Quantum Entanglement and Schrödinger's Cat — What the EPR Paper Started in 1935

Last time we followed Bohr and Einstein through the Solvay conferences (Part 5 is here). The uncertainty relation held, but one of Einstein's questions was left standing: does the theory say everything there is to say about a single event? This final part is about 1935, the year that question became a paper. Within a few months came four pages from Einstein and two colleagues, a reply from Bohr, and Schrödinger's cat. Out of that exchange came a name for something new: entanglement, a tie between two separated things that can only be described as one whole.

"If you can tell without touching it, it was already there"

On 25 March 1935 a manuscript reached the American journal Physical Review. Its authors were Einstein and his two assistants, Boris Podolsky and Nathan Rosen; from their initials it is known as the EPR paper. It ran to four pages in the issue of 15 May, and its title was a question: "Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?"

The argument starts from a yardstick. If you can predict the value of some quantity with certainty, without disturbing the system in any way, then that quantity was really there, on the system's side, before you looked. The paper took this as its test of what counts as real.

Next, take two particles. Let them interact once and then move far apart. Quantum mechanics allows a pair for which measuring the position of one tells you, with certainty, the position of the other. With the very same pair, measuring the momentum of one (how hard it would hit) tells you the momentum of the other.

Nobody has touched the distant particle. So by the yardstick, both its position and its momentum were settled from the start. Yet quantum mechanics cannot give definite values to position and momentum at the same time. If something is settled and the theory cannot say it, the theory's description is not complete. That was the paper's conclusion.

Einstein did not write it

The text was written by Podolsky. According to the philosopher Arthur Fine, who has studied the history of this dispute, Einstein apparently never checked the draft before it was sent, and he was not pleased with the result. On 19 June he wrote to Schrödinger that, for reasons of language, the paper had been written by Podolsky after several discussions; that it had not come out as he had wanted; and that the essential point was, so to speak, buried under learnedness.

Einstein's own argument, as he gave it in his letters, is shorter. There is no need for both position and momentum. Position alone will do. Measure the position of the particle at hand and you know the position of the distant one. Whatever is done here, the real situation of the particle over there cannot change (he called this the "separation principle"). So the distant particle was at that position before anything was measured. But the quantum formula gives the distant particle no definite position before the measurement. So the formula does not say everything about the real situation.

As for whether position and momentum can be fixed together, he told Schrödinger he could not care less. The EPR paper is sometimes presented as a trick for getting around the uncertainty relation. That was not what Einstein was after. His question has the same shape as the one in the 1927 proceedings and the 1931 box of light we saw last time.

Bohr's reply, under the same title

Bohr answered with a paper carrying exactly the same title. It reached the same journal on 13 July and appeared in the issue of 15 October. Its abstract states the answer: the EPR yardstick "contains an essential ambiguity" when it is applied to quantum phenomena.

The ambiguity lay in the words "without in any way disturbing". Bohr agreed that measuring the particle at hand does not push or pull the distant one. But choosing whether to set up the apparatus for position or for momentum, he said, does affect the conditions that decide what kinds of prediction can be made about the distant particle. An arrangement that measures position and one that measures momentum cannot be built at the same time. So one cannot say that position and momentum were both settled together. The arrangement of the apparatus is part of the phenomenon. This is the idea of complementarity from last time.

The reply is known for being hard to follow. Bohr himself, rereading it in 1949, wrote that he was deeply aware of its "inefficiency of expression", which must have made the line of argument very difficult to appreciate. No push or pull, and yet an effect on "the conditions": Fine's verdict is that the meaning of this claim is not at all clear.

Schrödinger's cat was written as a "ridiculous case"

The person most stirred by the EPR paper was Schrödinger. He wrote a long essay, "The Present Situation in Quantum Mechanics", which a German journal printed in three instalments in November and December 1935. A footnote says that the appearance of the EPR paper was what moved him to write it.

The cat appears in section 5, headed "Are the Variables Really Blurred?" There was, at the time, a tempting way to think: a quantity that has not been measured is not undecided, it is smeared out. As long as this stays inside the atom, no harm is done. Schrödinger remarked that one can also set up quite "ridiculous cases" where it does not stay there, and brought in the cat.

Shut a cat in a steel chamber. Out of the cat's reach, place a tube that counts radiation and a tiny amount of radioactive substance: so little that in the course of an hour one atom may decay, and with equal probability none may. If an atom decays, the tube fires, a relay releases a hammer, and the hammer breaks a small flask of hydrocyanic acid. Leave the box alone for an hour, and the quantum formula for everything inside it has the living cat and the dead cat blended together in equal parts.

His point was this. A vagueness that was supposed to be confined to the atomic world has turned into a vagueness you could see with your own eyes, and one that is settled the moment you open the box. So a "blurred model" cannot be naively accepted as a picture of what is there. In his image, a blurred photograph is one thing; a sharp photograph of clouds and fog is another.

The example had a model. On 8 August Einstein had sent Schrödinger an example of his own: a charge of gunpowder that may go off by itself. As time passes, the formula describes a blend of powder that has not yet exploded and powder that already has. In reality there is nothing in between. In his reply of 19 September Schrödinger wrote that he had built a very similar example, and went on to describe the cat.

