Quantum entanglement has been in the news (again), and in response to several puzzled enquiries, here is my attempt to disentangle the subject. Adapted from various bits of my previous writings, including Q is for Quantum, Schrödinger’s Kittens, and Science: A History in 100 Experiments. I also recommend George Musser’s book Spooky Action at a Distance.
Common sense tells us that if I hit a cricket ball on a playing field in England, this has no effect on a cricket ball in Australia, even if the two balls were manufactured in the same batch in the same factory and once nestled together in the same box. But does the same common sense apply to things in the quantum world, like photons and electrons? Bizarre though it may seem, in the twentieth century quantum physics proved by experiment that the answer is “no”.
It all started in 1935, when Albert Einstein and his colleagues Boris Podolsky and Nathan Rosen presented a puzzle (sometimes known as the “EPR Paradox”) in the form of a thought experiment.
Faster than light?
By 1935, Einstein was settled in Princeton, at the Institute for Advanced Study. He had been working with two younger colleagues, Boris Podolsky (1896-1966) and Nathan Rosen (1909-1995), and together (led by Podolsky on this occasion) they had come up with what seemed to them an unarguable refutation of the nonsense (as they saw it) inherent in the idea of collapsing wave functions and the Copenhagen Interpretation. This is the bizarre idea (still widely, but incorrectly, taught as the best way to understand the quantum world) that nothing is real until it is measured. An electron for example, exists (according to the Copenhagen Interpretation) as an indeterminate superposition of waves until someone looks at it, when it “collapses” into a point, before spreading out as waves again as soon as you stop looking. Their paper describing what became known as the “EPR Paradox”, even though it is not really a paradox, appeared under the title “Can quantum mechanical description of physical reality be considered complete?” in the journal Physical Review in May 1935. They described the puzzle in terms of measurement of position and momentum, but I shall use what seems to me a simpler example involving electron spin.
Imagine a situation in which two electrons are ejected from a quantum system (such as an atomic nucleus) in different directions, but required by the laws of symmetry to have opposite spin. According to the Copenhagen Interpretation (largely devised by the Dane Niels Bohr, hence the name), neither of the electrons possesses a definite spin until it is measured; each exists in a 50:50 superposition of spin up and spin down states, until it is measured. Then, and only then, the wave function collapses into one or the other state. But in this example the laws of symmetry require the other electron to have the opposite spin. This is fine when both electrons are in the superposition of states, but it means that at the instant one electron is measured, the other electron, which might by now be far away (in principle, on the other side of the Universe) collapses into the opposite state at the same instant. How does it know to do this? It seems that what Einstein called a “spooky action at a distance” links the two particles, which communicate with one another faster than light. And all quantum entities (which means everything) must be linked in the same way.
It is a key tenet of the theory of relativity, which has passed every test ever applied to it, that no signal can travel faster than light, so Einstein, in particular, saw this as a complete refutation of Bohr’s ideas. The EPR paper concluded that this makes the reality of properties of the second system “depend upon the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this.”
The alternative that Einstein favoured is that there is some kind of underlying reality, an invisible clockwork which controls the workings of the Universe and gives the appearance of uncertainty, collapsing wave functions and so on, even though “in reality” each of the electrons, in this example, always has a well-defined spin. In other words, things are “real”, not in a superposition of states, even when we are not looking at them. The idea that the Universe is composed, even at the quantum level, of real things that exist whether or not we observe them, and that no communication can travel faster than light, is known as “local reality”.
It is, perhaps, jut as well Einstein did not live to see a series of beautiful experiments carried out in the 1980s which proved that local reality is not a good description of the Universe; more of this later, but the implication is that we are forced to abandon either the local bit (allowing communication faster than light) or reality (invoking instead collapsing wave functions). But nobody knew this in 1935, and Erwin Schrödinger in particular was delighted when he saw the EPR paper. He wrote at once to Einstein, commenting that “my interpretation is that we do not have a q.m. that is consistent with relativity theory, i.e, with a finite transmission speed of all influences”, and in a paper published in the Proceedings of the Cambridge Philosophical Society later that year said “it is rather discomforting that the theory should allow a system to be steered or piloted into one or the other type of state at the experimenter’s mercy in spite of his having no access to it.” This was the genesis of Schrödinger’s famous cat, and also introduced the term “entanglement” into the quantum story.
