The long-running and generally excellent science documentary show on PBS, NOVA (funded in part by the David H. Koch Fund for Science, whose libertarian eponym -- despite evident philanthropic gifts all over New York City -- is a bête noire of the Left), began its 2019 season with a show about quantum "entanglement." This went back to the 1935 paper by Albert Einstein, Boris Podolsky, and Nathan Rosen that challenged quantum mechanics with the accusation that it would violate the limitation of the velocity of light postulated by Einstein's theory of Special Relativity. This is the "EPR Paradox." Hence the title of the show, "Einstein's Quantum Riddle."
The abstract of the show says this:
Einstein called it “spooky action at a distance,” but today quantum entanglement is poised to revolutionize technology from computers to cryptography. Physicists have gradually become convinced that the phenomenon -- two subatomic particles that mirror changes in each other instantaneously over any distance -- is real. But a few doubts remain. NOVA follows a ground-breaking experiment in the Canary Islands to use quasars at opposite ends of the universe to once and for all settle remaining questions.
In a way, this is old news, as the show seems to concede. Einstein's "riddle," whose terms I will consider in more detail below, was for many years only of remote theoretical interest. The complacency that attended the interpretation of quantum mechanics saw no real challenge in the EPR paper, and it could be ignored. As it was. However, when John Bell (1928-1990) wrote an equation, Bell's Theorem or Bell's Inequality, that could be used to test the predictive difference between standard quantum mechanics and the more realistic theory prefered by Einstein, this finally got some attention. The predictions of quantum mechanics were vindicated by the experimental tests, something that disappointed John Bell himself, since he thought that Einstein's objections made more sense.
The NOVA episode examines this history and moves on to matters of current interest, including the Canary Islands test of Bell's Theorem. However, the complacency about the interpretation of quantum mechanics persists; and some very precise stigmata can be identified in the show that betrays this attitude. Thus, the documentary includes no mention whatsoever of the "wave function," based on Schrödinger's Equation, or the phenomenon of the wave/particle duality. These are not optional features of quantum mechanics. Indeed, the picture of quantum mechanics presented, based on Bohr's "Copenhagen Interpretation," passes over Bohr's own "Complementarity" principle, which addresses the wave/particle duality.
The nature of the bias perhaps can be seen in a physics book from 1973, Physics, The Foundation of Modern Science, by Jerry B. Marion [John Wiley & Sons]. After some discussion of the "De Broglie Wavelength" [pp.218-219], by which Louis de Broglie (1892-1987) postulated that, just as Einstein had said that photons, previously understood as waves, exhibited the characteristics of particles also, particles like elections would also exhibit the characteristics of waves. This proved to be the case. Jerry Marion says:
It proves convenient to describe the electrons in terms of a wave function, denoted by the symbol . The value of the wave function depends on position and in the one-dimensional case is written as (x). The square of the wave function, |(x)|2, is proportional to the probability that a measurement will reveal the electron to be located at the particular position specified by x. In fact, the wave function itself, (x), has no physical significance and cannot be directly measured; only |(x)|2 can be determined by experiment and is therefore physically meaningful. [p.224, boldface added]
The statement "the wave function itself... has no physical significance" is false and betrays the nature of the bias we see in the NOVA documentary. But this is not an unusual idea, which we actually see in Carlo Rovelli and expressed by Richard Feynman, who says that "the wave theory collapsed" in the photoelectric effect. But Feynman also must acknowledge the wave/particle duality, and he expresses the hopelessness of explaining all this, as "theoretical physics has given up on that."
But things are not that hopeless, thanks to Bohr's "Complementarity." Jerry Marion introduces the principle in this way:
In 1928, Niels Bohr summarized the conclusions that had been reached concerning indeterminism in quantum theory by stating that if an experiment allows us to observe one aspect of a physical phenomenon, it simultaneously prevents us from observing a complementary aspect of the phenomenon. This statement is known as Bohr's principle of complementarity. [pp.228-229]
If we apply this to the wave/particle duality, as Marion immediately does, this contradicts the statement that "the wave function itself... has no physical significance"; for if the waves have "no physical significance," then they do not qualify as something where "an experiment allows us to observe one aspect of a physical phenomenon." If waves have "no physical significance," then they are not something that we could observe in a "physical phenomenon."
