’t understand why ammonia represents an example of symmetry breaking.  
  7. It appears that all three cases that have been claimed by the authors to not occur in a superposition, are potentially falsifiable.  One might argue that such falsifiability typically does not occur in quantum theory. However, there are notable exceptions.  For example, when considering quantum transitions between states of an atom using the Bohr and Einstein models, the photon energy that is emitted or absorbed is directly related to the energy eigenvalues of the matter which is the atom.  On the other hand, it was predicted by Jaynes-Cummings that if one puts an atom in a cavity, superposition eigenstates result that are a superposition of both the number of cavity photons and the original matter eigenstates.  An experiment was then performed  [2] in 1992 which confirmed the Jaynes-Cummings splitting of the matter eigenstates. Hence, while typically one does not observe superpositions of light and matter eigenstates, it is possible to occur.  So simply because some phenomenon hasn’t been observed to-date does not logically imply that it won’t be in the future.  Therefore, it would seem to us that if one were to make the claim that ammonia masers operate with a particular orientation and not in superposition, the ammonia maser would have to rely on a semiclassical principal of operation.  Essentially, jumps between the two orientations would have to periodically occur.  While this is an interesting possibility, one can formulate and conduct experiments to discriminate these two cases and thereby falsify one of the two possibilities—i.e. that the ammonia is always in one configuration with nitrogen at the top or the other, and performs jumps to make a transition, or that the ammonia can evolve unitarily into a physical superposition.  It seems to us the most likely scenario is that ammonia does exist as an actual superposition at least when operating in a maser configuration since these superposition eigenstates with different energies are found to create resonances.  Now, the authors also point to biological sugar molecules as symmetry breaking.  Maybe, but maybe not, particularly if the time for tunneling transitions is predicted to be very long. 
  8. The authors, based on Maudlin’s definition of the QMP, examine several quantum interpretations which they think can resolve the issues they raised on molecular structure.  The authors, in our view, do not have an understanding of what is required to resolve the QMP. The authors refer to the definition of the measurement problem given by Maudlin.  Maudlin’s definition in our view is too restrictive. The current quantum theory is based on two distinct von Neumann postulates, a measurement and unitary postulate. With the advent of quantum information, there has been substantial progress made regarding entanglement.  In Chapter 3 of our book, it is proven that the entanglement predicted by Schrödinger’s equation cannot account for measurement outcomes. The result is independent of the number of particles in the detector, i.e. the result holds for macroscopic systems. Hence one cannot obtain measurement results by Schrödinger evolution alone.  This shows that there is as-yet something unknown that is needed to account for measurement results and shows the necessity of having at least two distinct postulates.
    • Additionally, in applying these postulates there is an inherent assumption made that one knows whether or not a measurement has been made, and also that the precise operators that represent the measurement operation are assumed known. However, whether or not a measurement is made as well as the particular measurement operation that is occurring, can be experimentally investigated using tests that can discriminate measurement from Schrödinger’s equation.  Hence the current quantum theory is incomplete, as further experimental investigation of the root cause of measurement is possible within the current formalism! The existence of two postulates, while being necessary to explain both measurement and Schrödinger evolution, do not appear to be sufficient without augmentation to explain all quantum phenomenon. Our view is that with time, as more is learned both through new theory and new experiments, the current theory will be replaced with a more complete formulation. 
    • This allows us to define a stronger version of the problem, what we call the physical measurement problem.  In the physical measurement problem, the what, when, and why (WWW) of the physics of measurement must be determined to resolve the measurement problem. Note that philosophical quantum interpretations such as Bohm’s theory that are considered in this paper do not come close to resolving the measurement problem as we have defined it. These interpretations ultimately assume that a measurement is known to have occurred a posteriori i.e. after it occurred, in the manner of von Neumann’s two postulates, and then offer some explanation for it.  Such explanations provided no additional predictive power beyond the two postulates. Such explanations are interesting philosophically, but it is less clear what scientific use they have.
    • How does one know a measurement has even occurred and what operation has occurred? The two von Neumann postulates explain “what” to do, when a particular measurement is known a posteriori to have occurred and known a posteriori to have occurred in some particular basis.  The postulates fail to explain “when” and “why” the measurement has occurred in that particular basis.  When do measurements start occurring and why do they occur? What determines the measurement operation?  These questions are necessary to answer how to understand the root causes of measurement.  The conditions for which measurement occurs and the physics behind why it occurs are, in our view, the modern-day measurement problem, not proposing and comparing various interpretations and evaluating them based on philosophical concepts such as ontologies.
    • Other than super-deterministic theories which have been criticized as unscientific and spontaneous localization theories which typically do not conserve energy, there is currently no physical theory that has been put forward that resolves the measurement problem as we define it.
    • One might ask why would von Neumann make such assumptions in his postulates? One possibility is that von Neumann attempted to put the views of Bohr in a mathematical framework. Bohr also didn’t think any more could be predicted regarding the precise space-time evolution of the particles during the interaction between a quantum system and a macroscopic measurement device.  The very act of measurement for Bohr meant an uncontrollable interaction that necessitates resorting to a noncausal or statistical approach for a meaningful description, which he believed was enforced by the uncertainty principle.   The theory according to Bohr would therefore require a complementary description with the two modes of causal unitary evolution and resorting to a statistical non-causal approach when measurements are occurring.
    • Is Bohr’s complementary description, correct?  We believe partially correct, because the conditions expressed in the two postulates are necessary conditions that must be imposed on any resolution of the QMP. Does Bohr’s complementary description justify that no further progress can be made on the physics of the measurement process? No, because both Bohr and also von Neumann made additional (although different) assumptions in reaching their conclusions regarding the completeness of the theory. It is not guaranteed that the postulates are sufficient to explain all quantum phenomenon.  This will be explained in detail by us in future papers on 1) why the Copenhagen interpretation is incomplete and 2) on the implications of the von Neumann chain theorem. Essentially there is no logical rationale for the claim that these two postulates are complete. As well, the measurement process can still be investigated both theoretically and experimentally and progress on the WWWs of the QMP will inevitably occur.
    • Advertisement: If you still can’t understand this, why not purchase our book where we explain this in more detail? If on the other hand, if you don’t agree with what we’re saying and have no desire to purchase our book, we can’t help you further.  In this case, perhaps consider  Sir Roger Penrose.
  9. The authors utilize the definition of Maudlin of the QMP for which the QMP can be solved by various interpretations such as Bohm’s theory  [3]  However, in light of our viewpoint in Point 8. above, Maudlin’s definition of the problem that the philosophers are quoting in this paper, as well as other philosophers such as Lewis  [4], are defined in an overly restrictive manner, are outdated, and should be updated.  The key is to realize that the von Neumann postulates impose necessary conditions i.e. because von Neumann assumed that measurement has occurred and assumed the basis was known for the measurement. However, by making such assumptions one now has to admit that such postulates may not have sufficient strength to fully describe quantum phenomenon.  One cannot just assume that measurement has occurred as well as the basis and formulate what to do in such a case, and expect the theory to be complete in terms of predictability of all quantum phenomenon.  At the very least, one would have to further justify that such assumptions still render the postulates necessary and sufficient for prediction of all quantum phenomenon. On the other hand, if you strongly believe that these two postulates are clearly and undoubtedly necessary and sufficient for the description of all quantum phenomenon, we would like to talk to you about purchasing an old bridge we own in New York.
    • Certainly, if Maudlin’s definition of the QMP was adequate, we could understand the authors’ attempts to solve the problems of molecular structure by analyzing how the structure comes about by, for example, Many Worlds theory.  But we don’t agree that this definition is adequate to capture the essence of the QMP and that therefore the attempt to utilize quantum interpretations to resolve difficult issues of molecular structure is, in our view, dubious.

