This time it took all night for Bohr to discover the error in Einstein’s
reasoning.
Both times Bohr had succeeded in refuting Einstein’s arguments. But
Einstein remained unconvinced nevertheless. He wrote to Schrödinger:
“The soothing philosophy— or religion?— of [complementarity due to]
Heisenberg– Bohr is so cleverly concocted that for the present it offers the believers a soft resting pillow from which they are not easily chased away.
Let us therefore let them rest. … This religion does damned little for me.”3
Over the years the two battled it out. But their scientific disagreements
never became personal. Indeed, Einstein held great affection for Bohr. Writing to a friend: “Bohr was here, and I am as much in love with him as you are. He is like an extremely sensitive child who moves around the world in a sort of trance.”4
It cannot be said that the great debates between Einstein and Bohr ever
reached a definite resolution. Rather they just seemed to peter out. Some
people continued paying attention to the question, but by and large the
mainstream did not.
Maybe it was a matter of simple exhaustion. Einstein and Bohr had wrestled over the matter without reaching a conclusion: why go over the same ground yet again?
The Solvay Battles 25
Figure 4.2
Bohr and Einstein … in the midst of a furious battle? Although they disagreed profoundly, their disagreements were never personal. In fact, they had deep affection and respect for one another. Photo courtesy of the American Institute of Physics Emilio Segre Visual Archives.
26
Chapter 4
Or maybe it was like the famous paradox of Zeno: in order to go from
here to there, first you need to cover half the distance, then half the remaining distance, and so on. This seems to prove that motion is impossible. But do I care? Not at all: I can’t think of a satisfactory rebuttal, but that doesn’t stop me from walking across the room. Similarly, maybe you don’t have to
know what quantum theory means in order to use it.
At any rate, thinking about such issues was just “not done” in those days.
To many people it seemed a bit unprofessional, maybe even juvenile. Grownups did not waste time doing such things. Somehow, admitting to an interest in the nature of reality felt like admitting to a fascination with ESP or reincarnation.
On the one hand, the problem seemed to have no practical consequences. Whichever side you took made not the slightest difference to the conduct of your research. Accustomed to playing the hardball of theories
that made specific, testable predictions, of conducting experiments that
yielded detailed, verifiable results, stewing over such matters had been striking many people as just a bit fluffy.
It is also a matter of the technology available. In the great debates over the creation of quantum theory, the thought experiments of Einstein and others were just that: thought experiments. They could not actually be conducted.
It was technically impossible. And in science, experiment and observation
are paramount. Pure thought is all very well, but it gets you only so far.
The astonishing thing about the battle over the adequacy of quantum
theory is that the battle simply seemed to vanish for many years. In my
own experience, I can testify that when I was a student studying quantum
mechanics not a single professor so much as mentioned the enigmatic nature of the theory, the mysteries surrounding its interpretation, or the great
debates that had so animated Bohr and Einstein. The same is true of every
textbook I ever read. Indeed, it was not until 1985 that a single graduate
level textbook so much as mentioned Bell’s Theorem— more than two
decades after he had discovered it. Undergraduate texts took even longer to get around to the subject.5 And if our professors and our textbooks did not refer to the subject … why then, we students did not either. The subject was out of bounds.
The Science sections of bookstores nowadays are crammed with popular
expositions of the mysteries of quantum mechanics. This has not always
been so. For more than two generations following the close of World War II
The Solvay Battles 27
virtually no such books appeared discussing these issues.6 At the other end of the publishing spectrum, the Physical Review, one of the premier scientific journals in the world, had for years an explicit policy of refusing to publish any paper on such matters that did not explicitly make new quantitative
experimental predictions.7 Most of the great debates among the theory’s
founders would have remained forever unpublished under such a guideline.
So for decades the questions were relegated to the margins.
Einstein was trying to show that quantum mechanics was incomplete— a
mere half theory— and that it should be supplanted by a more complete
one that would describe in detail the hidden reality of the microworld. So far he had failed. But he had not given up. And the next step he took led
directly to Bell’s wonderful discovery into the nature of quantum reality.
5 Spin
The simplest exposition I know of what came next involves electron spin.
Every rotating object possesses an axis of spin, represented as an imaginary arrow. Normally you can fully specify the orientation of that arrow: the spindle of a top, for instance, might tilt off to the right by so and so many degrees from the vertical.