So what is the "physical phenomenon" that we can observe that gives the wave function a "physical significance"? First and most important of all, it is the interference effects that were observed by Thomas Young (1773-1829) that confirmed the wave nature of light, previously a matter of speculation, and the similar effects predicted by de Broglie that were then observed in the case of electrons.
But there is a lot more to it than that. A single electron going through Young's slot experiment, where the particle can go through one slot or the other, actually interferes with itself, and produces the same interference effects seen with multiple photons or electrons. How the hell does that happen? Well, somehow the electron must go through both slots at once. If we put detectors on the slots and determine where the electron goes, the interference disappears. And we cannot say that the detectors disturb the electron; for if only one detector is on only one slot, and it simply reports, by inactivity, that the electron didn't go through that slot, the interference still disappears. The electron knows that we know where it went.
This is a very bizarre result, but there is clearly a very simple way to explain it. The physical wave is extended in space, can go through both slots, and can interfere with itself. Jerry Marion's "the wave function itself... has no physical significance" is falsified by this. And Complementarity sorts it out quite nicely. When the cat is away, the mice will play. Thus, if we do anything that will locate the electron, it behaves as a particle, with a discrete, indeed a Dirac point-like location. But if we don't do anything to locate the electron, it behaves as a wave. Thus, even when the electron passes through both slots and interferes with itself, only a discrete particle can strike a phosphorescent screen and illuminate a location. The interference pattern in this is evident in the distribution of strikes, as individual electrons pass through the slots.
One would never know this from the NOVA episode. Instead, in the graphics of the show, we see a "probability cloud," like wisps of fog, moving along where the physical wave would be traveling. This is coupled with the Copenhagen Interpretation that "nothing exists" until it is observed and measured, leaving the obvious paradox that something that "doesn't exist" nevertheless is being shown as part of a physical process -- while the wave function has no "physical significance"?!
The metphysics of such a theory and presentation only allows for a "mind only" ontology, in line with the schools of "Idealism," like Hegel, where external objects only exist because of their presence in consciousness. Neither the producers of NOVA, nor perhaps the talking head physicists featured in the show, were advised by any perspicacious philosophers about the problem with such a thing. Bohr himself was philosophically naive enough not to follow through with the implications of the anti-realism of his Interpretation, which is what bothered John Bell (and Einstein) about him.
Nor can this "probability cloud" be used like the original wave function to explain interference effects; for the probability function is the square of the wave function, which eliminates any negative magnitudes, the very things that zero out the positive magnitudes in the interference effects.
Nevertheless, this muddle, as we see from Jerry Marion, Carlo Rovelli, and Richard Feynman, is not unusual. But in the case of the NOVA documentary, we want to see how this bias and confusion affects the presentation of the phenomenon of quantum entanglement.
Einstein's "quantum riddle" concerns the effects of superposition and the attendant indeterminacy in quantum mechanics. In the diagram at left, named after Richard Feynman, we have an event where an energetic photon has created a pair of particles, one as ordinary matter, an electron (e-), the other as anti-matter, a positron (e+). They shoot off in different directions. But which is which? We don't know. And this means that the wave function contains both, where there is a probability of 50% that either one can be the electron or the positron. We won't know until we look, or one hits some kind of detector. Then the wave function collapses, and we get discete particles. But if we look and find an electron, then the other particle, wherever it is, must be the positron.
