Quantum Theory and ALA: Hidden Variables Interpretations

What can hidden variables interpretations offer quantum theory? And how compatible are they with the worldview of the authorized version of Law of Attraction (ALA)?

In my previous article on stochastic ensemble interpretations, I started my survey of interpretations of quantum theory and their relationship to the worldview of the authorized version of Law of Attraction (ALA).

This time I am investigating theories with hidden variables. What are hidden variables interpretations? Are hidden variables theories recommended? Who has ever used such theories?

As usual, in addition to discussing the more general aspects of a particular type of interpretations in an “orthodox” quantum context, I am also highlighting their use in a possible scenario where theorists adopt some ALA-inspired idea of nonphysical aspects of the world.

To that end, I am here then presenting some fundamental ideas from the ALA framework, which may help quantum theory developers to find new paths to explore. Some of these ideas focus on unpredictability, closed systems, the reality of nonphysical consciousness, and the multidimensional spin of electrons.

PART 1: WHAT ARE HIDDEN VARIABLES INTERPRETATIONS?

The mainstream physicist’s answer to the question “Are there hidden variables to be discovered in quantum theory?” was more or less a “No” during the first half of the twentieth century (Bohm 1983, p. 65). But then, in 1952, came David Bohm’s own formulation of a hidden variables theory that seemingly might work.

So what are these “hidden variables”? And why would one need them, in the first place?

Motivation: Recovering Determinism

One of the main issues with the quantum mechanics of the Copenhagen interpretation is that of indeterminism. This is the idea, roughly, that “particles” are not entirely predictable [n1].

So instead of a definite value of, say, an electron’s position, we are only being offered certain probabilities (and probability amplitudes) of the whereabouts of the electron.

And since the idea of predictability is a definite hallmark of “excellent science”, it bothers many scientists that, in some circumstances, an exact deterministic way of locating a “particle”, or measuring its momentum, cannot be done. So the idea of “physical” causality (and of ultimate reductionism) seems to have no basis [n2].

To “repair” this undesired feature of the Copenhagen interpretation, we have have to come up with an interpretation that “recovers” determinism and the idea of “excellent science” [n3]. And that is where hidden variables enter the picture.

It’s All in the Theory

So what are the changes that we, as potential hidden-variables theorists, have to make in order to “recover” the desired determinism?

Well, the idea is that, even if the actual experimental results of quantum mechanics never will be any different than they already are, our theory and our explanation of what is going on will have to be different than the Copenhagen interpretation.

So the main work for a hidden variables theorist is therefore (mostly) a conceptual and philosophical one: In order to be able arrive at determinism, some serious theory adjustments will have to made.

Validating the Hidden Variables

The hidden variables theorist typically wants to abandon indeterminism. And one way to get more determinism (if not full determinism) is to postulate that nature has hidden things from us that we cannot detect, either in principle or in practice [n4].

Having accepted the idea that there might be hidden variables, the theorist can then develop a theory with these variables in it. This enables him or her to explain various phenomena in a new way, compared to how the orthodox interpretation understands the same phenomena.

But since these variables are hidden from us, we can never validate the hidden variables directly by experiment [n5].

PART 2: CAN HIDDEN VARIABLES INTERPRETATIONS WORK?

Here in Part 2 we will discuss various historically important theories and proofs that are connected to the idea of hidden variables. The purpose of this discussion is to answer the question whether or not hidden variables is a practical possibility for future interpretations of quantum theory.

Einstein’s Decision

Einstein had already at the end of the 1920s a sketchy hidden-variables scheme on his drawing board [n6]. Unlike the Copenhagen theory (which worked with the concept of either a wave or a particle), Einstein’s approach was to postulate that both a particle and a wave were at play simultaneously (Baggott 2020, pp. 247-248).

Eventually, however, Einstein decided to abandon the theory. For to him the idea of a hidden-variables theory was more of a “fix” [n7], and would sooner or later be replaced by a more solid theory framework anyway (Baggott 2020, p. 248).

So the question then could be posed: Might a hidden-variables theory work? After all, if Einstein already had discarded the whole idea, what hope for others would there be?

