Quantum Strangeness Read online

  reason, for radioactive nuclei are all alike— absolutely alike. And yet they behave differently.

  So my analogy was flawed. And why did I not use a better one? Because

  there isn’t any. In the world of our experience identical objects behave

  identically. And if two objects behave differently, it is because they only seem to be identical— were we to look more closely, we would eventually

  spot the difference. But for nuclei there is no difference.

  There is a lesson in all this. It is that nothing in the normal world of daily experience prepares us for quantum mechanics. The microworld is alien—

  absolutely alien. If there is anything I have learned about the world of the quantum, it is that normal thinking simply does not apply.

  So a brief warning. Throughout this book, I will often be using analogies.

  I will be doing this because I want to place the strange, unfamiliar world of quantum mechanics into a comfortable context. But some of these analogies are going to be misleading. I will try to warn you when they are, but it’s going to be an awkward situation.

  So be it.

  And while I am at it, I should warn you of something else. Even now, so

  many years after the creation of quantum mechanics, physicists keep on

  arguing about it. There is still a profound disagreement among researchers about how to understand what it is telling us about the world. There have even been alternative theories proposed, designed to replace standard quantum theory with something else. Some of these can be thought of as

  re­ interpretations of the theory, and some are outright modifications.a

  a. The most prominent of these are the “pilot wave” theory developed by Bohm, the “spontaneous collapse theory” of Ghirardi, Rimini, and Weber, and the “many worlds” theory of Everett.

  14

  Chapter 2

  I want to warn you that everything I am going to say in this book refers

  to the standard version of the theory. Which is to say, I am completely

  ignoring these alternative approaches. Why do I do this? Because that

  is what most physicists do. None of these alternatives has attracted the

  amount of attention that the standard theory has attracted.

  It is actually an unfortunate situation, for there is much to recommend

  each one of these other approaches. They are all worthy of more attention

  than they have received. As I am sure you will appreciate as this book goes along, standard quantum theory is utterly strange, and in the long run

  one of these alternative approaches may well prove to be a better way of

  dealing with the mysteries of the microworld. If so it will be that one that comes to attract the lion’s share of physicists’ attention.

  But as of now, they lie on the outskirts. So in this book I will confine

  myself to the standard approach.

  Here is something that I wish I could tell you: that back when I was a student, I simply could not reconcile myself to the Great Predictor’s silence. That in those days I wanted to grab him by the lapels and shake him to and fro. That I wished I could yell at him to “speak! Say something! Explain yourself!”

  But to be honest, I cannot really tell you this. Yes, I was sometimes irritated at the Great Predictor’s silence. But as I have already mentioned, mostly I was irritated at myself. Irritated and even perhaps ashamed. Ashamed that

  I was so dense. Ashamed that I was Just Not Getting It. Ashamed that I was not understanding what my professor was trying to teach me. That professor certainly seemed pretty sure of himself, striding so confidently back and forth in front of the blackboard as he filled it with all that weird stuff.

  And, glancing sideways at my fellow students, I could not help but feel that they also seemed pretty sure of themselves. Was I the only one so confused?

  It was true in most of my courses.

  Of course, I would never reveal such weakness in public. So I put on a

  brave face and soldiered on, writing in my notebook with a bored and superior mien. Who knows? Perhaps I even managed to fool myself.

  For truth to tell, it is hard being a student. There is so much you have

  to learn. Everything is unfamiliar, and often it is foreign to your customary way of thinking. (I will illustrate this a little in chapter 6.) Before the school year began you had felt pretty sure of things— but now you are out of your depth, in new and uncharted territory.

  Silence 15

  It is true of every form of learning. Some time ago I decided that I needed to improve my tennis game. So I took a few lessons. The serve was something I found particularly hard. To this day I remember vividly all the contortions I was putting my body through in my efforts. I found myself

  twisting this way and that, bending into the most bizarre poses. Everything I was trying to do felt unnatural and awkward. Meanwhile my instructor

  was utterly graceful and at home as he demonstrated the proper form.

  I now believe that the same is true of all learning. Tennis, quantum theory— it is all the same. To the newcomer it is alien and uncomfortable, and one’s self­ confidence can be undermined. In the long run, as the new material sinks in and is internalized, the sense of solidity and confidence returns.

  But in the first stages the whole situation can be very bruising to the ego.

  And so it was with me. I found myself floundering during my initial

  exposure to quantum mechanics. And while this was going on, I simply

  had no energy for anything more than learning the material. It would be

  pleasing to me to be able to tell you now that, even as a student, I had questioned the very foundations of what I was struggling to learn. But that is not really true. The questions, I would tell myself, could wait.

  But not always.

