In 1981, Mermin wrote the very popular and widely cited paper "Quantum Mysteries for Anyone."

Mermin wrote a similar and more provocative paper in Physics Today in 1985, "Is the Moon There When Nobody Looks?."

In these papers Mermin described what he called a "very simple version" of John Bell's "gedanken" experiment. Mermin says his "EPR Apparatus" exhibits all the experimental behavior of Bell's version, without any reference to the "underlying mechanism that makes the gadget work." He provides samples of (hypothetical) data produced by the apparatus, which presumably matches (statistically) the data produced in real experimental tests of Bell's Theorem.

Two years later, Mermin published a variation on his original apparatus at a 1987 Notre Dame conference on Bell's Theorem. In this work, "More Experimental Physics from EPR," his new device has different switch settings but more data is provided to exhibit the mysterious entanglement (perfect correlations) between widely separated measurements. In this paper, Mermin gave a definite answer to his earlier question about the moon, "We now know that the moon is demonstrably not there when nobody looks." (p.50)

In real EPR tests (e.g., the Aspect experiment), the settings of polarizers at A and B are adjusted to a few specific angles, for example 0°, 22.5°, 45°, 67.5°. The angles chosen are expected to show the greatest differences between Bell's inequality predictions and quantum mechanics. In particular, when the polarizers measure the same angle, so their angle difference is 0°, the photon spin correlation (or anti-correlation for spin-1/2 electrons) is perfect. In Mermin's EPR device, different polarizer angles are represented by different switch settings on the detectors (11, 12, 13, 21, 22, 23, 31, 32, 33). But he does not tell us the angle difference between the measurements. Mermin's cases of "switches set the same" correspond to detectors measuring the same angle. For Mermin's device, lights flashing the same color (RR or GG) shows the correlations are perfect. When polarizers are set at different angles, it is well known that the transmission of light falls off as the square of the cosine of the angle difference θ, cos2θ. This is known as the "law of Malus." At 45 degrees, only half of the photons pass through. The other half is absorbed. At 0° all pass through. At 90° all are absorbed. For Merlin's device, when lights are different colors, there is a loss of correlation. Mermin's hypothetical data illustrate the fact that at some polarizer angles (when detector switches are set the same) the correlation between measurements is perfect. (For Bohm's electron spins it is perfect anti-correlation - if one spin is up, the other is down.) Mermin's data are for Aspect spin-1 photons, which are initially entangled with spins in the same direction.) Mermin divides his results into two cases: Case (a). In those runs in which each switch ends up with the same setting (11,22, or 33) both detectors always flash the same color: RR and GG occur with equal frequency; RG and GR never occur. Case (b). In those runs in which the switches end up with different settings (12,13, 21, 23, 31, or 32) both detectors flash the same color only a quarter of the time (RR and GG occurring with equal frequency); the other three quarters of the time the detectors flash different colors (RG and GR occurring with equal frequency). (Mermin, 1981, p.941) The quantum physics behind the reduced correlations in Mermin's case (b) is that light passing through polarizers falls off as the square of the cosine of the angle between the polarizers. This is the "law of Malus." See Stuckey et al (2020). In his classic book Principles of Quantum Mechanics, Paul Dirac describes photons in terms of his quantum state vectors. He tells us a diagonally polarized photon can be represented as a superposition of vertical | v > and horizontal | h > quantum states, with complex number coefficients 1/√2 that represent "probability amplitudes," which are squared to get probabilities. Thus, a diagonally polarized photon is | d > = ( 1/√2) | v > + (1/√2) | h >          (1) Dirac illustrates this The physical meaning of a superposition of quantum states is that in a large number of identical experiments, the probability of a | d > photon passing through a vertical polarizer is 1/2.

Switches set the same: highlighted to pick out those runs in which both detectors had the same switch settings as they flashed. Note that in such runs the lights always flash the same colors.

David Bohm and Yakir Aharonov wrote in 1957,

We consider a molecule of total spin zero consisting of two atoms, each of spin one-half. The wave function of the system is therefore

ψ = (1/√2) [ ψ₊ (1) ψ_- (2) - ψ_- (1) ψ₊ (2) ]

where ψ₊ (1) refers to the wave function of the atomic state in which one particle (A) has spin +ℏ/2, etc. The two atoms are then separated by a method that does not influence the total spin. After they have separated enough so that they cease to interact, any desired component of the spin of the first particle (A) is measured. Then, because the total spin is still zero, it can immediately be concluded that the same component of the spin of the other particle (B) is opposite to that of A.

"Discussion of Experimental Proof for the Paradox of Einstein, Rosen, and Podolsky,” Physical Review, vol.108, no.4. p.1070, 1957

Bohm and Aharonov also wrote that in classical mechanics, the molecule could have all three components of the spin well-defined, but this is impossible for quantum mechanics, since at most one component of the spin can be well-defined...