Relationship to other work

In  [5] this paper is also critically examined. Some of our comments overlap with that in  [5] such as the importance of how the measurement basis occurs in the QMP.

Conclusions

The authors bring to attention three problems of molecular structure for which no clear path exists to derive the solution within standard quantum theory.  The QMP is proposed to resolve these problems, but we believe this claim should be regarded in our view as a conjecture or speculation at this point, not a fact.  The manner in which the authors state the QMP is, in our view, outdated and wrong.   Therefore, the use of interpretations to resolve the problems of molecular structure, is in our view, dubious.  All-in-all the paper does bring to the forefront of discussion interesting issues of molecular structure. However, the methodology utilized to obtain many statements made in this paper, while perhaps acceptable in the philosophical community, does not appear to us to be sufficiently rigorous to draw scientific conclusions.

Remark

Note that it may seem that we are being overly critical regarding this paper. In fact, we are mainly pointing out the importance of applying scientific methodology. The QMP is a difficult problem that we believe requires a deductive approach rather than the use of induction to solve.  Deduction is a process of reducing the many potential approaches down to a single correct solution. By its very nature, deduction is a process that is error-prone.  It is mainly in the process of making errors and recognizing these errors that one makes progress on deductive problems.  It may very well be that some problems of molecular structure are related to the QMP; this is not ruled out by what we have said in this review.  In this sense, the paper is a positive contribution.  A healthy dialog is critical for progress on such difficult problems.  In fact, all the interpretations put forward as well as physical theories that have been proposed and the many mesoscopic experiments that are being carried out are useful towards reaching the end goal, which is to ultimately solve the problem.  One does however need to recognize the importance of being willing to make errors, work to identify them, and correct them.

References

[1]        T. Maudlin, Three Measurement Problems, Topoi 14, 7 (1995).

[2]        R. J. Thompson, G. Rempe, and H. J. Kimble, Observation of Normal-Mode Splitting for an Atom in an Optical Cavity, Phys Rev Lett 68, 1132 (1992).

[3]        T. Maudlin, Why Bohm’s Theory Solves the Measurement Problem, Philos Sci 62, 479 (1995).

[4]        P. J. Lewis, How Bohm’s Theory Solves the Measurement Problem, Philos Sci 74, 749 (2007).

[5]        S. Fortin and O. Lombardi, Is the Problem of Molecular Structure Just the Quantum Measurement Problem?, Found Chem 23, 379 (2021).

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