Guido Bacciagaluppi is a Senior Research Fellow at the Centre for Time, University of Sydney. He was previously professor at Utrecht University with a specialty in the philosophy of physics.

He is a prolific author with two critical books on the history of the development of quantum mechanics. The first was Quantum Theory at the Crossroads with co-author Guido Valentini and the second was The Einstein Paradox, with co-author Elise Crull.

In "Crossroads" we learned what Einstein said at the 1927 Solvay conference...

The Fifth Solvay Conference, On Electrons and Photons (1927)

Sadly, despite Einstein's two decades of pioneering work on the interaction of photons and electrons, his ideas and concerns were given little attention at this Solvay, though the conference was dedicated to electrons and photons.

The conference was dominated by papers on the new quantum theory delivered by Louis de Broglie, Niels Bohr, Max Born and Werner Heisenberg. It is best known for Einstein's after-hours suggestions to Niels Bohr and Werner Heisenberg probing for faults in the uncertainty principle. Accounts of these events have been told largely by the victors (there are no holes in uncertainty) but Einstein has said they often missed or ignored his important point. That point was the nonlocal behavior of a spherical light wave as it collapses to get absorbed by a single electron. This was Einstein's only contribution mentioned in the published proceedings.

Here are the notes on Einstein's original remarks at the conference and Bohr's brief response. They contain much of Einstein's 1935 EPR paper, except in 1927 only one particle is involved. Entanglement in EPR requires two identical particles.

Notice how Einstein's diagram clearly shows his concerns of over two decades about reconciling a spherical wave (his example is now an electron) and its collapse to being measured at just one point as if it is a particle. At this point in the history of quantum mechanics, wave-particle duality is seen as the debate between Schrödinger's wave mechanics and Heisenberg's particle mechanics.

MR ElNSTEIN. - Despite being conscious of the fact that I have not entered deeply enough into the essence of quantum mechanics, nevertheless I want to present here some general remarks.

One can take two positions towards the theory with respect to its postulated domain of validity, which I wish to characterise with the aid of a simple example.

Let S be a screen provided with a small opening O, and P a hemispherical photographic film of large radius. Electrons impinge on S in the direction of the arrows. Some of these go through O, and because of the smallness of O and the speed of the particles, are dispersed uniformly over the directions of the hemisphere, and act on the film.

Both ways of conceiving the theory now have the following in common. There are de Broglie waves, which impinge approximately normally on S and are diffracted at O. Behind S there are spherical waves, which reach the screen P and whose intensity at P is responsible [massgebend] for what happens at P.

We can now characterise the two points of view as follows.

The waves give the probability or possibilities for a single electron being found at different locations in an ensemble of identical experiments. A wave does not describe a cloud of electrons as Schrödinger had hoped. Einstein's ensemble theory is the correct interpretation.

1. Conception I. - The de Broglie-Schrödinger waves do not correspond to a single electron, but to a cloud of electrons extended in space. The theory gives no information about individual processes, but only about the ensemble of an infinity of elementary processes.

Quantum theory is not complete in this sense. Representing each particle as a narrow wave packet aiming at the point P is mistaken.

2. Conception II. - The theory claims to be a complete theory of individual processes. Each particle directed towards the screen, as far as can be determined by its position and speed, is described by a packet of de Broglie-Schrödinger waves of short wavelength and small angular width. This wave packet is diffracted and, after diffraction, partly reaches the film P in a state of resolution [un etat de resolution].

According to the first, purely statistical, point of view | ψ |² expresses the probability that there exists at the point considered a particular particle of the cloud, for example at a given point on the screen.

If by the same particle, Einstein means that the one individual particle has a possibility of being found at more than one (indeed many) locations on the screen. This is so, but this seems to be conception I?

According to the second, | ψ |² expresses the probability that at a given instant the same particle is present at a given point (for example on the screen). Here, the theory refers to an individual process and claims to describe everything that is governed by laws.

The second conception goes further than the first, in the sense that all the information resulting from I results also from the theory by virtue of II, but the converse is not true. It is only by virtue of II that the theory contains the consequence that the conservation laws are valid for the elementary process; it is only from II that the theory can derive the result of the experiment of Geiger and Bothe, and can explain the fact that in the Wilson [cloud] chamber the droplets stemming from an α-particle are situated very nearly on continuous lines.

Einstein is right that the one elementary process has a possibility of action elsewhere, but that could not mean producing an actual second particle. That would contradict conservation laws.

The "mechanism" of action-at-a-distance is simply the disappearance of possibilities elsewhere when a particle is actualized (localized) somewhere

But on the other hand, I have objections to make to conception II. The scattered wave directed towards P does not show any privileged direction. If | ψ |² were simply regarded as the probability that at a certain point a given particle is found at a given time, it could happen that the same elementary process produces an action in two or several places on the screen. But the interpretation, according to which | ψ |² expresses the probability that this particle is found at a given point, assumes an entirely peculiar mechanism of action at a distance, which prevents the wave continuously distributed in space from producing an action in two places on the screen.

When a particle appears - just one of the multiple nonlocal possibilities becomes actual or localized - at a specific point P , what becomes of the wave that was going off in all other directions? Its "collapse" - the instantaneous going to zero of probabilities - mistakenly appears to Einstein to violate his relativity principle.

In my opinion, one can remove this objection only in the following way, that one does not describe the process solely by the Schrödinger wave, but that at the same time one localises the particle during the propagation. I think that Mr de Broglie is right to search in this direction. If one works solely with the Schrödinger waves, interpretation II of | ψ |² implies to my mind a contradiction with the postulate of relativity.

The permutation of two identical particles does not produce two different points in multidimensional (configuration space).
Einstein and Bose discovered the new quantum statistics and indistinguishability. Dirac and Fermi extended it to electrons.
For example, interchange of the two electrons in the filled first electron shell, 1s², just produces a change of sign for the two-particle wave function.

I should also like to point out briefly two arguments which seem to me to speak against the point of view II. This [view] is essentially tied to a multi-dimensional representation (configuration space), since only this mode of representation makes possible the interpretation of | ψ |² peculiar to conception II. Now, it seems to me that objections of principle are opposed to this multi-dimensional representation. In this representation, indeed, two configurations of a system that are distinguished only by the permutation of two particles of the same species are represented by two different points (in configuration space), which is not in accord with the new results in statistics. Furthermore, the feature of forces of acting only at small spatial distances finds a less natural expression in configuration space than in the space of three or four dimensions.

(Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference, G. Bacciagaluppi and A. Valentini, 2009. p.442)

In "The Einstein Paradox," we learned of a third physicist who cited conservation of momentum as an explanation of entanglement, Edwin C.Kemble.

In addition to Eugene Wigner and C.S.Unnikrishnan, Bacciagaluppi and Crull reported that Kemble had said in a letter to the editor of the Physical Review, published June 15, 1935, shortly after the appearance of the EPR paper...

Thus in the case of a pair of systems with a definite total energy or a definite linear momentum we can infer from the measured value of the energy or momentum of one system after another collision what the value of the corresponding quantity for the other system must be.

It is quite true, as pointed out by E., P., and R., that the act of observing the system α can hardly be supposed to change the state of a system β which may be widely separated from it in space, but it can and does reveal something abut the state of β which could not have been deduced from the initial wave function of the combination system without such an observation. Thus each possible wave function for system β gives a correct description of the corresponding state of that system [α].

(The Einstein Paradox, G. Bacciagaluppi and E.Crull, 2024. p.258)

This we explain by a sequence of causes and conditions between the initial entanglement and the final measurements which are a common cause that involves no "hidden variables" but what we might call a "hidden constant of the motion."

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