Von Neumann’s Proof

And Einsten was not the only one who abandoned the idea of hidden-variables theories. For the famous mathematician John von Neumann believed that he had proven (in 1932) [n8] that hidden-variables interpretations of quantum mechanics could never work [n9] (Baggott 2020, p. 248; p. 184; Nagel 1961, pp. 311-312; Berofsky 1971, pp. 288-289).

However, even though von Neumann certainly enjoyed a “superstar” reputation in the academic world of mathematics at the time, it turned out that there was a mistake in his reasoning. And that took many years to detect (Polkinghorne 2002, p. 43; Treiman 2002, p. 184; Gribbin 2002, p. 214).

This meant, practically speaking, that the idea of hidden variables was basically off the table for most physicists during the 1930s, 1940s, and 1950s.

David Bohm’s Ideas

But David Bohm did not stop his own investigations due to von Neumann’s proof. Bohm continued looking for hidden-variables interpretations that could provide a more “classic” picture of the world which might save determinism. He was convinced that von Neumann’s proof was not correct, but he also could not say exactly what was wrong with it (Gribbin 2002, p. 214).

Nevertheless, in the early 1950s Bohm presented his first hidden-variables theory. In 1951 he had published his own quantum physics textbook called Quantum Theory, which was well-received even by Einstein himself. But since that textbook was based on the Copenhagen interpretation, Bohm felt that something had to be done. (Baggott 2020, p. 249; Talbot, p. 39).

Bohm’s main discontent with the Copenhagen interpretation was not that it offered only a probabalistic solution and therefore made strict determinism impossible; the main difficulty for Bohm was that the Danish system only permitted “reality” to be viewed as a set of phenomena, resulting from a particular measurement or observation (Bohm 1991, p. 33). In other words, the idea of an objectively and continuously existing physical world with actual “solid” particles was no longer on the table.

In order to “restore” continuous reality and classical determinism, Bohm then, in 1952, conceived of an interpretation in which both particles (electrons, photons, etc.) and waves exist simultaneously, continuously, and objectively, thus independent on whether any measurement (i.e., observation) is going on, or not.

In this setup, the real particles are following classical Newtonian mechanics, but seemingly are also “guided” by a wave, somewhat like in de Broglie’s case with his “pilot waves” (Polkinghorne 2002, p. 54; Walker 2000, pp. 110-111; Baggott 1992, pp. 160-161). This system was then later refined and expanded into his wholeness-inspired “implicate order” theory (Bohm 1983).

In Bohm’s interpretation, then, it is the positions of the particles that represent the hidden variables. (Polkinghorne 2002, p. 54; Baggott 1992, pp. 162).

Bell’s Inequalities

In the mid 1960s John Bell analyzed von Neumann’s original conclusion that hidden variables could never work with quantum theory. With rigorous mathematics and logic (that I will not try to discuss further here), he came to the conclusion that hidden variables are possible, but that there are certain restrictions.

Bell’s inequality theorem thus results in two basic scenarios: If we are using local hidden variables, such a system will never be able to replicate the experimental results of quantum mechanics. Only if we are using nonlocal hidden variables can we device a theory that produces the same results that “raw” quantum mechanics does (Baggott 2020, p. 256.

Thus, as Myrvold et al. point out, although some people seem to believe otherwise, Bell’s theorem is not a complete no-go for all types of hidden-variable theories, “since, as Bell himself repeatedly emphasized, there is a functioning hidden-variables theory, the de Broglie-Bohm theory” (2021, introduction).

So the “takeaway” here is that Bohm’s theory is not just any (internally consistent, nonrelativistic) hidden-variables theory, but a nonlocal one (Treiman 2002, p. 187).

Mainstream Consensus: Are Hidden Variables Possible?

So what is the current mainstream conception of the state of hidden variables as a way to “complement” or “complete” quantum theory? Can hidden variable solutions work?

After Bell’s inequality theorem (and after Aspect’s experiments and the more recent experiments done in Geneva and the Canary Islands; Baggott 2020, p. 260), it seems as if there is plenty of room left for certain types of nonlocal hidden-variables theories. But local hidden-variables theories seem to be basically ruled out.

