Born into a poor family in the Northern Irish capital of Belfast, Bell was encouraged by his mother to continue his education after leaving school at sixteen. Consequently, after working for a year as a laboratory assistant in the physics department of Queen's University, Belfast, he enrolled as a student and graduated in 1949. Rather than pursue a PhD and burden his family further, Bell began work immediately at the Atomic Energy Research Establishment at Harwell. He worked initially on the design of CERN's first accelerator, the Proton Synchrotron. He was also given a year's leave of absence to work on a doctorate at Birmingham University. On his return to Harwell he turned to the theoretical study of elementary particles. Bell moved to CERN in Geneva in 1960 where he remained for the rest of his life. He was accompanied by his wife, Mary Bell, also a physicist, who worked at CERN on accelerator design.

In 1964 Bell published what for many has become the single most important theoretical paper in physics to appear since 1945; it was entitled On the Einstein Podolsky Rosen Paradox. The title referred to a thought experiment proposed by Einstein and others in 1935 sharply challenging the basis of quantum theory. He proposed a principle of reality stating that: “If, without in any way disturbing a system we can predict with certainty … the value of a physical quantity then there exists an element of physical reality corresponding to this physical quantity.” For example, electrons have a spin that can take one of two values, conveniently classed as positive or negative. Spin, like angular momentum, is conserved. Consequently, if a particle with zero spin decays into an electron/positron (e^–/p⁺) pair, the two particles must have equal and opposite spins. Knowing, for example, that the electron has a negative spin, it can be inferred that the positron must have a positive spin.

But this, according to Einstein, gives us a way to measure the spin of a particle without disturbance. If the p+ spin is measured and found to be positive, the measurement may well disturb the p+, but on this basis the spin of the e^– can be concluded to be negative without in any way disturbing the e^–. It follows from Einstein's reality principle that the negative spin of e^– is a real property of the electron. This view, however, conflicts with the usual interpretation of quantum mechanics, which sees the spin of the electron as a superposition of both spin states, a condition only resolved when the electron is observed and the wave function collapses. Nor can it be said that the state of the electron is in any way influenced by the outcome of the observation of the positron's spin for, as no signal can travel faster than the speed of light, instantaneous communication between separated particles is impossible.

The theoretical physicist is therefore presented with an uncomfortable choice. He or she can accept that electrons have intrinsic spin, in accordance with the reality principle and against quantum mechanics, or adopt what Einstein scornfully termed a “spooky action at distance.” One weekend in 1964 Bell saw a way in which the matter could be resolved.

The spin of a particle is complicated in that it can be independently measured along three coordinates x, y, and z at right angles to each other. Further, a measurement of the electron's spin in the x direction will influence the spin of the positron in the x direction also; it will, however, have no effect on measurements along the y and z directions. Similar rules apply to measurements along the y and z axes. Bell argued that, if the reality principle is correct, then one would expect to find for a large number of observations:

x ⁺ y ⁺ łe; (x ⁺ z ⁺ + y ⁺ z ⁺)

That is, the number of particles with a positive spin along the x and y axes, is smaller than the number found on both the x ⁺ z ⁺ and y ⁺ z ⁺ axes. The result is known variously as Bell's inequality and Bell's theorem. Although it proved impossible to test Bell's inequality in terms of the reactions described in the 1964 paper, later workers have produced equivalent formulations that are testable. The most convincing of these, the Aspect experiment performed by Alain Aspect of the Institute of Optics at the University of Paris in 1982, using correlations between polarized photons, established that the inequality did not hold. The conclusion seemed to be that nature preferred to act ‘spookily’ at a distance rather than using Einstein's reality principle.

At first Bell's five-page paper was ignored. Only when experimentalists such as John Clauser at Berkeley in 1969 took his work up did Bell's argument become widely known. Bell's views on his own work, more tentative and less extreme than those of many of his followers and popularizers, were collected in his Speakable and Unspeakable in Quantum Mechanics (1987).