Quantum Strangeness

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Quantum Strangeness Page 13

by George Greenstein


  the first time how utterly strange quantum theory is. A student learning

  quantum theory must learn a whole new way of doing things. The way

  involves mathematics that seems to have nothing to do with the subject at

  hand. An example is those matrices of chapter 6— nowhere within them do

  you find the slightest image of a spinning object. And the same is true of all the rest of the theory.

  And then one day I had an epiphany.

  The amazing thing about that epiphany is that it happened in a flash— at a precise instant of time. As a matter of fact, so momentous was that instant that I took note of it. Even now a small sign sits above my desk:

  The Epiphany

  11 AM, Friday July 10, 2015

  Another bright and sunny day

  (Big thunderstorm last night)

  I don’t want to give the wrong impression. I don’t want to imply that in

  order to understand something hard, all you have to do is sit around and

  wait for inspiration to hit. My epiphany would never have come had I not

  spent all those years of work stewing things over. The epiphany was just

  the final step.

  Nevertheless, it was a climactic moment. It felt as if I had been wandering around for years through a darkened house, and that I had ultimately found myself in a pitch­ black room, a room I had never been in before—

  and suddenly the lights turned on.

  Here is what I saw.

  I saw what had been confusing me so thoroughly. It was that I had developed in my mind two completely different spheres of thought. One was the new language of quantum mechanics that I had learned so many years

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  ago. The other was the normal way of thinking that we all employ: the

  automobile is right there and it is going that way at such- and- such a speed; the golf ball is spinning so fast in this direction. And what I suddenly realized was that all along I have been thinking in both ways at once. I was moving seamlessly and smoothly from one sphere of thought to the other. And most important of all: this moving from one to the other was unconscious.

  If something is unconscious it just might cause you trouble. That, I suddenly saw, was what had been giving me so much grief for so very long.

  Indeed, I had been actively preventing myself from realizing how utterly

  incompatible those two ways of thinking are. This incompatibility is the very essence of this book. It is the essence of Bell’s Theorem. What Bell’s Theorem proves is that quantum mechanics is not a local hidden­ variable theory— and that’s just a fancy way to say that it is not a theory of normal reality. And the experiments testing Bell’s Theorem— metaphysical experiments— are telling

  us that the hypothesis of normal reality is untenable. There ain’t no such thing.

  This “doublethink” had been infecting all my thinking over the years.

  Indeed, it has infected this very book. In the first chapter I wrote of my youthful amazement that something could be in two places at once. Indeed,

  I was frustrated that the Great Predictor refused to tell me how this could be.

  Later on, in chapter 6, I had advanced in my thinking somewhat, and

  wrote that the problem lay with the language the Great Predictor spoke.

  It was, I wrote, a strangely impoverished language, and my poor Predictor

  was simply tongue­ tied: his language was incapable of expressing certain

  things. But now I suddenly realize that the truth is far stranger than that: it is that my very question was misguided. “How can a thing be in two places

  at once?” I had asked— but buried within that question is an assumption, the assumption that a thing can be in one place at once. That is an example of doublethink, of importing into the world of quantum mechanics our normal

  conception of reality— for the location of an object is a hidden variable, a property of the object … and the new science of experimental metaphysics

  has taught us that hidden variables do not exist.

  Another example of how I had been unconsciously moving between

  these two spheres: radioactive decay. In chapter 2 I discussed how one

  nucleus would decay rapidly while another would decay more slowly.

  What enables one nucleus to survive for longer than the other? The Great

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  Predictor refused to say. I was frustrated by this refusal, but now I see that contained within my frustration was another assumption: the assumption that there is a reason— some property that distinguishes the short­ lived nucleus from the long­ lived one. And now I realize that reasons are hidden variables … and hidden variables do not exist.

  I would not be wasting the reader’s time on my own personal history had

  I not felt that it has a wider moral. For in truth I believe that what I have been recounting in this book is not just my own story: I believe it is every scientist’s story. Einstein believed utterly in a real physical situation, and he fought for that view to the end of his life. Bell did too: “Everything has definite properties,”1 he would often say. And perhaps you recall my earlier quote from the quantum physicist E. T. Jaynes, who termed the view that there was no such reality “a violent irrationality” (chapter 13) So I am not ashamed of thinking according to our normal conception of reality. That is how these

  people thought, and if it was good enough for them it is good enough for me.

  As a matter of fact, I believe that the real point goes beyond what I

  myself think, or what this person or that person thinks. I believe that in truth we cannot help thinking that way. That is the only way we know how

  to think. It is how our minds work.