However, by setting up a non-local hidden-variables theory one automatically seemingly needs to accept the idea of the idea that Einstein did not like, namely “spooky action at a distance”.

Furthermore, it also seems to follow that a non-local hidden variables theory in some sense seems to be incompatible with relativity, or at least be problematic to incorporate in a relativistic theory of quantum mechanics (Baggott 1992, p. 162).

And it also seems that the adoption of nonlocality has other problematic effects: “specifically, the ability for signals to travel backwards into the past. This would open the way to all sorts of causal paradoxes” (Davies and Brown 1993, p. 39).

Issue: What Is a Quantum System?

Are the possibilities for hidden-variables interpretations now once and for all settled with Bell’s theorem and subsequent experiments? I do not think so. I think there are many things one might discuss.

One potential avenue of investigation is Wallace’s observation about the meaning of “a quantum system”. Consider the definition of Polkinghorne’s “Locality Principle” (1986, p. 73): “If two systems have been for a period of time in dynamical isolation from each other, then a measurement on the first system can produce no real change in the second”.

The question can then be raised: How do we know that the two systems are not, in fact, two parts of the same system? This is, says Wallace, especially important to note, since Bell thinks the word “system” has (or should have) no place in the foundation of the principles of quantum theory (Wallace 1996, p. 91).

Issue: Locality vs Nonlocality (1)

And even if one nicely categorizes nonlocality in three categories (nonlocal forces, nonlocal correlations, and physical holism), as Peter Gibbins does, one seemingly still has to be concerned with the definition of where the limit between “local” and “nonlocal” goes [n10].

So if look at Gibbins’s categorization of the Pauli exclusion principle as a “holistic nonlocality”, must we really accept it as it stands? Doesn’t it just depend on how we understand the word “adjacent” in relation to the “topography” of the nanomicroscopic world of electrons, atoms, and molecules (Gibbins 1987, pp. 116-117)?

Or is “locality” and “nonlocality” simply some sort of philosophical “definition game”, where “locality” merely boils down to the consideration of the possible internal quantum states of a certain type of particle?

Consider Susskind’s statement (2015, pp. 37-38): “The idea that there are no hidden variables has a very simple mathematical representation: the space of states for a single spin has only two dimensions . . . All possible spin states can be represented in a two-dimensional vector space”.

In that case, since all the possible quantum states for any particle (here: the two possibilities “spin up” and “spin down”) and any plane (here: the z axis) already have been determined a million times by laboratory experiments, there seems to be no room for any adjustments of that outcome.

In other words, Susskind seems to imply that with hidden variables we might end up with more than a two-dimensional state space (i.e., three-dimensional, four-dimensional, etc.). But since quantum theory has already experimentally verified that the state space is exactly two-dimensional (i.e., just “spin up” and “spin down”), the idea of (local) hidden variables in this sense is automatically ruled out.

Consequently, we don’t need Bell’s proof to tell us that local hidden variables are impossible. It is guaranteed by definition.

Issue: Locality vs Nonlocality (2)

Here the objection can made that my reading of Susskind’s statement was not correct. For (local) hidden variables are not about adding any new possible quantum states to the two we already have (i.e., “spin up and “spin down”). Rather, it is about using the exact same quantum states that we have already have, and to produce identical experimental results that quantum theory has demonstrated, but now with hidden variables inserted into the theoretical framework.

My reply to this objection is that this may very well be. And an example of the general procedure, involving the hidden variable ‘lambda’, can be seen in Baggott 1992 (pp. 110-113 and 127-131). Baggott’s photon polarization example, however, demonstrates that the theory with the local hidden variables does NOT reproduce the results from quantum theory.

But, according to Baggott, that is expected. This is because “more complicated local hidden variable theories are indeed possible, but, in fact, none can reproduce all the predictions of quantum theory. The truth of this statement is demonstrated in a celebrated theorem devised by John S. Bell” (1992, pp. 130-131).

But can we really be sure that all aspects of Bell’s reasoning are flawless?