Notice that in giving this specification I have made use of two different
reference directions: one running right and left and one up and down. Fewer reference directions would not be enough to fully describe the orientation of the arrow: it would not be sufficient to say that the spin made such and such an angle to the vertical, had I neglected to also mention that it leaned right instead of left.
But quantum mechanics speaks a language all its own, and it is a strangely limited one. That language possesses no means of giving both specifications.
Quantum mechanics can describe the fact that an electron’s spin is up as
opposed to down— but in such a configuration the theory is incapable of telling us whether it leans right or left. Alternatively, the language of quantum mechanics can express the fact that an electron’s spin points to the right, but it cannot then specify the vertical component. If quantum theory is a
language, it is an impoverished one, incapable of expressing many things.
Perhaps we should just try harder. Maybe with a little more work we
could cook up a quantum mechanical description of an electron with its
spin arrow pointing in a definite direction. Unfortunately, no matter how
hard we try we find ourselves unable to find such a specification— and
indeed, it can be shown that the mathematical structure of quantum theory
is such as to prohibit such descriptions. It is the Heisenberg uncertainty principle all over again.
30
Chapter 5
Figure 5.1
A spinning object and its axis of spin.
Sometimes things are even more ambiguous than that. There are
quantum mechanical states in which even the component of spin along a
single reference direction is undefined. Imagine an electron gun— a device that shoots out electrons. (These guns used to be very common: they were
constituents of television sets before the advent of flat screen technology.) Suppose that such a gun produces electrons in such a strangely ambiguous state. It fires one off in the direction of an experimenter. That experimenter is equipped with a detector that measures the component of the electron’s spin along a particular reference direction. What will it find? Will the
electron’s spin turn out to be this way or that? There is no way to know.
Nothing in the quantum mechanics of such a state predicts the result the
detector will get.
All the theory gives is the probability of a particular result. It is precisely this refusal to go further that is so frustrating about the theory. It seems to avoid all the interesting questions. Would you like to find a description of what is going on in the experiment? Do you find yourself beset by the urge to make up for quantum theory’s lack? Do you want to posit some property
of the electron flying toward the detector that explains the result that it gets? If so, then you are not alone. In the old days many people agreed with you. Einstein agreed with you.
Indeed, you may be feeling that the whole thing is trivial. Perhaps you
feel that you already know what this property is. Perhaps you carry in your mind’s eye an image— an image of a tiny speck hurtling away from the
electron gun, aimed precisely at the detector. Perhaps in your imagination you lean forward to gaze closely at this speck— and you notice that it is
Spin 31
spinning. Spinning about an axis that you can see in your mind’s eye. An
axis that points in a perfectly definite direction.
I too find it hard to resist this image. After all, it is what figure 5.1 shows.
But that image is not provided by quantum theory. It is provided by a lifetime of experience in the large scale world, a world that does not partake of the slippery, endlessly ambiguous nature of the microworld, a world that may be entirely inappropriate to this new zone of experience.
Indeed, quantum mechanics has no place for the image. It lies utterly
outside the theory. It belongs to that world of which my Predictor refuses to speak— a world of real objects, of actual physical situations. A world of hidden variables. A world in which Einstein believed, but Bohr did not.
A world whose very existence is in doubt.
For make no mistake: that apparently trivial figure carries with it a profound assumption about the very nature of reality. It is an assumption that I find almost impossible to question, but that I am being forced to question as I replay in my mind that long ago battle over the completeness of quantum theory. An assumption about metaphysics. An assumption that John Bell realized could be tested by experiment.
6 An Impoverished Language?
What does quantum mechanics say about spin? I like to think of quantum theory as a kind of language. It is a strange, abbreviated tongue. Nothing in it seems to correspond to anything that we have ever experienced, and it is utterly incapable of expressing many things. Perhaps this is not surprising: it was designed to fit the strange new world of submicroscopic entities such as electrons and photons, not normal life.
One entity in this new form of discourse is something known as a matrix.
It describes the electron’s spin. A matrix like this
1
0
vertical
Figure 6.1
represents an electron whose spin lies upward along the vertical direction.