  Every so often, I would approach my professor after class and try to

  speak about these mysteries. I wanted to ask him how an object could be in two places at once, or how something could happen without a cause. And

  although he was being polite, I could tell that my questions did not really interest the professor.

  And more than that: I had a faint but unmistakable feeling that he

  regarded my questions as juvenile. “Kids,” I would imagine him thinking.

  “You’ve got to love them— aren’t they great? But in the long run this guy

  Greenstein will have to grow up.”

  Even then, at the very beginning, I had encountered a stigma— the faint

  but all­ pervasive sense that I’d better not spend too much time asking such questions. I had encountered a second kind of silence. It was a silence that had paralyzed the field for decades.

  3 Half a Theory?

  This reticence is unique to quantum mechanics. No other theory of

  physics is so reticent. Newton’s theory of gravitation speaks of the solar system as sort of a gigantic clock, a smoothly functioning machine. Statistical mechanics describes a gas as a swarm of particles, rapidly zooming about every which way. Electromagnetism tells of space filled with invisible fields. Each of these theories gives us a vivid picture of the world.

  But quantum theory tells us nothing of the sort: it leaves us no picture

  at all.

  The refusal of the theory to give a picture of reality, to respond to certain questions, and its seeming inability to describe any mechanisms lying behind its predictions, deeply disturbed the theory’s creators. One of those creators was Albert Einstein. He was so disturbed that he decided that there was something wrong with the theory. To him no respectable theory of

  physics should be so speechless.

  Is there something wrong with quantum mechanics? It seems so limited!

  Is it too limited? Is there something wrong with it? Maybe it is not a theory but half a theory.

  For surely there must be some way to penetrate beyon
d the silence of

  the theory! Surely something is missing from quantum mechanics. Could

  it be that it is only a partial theory, that underlying it there is a deeper understanding, a fuller and more complete explanation of the workings of

  the microworld? In this view quantum mechanics is only a start, and we

  need to search for a better theory that will speak of all those things that the Predictor fails to address. This new theory, if we could find it, would clearly describe the invisible reality— the actual physical situation, the real state of affairs— of which we would dearly love to learn.

  18

  Chapter 3

  Figure 3.1

  Albert Einstein. Although he was one of the creators of quantum mechanics, he never accepted it. Over and over again, Einstein argued that the theory was incomplete because it failed to describe subatomic reality. The arguments that Einstein advanced are the fertile soil from which grew the discoveries described in this book. Photo courtesy of the American Institute of Physics Emilio Segre Visual Archives.

  Half a Theory? 19

  Does this view make sense to you? If you feel that it does make sense,

  then you believe in hidden variables. And it made sense to many people

  before Bell’s Theorem and the experiments that it inspired came along.

  In particular, it made sense to Albert Einstein. In his view quantum

  mechanics, successful though it may be, was incomplete. The theory was perfectly good so far as it went, he felt— but “so far as it went” was not good enough for him. Einstein wanted something more: a complete theory.

  Is quantum theory incomplete? Or are there are reasons to think that it

  is all that we will ever get?

  On the one hand, if we are going to revise quantum mechanics to make

  it into a complete theory, the task won’t be easy. It won’t be a matter of making a few tweaks here and there. The very structure of the theory, the

  way in which it is formulated, is antithetical to the goals of such a revision. If we are looking for a more talkative Predictor, it’s an utterly different person that we’re after. And if we do decide to go looking for a new one,

  we’d better remember that she’s got some pretty big shoes to fill. Quantum mechanics as it stands is that good.

  Furthermore, it seems inconceivable that such a Predictor— a talkative Predictor, one who describes what is really going on— could ever be found. What sort of description could there be of a particle existing in many places at once, of an atom with a broad range of energies, of an object most definitely spinning on an axis but of that axis having no particular direction until it is observed? The more we probe the quantum world, the more we learn that its

  properties simply cannot be described in anything like the ordinary manner.

  Many of the theory’s creators felt that the refusal of quantum theory to

  provide a detailed account of the workings of the microworld is not a problem but a discovery. It is not a limitation but an advance. In this view the theory is profoundly right in confining itself to doing only what can be done, and avoiding what cannot. These people insist that the question “What is the reality that the Predictor perceives so clearly?” is misguided— that there simply is no such thing. They insist that the idea of a reality that can be explained is a naive notion that we need to outgrow, on a par with another intuitively obvious concept that turned out to be wrong— that of a flat Earth beneath our feet.

  Einstein, on the other hand, thought that these people were just spouting

  nonsense. He set out to prove them wrong. And it was the arguments that

  Einstein brought to bear that led in the long run to Bell’s famous theorem, a theorem that, in a supreme irony, almost certainly showed that Einstein had been wrong.

  4 The Solvay Battles

  The issue around which Einstein chose to launch his attack involved one

  of the cornerstones of quantum theory: Werner Heisenberg’s famous uncertainty principle.