Issue: Are Bell’s Inequalities Correct?

Although Bell’s inequality proofs typically have been very highly regarded by the academic community, it is still possible that there is some strange definition or premise that is not “stringent” or “precise” enough to really support the kind of conclusion that Bell has previously presented.

For if an illustrious mathematician such as von Neumann could make a mistake that took decades to find, it is certainly possible that a similar thing could happen again.

But there could also, of course, be more broader issues with Bell’s work, as Lazar Mayants seems to indicate. In particular, he proposes that Bell’s inequalities for the Aspect case “were doomed to failure beforehand”, and could have been replaced simply by considering Malus’s law alone (1994, p. 84).

Another point by Mayants is the idea that “Bell’s challenge is a total failure” (1994, p. 85). This comes from the commonly accepted notion that Bell’s inequalities deal with ‘local realism’, and that quantum physics is NOT ‘local realism’.

But Mayants claims it is just other way around: it is quantum physics that deals with reality in the form of experiments, “whereas Bell’s inequalities fail the experimental test just because they result from unrealistic assumptions” (1994, p. 85).

A more general point that Mayants also brings up is the distinction between determinism and realism. His idea is that arguments such as Bell’s have only the inherent capability to prove that quantum mechanics is incompatible with determinism (as opposed to realism) [n11]. But that is no great feat, since it is so obvious that quantum physics is linked to probabilities, which then immediately suggests inconsistency with determinism (1994, p. 85).

PART 3: DO WE NEED HIDDEN VARIABLES IN AN ALA-BASED THEORY?

One of the more common reasons for wanting to implement a hidden-variables theory is to save classical determinism and the idea of a type of naive billiard-ball causality. But since ALA always have embraced probabilities, not strict determinism, the need for a hidden-variables theory for that reason does not exist.

This, however, does not mean that an ALA interpretation would necessarily be devoid of hidden variables. For there are many more degrees of freedom in the worldview of ALA than there are in the theories of contemporary quantum mechanics.

To get a more correct framework to work, though, one would most probably need (much) more fundamental changes than hidden variables can provide. Nevertheless, perhaps hidden-variables scenarios might work as preliminary solutions until better frameworks are presented.

PART 4: HOW CAN WE IMPROVE QUANTUM THEORY WITH ALA?

Here in part 4 I am presenting various pieces of information that illustrate some of the current misconceptions of mainstream quantum physics. Note, however, that the following points are merely a microscopic part of a veritable galaxy of information to be explored in the ALA corpus, with the material given to us by Seth and Abraham-Hicks.

In any case, the idea is that these pieces of ALA information might help physicists to adjust their theories so that they become more true to the actual state of affairs in all dimensions of existence (physical and nonphysical).

Whether hidden variables or not are used to implement such new interpretations may of course be a matter of taste. Some physicists may choose to use hidden variables to implement certain new features, while others may instead decide to modify some aspects of the orthodox equations in a more fundamental fashion.

Unpredictability and Probability

Probabilities and the multidimensional activities of electrons are both highly relevant to the lives of human beings (The Unknown Reality, V1, Session 704, p. 209):

In fact, the nature of all existences is based on unpredictability. This is especially interesting for scientists to observe, since it is a propensity that is exactly opposite to the overall mentality of the so-called scientific project. For science usually is portrayed as a discipline where the ability to predict things is the norm for excellence.

But it is important to realize that the “loss” of classical determinism is not really a loss. For it is the origin of true order in all realms of existence (p. 209):

Because probabilities and unpredictability are so important, it is imperative that physicists do not try to avoid indeterminism by imposing classical Newtonian thinking into their quantum-mechanical theories.

In other words, quantum theorists should not use hidden-variables interpretations (or any other schemes) to try to “cover up” the innate unpredictability of the positions or momentums of various subatomic particles (electrons, photons, etc.). For that would only prove that they themselves do not understand how the universe works.

So in order to move quantum physics forward, not backward, we need to firmly accept that probability and unpredictability are the basic, fundamental principles that not only keep our own physical space-time reality going, but also keeps all other physical and nonphysical worlds in All That Is in perfect, creative motion.