A matrix with the “zero” on top and the “one” on the bottom represents
the opposite case of a spin pointing downward against the vertical. Similar matrices describe other directions— horizontal, say, or tilted. We can add such matrices, each multiplied by a number from which can be calculated
the probability that a detector will yield the corresponding result.
All in all, it is a peculiar language, and one far removed from normal
experience. This is what was giving me so much trouble when I was first
introduced to it as a student. Nothing in this language corresponds to our customary, everyday notion of spin. And if we search through quantum
34
Chapter 6
theory, looking for the slightest mention of that notion, we will not find it.
We will find no rotating bodies, no axes pointing off in definite directions.
Rather, what we find are matrices— utterly foreign, and utterly abstract.
If you are of a certain frame of mind, such a way of thinking will be good enough for you. Mathematicians, for instance, are perfectly comfortable
speaking in terms of abstractions with no counterpart in experience. (I once met a mathematician who mentioned that she was studying non Euclidian
geometry. “What a joy! It is so delightfully concrete!”) For example, a mathematician is just as happy speaking of a negative number as a positive one.
Maybe you are too. But should you be? We all know what four apples look
like— but what do minus four apples look like?
The difficulty is that our normal way of thinking about a situation brings with it a mental picture of what is going on— but abstract thinking like this does not. Suppose, for instance, we ask “If there are ten apples in a bag, and four are removed, how many will be left?” Normally we would subtract to
find the answer. But if you are of a mathematical bent of mind you might
want to play with a second way of answering that question: that of adding a negative number of apples to the original ten. You will get the right answer.
Notice, however, that this alternate way of dong the calculation fails to
carry with it any such picture. Nobody has ever tossed a negative number
of apples into a bag. Not even a mathematician.
In the same way, the language of quantum mechanics fails to carry with
it a description of what might really be going on. Nothing in the matrices that constitute the quantum mechanical description of spin corresponds to the sort of intuitive picture of figure 5.1. Do you find this a defect? Are you looking for more than matrices? If so, then you are looking for something
that goes beyond quantum mechanics, something not contained within
the theory and that encapsulates our normal conception of spin, our normal metaphysical assumption about reality.
Which is to say that you are looking for a theory better than quantum
mechanics. You believe that quantum mechanics is incomplete. You are
saying that it is half a theory, and it is not enough for you.
I don’t want to give the wrong impression here. Many areas of physics use abstract mathematics. You will find the square root of minus one all over the place in the theory of electromagnetism, and non Euclidian
geometry in relativity. The point is that, in all these other areas, the math is about something that can be pictured.
An Impoverished Language? 35
In chapter 2 I spoke of the “reticence” of the Great Predictor, and of his
“refusal” to answer my questions. In truth it is not really a question of reticence or refusal. Rather it is a question of his being incapable of speaking.
The language that the Predictor speaks simply has no means of expressing
all those things that constitute the reality concerning which Einstein wanted him to speak.
But maybe you— and Einstein— are wrong in your wish. For notice that,
for all its abstractness, quantum mechanics makes perfectly definite predictions about the results of experiments. It predicts the probability that such and such a measurement will yield such and such a result. And if I make that measurement, I find that the prediction was correct. Isn’t that
enough? The Great Predictor got it right yet again: why isn’t that good
enough? If a theory predicts what I will find when I do something, is that not everything I should want of a theory?
There are times when I think that the language of quantum mechanics
is not impoverished at all. To the contrary, it is perfectly adapted to the microworld— a realm utterly different than that of everyday experience, a
realm in which our old ways of thinking are no longer appropriate. As with the uncertainty principle, perhaps the strange new language
that the Predictor speaks is not a problem but a discovery— a profound insight into the very nature of physical reality.
I understand that Eskimos have many different words for snow. Quantum
mechanics is like a language that has no words for snow. And the question is whether this is a failing of that language. Maybe not! Perhaps we should recognize it as a positive benefit of this way of speaking. For after all— maybe there is no such thing as snow. Maybe snow is like Santa Claus: a fiction that we are so accustomed to that we have mistaken it for the truth.
In this view, the image in figure 5.1 and the desire we may feel for a fuller description of what is really going on are instances of a naive, outmoded
way of thinking. They are relics from an earlier time, from an earlier metaphysics, a metaphysics not yet informed by the wonderful discovery that is quantum theory. Better we should grow up.
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
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