  And it is how science works— all of science: biology and geology and

  chemistry and, indeed, every facet of physics other than quantum mechanics. I want to emphasize this. Never before have we encountered a situation like the one that experimental metaphysics has forced on us. Relativity,

  the space program, the genomic revolution, artificial intelligence— none

  of these have required so great a shift in our thinking. Earlier in my career I worked on neutron stars: monstrously dense, exotic in composition,

  ferociously magnetic … but each one of which sits in a perfectly definite

  place and spins at a perfectly definite rate in a perfectly definite direction.

  A geologist might be concerned with the motion of magma hundreds of

  miles beneath her feet— a magma that neither she nor anybody else has

  ever seen … but nevertheless a magma that has a perfectly definite temperature and pressure. A biologist might study the evolution of creatures now extinct: creatures that no one has ever seen … but creatures whose size and shape and mating habits most definitely existed.

  No matter how exotic and unfamiliar the objects that scientists study,

  until now all of them have conformed to our normal conception of reality.

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  There is only one small problem: the new science of experimental metaphysics has shown that within the microworld this normal conception of reality does not apply.

  “Shut up and calculate.” That is the way people often refer to the standard approach to quantum mechanics. “Don’t waste time thinking about all this stuff” might be a good translation. “Just get going and do the calculations.” I used to think the phrase was pejorative. Now I am not so sure.

  Maybe it is not pejorative. Maybe it is great wisdom.

  The astute reader will have noticed that I have not solved the mystery of

  quantum theory. I have not explained how things can have no properties.

  I have not explained how nonlocality can bind the universe together. No

  matter: I am content to rest. At long last, I have achieved what to me is a great vi
ctory. I have expressed to myself clearly what the mystery is.

  Because in truth I wonder if it is a mystery. Perhaps it is just a fact. This is the way the world is.

  Do I like this new cosmos that we have stumbled into? Do I dislike it? Is

  it congenial to my thoughts, or utterly alien to them? Well, I guess I would say that it makes no difference: this is the new world— get used to it.

  Listen to the words of Richard Feynman:

  We always have had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I’m an old enough man that I haven’t got to the point that this stuff is obvious to me. Okay, I still get nervous with it. … You know how it always is, every new idea, it takes a generation or two until it becomes obvious that there’s no real problem. It has not yet become obvious to me that there’s no real problem. I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.2

  Not long ago I had a dream. In that dream I was on a powerboat far out to

  sea. The engine was off. No breeze blew: we drifted aimlessly. An immense

  silence reigned. The sky was gray and vague, the horizon obscured by haze.

  Nothing was happening. Everything was listless.

  At long last I roused myself to wonder where we were. Reaching down

  into the water I gave a sideways paddle. Slowly the boat spun about— and

  suddenly there came into view a stone jetty. It was a mere few feet away!

  While I had been listlessly waiting, the boat had drifted right up against the shore.

  The boulders of the jetty were hard and clear, utterly solid and picked

  out in vivid relief. Looking upward I saw that the haze had lifted, and that

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  the sky was now a crystalline blue. Gazing down into the water I saw that

  it too was clear and lovely. I could see the bottom. Could I reach it and so give us a push? Leaning over, I found the water just slightly too deep. Or could I reach the jetty, and push off against it? Leaning sideways, I found it just slightly too far away.

  Not a problem— we had an engine. I reached for the starter switch.

  There was a mirror. I looked at my reflection in it. “Time to get going”

  I told my reflection.

  And I did. And we are.

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  Chapter 16

  The epigraph of this book is a quotation from a lecture by Richard Feynman.

  Actually, I took that quote out of context. Here is a bit more of it:

  I think I can safely say that nobody understands quantum mechanics. So do not take the lecture too seriously, feeling that you really have to understand in terms of some model what I am going to describe, but just relax and enjoy it. I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing.1

  Appendix 1: The GHZ Theorem

  It is a complicated matter even to write down Bell’s Theorem— the particular mathematical relation between the various quantities that he proved every hidden­ variable theory must obey. And the proof of his theorem is

  harder still. But some time after Bell’s work, an extension of his theorem was discovered— an extension so simple that it is actually possible to describe the theorem, and to give a nontechnical proof.

  The authors of this new theorem are Daniel Greenberger, Michael Horne,

  and Anton Zeilinger— hence their result’s name: the GHZ theorem. It is an

  extension of Bell’s work. Recall that Bell had envisaged two particles: in the GHZ analysis there are three. Similarly, the old argument had envisaged

  two experimenters, Alice and Bob, while the new one has a third— Chris,

  let’s say. In both theorems the experimenters measure the spins of the particles heading toward them and, as with all quantum measurements of spin, there are only two possible results: the spin is found to lie either along the reference direction of the detector, or against it.

