by Lee Smolin
Bell introduced an assumption which expressed the idea that physics is local, in that information cannot travel faster than light. This requires that when the two photons are very far apart, the questions I choose to ask one photon cannot affect the answers the other will give.
From this assumption, Bell derived a restriction on the proportion of cases in which both photons pass their polarizers. This restriction depends on the angle between the two planes of polarization.
Bell asked first whether the restriction is violated by the predictions of quantum mechanics. He found that for certain angles it is violated. This means that quantum mechanics violates Bell’s principle of locality. We can easily see that this is the case in the story of our couple. When Anna and Beth each go off to work, they share a single quantum state, the state CONTRARY. This is not a property of either of theirs as individuals. It is a shared property; it makes sense only when it is ascribed to the couple. This situation is already in tension with the philosophy that physical properties are local.
But it gets worse. When Beth’s coworkers ask her about her pet preference she says she loves cats. This immediately changes her quantum state, as prescribed by Rule 2. It was originally indefinite, but now she is purely a cat person. If asked again about pet preference she is certain to say “cat,” so the state CAT defines her.
But by the same logic, because they started the day in the CONTRARY state, Anna became at that moment a person with a definite preference for dogs. If asked by her colleagues which pets she prefers, Anna is now 100 percent certain to say “dogs.”
Thus the measurement of Beth’s preference appears to instantly affect Anna’s state. In spite of the fact that it was Beth who was measured, and Anna has talked to no one, Rule 2 applies to Anna as well. This is an example of the phenomenon known as quantum nonlocality.
The story would be exactly the same if Beth were asked her political leanings. Whichever way she answered, Anna would instantly become the other.
Once Beth is asked about one of her preferences, she and Anna no longer share a state. Beth now has a definite state of her own, and you can say this was the result of her being measured. What is weird is that, because they were originally together in the entangled state CONTRARY, when Beth is queried this immediately changes Anna’s state as well. By virtue of the answer that Beth gives, Anna is immediately defined as being in a quantum state of her own, to wit, the opposite of whatever answer Beth gives.
This happens even though no one has yet asked Anna anything. Beth and her colleagues may be light-years away, so no information about what Beth was asked and what she answered could reach Anna for years, assuming the usual restriction on the transmission of information. This is to say that Anna herself cannot know yet that her quantum state has changed. But it has, if quantum theory is correct.
Of course, the story would be the same if it were Anna who had been asked first. The consequences of sharing an entangled state are entirely symmetric.
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THE STRANGE BEHAVIOR of the quantum state CONTRARY was discovered by Einstein, and it was the centerpiece of a paper he wrote in 1935 with two younger colleagues, Boris Podolsky and Nathan Rosen.1 The three authors (sometimes abbreviated as EPR) used an experiment like I’ve described to argue that quantum mechanics must be incomplete. To arrive at that conclusion they gave a criterion for when a property of a physical system must be considered real. Here is their criterion:
If, without in any way disturbing a system, you can determine a property of it with 100 percent certainty, there must be an element of physical reality associated to that property.
Einstein and his collaborators also assumed that you could only disturb a system by doing something physically to it. Most importantly, they also assumed that any physical disturbance is local, and is hence restricted to traveling at the speed of light or less. This implies in particular that
Anna cannot be physically affected by the choice of questions Beth is asked until enough time has passed for a light signal to have carried the information about which question Beth was asked from Beth to Anna.
We have just seen that once Beth’s colleagues query Beth about her pet preference, they also know Anna’s pet preference. However, Einstein and his friends believed strongly in the principle of locality, which implies that, because they are far apart, Anna cannot have been disturbed by questions asked of her faraway friend Beth. Hence, the criterion for reality just enunciated is satisfied and we can conclude that Anna’s pet preference is an element of reality.
Moreover, what is real concerning Anna can’t be affected by anything that happens or doesn’t happen to Beth. So Anna’s pet preference must be real whether or not Beth’s pet preference was queried.
Now, notice that Beth’s colleagues might instead have asked about her politics. The same argument works and we must conclude that Anna’s political preference is also an element of reality. And again, this is true whether or not Beth’s politics was queried.
So we must conclude that both Anna’s pet preference and her politics are elements of reality!
But quantum states cannot simultaneously describe both someone’s politics and their pet preference. Hence, Anna’s quantum state incompletely describes her.
And so, concluded Einstein, Podolsky, and Rosen, the description of the world in terms of quantum states is incomplete.
I’ve been thinking about this argument since my first year of college. So far as I can tell it’s logically correct. But notice that it depends on the assumption that physics is local. Einstein and his young friends assumed locality when they posited that Anna cannot be physically affected by the choice of questions Beth is asked when they are far apart.