There Are No Closed Systems

According to the authorized version of Law of Attraction, there are no closed systems anywhere in the totality of all universes (The Unknown Reality, V1, Session 698, p. 170):

So the probable actions that manifest into our everyday experience are not a result of “chance”. Rather, they are a natural consequence of an incredible amount of multidimensional calculations of probabilities, from all probable universes and realms of existence.

This is possible only because there are, in reality, no closed systems. Because energy can flow freely, a maximized degree of spontaneity can be maintained (Seth Speaks, Session 581, p. 305; my square brackets; my punctuation):

So we can therefore say that Wallace’s point (mentioned above) about the meaning of a “quantum system” is well taken: for since all systems (i.e., all probable universes and dimensions and spheres of existence) are interconnected, there is only one system: everything.

In other words, the idea of “locality”, on the nanomicroscopic scale, is simply an illusion (i.e., “camouflage”), when we are talking in terms of “what is real” and “what is not real”.

Thus, for all practical purposes, some version of the Copenhagen interpretation must be accepted. There is no room for the idea that “billiard-ball” determinism must be saved. Everything is interconnected and nonlocal.

So hidden-variables theories, even if they are nonlocal, should not be pursued with the motivation to try to restore classical determinism. Thus, an interpretation like the de Broglie-Bohm variant is not a helpful philosophical system in that sense. It does not amount to a good approximation of how the totality of all universes work.

But this, of course, does not mean that parts of the later versions of Bohm’s theory does not have merits. For ideas such as “wholeness” and “the implicate order” are on the right track.

Consciousness is Real, Electrons & Waves Are Not

The important general point to grasp, for quantum physicists and other science researchers, is that the only reality that deserves being categorized as “fundamental” is the realm of consciousness. The physical world we live in is just phenomenological in nature. There is no “solidity” to the physical world; it is just a type of television broadcast, which we, on an individual basis, tune in to (The Unknown Reality, V1, Session 702, p. 197):

So, in reality, then, there are, strictly speaking, no solid subatomic particles such as electrons or photons or quarks; they are merely the standardized “visualizations” of individual consciousness units (CUs), as they “interact with the physical atmosphere”, so to speak, from their nonphysical vantage point.

For it is from the nonphysical realm of consciousness that our own physical space-time reality emerges (The Unknown Reality, V1, Session 702, p. 197; square brackets in original):

The most important challenge that quantum physicists must face, then, if they want to understand what quantum theory really means, is to realize the enormous role that consciousness plays.

It is certainly true that some quantum theorists have considered the role of consciousness in terms of the strange behavior of the quantum world. But, in my own estimation at least, most physicists do not want to go there. Instead, they hide behind concepts such as “measurement”, so that they do not have to bother with mind and consciousness.

But it is, of course, inevitable that the quantum community, sooner or later, will have to accept the idea that consciousness is heavily involved. For the more “anomalies” the researchers find, the more they will have to contemplate new theories. So even if a new Kuhnian paradigm typically is meeting lots of resistance before it finally is generally accepted, it is certainly on its way.

Electron Spin and Time (1)

The spin of electrons is connected to the notion of time (The Unknown Reality, V1, Session 702, p. 198):

Seth here explains, from his nonphysical perspective, that it is difficult to describe to us what is going on. This is not due to any ignorance on his part, but is a consequence of the way our verbal language is structured. The complete picture cannot easily be “funneled down” (or translated) from his broader understanding to our limited, sequential thinking.

In any case, he does emphasize the point that electrons spin in many directions at once (The Unknown Reality, V1, Session 702, p. 198; emphasis in original):

And the spin of the electron is also connected with the direction of time (The Unknown Reality, V1, Session 702, p. 198; emphasis in original):

The expression “many directions at once” is presumably not referring merely to the usual setups in quantum mechanics with three spatial directions (x, y, z) and their respective quantum states (i.e., “spin up”, “spin-down”).