The truth about the cat in the box
The ideas encapsulated in the famous “thought experiment” involving Schrödinger’s cat actually came in no small measure from Einstein, in the extended correspondence between the two, triggered by the EPR paper, and preserved in the Einstein Archive at Princeton University. Einstein introduced the idea of two closed boxes and a single ball, “which can be found in one or the other of the two boxes when an observation is made” by looking inside the box. Common sense says that the ball is always in one of the boxes but not the other; the Copenhagen Interpretation says that before either box is opened a 50:50 wave function fills each of the boxes (but not the space in between!), and when one of the boxes is opened the wave function collapses so that now the ball is in one box or the other. Einstein continued “I bring in the separation principle. The second box is independent of anything that happens to the first box.”
In a later letter, Einstein came up with another reductio ad absurdum. He suggested to Schrödinger the idea of a heap of gunpowder that would “probably” explode some time in the course of a year. During that year, the wave function of the gunpowder would consist of a mixture of states, a superposition of the wave function for unexploded gunpowder and the wave function for exploded gunpowder:
In the beginning the -function characterises a reasonably well-defined macroscopic state. But, according to your equation, after the course of a year this is no longer the case at all. Rather, the -function then describes a sort of blend of not-yet and of already-exploded systems. Through no art of interpretation can this -function be turned into an adequate description of a real state of affairs . . . in reality there is just no intermediary between exploded and not-exploded.
Stimulated by the EPR paper and his correspondence with Einstein, Schrödinger wrote a long paper, published in three parts in the journal Die Naturwissenschaften later in 1935, summing up his understanding of the theory he had helped to invent. It was titled “The Present Situation in Quantum Mechanics”, and it introduced to the world both the term entanglement and the cat “paradox” that (like the EPR “paradox”) is not really a paradox at all. An excellent English translation of the paper, by John Trimmer, appeared in the Proceedings of the American Philosophical Society in 1980, and can also be found in the volume Quantum Theory and Measurement edited by John Wheeler and Wojciech Zurek. Many garbled accounts of the cat in the box “experiment” have appeared over the years, but it is best to go back to this source and Schrödinger’s own words (as interpreted by Trimmer) to get the puzzle clear:
One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The -function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.
It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation.
In other words, according to the version of quantum mechanics that was generally taught and widely (but not universally) accepted for the rest of the twentieth century, the cat is both dead and alive (or if you prefer, neither dead nor alive) until somebody looks inside the chamber and by the act of observation “collapses the wave function”. But there is nothing in the equations about collapsing wave functions. This collapse business is an entirely ad hoc idea, introduced by Bohr, with no basis in reality. That is the single most important message to take away from Schrödinger’s thought experiment (which, I stress, is indeed “all in the mind”; nobody has ever done anything like this to a real cat). Although the “cat-in-the-box” idea did not generate widespread interest in 1935, Einstein at least fully appreciated the importance of Schrödinger’s puzzle; Schrödinger described the idea to him in a letter, before his paper was published, and Einstein replied:
Your cat shows that we are in complete agreement concerning our assessment of the character of the current theory. A [wave]-function that contains the living as well as the dead cat just cannot be taken as a description of a real state of affairs.
Schrödinger was right to point out the nonsensical nature of the concept of the collapse of the wave function, and there are much better ways to understand the workings of the quantum world – the most intriguing of which Schrödinger himself later came close to developing (my own preferred explanation, which involves the Many Worlds Interpretation; but that is anther story).
The EPR puzzle itself was later refined by David Bohm, and later still by John Bell. In its later form, the puzzle concerns the behaviour of two photons (particles of light) ejected from an atom in opposite directions. The photons have a property called polarization, which can be thought of as like carrying a spear pointing either up, down or at any angle across the direction of travel; the key feature of the puzzle is that the photons must have different polarization, but correlated in a certain way. For simplicity, imagine that if one photon is vertically polarised the other must be horizontally polarised.