Bell made exactly the same assumption, regarding photons rather than people, in deriving his restriction.
When the two photons are very far apart, the questions I choose to ask one photon cannot affect the answers the other will give.
This is, indeed, the only non-trivial assumption in Bell’s argument. So since, as I said, Bell’s restriction disagrees with quantum mechanics, it must be that quantum mechanics itself disagrees with locality.
But we can go further and test directly whether locality, as assumed by EPR and Bell, is violated by nature.
The importance of Bell’s restriction is that it applies not only to quantum mechanics. The restriction he derived constrains any theory that satisfies Bell’s and EPR’s principle of locality. This includes theories that are intended to replace quantum mechanics. It will apply equally to any theory which might be invented in the future. This means that we can set up experiments that directly test the locality principle.
Fortunately, Bell’s restriction could be tested by a relatively inexpensive device, hand-built in a single room. A few brave souls began the work of building experiments to test the theorem. After several attempts got partial and contradictory results, the definitive experiments were carried out in Orsay, near Paris, in the early 1980s by Alain Aspect and his collaborators, Jean Dalibard, Philippe Grangier, and Gérard Roger.2
In Aspect’s experiments the entangled particles are photons and the questions asked are about their planes of polarization. These experiments begin with an atom raised from its ground state into an excited state, by a photon from a laser. These are chosen so that when the excited atom decays back to the ground state, it does so in a way that produces a pair of entangled photons, in the state CONTRARY. The photons fly off in opposite directions and after a few feet encounter polarizers, which measure their polarizations relative to a plane. The plane of each polarizer can be set freely, in whatever position the experimenter chooses, so the correlations of the polarizations of the two photons can be measured. The results cleanly violated Bell’s restriction while agreeing precisely with the predictions of quantum theory.
The experiments tell us that the assumption of Bell locality hi
ghlighted above is false! The quantum world does not obey the principle of locality.
If this is not the most shocking news you have heard from the world of science, you have perhaps not understood it. Nature does not satisfy the idea of locality. Two particles, indeed two objects in the world, situated far from each other, can share properties that cannot be attributed to properties separately enjoyed by either.
At this point it is natural to wonder if the principle that information cannot be transmitted faster than light could be violated, by taking advantage of the circumstance that Beth and Anna share an entangled state. Could the fact that Anna’s state is changed abruptly, based on which question Beth is asked, be used by Beth’s colleagues to send a message instantaneously to Anna’s colleagues?
The answer is that information cannot be sent faster than light, because the relation between Anna’s state and the answers she gives is random. No matter what question Anna is asked, her answers are 50 percent either way. This is true before Beth is queried, when she shares the state CONTRARY with Anna, and it remains true afterward. It is only when the lists of answers each gave to a series of questions are brought together and compared that evidence of mysterious correlations appears. And the lists are ordinary classical objects that cannot be transmitted faster than light.
There is another, related possibility, which Aspect and his colleagues could also test. Perhaps, at some deeper level than that described by quantum theory, the two atoms are in communication, so that the first photon to be measured transmits information to the other photon about what question it was asked. Then the principle of locality could still be satisfied. But now we have to reckon with special relativity, which maintains that no information can travel faster than light. To test for this possibility, the experiment was redone with a random switch on one side, which could very rapidly choose which question would be asked of its photon. This switch was fast enough that the choice was made while the photons were in flight. Thus the switching happened faster than could be communicated to the other photon by any signal traveling at light speed or less. The result was unchanged. If the two photons are in communication, their messages are being transmitted much faster than light, and relativity theory is violated.
What are we then to make of the argument of Einstein, Podolsky, and Rosen? As clever as it was, the argument must be considered, in light of the experimental findings, to be wrong, because it relies on an incorrect assumption, which is the assumption of locality. The experimental tests of Bell’s inequality show us that, once Anna and Beth are entangled in the state CONTRARY, Anna in fact is physically affected by the choice of questions Beth is asked. This remains true even when they are far apart. This is true in quantum mechanics, and, the experiments imply, it must be true in any deeper theory that completes quantum mechanics.
Nevertheless, EPR’s paper was enormously important, because it exposed an unexpected aspect of quantum physics, which was entanglement. This took decades to appreciate; indeed, the EPR paper was way ahead of its time. Apart from the discovery of entanglement, the paper was the starting point for Bell and hence for the shocking experimental discovery that physics violates the principle of locality.
Bohr, the great anti-realist, replied right away to the EPR paper, with an especially obscure example of his style of reasoning.3 He took issue with EPR’s criteria for reality by pointing out that a measurement of one of the particles disturbs the other particle indirectly, by disturbing the context within which the properties of the other particle make sense.