If this were a classical system, there would be no difficulty in interpreting the above results, because all components of the spin of each particle are well defined at each instant of time. Thus, in the molecule, each component of the spin of particle A has, from the very beginning, a value opposite to that of the same component of B; and this relationship does not change when the atom disintegrates. In other words, the two spin vectors are correlated. Hence, the measurement of any component of the spin of A permits us to conclude also that the same component of B is opposite in value. The possibility of obtaining knowledge of the spin of particle B in this way evidently does not imply any interaction of the apparatus with particle B or any interaction between A and B.

In quantum theory, a difficulty arises, in the interpretation of the above experiment, because only one component of the spin of each particle can have a definite value at a given time. Thus, if the x component is definite, then the y and z components are indeterminate and we may regard them more or less as in a kind of random fluctuation.

ibid.

Both photons must have had definite polarizations along α. Furthermore, since the conclusion that one photon has a definite polarization along the direction α does not require an actual measurement of the polarization of the other along that direction (again, in the absence of spooky connections), and since not measuring polarization along a direction α is the same as not measuring it along any other direction, we are led to conclude that both photons must have definite polarizations along every conceivable direction.

"Spooky actions at a distance, mysteries of the quantum theory" The Great Ideas Today 1988. p.2 (Encyclopedia Britannica) Reprinted in Boojums All The Way Through (1990), Cambridge University Press, p.110

In our analysis we show how a hidden constant of the motion can carry common causes of entanglement to the "separated" particles. It is not that atoms and electrons must have spins along all three directions or that both photons must have definite polarizations along every conceivable direction.

It is that the two-particle wave function is spherically symmetric with no definite spins in any direction, that is, until the measurements, which each create one bit of information and the perfectly correlated spins.

Eugene Wigner wrote in 1962

If a measurement of the momentum of one of the particles is carried out — the possibility of this is never questioned — and gives the result p, the state vector of the other particle suddenly becomes a (slightly damped) plane wave with the momentum -p. This statement is synonymous with the statement that a measurement of the momentum of the second particle would give the result -p, as follows from the conservation law for linear momentum. The same conclusion can be arrived at also by a formal calculation of the possible results of a joint measurement of the momenta of the two particles.

Writing a few years after Bohm, and one year before Bell, Wigner explicitly describes Einstein's conservation of linear momentum example as well as the conservation of angular momentum (spin) that explains perfect correlations between angular momentum (spin) components measured in the same direction

One can go even further: instead of measuring the linear momentum of one particle, one can measure its angular momentum about a fixed axis. If this measurement yields the value mℏ, the state vector of the other particle suddenly becomes a cylindrical wave for which the same component of the angular momentum is -mℏ. This statement is again synonymous with the statement that a measurement of the said component of the angular momentum of the second particle certainly would give the value -mℏ. This can be inferred again from the conservation law of the angular momentum (which is zero for the two particles together) or by means of a formal analysis.

(The Problem of Measurement, Eugene Wigner, in Wheeler and Zurek, p,340)

John Bell wrote in 1964,

With the example advocated by Bohm and Aharonov, the EPR argument is the following. Consider a pair of spin one-half particles formed somehow in the singlet spin state and moving freely in opposite directions. Measurements can be made, say by Stern-Gerlach magnets, on selected components of the spins σ₁ and σ₂. If measurement of the component σ₁ • a, where a is some unit vector, yields the value + 1 then, according to quantum mechanics, measurement of σ₂ • a must yield the value — 1 and vice versa. Now we make the hypothesis, and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the result obtained with the other.

"pre-determination" is too strong a term. The first measurement just "determines" the later measurement. We shall see that the second measurement is synchronous with the "first" in a "special" frame

Since we can predict in advance the result of measuring any chosen component of σ₂, by previously measuring the same component of σ₁, it follows that the result of any such measurement must actually be predetermined.

Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.

("On the Einstein-Podolsky-Rosen Paradox," Physics, 1.3, p.195.)

Just like Bohm and Wigner, Bell is implicitly using the conservation of total spin.

Albert Einstein made the same argument in 1933, shortly before EPR, though with conservation of linear momentum, asking Leon Rosenfeld,

Suppose two particles are set in motion towards each other with the same, very large, momentum, and they interact with each other for a very short time when they pass at known positions. Consider now an observer who gets hold of one of the particles, far away from the region of interaction, and measures its momentum: then, from the conditions of the experiment, he will obviously be able to deduce the momentum of the other particle. If, however, he chooses to measure the position of the first particle, he will be able tell where the other particle is.

