The ideal of science is that we are investigating a real situation that exists independently of us. But if we are not … then what are we scientists doing?
14 Nonlocality
What are we scientists doing? Before quantum mechanics came along we
would have replied that we are studying the properties of the world. But if there is anything that we have learned from Bell’s Theorem and the experiments that test it, it is that the microworld does not necessarily have certain properties.
To be specific, let us return to the EPR scenario in which Alice and Bob’s detectors are parallel. In this configuration they always get opposite results.
But why? We used to think that it was because the two particles heading
toward those detectors had spins pointing in opposite directions. But as
we saw in chapter 9 that simple picture does not work. Furthermore, as
Bell’s Theorem and the experiments that test it have shown, if we make the locality assumption no picture will work that attributes definite properties to those particles. So once again— what makes Bob’s detector get different results than Alice’s?
It used to be a trivial question. Suddenly it is not so trivial.
If the answer to that question does not involve the properties of the
particle heading toward the detector, then it must involve something else.
What else? There is only one possibility. This possibility has to do, not with particles, but with measurements. It is that in some strange way Bob’s result is connected to a result— the result of Alice’s measurement. We are forced to conclude that the very fact that Alice’s detector gets one result influences Bob’s to get the other.
We must cease thinking about the particles heading toward detectors,
and start thinking about something else— about the behavior of these
detectors. We must realize that these behaviors are connected— invariably
connected, perfectly connected. Our discovery is that Alice’s and Bob’s
detectors always behave in ways that are synchronized, and that they do so
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even if there are no wires leading from one to the other, even if there are no radio transmissions from one to the other, and even if they are thousands
of miles apart. We must understand that the world is utterly connected.
Physicists term this connection “nonlocality.” Things happening far
away are linked to things happening right here.
In proving his result, Bell was careful to analyze theories in which nonlocality had no place. It is only local theories that his theorem and the experiments that test it have ruled out. If, on the other hand, we recognize that the world actually is nonlocal, then Bell’s Theorem has no validity. In such a case, particles in the quantum world can possess perfectly definite properties.
(A theory along these lines was long ago developed by the physicist
David Bohm— indeed, it was by thinking about this theory that Bell was led to his discovery. Within Bohm’s picture quantum particles have perfectly
definite attributes. But even so, his world is utterly unlike the normal world of daily experience, for it is profoundly nonlocal.)
Quite aside from Bohm’s theory, nonlocality denotes an intimate connection between widely separated events. At first glance this linkage might not seem so very strange. Perhaps it reminds us of the utterly connected nature of everyday life, in which we stay in touch with friends through Facebook, follow events in China through CNN, and buy avocados grown in Mexico.
But quantum nonlocality is not like all this. It is not like anything we have ever encountered before.
On the one hand, the nonlocal influence must be able to exert itself
across gigantic gulfs of space. This is because Alice and Bob get opposite results even if they are very far away from one another. Nonlocal connections grow no weaker with distance. Even were Alice located on some distant planet in a faraway galaxy, this invisible agency must be able to exert its controlling sway.
Furthermore, it must do so instantaneously. Our daily connections,
whether by telephone, internet, or the like, travel at the speed of light or slower— but this influence must travel faster than light. For suppose the two electrons in our experiment were set forth on their journeys from a point
half way between Alice and Bob— and then Alice were to take one small step forward. She would receive her electron a fraction of a second before Bob. So the influence we are postulating must travel from her to him in that fraction of a second. Indeed, Alice and Bob could be located at enormous distances
from one another. Alice’s home might lie in a galaxy a million light years
Nonlocality 99
distant, so that a ray of light from her to Bob would require a million years to arrive— but her influence would still get there in no time flat.
Indeed, we are forced to postulate that our mysterious influence travels
at a literally infinite velocity. So this strange new phenomenon has nothing to do with the “telephone calls” between particles that Alain Aspect’s experiment had dealt with (chapter 11). It is another matter altogether.
And yet, according to Einstein’s theory of relativity the very concept of
“no time flat” has no meaning— because while two events may happen at
the same instant to one observer, they do not for another. Many people
believe that we are facing here a major conflict between the two great discoveries of twentieth century physics, relativity and quantum theory.
And finally, it is not at all clear who is doing the influencing. If Alice receives her particle first we might be willing to say that the result of her measurement caused the result of Bob’s. But if she takes a few steps back then Bob would be the first to register a measurement. Is it now Bob’s detector that is calling the shots? And finally, what would we say if Alice and Bob receive their particles at the very same instant? Then what is influencing what?