For the next fifteen years there is just one paper written which cites the EPR paper. The next several citations are by Bohm and Everett in the 1950s. John Bell was just the sixth author to cite EPR, which he did in his great paper of 1964, almost thirty years later. Yet the paper was cited more than sixty times in 2015, and again in 2016. We now, finally, live in the era of entanglement.
In recent years, the sharing of properties among entangled pairs has been confirmed in experiments in which the pairs are separated by hundreds of kilometers. Entanglement is fast evolving from a laboratory curiosity into a technology. It is now considered a resource, which is at the heart of a new kind of computer—a quantum computer. In the near future entanglement may allow us to break codes long thought secure as it also makes possible new kinds of codes that are truly unbreakable. There are already in orbit quantum communications satellites, which employ entangled pairs to encrypt messages they transmit.
Einstein’s first revolutionary papers appeared in 1905, when he was twenty-six. Thirty years later, the EPR paper was the last paper by Einstein to shake physics to the core. It is given to very few to lead science over three decades. Einstein never ceased trying to find the deeper theory beyond quantum mechanics, and two decades further on, he was still working in his notebook in the hospital the night he died. But he failed, and the simple reason was that he never understood that the central assumption behind many of his great papers—the principle that physics is local—was wrong.
There is no reason Bell’s 1964 paper could not have been written in the late 1930s, shortly after EPR. And the experimental disproof of locality could have happened shortly after. One can only wonder what Einstein would have thought had he learned of Bell and Aspect in the 1940s.
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TOGETHER THE STORIES I have told so far illustrate the strangeness of the quantum world. They have taught us about the wave-particle duality, superposition, and the uncertainty principle.
Stranger still was how quantum properties can be entangled and shared among systems that are widely separated in space. This was the ultimate lesson of the story told by Einstein, Podolsky, and Rosen. But it was only in John Bell’s retelling that the true moral of the story was revealed to be the radical nature of quantum nonlocality.
As we saw, superposition can be understood as a quantum version of “or,” which I will indicate as or. When we combine two systems, we use a quantum version of “and.” I will write this as and. Each behaves differently from the ordinary usage of “or” and “and” that we are used to from everyday life. But it is when they act together that truly strange things happen. We see this in a famous experiment called Schrödinger’s cat.
Let us start with a very simple model of an atom, which can exist in two states: an excited, unstable state, which we call EXCITED, and a stable ground state with lower energy, called GROUND. EXCITED, being unstable, will decay into GROUND by emitting a photon, which carries away the energy. These decays take place at a rate measured by the half-life of the excited state.
Let us put an atom in the state EXCITED in a box and wait a time comparable to the half-life. If we don’t look in the box, we can deduce only that the probability is about half that if we open the box we will see that the atom has decayed to the state GROUND. But what is the state before we look inside the box? According to quantum mechanics, it is neither EXCITED nor GROUND, but a superposition of them. We can write this as
ATOM = EXCITED or GROUND
According to Rule 2, this superposition has the potential of becoming, when we look, either of the two states: EXCITED or GROUND. If we have a large collection of such states, then we can determine probabilities for each of these outcomes. These probabilities change in time. Just after making the atom, the probability that it has decayed is very small. Many times the half-life later, it has almost certainly decayed.
A superposition is not the same as having one or the other state with varying probabilities. One reason is that when we make the energy uncertain by superposing two states of different energies, another observable will be made certain. This is like the way we made our visitors have definite political views by superposing their states with different pet preferences. So we can always find a question complementary to the energy that the answer to will be YES with certainty. That would not be the case if we were just dealing with the probabilities of being EXCITED or GROUND.
We next put a Geiger counter in the box, and set it up to send out a pulse of electricity whenever it sees a photon.
From the point of view of quantum mechanics, the Geiger counter can also exist in two different states. There is the state NO, in which it hasn’t seen a photon, and the state YES, when it has. It can also exist in superposition of these two states.
We put the atom in the box with the Geiger counter. We must be careful to set them up so that initially the atom is in the state EXCITED and the Geiger counter is in the state NO.
INITIAL = EXCITED and NO
By and we understand that these states, being states of two different systems, are being combined, not superposed.
Much later, if everything is working well, we expect to see the atom in the state GROUND and the Geiger counter in the state YES. This corresponds to the Geiger counter having detected the photon emitted when the atom decayed.
FINAL = GROUND and YES
In between, the system is in a superposition of these two states.
IN BETWEEN = (GROUND and YES) or (EXCITED and NO)
The total system is a superposition of a state where the atom is in the undecayed state EXCITED and the Geiger counter is in the state NO with the other possibility, which is the state in which the atom has decayed to GROUND and the Geiger counter is in the state YES, in which it has seen the photon.