Rather, what Seth most probably is referring to here is the multidimensional spin in nonphysical dimensions. So he is referring to a many-worlds scenario in which there is spin in all dimensions in the universe. This is how I interpret his phrase “into all probabilities simultaneously” in the quotation just above.

Electron Spin and Time (2)

Here the following objection can be made: If the behavior of electrons is just a “facade” or “illusion” or “camouflage” as seen from our physical space-time perspective, why speak of the multidimensional spin of electrons in nonphysical dimensions? If electrons aren’t really real even in our physical reality, how can they be real anywhere else, and be spinning there?

My reply to this objection is this. What Seth is doing here, as I understand it, is to talk about electrons as disguised nonphysical consciousness units (CUs). So using a simple analogy from the theater world, the real actor is the CU, and he is wearing an electron outfit, to play the part of an electron.

Thus, in the quotations above, Seth is talking about the character in the play, instead of the actor who is playing that character. But we all know that the character in the play cannot be animated without the actor himself. So any perceived physical action of the character in the play is, of course, in reality carried out by the hidden actor inside the costume.

Consequently, although Seth is referring to “electrons” and their spin, he is actually saying that it is the nonphysical individualized consciousness units, dressed up as electrons, that are doing the spinning in all nonphysical dimensions (i.e. in all possible or probable worlds) at once.

CONCLUSION

Hidden variables theories might very well be used if quantum physicists want to make new theories that, for example, are more true to how the universe really works.

However, such theories should not be built upon a philosophical foundation that tries to rescue the idea of determinism. For, according to ALA, the totality of existence (All That Is) is intrinsically probabilistic in nature.

And since time and space, as we know them here in our physical space-time world, are basically nothing else than illusions (i.e., “camouflage”), nonlocality is the name of the game.

Therefore, if some pure-hearted scientists have the aim to devise better theories that are more true to reality as it really is, then the only possible theories are those that are based on nonlocality.

By using such theories one might therefore, for instance, try to spice up the current theoretical framework with the most important component of all: consciousness. For without consciousness in the mix, one cannot really claim to have a “complete” (and philosophically correct) framework of how the world really operates.

For further details about consciousness, electrons, atoms, molecules, cells, alternate dimensions, and nonphysical realms, please consult the ALA corpus. There are many pieces of information that can be used in order to create much better quantum theories (and accompanying philosophical understanding) than those we are currently faced with.

Chris Bocay

NOTES

“particles” are not entirely predictable [n1] There is more to the idea of the indeterminism of the Copenhagen interpretation. Another important feature is the idea that the “particles” may have no existence at all, other than at the time of measurement or observation (cf. ideas such as “the collapse of the wave function” and “superposition”). Also see Dirac’s description of “the breakdown of classical mechanics” (1981, p. 3).

“physical” causality . . . seems to have no basis [n2] Alex Rosenberg writes (2000, pp. 53-54; my square brackets) : “Since these probabilities [of quantum mechanics] are propensities or dispositions, and are the most fundamental ‘basement’-level properties physics reports, there cannot be a more basic level of structural properties to causally ground these probabilities. They are therefore ‘free-floating’ powers of microphysical systems, which the systems probabilistically manifest, but which when not manifested, exist without any actual further causal basis”. Note, though, that Rosenberg’s statement, seemingly only pertains to some typical billiard-ball model of causality where hard, solid entities bumb into each other. In other words, even though Rosenberg apparently excludes such a possibility, there might very well be a ‘soft’, non-solid, nonphysical causal basis, in which probabilities are involved, as the authorized version of Law of Attraction has it.

an interpretation that “recovers” determinism [n3] When describing in what sense an “hidden variables” solution could be a part of an (Einsteinian-type) ensemble interpretation of quantum mechanics, Peter Gibbins says (1987, p. 9; parentheses in original): “The hidden-variables idea has it that there reallly is a (presumably deterministic) underpinning of quantum mechanics analogous to the underpinning of classical statistical mechanics by classical mechanics”.

