JOVANA
Library Glossary Getting Started Three Levels Fields How it works Mission
Join the mission
Back to the library
Physics 1935

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?

Albert Einstein, Boris Podolsky & Nathan Rosen

If measuring one particle fixes a distant partner, quantum theory must be incomplete.

Choose your version
In depth · the introduction

Measure one particle here, and its faraway partner seems to make up its mind in the same instant — a link Einstein could not stomach, and used to argue that quantum theory must be missing something.

The big idea

Quantum mechanics says a particle has no definite position or momentum until you measure it — only odds. Einstein, with Podolsky and Rosen, thought that couldn't be the whole story. They imagined two particles born together and sent far apart, their fates locked: whatever you find for one, you instantly know the matching answer for the other.

Here is the trap they set. Suppose by measuring particle A you could predict particle B's outcome with total certainty, without touching B at all. Then surely B already had that property — it was real, sitting there, before you looked. But quantum mechanics refuses to assign B that definite value in advance. So, EPR concluded, the theory must be incomplete: there must be hidden details it leaves out. Einstein wanted reality to be local — no instant influence across a distance — and definite. Quantum mechanics seemed to offer neither.

How it came about

By 1935 Einstein had helped build quantum theory but had come to distrust its picture of the world. Settled at the Institute for Advanced Study in Princeton, he worked with two younger colleagues, Boris Podolsky and Nathan Rosen, to turn his unease into an argument no one could wave away. Podolsky wrote it up and, it turned out, slipped it to the press before publication — a New York Times headline appeared, and Einstein was annoyed at the framing.

Niels Bohr, the great champion of quantum mechanics, was reportedly thrown into weeks of intense work and fired back a reply with the very same title. He argued that EPR's idea of a particle having properties on its own, independent of how you choose to measure it, simply doesn't apply to entangled systems. For thirty years the debate sat there: two brilliant readings of the same equations, with no experiment to choose between them.

Why it mattered

EPR did something rare: they made a philosophical question about reality into a precise, answerable one. They were trying to expose a flaw in quantum mechanics. Instead, in 1964 the physicist John Bell found a way to turn their thought experiment into a real test — and decades of experiments delivered a verdict Einstein would have hated. Nature really is as strange as the equations say; the cozy local, definite world EPR hoped to rescue does not exist.

Their honesty is the point. EPR's logic was flawless given their assumptions; it was one of those assumptions — that influences can't outrun the speed of separation — that nature declines to honour. Few papers meant to win an argument have been so productively wrong.

A way to picture it

Imagine a pair of gloves split into two sealed boxes and shipped to opposite ends of the Earth. Open one box, see a left glove, and you instantly know the far box holds the right — no signal travelled; the answer was sealed in from the start. Einstein wanted entangled particles to be exactly like that: the answer decided at the source, just hidden.

But quantum particles fail this picture. With gloves you can check left/right, and that's that. With entangled particles you get to choose, at the last moment, which question to ask — and however you choose, the distant partner's answer matches up too perfectly. No set of pre-sealed gloves can pull that off. That mismatch, made testable by Bell, is what finally settled it.

An interactive EPR experiment: an entangled source sends a pair to two distant detectors, Alice fixed and Bob set by a slider; as paired results stream in, a marker shows how strongly the two outcomes agree, settling on −cos of the detector angle, and at zero angle they are always exactly opposite.

Where it sits

This paper is the hinge between the founding of quantum mechanics — Planck, Bohr, Heisenberg, Schrödinger — and the quantum-information age. It crystallised entanglement as a concept, prompted Bell's 1964 theorem, and led to the experiments of Clauser, Aspect and Zeilinger that won the 2022 Nobel Prize. The very weirdness Einstein rejected now powers quantum cryptography and quantum computers. In the Library it stands beside the work it questioned and the technologies it unwittingly seeded.

The original document
Original source text
A. Einstein, B. Podolsky, N. Rosen · Physical Review 47 (1935): 777–780 · Received March 25, 1935
Abstract
In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system.
In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.
§1 — The condition of completeness and the criterion of reality
Whatever the meaning assigned to the term complete, the following requirement for a complete theory seems to be a necessary one: every element of the physical reality must have a counterpart in the physical theory. We shall call this the condition of completeness. The second question is thus easily answered, as soon as we are able to decide what are the elements of the physical reality.
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.
[ … ]
§2 — The two-particle thought experiment
Suppose now that we have two systems, I and II, which we permit to interact … after which the systems no longer interact. We assume that the states of the two systems … are known. We can then calculate … the state of the combined system. … By measuring either A or B we are in a position to predict with certainty, and without in any way disturbing the second system, either the value of the quantity P (that is p_k) or the value of the quantity Q (that is q_r). In accordance with our criterion of reality, in the first case we must consider the quantity P as being an element of reality, in the second case the quantity Q is an element of reality. But, as we have seen, both wave functions … belong to the same reality.
Previously we proved that either (1) the quantum-mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality. Starting then with the assumption that the wave function does give a complete description of the physical reality, we arrived at the conclusion that two physical quantities, with noncommuting operators, can have simultaneous reality. Thus the negation of (1) leads to the negation of the only other alternative (2).
We are thus forced to conclude that the quantum-mechanical description of physical reality given by wave functions is not complete.
One could object to this conclusion on the grounds that our criterion of reality is not sufficiently restrictive. … This makes the reality of P and Q 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.
While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.
Institute for Advanced Study · Princeton, New Jersey · received March 25, 1935