The lesson we must take from this is that we cannot think of one result
“causing” the other. We must think only of a synchronization between the
results. Of a correlation between the behaviors of the detectors.
Doesn’t this correlation violate Einstein’s principle that nothing can
travel faster than light? After all— something that travels at an infinite velocity certainly seems to be achieving this remarkable feat. It does not—
for three reasons. In the first case, Einstein’s principle applies to objects (spaceships and the like) but our postulated influence is not an object. In the second case, Einstein’s principle applies to causes— to physical processes that exert a causative effect. But the influence we are postulating is not a cause in anything like the ordinary sense of the term. There is nothing Alice can do to make Bob’s detector do anything. She cannot cause his detector
to obtain a certain result— because she cannot cause her detector to obtain its result. It is not Alice who influences Bob’s detector: it is the result she obtained. And finally, Einstein’s principle applies to information— to messages that we send one another. But even though Alice and Bob might have a prior agreement that, say, receipt of an electron with spin up means “sell all your stock in Facebook,” the fact that Alice cannot control the result Bob’s detector gets means that she cannot control the message he gets …
and an uncontrollable message is no message at all.
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Perhaps strangest of all is that Alice and Bob might not even know that
their electrons are connected in this strange fashion. If Alice studies only her particle, nothing she can do will alert her to the fact that it is associated with Bob’s. The same applies to Bob. Both experimenters believe themselves to be studying isolated, individual particles. Only if they were to get together and compare notes would th
ey realize that the electrons they were studying were actually connected. The same applies to any pair of particles.
Perhaps the electrons in your prefrontal cortex are intimately linked with those in the brain of that person across the room— a person you have never met before. Or perhaps they are linked with electrons in the body of some
alien creature living on a world in a distant galaxy of which we are entirely unaware.
The message of nonlocality is that the world is utterly connected. The
fall of a tree in Chile might be linked with the rising of a plume of dust on Mars. The fall of a sparrow in Norway might be linked with the birth of a
baby next door.
15 Quantum Machines
The birth of a baby next door … or the secure transfer of funds from Vienna’s city hall to the Bank Austria Creditanstalt— a transfer initiated by the city’s mayor, executed by the bank’s director, and announced at a press conference. That was in 2004.
What began as a philosophical difference among a small group of
physicists nearly a century ago has blossomed into what promises to be a
worldwide industry— an industry based on quantum mechanics. Billions
of dollars are involved. Google is interested in quantum nonlocality. So are Facebook and MIT. Venture capital firms are sitting down at the table, as well as the CIA. Above the boardrooms of mighty governments and corporations
float the ghosts of Einstein, Bohr, and Bell. Mild, philosophical, perhaps a bit otherworldly, they have been shoved aside by the new breed: those cando types who roll up their sleeves, brush aside the niceties, and get down to cases. The old stigma has passed— passed with a vengeance.
But why? What has happened to the old antipathy to philosophically
tinged questions, the antipathy that stifled the field for years? Part of the answer is a simple matter of time. A new generation of researchers has
come of age— researchers no longer in thrall to Von Neumann’s erroneous
proof or to the necessities of the Cold War. These people never experienced the old days, were hardly touched by that subtle, all pervasive amusement that once greeted those who asked such questions— an amusement I must
have unconsciously sensed when I was a student, and that steered me away
from these matters for so many years.
But I think there is another factor at play. As I wrote in chapter 12, I think it is also a matter of the advance of technology. In the intervening years technology has progressed so rapidly that it is now possible to actually do the experiments of which previous generations could only dream. Thought
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experiments have been replaced by real ones. It is no longer a matter of
arguing about what such and such an experiment might reveal: now you
can actually find out. There it is again: the thing I love about science— the wonderful sense of freedom and openness and possibility to the business of research. If you can do something you do do it, and all those psychological and historical issues be damned. Science is a can do enterprise. So philosophy is invading industry.
And strange to say, all this has been made possible by a breed pretty much uninterested in philosophy. The new age of experimental metaphysics has
been made possible by people in love, not with philosophy, but with gadgets.
These are people who delight in inventing new devices, new procedures, and new ways of doing experiments. If their wonderful new gadgets can be pressed into service to answer a primarily philosophical question, all well and good.
But it was never their primary concern. So industry is invading philosophy.
And so experimental metaphysics.
If you are transferring funds you are transferring information— information about your bank account number, let us say. This might be done in person,
or by email. But if your name happens to be Alice, and the teller at the bank is named Bob, a whole new dimension of the situation just might occur to
you. Can information be conveyed by quantum particles?