nature has hidden things from us that we cannot detect [n4] This reading is supported by, for example, Jim Baggott, who states (1992, p. 107): “As these variables are not revealed in laboratory experiments, they are necessarily ‘hidden’ from us”. However, Colin Bruce presents a slightly different reading of “hidden” (2004, p. 26): “All the phenomena . . . can be explained merely by postulating some kind of fine structure to space that is too delicate to measure directly, at least with present-day instruments.” Thus, Bruce’s idea is that this fine structure (i.e. the hidden local variables) is currently unverifiable in practice, but that it, in principle, could be detected some day if the technology only were more advanced. Thus, Bruce seemingly describes a Type A scenario, where the hidden variables suddenly are not ‘hidden’ anymore (cf. Susskind 2015, p. 36; see also below).

we can never validate the hidden variables directly by experiment [n5] Note that Leonard Susskind discusses two kinds of hidden-variable theories: Type A, where the hidden variables are hard to measure, but still possible to measure in laboratory experiments; and Type B, where the hidden variables are undetectable (2015, p. 36). The problem here is if we have already defined a hidden variable as something that nature hides from us, either in principle or in practice, then, of course, the only possibility would be Susskind’s Type B. So Susskind’s Type A then does not really refer to hidden variables proper in this sense, but merely to some very-hard-to-find variables that hitherto have not yet been experimentally found but which might be found in the future.

a sketchy hidden-variables scheme on his drawing board [n6] Although de Broglie already in 1923 had published an idea of “a fictitious associated wave” (Krips 1987, p. 63) and also had had Einstein scrutinizing (and approving) his 1924 doctoral dissertation (Hey and Walters 1987, p. 27), Einstein is still, by Krips at least, considered to have independently come up with a similar idea (Krips 1987, p. 63).

a hidden-variables theory was more of a “fix” [n7] Einstein seemingly had several reasons for abandoning the theory. So it was not just that the hidden-variables theory felt like a “fix” or a “patchwork”. It was also that it involved the idea of “spooky action at a distance”, which Einstein did not like. So he withdrew his 1927 paper before it got published (Baggott 2020, p. 248).

John von Neumann believed that he had proven (in 1932) [n8] Peter Gibbins gives the year for von Neumann’s discovery as 1932, but gives no reference to the title of the work (1987, p. 122). However, Ernest Nagel does provide us with such a reference. The German title is Mathematische Grundlagen der Quantenmechanik and was published in Berlin in 1932 (1961, p. 312, note 24). This then explains why Jim Baggott does not mention 1932 in his note on von Neumann’s proof, but instead uses 1955 (2020, p. 262, note 9). For it would take 23 years for von Neumann’s work to be translated into English, as Mathematical Foundations of Quantum Mechanics, published by Princeton University Press in 1955.

hidden-variables interpretations . . . could never work [n9] John von Neumann’s proof is complicated. But Baggott has presented a simplified variant, which he presents in the section called “Von Neumann’s ‘impossibility proof’” (1992, pp. 113-116). Note, though, that it is not a mathematics-free exposition, and that it still requires that the reader is comfortable with the usual Dirac notation in quantum mechanical computations, using kets (column vectors) and bras (row vectors), operators, eigenstates, etc.

where the limit between “local” and “nonlocal” goes [n10] Hrvoje Nikolic at the Theoretical Physics Division of Rudjer Boskovic Institute has written a very interesting article called “Quantum Mechanics: Myths and Facts”, where he discusses, among other things, the concepts of “locality” and “nonlocality”, both in relation to hidden variables and in relation to quantum theory in general. He says: “However, it is important to emphasize that the principle of locality is an assumption.” And although the Schrödinger equation “satisfies this principle”, we cannot be sure that “this principle must be valid for any physical theory” (Nikolic 2007).

incompatible with determinism (as opposed to realism) [n11] Mayants’s idea is thus that Bell’s inequalities only pertain to determinism, not realism. So a conclusion such as Manner’s (2008, p. 177), “Bell’s theorem tells us that the days of EPR-style local realism are gone forever” should presumably be read instead as “Bell’s theorem tells us that the days of EPR-style local determinism are gone forever”. But that is obvious anyway, according to Mayants, without having to invoke Bell’s inequalities.

REFERENCES: A-M

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