7 The EPR Paradox
The year 1935 witnessed Einstein’s most powerful salvo in his battle against Bohr. Referred to as “the EPR Paradox,” this attack set the stage for positively endless arguments, disagreements, confusion, and fascination on the part of physicists for decades—and it directly led to John Bell’s discovery. Indeed, Bell’s Theorem is a direct extension of the EPR scenario.
The paradox appeared in a physics journal in the form of a brief paper bearing the forbidding—and ungrammatical—title “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” Written together with Boris Podolsky and Nathan Rosen—hence the paper’s acronym, EPR—it is one of the most historic scientific papers ever written. I can testify from personal experience that it is also one of the hardest to understand. I have pored over it for years, and I cannot say that I comprehend it in any depth. To me reading the EPR paper is a bit like wrestling with difficult poetry, or with prose lifted from some obscure Journal of Heavy Thought. It contains one of the most widely quoted—and, to me at least, incomprehensible—sentences of any scientific paper in any field:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.1
Succeeding work has clarified their argument. The simplest exposition I know of involves spin.
In their paper, Einstein, Podolsky, and Rosen provided an argument that shows that quantum spin was just like normal spin, and that it pointed in a perfectly definite direction. Since the language of quantum theory was incapable of expressing this fact, they argued, quantum theory was incomplete. It did not express all there was to be known. They claimed to have proven that the Great Predictor might be perfectly good at making predictions—but that he was utterly blind to the underlying reality about which he was so prescient. A new predictor was urgently required.
They did this by inventing yet another thought experiment, one designed to measure a spin’s components along both the vertical and horizontal reference directions—again, just what the uncertainty principle forbids. Their experiment involves a sort of modified electron gun—a device that produces not one but two electrons. The device sits in the middle of a room. At opposite ends of the room are two experimenters. Let’s give them names: Alice and Bob, say. The device in the middle shoots one of its particles toward Alice and the other toward Bob. As for the experimenters, each has a detector, and the two detectors are oriented the same way: both are vertical, say, or both horizontal. Each detector reveals whether the spin of the electron it observes points along this reference direction or against it.
The electrons produced by the emitting device are in something known as an “entangled state.” Such a state has the property that the two detectors always yield opposite results. If one detector finds a spin pointing along its reference direction, the other is sure to find a spin pointing against it. We might liken such an entangled state to an angry couple. They are furious with each other, and they disagree constantly. If the husband is in the mood for seafood the wife will shudder at the very thought. If she wants to play golf, he wants to lie in the backyard. But it’s not just a matter of his liking seafood, or of her feeling active—because he might just as well have hated seafood, and she might have been feeling lazy. Indeed, the only thing each of them really wants is, not this or that, but a fight. They want to disagree. So too with the EPR entangled state: the two detectors always disagree.a
In the EPR scenario Alice and Bob orient their detectors along the vertical direction, the button on the emitting device is pressed, and it shoots out such an entangled pair of electrons. Imagine that Alice is slightly closer to the device than Bob. She performs an observation: is her electron’s spin up or down? Whatever she gets, she can predict the result that Bob will get: the opposite. And if Bob then performs his measurement, they will find that she had been right.
By observing what happens at her detector, Alice has found out something about the spin of her electron. But she has also done more: she has found out something about the spin of Bob’s. And she did this without ever touching it. Einstein, Podolsky, and Rosen argue that Bob’s electron must have had this property even before Alice had made her measurement.
For after all, they say, Alice and Bob’s detectors were far away from each other, and hers could not possibly have influenced what was about to happen at his.
(As an aside, let me direct your attention to the forgoing sentence. Does it make sense to you? It certainly did to Einstein, Podolsky, and Rosen … and yet, as we will see, it contains an assumption—an assumption that seems utterly obvious, and yet that in the long run will turn out to be false. Let us give that assumption a name: locality. We will return to the subject of locality in chapter 14. But for now let us proceed.)
Now Alice and Bob twist their detectors about so that they lie along the horizontal direction. They repeat the procedure. As before, Alice can now determine not just the vertical, but also the horizontal component of the spin of Bob’s electron. So, say EPR, both the vertical and the horizontal components of the spin of his particle exist—in contradiction to the uncertainty principle.
The argument seems to make a lot of sense. If the experiment is repeated over and over again, Alice always succeeds in predicting the result of Bob’s measurement. But why? Why does Bob’s detector keep on getting the predicted result? What influences his detector’s behavior when a particle arrives? The only possibility seems to be the particle itself. This is the only thing that can “tell Bob’s detector what to do.” If this seems reasonable to you, reflect that we are now speaking of some attribute, carried by this particle, that influences Bob’s detector. Does this strike you as a correct way to think? If so, then you believe in hidden variables. You believe that the spin of the particle had a perfectly definite value even before Bob observed it.
It might appear to be a trivial argument. As an analogy, imagine that you are holding a coin. Cut it carefully along its flat plane, so that you end up with two half-coins: one is heads and the other tails. The half-coins are analogous to the spins of the entangled particles, and of the states of mind of the angry couple.
Take two envelopes: slip the “heads” half-coin into one and the “tails” into the other. Shuffle the envelopes and then mail them off. One goes to Alice and the other one to Bob. Alice gets to her mailbox first: when she opens her envelope she finds herself able to predict with certainty what Bob will find when he opens his.
It seems almost churlish to point out that, in attributing a “headness” or “tailness” to the content of an envelope, we are doing precisely what quantum theory is incapable of doing. Those faces are hidden variables. They are properties of the half-coins. The very existence of such a property was what Einstein and Bohr were fighting over. It is what everyone has been fighting over since the creation of the theory.
They are what the Great Predictor will not speak about. And if he will not speak about them … then maybe he is not so very Great after all.
A colleague of Bohr has given us a description of the EPR paper’s effect:
This onslaught came down upon us as a bolt from the blue. Its effect on Bohr was remarkable. … A new worry could not come at a less propitious time. Yet as soon as Bohr had heard my report of Einstein’s argument, everything else was abandoned: we had to clear up such a misunderstanding at once. We should reply by taking up the same example and showing the right way to speak about it. In great excitement, Bohr immediately started dictating to me the outline of such a reply. Very soon, however, he became hesitant. “No, this won’t do, we must try all over again … we must make it quite clear. …” So it went on for a while, with growing wonder at the unexpected subtlety of the argument. Now and then, he would turn to me: “What can they mean? Do you understand it?” There would follow some inconclusive exegesis. Clearly, we were further from the mark than we first thought. Eventually, he broke off with the familiar remark that he must sleep on it.2
In the days that followed Bohr developed a counterargument to that of E, P, and R. It was rapidly published. Very few colleagues whom I have consulted claim to understand this paper.
Indeed, much of Bohr’s thought seems to be obscure to the point of incomprehensibility. One contemporary physicist has grumbled, “Whatever the merits of Bohr’s approach, it did not really facilitate answering awkward questions; it was better at giving verbally dexterous accounts of why they could not be answered.”3 And John Bell has commented, “Bohr was inconsistent, unclear, willfully obscure, and right. Einstein was consistent, clear, down-to-earth, and wrong.”4 Finally, a quote from the Nobel Prize winning physicist Murray Gell-Mann: “Niels Bohr brainwashed a whole generation of theorists into thinking that the job [of understanding quantum mechanics] was done 50 years ago.”5
a. This is another instance of a poor analogy of which I warned earlier. In my analogy the husband and wife are able to disagree because each knows what the other wants. But in reality they do not know (I will explain why we are so sure of this in chapter 12). So even though they do indeed disagree, that disagreement is a mystery.
Notes