In May 1935 the journal Physical Review published a four page paper by Albert Einstein and two younger colleagues at the Institute for Advanced Study in Princeton, Boris Podolsky and Nathan Rosen. Its title asked whether the quantum mechanical description of physical reality could be considered complete. The EPR paper argued that quantum mechanics, though correct in its predictions, must be incomplete: it leaves out parts of reality that a full theory would describe.

What complete means

Einstein did not claim quantum mechanics was wrong. Its predictions were already spectacularly successful. A theory is complete, the authors said, if every element of physical reality has a counterpart in the theory. So they needed a way to spot an element of reality. They offered a test, now called the reality criterion: if, without disturbing a system in any way, we can predict a quantity with certainty, then there is an element of reality corresponding to that quantity. The test does not say what reality is, only how to recognize a piece of it.

The argument

The paper imagined two particles that interact and then separate, prepared so that their positions are tightly linked and so are their momenta. Measure the position of particle A and you can predict the position of particle B with certainty. Measure the momentum of A instead and you can predict the momentum of B with certainty. Either way, you never touched B.

Now apply the criterion. Because either quantity of B could be predicted without disturbing B, EPR concluded that both its position and its momentum must be real. But quantum mechanics, through Heisenberg's uncertainty principle, says no state can assign both a sharp position and a sharp momentum at once. So the theory fails to describe properties that, by the criterion, B really has, and therefore it is incomplete.

The argument rests on a premise that Einstein later made explicit: locality. Locality, in Einstein's sense, means that what is done to one system cannot immediately affect the real state of a distant system. If measuring A could reach out and alter B, the criterion would not apply, because B would be disturbed after all. In a 1947 letter to Max Born he mocked it as a kind of ghostly action at a distance.

The dilemma

Seen clearly, EPR posed a choice. Either quantum mechanics is incomplete, so that particles carry properties the theory leaves out, or nature is nonlocal, so that a measurement here can affect reality there. Einstein chose incompleteness, hoping a deeper theory would one day fill in the missing details.

Bohr's reply

Niels Bohr, the Danish founder of the Copenhagen school, answered within months in a paper with the same title in the same journal. Its core claim was that the EPR criterion is ambiguous, because what can be predicted about B depends on which measurement is chosen at A. For Bohr, position and momentum are not properties a particle simply has; they are meaningful only within a complete experimental arrangement, and the arrangements for measuring them exclude each other. There is no mechanical disturbance of B, he granted, but there is an influence on the very conditions that define what can sensibly be said about it.

Defenders saw this as a deep insight about the limits of classical concepts. Critics felt Bohr had changed the subject: EPR asked about reality, and Bohr answered about language and procedure. Most physicists accepted that Bohr had won, largely because they cared more about using the theory. Einstein and Bohr remained friends who argued for the rest of their lives.

Schrödinger's cat

Schrödinger took EPR more seriously. Corresponding with Einstein in 1935, he developed his own critique, and in a long article that year he introduced a thought experiment that became far more famous than EPR itself. Schrödinger's cat was meant to show how absurd it would be to say a large object has no definite state. A cat sealed in a box, whose life depends on a single atomic decay, would on a literal reading of the theory become entangled with the atom and be neither alive nor dead until someone looked. What the cat shows about measurement belongs to QUAN 202; here it matters as a sign that the founders saw entanglement as the heart of the puzzle.

Worked example: a simpler EPR

Positions and momenta are awkward to picture, so in 1951 the American physicist David Bohm recast EPR using a property called spin, which can be measured along any direction and always gives one of two results, up or down. Imagine two particles created with opposite spins along every direction. Ana in one city measures her particle along the vertical axis and gets up. She can now predict with certainty that Ben's particle, a hundred kilometers away, will show down if measured vertically.

Had she measured horizontally, she could have predicted Ben's horizontal result instead. Ben's particle was not disturbed either way, so by the EPR criterion it must have definite answers for every direction, which quantum mechanics does not assign. The EPR reasoner concludes that each particle secretly carries a full set of answers, like an instruction card, and that the theory is silent about the card. Bell later used this version, and it sharpens the question: could such cards explain everything?