  In Bell’s scenario the particles were in a special entangled state in which Alice and Bob’s measurements yielded opposite results if the detectors were parallel. So in this configuration Alice was able to predict the result of Bob’s measurement prior to his making it— it would be the opposite of what she

  had obtained. Recall the central point of the old EPR argument that had so disturbed Bohr: Einstein and his coworkers claimed that this demonstrated

  that the spin of Bob’s particle must have existed all along, contrary to the principles of quantum mechanics.

  Similarly, in the Greenberger, Horne, and Zeilinger scenario the particles are also in an entangled state, so the results of measurements can also be predicted and the same conclusion would follow. And just as Bell had found

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  Appendix 1

  a way to experimentally test the EPR conclusion, so too do Greenberger and colleagues. Thus experimental metaphysics.

  The GHZ scenario goes as follows. Alice, Bob, and Chris measure the

  components of spin of the particles entering their detectors, and each of

  them writes down on a slip of paper the result. They do so adopting a particular shorthand:

  • If the result was that the spin lay along the detector reference direction, write down the number one.

  • If the spin lay against the direction, write down minus one.

  Finally, the three experimenters collect their results and multiply them

  together. The result is itself a single number: let us call it their final combined result. What might this combined result be? It can only be plus or minus one, since each of its three individual components were either plus or minus one.

  Greenberger, Horne, and Zeilinger envisage measurements in which the

  experimenters orient their detectors so that one is horizontal, and the other two vertical. In this particular configuration their entangled state has an important property: the final combined result can only be plus one. It can never be minus one.

  Follow now the Einstein, Podolsky, and Rosen argument and see what

  it makes of this. Imagine with them that Alice moves far off into the distance, so that Bob and Chris make their measurements before she makes hers. Then they can predict the result she will get! For suppose that Bob

  had obtained, say, spin along the reference direction, and so jotted down

  +1, while Chris had found spin against it and so written – 1. Then, since the product of all three results must be +1, they know that, when Alice makes

  her measurement, she is sure to obtain – 1. So Bob and Chris have determined the spin of Alice’s particle: its spin is against her axis.

  The same is true for the various other results Bob and Chris might have

  obtained. So the usual EPR argument leads to the conclusion that the hidden variable corresponding to Alice’s measurement exists.

  Greenberger, Horne, and Zeilinger realized that they could test this conclusion. They would do so as follows.

  Notice that there are three different ways in which Alice, Bob, and Chris

  can orient their detectors. Two are vertical, and only one of them horizontal—

  but which is the horizontal one? It might be Alice’s. Alternatively, it might be Bob’s that is horizontal, or finally Chris’s. So there are three possible cases.

  The GHZ Theorem 123

  In the first case we can write the final combined result as

  Ahorizontal Bvertical Cvertical

  where by “A” we mean the number Alice wrote down, “B” the number Bob

  wrote down, and so too for “C.”

  In the second case the final result is

  Avertical Bhorizontal Cvertical

  And in the third

  Avertical Bvertical Chorizontal

  Each of these expressions is the product of three things— the three
results that Alice, Bob, and Chris had jotted down on their slips of paper. Recall that these results (plus or minus one) are just shorthand ways to express the fact that the electron’s spin lay along or against the direction of their detectors. And recall that the usual EPR argument was that they must have been real properties of the electrons. If this is so— and here is the hidden­ variable hypothesis in action— then we can treat these three results as simple numbers, and we can rearrange them in any way we wish. That is what Greenberger and coworkers proceeded to do.

  They knew that in their special entangled state each of these products

  equals plus one. So if they were to multiply them together they would still get plus one:

  (Ahorizontal Bvertical Cvertical) (Avertical Bhorizontal Cvertical) (Avertical Bvertical Chorizontal) = +1

  They rearranged this:

  Ahorizontal Bhorizontal Chorizontal (Avertical)2 (Bvertical)2 (Cvertical)2 = +1

  And they recalled that no matter what the three experimenters obtained,

  the numbers they wrote down— A, B, and C— could only be plus or minus

  one. But the square of minus one is plus one, and so of course is the square of plus one. So they realized that they could simply leave out the terms

  involving the parentheses— they were just plus one. And they got a most

  interesting result:

  Ahorizontal Bhorizontal Chorizontal = +1

  In words: if all three experimenters were to orient their detectors horizontally, their final combined result is guaranteed to be plus one. This is a prediction of the hidden­ variables theory, and it can be tested.

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  Appendix 1

  There’s more. Greenberger, Horne, and Zeilinger realized that quantum

  mechanics makes the opposite prediction:

  Ahorizontal Bhorizontal Chorizontal = − 1

  So the final combined result of three horizontal measurements is sure to

  be minus one. So, just as in Bell’s analysis, quantum mechanics disagrees

  with the postulate of hidden variables. Here too, an experiment to measure this result of this configuration would have metaphysical implications.

  That experiment has been done. Its results agree with quantum mechanics, and not with the hidden­ variable hypothesis.

 

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