Now comes the twist. Quantum physics tells us that the polarization of the photon is not determined – it does not become “real” – until it is measured. The act of measurement forces it to “choose” a particular polarisation, and it is possible (indeed, straightforward) to set up an experiment which measures a photon to decide if it vertically polarised, or horizontally polarised. The essence of the EPR “paradox” is that according to all this, measuring one of the pair of photons and forcing it to become, say, vertically polarised instantaneously forces the other photon, far away and untouched, to become horizontally polarised. Einstein and his colleagues said that this is ridiculous, defying common sense, so quantum mechanics must be wrong.
After John Bell presented the puzzle in a particularly clear form in the 1960s, the challenge of testing the prediction was taken up by several teams of experimenters, leading up to a comprehensive and complete experiment carried out by Alain Aspect and his colleagues in Paris in the early 1980s. Although such experiments have since been refined and improved, they always give the same results that emerged from the Aspect experiment itself.
The key feature of the experiment is that the choice of which polarisation will be measured is made automatically and at random by the experiment, after the photons have left the atom. At the time the photon arrives at the polariser, there has not been long enough for any signal, even travelling at the speed of light, to have reached the other side of the experiment. So there is no way that the detector used to measure the second photon “knows” what the first measurement is.
It would be very difficult (just about impossible with present technology) to do the experiment literally with pairs of photons, two at a time; but in the Aspect experiment and its successors very many pairs of photons are studied, with more than two angles of polarisation being investigated, and the results analysed statistically. John Bell’s great contribution was to show that in this kind of analysis if one particular number that emerges from the statistics is bigger than another specific number, common sense prevails and there is no trace of what Einstein used to call “spooky action at a distance”. This is what Bell expected to happen, and it is known as Bell’s Inequality. But the experiments show that Bell’s Inequality is violated. The first number is smaller than the second number. Experiments are somehow particularly convincing when they prove the opposite of what the experimenters set out to find – it certainly shows that they were not cheating, or unconsciously biased by their preconceptions! And as Richard Feynman pithily summed up the essence of science, “if it disagrees with experiment, then it is wrong”. So Einstein was wrong. But what does it mean?
The pairs of photons really are linked by spooky action at a distance, confounding “common sense”, in the state quantum physicists call entanglement. What happens to photon A really does affect photon B, instantaneously, no matter how far apart they are. This is called “non-locality”, because the effect is not “local” (specifically, it occurs faster than light}. But (and it is not just a big “but” but an absolutely crucial “but”) it turns out that no useful information, such as the result of the 3.30 race at Newmarket, can be transmitted faster than light by this or any other means). The polarizations of the photons are determined at random. Measuring the polarization of photon A determines the polarization of photon B, but someone who can only detect photon B still sees a random choice of polarization. It might be different random choice from the one that would have occurred if photon A had been affected differently, but it is still random. The only way to extract useful information from studying photon B is to send a message (slower than light) from A to B informing the observer what was done to photon A. Nevertheless, the Aspect experiment and its successors show that the world is non-local. And this strange property even has practical implications, in the rapidly developing world of quantum computing. This may not be a “reasonable definition of reality”, but it is the way the world works.
Feynman was particularly delighted by this definitive experimental evidence of the way the quantum world works. “I’ve entertained myself always,” he said, “by squeezing the difficulty of quantum mechanics into a smaller and smaller place, so as to get more and more worried about this particular item. It seems to be almost ridiculous that you can squeeze it to a numerical question that one thing is bigger than another. But there you are.”
Don’t worry, though if you do not understand how the world can be like that. As Feynman also wrote, in The Character of Physical Law, “I think I can safely say that nobody understands quantum mechanics . . . Do not keep saying to yourself, if you can possibly avoid it, ‘But how can it be like that?” because you will go ‘down the drain’ into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.”