  The inability to give us a picture of a real physical situation (aka hidden variables) is built into the very structure of quantum mechanics. Perhaps

  the strongest evidence for this is provided by the uncertainty principle.

  This principle, formulated in 1927, deals with a strange limitation of the language of quantum theory: it cannot speak of certain pairs of properties. One example is the specification of the position and velocitya of an electron. Using the language of quantum mechanics we can write down a

  description of an electron being at some definite place— but that description will specify that the electron can have any velocity at all. Conversely, we can elect to write down a quantum­ mechanical statement of the fact

  that the electron is moving at a definite velocity— but that description will specify that it can be at any location at all.

  Are we just being stupid? Maybe with a little more work we could cook

  up a quantum­ mechanical description of an electron with a perfectly definite position and velocity. 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.b My Predictor does not even talk our language.

  a. Technically the theory speaks of momentum, but momentum is just the electron’s velocity multiplied by its mass so the distinction doesn’t matter.

  b. Years later a variant theory was proposed by David Bohm that evaded this problem.

  (It is briefly discussed in chapter 14.) This theory does not, however, succeed in providing the sort of mechanistic description of the microworld that Einstein was looking for.

  22

  Chapter 4

  But perhaps we have been misunderstanding the nature of the electron.

  Perhaps the electron is just not the sort of thing that has a definite location.

  Could it be a little fuzzy, or have a fluctuating shape, so that it is impossible to specify with perfect accuracy its position? Maybe an electron is less like a tiny, point­ like particle and more like a region of bad weather. Things might be pretty stormy across the Northeast— but a more precise specification of the bad weather’s location is simply impossible.

  But this will not do, for quantum theory is perfectly capable of describing an electron located at a precisely specified place. It is only pairs of properties that cannot be simultaneously described. Such pairs are termed “complementary.” Furthermore, it is only some pairs that are complementary: the theory is perfectly capable of simultaneously specifying the position and

  mass of an electron, for instance.

  Is this a fatal limitation of quantum mechanics? Or is it some kind of

  insight into the very nature of the microworld? Is the uncertainty principle a problem or a discovery? Is it an expression of the fact that quantum mechanics is incomplete, a mere half­ theory that must be supplanted by a fuller theory? Or is it a profound insight into metaphysics and the nature of reality?

  Einstein took the first view. Another of the creators of quantum mechanics, Niels Bohr, took the second. Einstein wanted a more talkative Predictor; Bohr thought that this desire was naive. They battled it out for years.

  Two memorable interchanges took place at historic “Solvay” conferences

  in the years just following the creation of quantum theory. Founded by

  the Belgian industrialist Ernest Solvay in 1911, these meetings take place in Brussels and have been devoted to fundamental issues in physics and

  chemistry. Meeting at irregular intervals, they continue to this day.

  At the Solvay Conference in 1927— the very year in which Heisenberg

  enunciated his uncertainty principle— Einstein came up with a “thought

  experiment” that he felt revealed a way to circumvent it. Such thought experiments do not need to be performed: the
y are mental exercises designed to bring out certain elements of a situation, just as a novelist might place

  characters in a particular state of affairs to watch what they do. Einstein invented a series of steps designed to reveal to the experimenter two complementary quantities that, according to Heisenberg’s principle, could not be so revealed.

  The Solvay Battles 23

  Figure 4.1

  Niels Bohr. Also one of the creators of quantum mechanics, Bohr argued that Einstein’s search for a more complete theory— one that would describe microscopic reality— was misguided. Indeed, Bohr argued, the refusal of quantum theory to do so was not a problem but a discovery— a profound philosophical insight. Photo courtesy of the American Institute of Physics Emilio Segre Visual Archives.

  24

  Chapter 4

  A participant has given a first­ hand description of what happened.

  Each day

  Einstein came down to breakfast and expressed his misgivings about the new quantum theory, every time [he] had invented some beautiful [thought] experiment from which one saw that [the theory] did not work. … Pauli and Heisenberg, who were there, did not pay much attention, “Ah well, it will be all right, it will be all right.” Bohr, on the other hand, reflected on it with care and in the evening, at dinner, we were all together and he cleared up the matter in detail.1

  Three years later, at the next conference, Einstein arrived armed with a

  second thought experiment.

  It was quite a shock for Bohr— he did not see the solution at once. During the whole evening he was extremely unhappy, going from one to the other, trying to persuade them that it couldn’t be true, that it would be the end of physics if Einstein were right; but he couldn’t produce any refutation. I shall never forget the sight of the two antagonists leaving [the meeting], Einstein a tall majestic figure, walking quietly, with a somewhat ironic smile, and Bohr trotting near him, very excited.2