So far, this is not so mysterious. When we look, we just find out which is which -- the way they were already. In quantum mechanical terms, however, each particle must be both particles before we observe either one. Neither is already the kind of particle we find when we observe -- that is ruled out as a "hidden variable" theory. Nothing is "hidden" in quantum mechanics. In the diagram, we see the sum of both particles divided by 2 because the probability, when the expression is squared, must be one -- i.e. (1+1)/2=1. This was the point of Schrödinger's Cat, that, if the cat might be dead, the cat must be both dead and alive until we observe it. Schrödinger found this bizarre, and falsifying, as would Einstein.
What turned this into the EPR Paradox is two things: (1) When the wave function collapses, its does so instantaneously, even across cosmological distances. This violates Special Relativity, where nothing can propagate faster than the velocity of light. And (2) One particle assuming definite form would seem to cause the other particle to react, even across, indeed, cosmological distances. This is what Einstein called "spooky action at a distance."
Bell's Theorem made it possible to test (1), and it turned out that the predictions of quantum mechanics, instantaneous collapse and all, are born out. Testing (2) is a different matter altogether. Violating the velocity of light is not "spooky" the way an invisible influence through empty space is. The metaphysics of this is the real hang-up, among people who don't know anything about metaphysics and probably want nothing to do with it.
But there is really nothing "spooky" about action at a distance. This was Newton's entire theory of gravity. The Earth, Moon, and Sun all attracted each other across the Void; and the only explanation that Newton ever had for this was that it is the Will of God -- something also invisible. At the time, nobody liked this very much; but, as with quantum mechanics, the math worked. But neither Einstein's theory of gravity, in General Relativity, nor the principle of the interactions of forces in quantum mechanics, using virtual particles, were theories of action at a distance. Something mediated them -- space itself with Einstein, those virtual particles in quantum mechanics.
The device of neither theory, however, seems to cover this case. Einstein's space doesn't fit the quantum setup; and quantum mechanics is not positing that virtual particles pass instantaneously from the electron to the positron. This leaves us with Feynman's confession that, "the way we have to describe Nature is generally incomprehensible to us." Or is it?
What is the cost of the NOVA documentary ignoring the wave function and the wave/particle duality? Well, it leaves out the "physical significance" of the wave function. The quantum "entanglement" of the particles with each other is an artifact of their both being part of the same wave function. The same electron cannot go through both of Young's slots as a particle; but the same electron can go through both slots as a wave. The same electron and positron cannot be in both locations as particles, at possibly cosmological distances, but they can be at both locations as waves. The particles are not just "entangled," they are superposed, i.e. they are mixtures of each other, as (e-+e+)/2 -- like Schrödinger's Cat being both dead and alive.
There was no hint of this in the NOVA episode, but superposition (or Schrödinger's Cat) is not an optional part of quantum mechanics. Leaving out the wave function, the wave/particle duality, and superposition means that only a fragment of quantum mechanics is presented, a fragment that offers nothing more than the foggy wisps and non-existence of the "probability cloud" to explain how the electron and positron get to the positions where their identities are specified.
|Gödel and Einstein walking to work at the Institute for Advanced Study|
When the answer, in a way, is really so simple, that the wave function bridges the "spooky action at a distance," we must ask why it is so obviously overlooked. Something about the wave function makes a lot of people nervous, and perhaps it is because of the dualistic metaphysics that is implied by it, a dualism described by Roger Penrose and Freeman Dyson, and examined in these pages as "Kantian Quantum Mechanics." The ontological absurdity, or Hegelianism, of the Copenhagen Interpretation is something people can avoid facing, even as it stalks their speculations and reasoning. But the avoidance is either bad faith, or fear. The fear, perhaps, is that if they looked, the trap would spring and they would be caught in a "mind only" metaphysics. Or the fear may be the unconscious sense that something ought to be done to avoid that trap, even while their physics or math degrees never prepared them for a task involving metaphysics. They might have done better walking to the Institute for Advanced Study with Einstein and Gödel, discussing Kant.
Seven Brief Lessons on Physics, by Carlo Rovelli
Philosophy of Science