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
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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.
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.
The EPR Paradox 39
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
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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 g
rumbled, “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
8 Hidden Variables
Figure 5.1 is precisely what we might imagine my Great Predictor sees as he peers beyond the veil of appearances to see the underlying reality— that reality of which he so adamantly refuses to speak. Vividly obvious in that figure is something that quantum theory fails to give us: an actual situation. We see in this figure a full specification of the direction to which the spin points.
We can even measure that direction, and come up with a definite number:
so and so many degrees off to the right.
That number is the hidden variable describing the electron’s spin. We call it a “variable” because it could have one value or another— fourteen degrees, for instance, or maybe one hundred and ten. And it is “hidden” because it
is tucked away, hidden from the theory’s gaze. Quantum mechanics cannot
give us the value of a hidden variable. Indeed, it seems to have no place for them within its way of doing things.
The problem goes beyond spin. It infects everything that quantum theory addresses. Consider as another example the matter of radioactive decay, in which an atomic nucleus spontaneously breaks apart into pieces. Such
nuclei are found to possess a certain half life— the length of time during which half of them decay. There is an isotope of radium, for instance, that has a half life of a bit more than eleven days. Start out with a chunk of pure radium: if you come back eleven days later, half the atoms will have
decayed. If you wait yet another eleven days, half the remaining ones will be gone.
Quantum theory can make predictions about this half life. But what the
theory cannot tell us is when any given radium nucleus will decay. Imagine that two such nuclei lie before you. They are identical: nevertheless, if you come back a couple of weeks later, you might find that one of them
has decayed while the other is still intact. But why? What is the difference
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between the two, which allowed one to survive longer than the other? The
theory has nothing to say on the matter.
In speaking of radioactive decay I have already used the analogy of
leaves falling from a tree (chapter 2). Here is another analogy. Suppose that the weather bureau has predicted a 50 percent chance of rain on Monday—
but that when Monday rolls around, you find that it fails to rain. Suppose further that again on Tuesday the prediction is for a 50 percent chance of rain, and that again Tuesday remains sunny. So it might go for several days until, on Saturday (for which the prediction is still a 50 percent chance of rain), the rain finally comes.
What was different about Saturday? We do not know, but we have some
suspicions. Maybe it was a sudden incursion of cooler air from Canada,
which the weather bureau had not foreseen. Or maybe it was a lower than
usual air pressure coming up from the south. Weather is complicated, after all, so we forgive the weather bureau.
We may not know the reason for Saturday’s rain, but we are positive that
this reason exists. That reason is a hidden variable. If we ever managed to figure out why it rained on Saturday, it would no longer be hidden. It would be a “seen variable”— a known variable.
In terms of radioactive decay, if there is a reason, quantum theory does
not give it to us. Just as the theory has no way within its language to give a precise specification of the direction of spin, it has no way to predict when any given nucleus will decay. If you are looking for such a reason, you are looking for a hidden variable. And if you are looking for a hidden variable, you are looking for a more complete theory than quantum mechanics.
A better theory. A loquacious Predictor, one willing to speak more openly.
John Bell’s Theorem dealt with the question of hidden variables. Do they
exist? Is there a reality that my Great Predictor sees, but refuses to speak of? Is quantum mechanics a mere half theory, destined to be replaced by a clearer view of reality? Or are hidden variables and the reality they represent a naive fantasy, a leftover from an earlier and outmoded picture of the world?
We are ready to turn to Bell’s Theorem.
Bell’s Theorem
9 A Hidden Variable Theory
It was many years ago that I first encountered the Great Predictor.
I was thrilled to meet him. I’d been looking forward to the encounter for
years. The Predictor was famous— world famous. He was legendary for the
number of his predictions, and for their amazing accuracy. Many people
had relied on those predictions, and always with profit.
What intrigued me the most, however, was how bizarre were some of his
predictions. “Tomorrow you will be in two places at once” was one. “On
Wednesday an event will occur for which there is no cause” was another.
How could such things be? I was captivated by the strangeness of these
prognostications. Could such weird things really come to pass? That’s why
I had been so anxious to meet the Predictor. For years I had looked forward to finally getting to know him.
At long last I was getting my wish. I was twenty years old, and I was
thrilled. I was sitting in a classroom, in college, on the first day of a course called Introduction to Quantum Mechanics.
That was many long years ago. And throughout my career I have maintained my early fascination with quantum mechanics. Somehow, though, I never felt that I really understood the theory. It always sat lodged in the back of my mind— enigmatic, mysterious, enticing. Over and over again, I found
myself thinking that someday I really ought to go back and figure it all out, and finally put all those early juvenile confusions to rest.
Part of that project was an effort to understand Bell’s Theorem. To be
honest I found myself dreading getting to work on that particular topic.
While I had never felt comfortable with quantum mechanics in general,
Bell’s Theorem was a topic that I felt positively unnerved by. Over and over again I had tried to master it, and over and over again I had failed.
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Eventually I did come to some sort of understanding of Bell’s work.
I recall feeling pretty pleased with things … until the fateful day when I looked at my reflection in the mirror— and this is literally true— and I spoke aloud. “Greenstein,” I said to my reflection, “you were just kidding yourself, weren’t you? You never really understood Bell’s Theorem at all, did you?”
“Time to get going,” I told my reflection.
And I did.
What did I do? I read some books. I read some scientific articles. Among
all my readings, one stood out: an article provocatively entitled “Is the
Moon There When Nobody Looks?,” whose explicit function was to make
Bell’s Theorem as accessible and as comprehensible as possible. I found it wonderful: immensely readable and immensely informative.a I read that
article— not just once, but over and over again. It was helpful … and yet, no matter how many times I returned to it, I still felt that something was eluding me. Some central insight, some clear understanding I still found
out of reach.
Eventually I realized the error I had been making. I had been trying to
adopt someone else’s thoughts and make them my own. And then I realized
that it was time for me to stop heading down this other person’s path, and strike out by myself. It was time to take seriously the central mystery, and try to think about it in my own personal terms.
I decided to tackle the famous and intimidating EPR paradox.
At first glance it might be hard to see what the fuss over the EPR Paradox is all about. Why do people even call it a “paradox?” Perhaps you, the reader, feel this way. After all, is it not obvious what is going on in the EPR thought experiment? Is it not clear that the source of electrons, however it may
work, is merely shooting out a pair of particles, one flying toward Alice and the other toward Bob, set spinning in opposite directions (figure 9.1)?
Figure 9.1 illustrates the underlying reality that we might think our Great Predictor sees, but of which he so adamantly refuses to speak. And isn’t this simple picture all we need to explain the fact that Alice’s and Bob’s results disagree?
I decided to take seriously this picture, and see how well it dealt with
the EPR scenario. I decided to see if I could create the very hidden variable a. You will find a reference to this article in the “Further Reading” appendix.
A Hidden Variable Theory 47
To Alice
To Bob
Figure 9.1
Naive view of the entangled state. It makes intuitive sense, but it will turn out to be wrong.
theory that Einstein sought, and Bohr declared impossible— a theory that
made the same predictions as quantum theory, but that went further and
described in full detail the workings of the microworld. I would create my own predictor— a new predictor, a loquacious predictor, one who was willing to speak up: a “Greater Predictor.” Notice that in doing so I was doing just what quantum theory failed to do.b
Quantum Strangeness Page 5