Today the cat is a mascot for quantum strangeness: a cat that is alive and dead at once. It was first aimed the other way. The formula comes out in that form, and for that very reason it will not do as a description of what is really there; something is still missing from the account. That was what the cat was for. Fine, too, points out that it began as an argument for incompleteness.

The word "entanglement"

Later in the same essay Schrödinger returned to the two particles of the EPR paper, and gave what happens there a name. In German it was Verschränkung. In an English paper that reached the Cambridge Philosophical Society on 14 August, it was entanglement.

Here is what the word covers. In everyday life, if you know all there is to know about a whole, you know all there is to know about its parts. In quantum mechanics, once two things have interacted and separated, you can know everything knowable about the pair and still not know everything about either one. The best possible knowledge of the whole need not include the best possible knowledge of the parts. In the English paper Schrödinger wrote that he would call this not one but rather "the characteristic trait" of quantum mechanics, the one that forces a complete break with the older ways of thinking.

He did not hide his unease. Simply by choosing what to measure here, an experimenter can steer something out of reach into one type of state or another. That the theory allows this, he wrote, is "rather discomforting".

Einstein held that the theory is incomplete. Bohr held that it is complete and that the question was ambiguous. Schrödinger took neither side and named the oddity. In 1935, though, this was a dispute in words. Whichever side you took, the predicted results of every experiment were the same.

1964: the question goes to the laboratory

Twenty-nine years later the physicist John Bell turned the dispute into something an experiment could decide. David Bohm had prepared the ground by recasting the EPR pair: instead of position and momentum, use the direction of the tiny magnet each particle carries (its spin).

In his 1964 paper Bell tried thinking as Einstein wished. Suppose the particles carry values that do not appear in the formula, so that every result is fixed in advance. Suppose also that distant places do not influence each other. Then there is a ceiling on how closely the results from the two particles can match. But for some choices of measuring direction, quantum mechanics predicts a match above that ceiling. Bell's conclusion: if values are added so as to reproduce the quantum predictions, there must be a mechanism by which the setting of one instrument influences the reading of the other, however far away.

In 1969 John Clauser and three colleagues put this into a form a real experiment could use. Offer two measuring directions on each side, and combine the agreement between results over the four pairings into a single number. In any theory without influence between distant places, that number cannot exceed 2. In quantum mechanics it can reach about 2.83.

In 1972 Stuart Freedman and Clauser measured pairs of light particles emitted one after the other by calcium atoms. The ceiling was broken, and the results agreed with quantum mechanics. In 1982 Alain Aspect, Jean Dalibard and Gérard Roger switched the measuring directions while the light was in flight, and broke the ceiling again, by five standard deviations. The switching was there to weaken the suspicion that one side's setting had somehow reached the other in advance.

Loopholes remained. Most of the light particles went undetected, so it could not be ruled out that only a skewed sample was being counted. Experiments that closed both loopholes at once came in 2015. A group in Delft entangled electrons in two diamonds 1.3 kilometres apart and, in 245 trials, found a value of 2.42 ± 0.20. In the same year groups in Vienna and in the United States reported the same conclusion with light. The 2022 Nobel Prize in Physics went to Aspect, Clauser and Anton Zeilinger.

What could be done by then, and what could not

First, what was done. The three pieces of 1935 contained no new experiment and no new prediction. What they contained was a question and a name. Twenty-nine years later the question became the blueprint for an experiment, and eighty years later an experiment without loopholes.

What was learned is this. "Particles carry values that fix the results before they are measured" and "distant places do not influence each other": no theory that keeps both agrees with experiment. The theory could not be made complete in the way Einstein hoped. One caution: in the Delft result the error bar comes down close to the ceiling of 2 (the paper puts the chance of getting this by luck at 0.039, about 4 per cent). What settled the matter was not one experiment but three, done in different ways and agreeing (in the Vienna experiment the gap was 11.5 standard deviations).

Entanglement also became a tool. In 1991 Artur Ekert proposed a cryptography scheme in which the violation of Bell's ceiling serves as the test for eavesdropping. For quantum computers, Richard Jozsa and Noah Linden proved in 2003 that a quantum computation can only be exponentially faster than an ordinary one if the number of entangled qubits (the units a quantum computer works with) keeps growing with the size of the problem. Their proof is for ideal, noise-free states. In the same year Guifré Vidal showed that a quantum computation with only a little entanglement can be imitated efficiently on an ordinary computer. Entanglement is an ingredient you cannot do without. Yet Jozsa and Linden say in the same paper that it is misleading to regard entanglement as the key resource behind the power of quantum computing. Necessary, but not by itself the reason for the speed.

What could not be done is just as clear. The cat's question is still open. The formula gives the half-and-half blend, but anyone who opens the box sees one result. Where, and why, does the blend become a single outcome? The formula does not say. Nor is there one agreed reading of Bell's result. Accept that distant places do influence each other? Give up the idea that values exist before measurement? Read it some other way? The experiments did not choose among these.

This series has followed the quantum mechanics completed in 1927 as it spread to the chemical bond, the nucleus, the positron and the electrons in solids. In every part there was a gap between getting the answer and understanding it. The three people in this last part asked about that gap directly. Their question did not bring the theory down. It was given the form of an experiment, and then became a component of cryptography and computing. The calculations come out right. What is actually happening still cannot be said outright. The gap between those two got its name in 1935, and it has not been closed.