When we measure the spin of a particle, we learn whether that spin is
along or against the direction of our detector. Suppose we agree that a spin along represents a “0” and a spin against a “1.” Then our measurement has
told us a number.
That number is in binary— the number system of base two. We are used
to writing numbers in base ten. But the translation is straightforward:
Base 10
Base 2
0
0
1
1
2
10
3
11
4
100
.
.
.
.
.
.
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Suppose Alice sends Bob three electrons, the first with spin against his
detector’s axis– that’s a “1”— and the next two along the axis— these are
“0s.” Then this represents the sequence “100”— which, if we think of it as the binary representation of a number, we would interpret as a “4.” Using
those electrons, Alice has told Bob a number.
We can also transfer letters of the alphabet. It can be so simple a matter as agreeing that “1” represents the letter “a,” “2” represents a “b,” and so forth.
There are more sophisticated codings, but the principle is the same. In every case we can find a means of translating the information we wish to convey
into binary numbers, and then we can use electron spins to encode those
numbers. Alternatively, we can use particles of light— photons.
It’s not enough to transfer information. The transfer needs to be secure.
We need to make our information available to the intended recipient, but
not available to anybody else. The world is full of eavesdroppers— hackers trying to steal our credit card numbers, wartime enemies trying to steal our battle plans. If you are a certain soft drink company, you might wish to
keep the formula for Coca Cola secret from competitors, while revealing it to your factories worldwide. How to guard against snoops?
Secrecy in the transfer of information has a long and fascinating history.
In one ancient method, the head of a courier was shaved, the message was
written on his scalp, and his hair was allowed to grow back. The courier
could then travel to the intended recipient, where his head was shaved,
thus revealing the message. A more recent technique was to lock the secret message into a briefcase, handcuff the briefcase to a courier, and send the courier off to the recipient— a recipient who had the only key to the briefcase. I recall sitting next to such a courier once in an airplane.
Both of these methods entailed trusting the couriers— and a long trip
too, one that might very well be expensive and time consuming. Far
cheaper, and far more rapid, would be something like a telephone call
or a transfer over the Web. How to guard against eavesdroppers in these
situations?
The method is to encrypt the message— to scramble it in some way. Suppose we send the message “MN.” An eavesdropper could easily intercept it, but she would not have the slightest idea what it means. If, however, you
and your intended recipient had agreed beforehand that you would send the
letter of the alphabet lying before each letter of your message, the recipient would know that in fact you had sent the word “NO.”
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Such a method of encryption is known as the “key”— it unlocks the message. This one, of course, is very simple, and it is one that any smart eavesdropper could foil with ease. It is far better to use a more complicated key.
&n
bsp; Suppose, for example, that we use some random string of numbers, such as
726 …
and suppose we simply add each digit to the corresponding digit in the
message we wish to send. If, for instance, Alice’s credit card number begins with the digits
547 …
then she would add the key to her number
7 + 5, 2 + 4, 6 + 7 …
and send the message
12,6,13 …
If Bob knew the key, he could decode the message and so learn the first
three digits of Alice’s credit card number. And if nobody else knew the key, eavesdroppers would be foiled.
Of course, Alice has to tell Bob about the key she used— and this “telling” itself must be secret. There is a whole branch of mathematics devoted to the study of encrypting and decrypting messages. It is known as cryptography. No cryptographic method is foolproof. Some brilliant new technique is invented … and then, far sooner than anybody expected, some brilliant
hacker finds a means of circumventing it. For obvious reasons, large corporations are interested in cryptography, as are governments. Billions of dollars are involved.
People’s lives are involved as well. During the Second World War, Germany encrypted its messages using a devilishly complicated device known as the “enigma” machine. In absolute secrecy, code breakers stationed at
Bletchley Park in England succeeded in deciphering the code, revealing
vitally important military plans. Their triumph shortened the war, probably by several years, saving untold numbers of lives. Had they failed, would an atomic bomb have been dropped on Berlin?
In 1991 the physicist Artur Ekert invented a way to encrypt a key relying on quantum mechanics. The method is to use our old familiar pair of entangled particles, for which measurements of spins always yield opposite results. Suppose we send out a series of such entangled pairs. For each one,
Quantum Machines 105
Alice and Bob can translate the results of their spin measurements into
binary numbers— and then, if Bob simply reverses his digits, his number
is guaranteed to be the same as Alice’s. After measuring all the particles, Alice and Bob will have the same series of numbers— the same key. If Alice uses her key to scramble the message she wishes to send, Bob can use his
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