(Niels Bohr, His Life and Work as seen by His Friends and Colleagues, 1967, S. Rozental, pp.128-129)

Supporters of the Copenhagen Interpretation (including Mermin?) claim (correctly) that the properties of the particles (like angular or linear momentum) do not exist until they are measured. It was Pascual Jordan who claimed the measurement creates the value of a property. This is true when the preparation of the state is in an unknown linear combination (superposition) of quantum states.

In our case, the entangled particles have been prepared in a superposition of states, both of which have total spin zero. The two-particle wave function is

So whichever of these two states is created by the preparation, it will put the two particles in opposite spin states, randomly + - or - + , but still supporting the views of Bohm, Wigner, and Bell, that they will be perfectly (anti-)correlated when measured.

As long as nothing interferes with either entangled particle as they travel to the distant detectors, they will be found to be perfectly correlated if (and only if) they are measured (by prior agreement) at the same angle. Otherwise. the correlations should fall off as the square of the cosine of the angle difference. Oddly, Bell's inequality predicts a linear falloff with the angle difference, and a strange non-physical "kink" at angles 0°, 90°, 180°, and 270° (which Bell himself pointed out).

It shows Bell’s local hidden variables prediction as four straight lines of the inner square. The circular region of quantum mechanics correlations are found outside Bell's straight lines, "violating" his inequalities. Quantum mechanics and Bell's inequalities meet at the corners, where Bell's predictions show a distinctly non-physical right-angle that Bell called a "kink."

All experimental results have been found to lie along the curved quantum predictions called the "Tsirelson bound."

In 1976, Bell gave us this diagram of the "kinks" in his local hidden variables inequality. He says,

Unlike the quantum correlation, which is stationary in θ at θ = 0, at the hidden variable correlation must have a kink there

("Einstein-Podolsky-Rosen Experiments," republished in Speakable and Unspeakable in Quantum Mechanics," 1987, p. 85)

the predictions of quantum mechanics are fundamentally probabilistic rather than deterministic, quantum mechanics only can make sense as a theory of ensembles. Whether or not this is the only way to understand probabilistic predictive power, physics ought to be able to describe as well as predict the behavior of the natural world. The fact that physics cannot make a deterministic prediction about an individual system does not excuse us from pursuing the goal of being able to construct a description of an individual system at the present moment, and not just a fictitious ensemble of such systems.

I shall not explore further the notion of probability and correlation as objective properties of individual physical systems, though the validity of much of what I say depends on subsequent efforts to make this less problematic. My instincts are that this is the right order to proceed in: objective probability arises only in quantum mechanics. We will understand it better only when we understand quantum mechanics better. My strategy is to try to understand quantum mechanics contingent on an understanding of objective probability, and only then to see what that understanding teaches us about objective probability.

So throughout this essay I shall treat correlation and probability as primitive concepts, “incapable of further reduction . . . a primary fundamental notion of physics.” The aim is to see whether all the mysteries of quantum mechanics can be reduced to this single puzzle. I believe that they can, provided one steers clear of another even greater mystery: the nature of ones own personal consciousness.

Now Richard Feynman, a great admirer of Mermin's "contraption", said the only mystery was exhibited by the two-slit experiment. Does Mermin agree? Mermin is correct that "the predictions of quantum mechanics are fundamentally probabilistic" and that the probability of different possibilities is "objective." The first desideratum of his Ithaca interpretation of quantum mechanics is "The theory should describe an objective reality independent of observers and their knowledge."

[K]nowledge is not on Bell's now famous list of

"words which, however legitimate and necessary in application, have no place in a formulation with any pretension to physical precision".

But "information" is on the proscribed list, the charge against it being

"Information? Whose information? Information about "what?"

Quantum [Un]Speakables, p.272

Mermin asked

Suppose Alice now goes to the right qubit and secretly measures it in the computational basis. She does not report to Bob the result of her measurement or even whether she has measured at all. Since the right qubit is far away and does not interact with the left qubit...

Quantum [Un]Speakables, pp.274-275

The fundamental theory of standard quantum mechanics is that any measurement of, or even an environmental interaction with, the two-particle wave function Ψ₁₂, it "collapses" instantaneously into the product of single-particle wave functions Ψ₁•Ψ₂. Mermin is correct that it is not an "interaction." It is not Einstein's "spooky action at a distance." It is instead "knowledge at a distance."

Alice's measurement of the right qubit now gives her knowledge of the state of Bob's left qubit, as both David Bohm and John Bell said clearly.

I argue that this knowledge is the consequence of the conservation of total spin angular momentum that I call a "hidden" constant of the motion, a common cause emanating from the apparatus located between Alice and Bob (in their past light cone) which entangled the qubits in a non-separable two-particle wave function.

The questions with which Einstein attacked the quantum theory do have answers; but they are not the answers Einstein expected them to have. We now know that the moon is demonstrably not there when nobody looks.

"Quantum Mysteries For Anyone," The Journal of Philosophy, 78(7), (1981) 397