Bell's Theorem

Bell's theorem, first proved by John Stewart Bell (1928–1990) [1] in 1964, is probably the most celebrated result in the whole of twentieth-century physics. Briefly stated, it demonstrates that a whole class of theories about the physical world (“objective local theories”, see below) defined by the conjunction of three apparently plausible general principles, must yield experimental predictions which under certain conditions are inconsistent with the predictions of quantum mechanics. Over the last 35 years a series of experiments motivated by the theorem have shown that under the relevant conditions the experimental properties of the world are consistent with the predictions of quantum mechanics and thus, subject to certain caveats, inconsistent with those of the alternative class of theories, so that the latter must apparently be rejected.

Let's first define an idealized experimental arrangement which is useful for the discussion of the theorem (see Fig. 1). A source emits pairs of particles (let us say for definiteness photons (► light quantum) as is usually the case in the real-life experiments). The photons travel to two different experimental “stations” S₁ and S₂ which are distant not only from the source but from one another, so that the space-time points at which they are detected at the stations are spacelike separated in the sense of special relativity (i.e. there is no time for a light wave, or anything slower, to pass between them). At (say) station 1 the relevant photon (1) encounters a randomly activated switch which directs it into one of two “measurement devices”. Each measurement device gives a binary output (“yes” or “no”), but to two different “questions”. To put a little flesh on this rather abstract formulation, let us imagine (as is usually the case in practice) that the “measurement” is of photon polarization; then one measurement device (call it M_a) would consist of a polarizer set to transmit photons polarized along direction a in the plane orthogonal to its propagation direction and reflect photons with the orthogonal polarization, together with counters [C_a(+) and C_a(−)] to detect both the transmitted and reflected photons. The second measurement device, M_a′, is similar except that the polarizer now has a transmission axis a′ which is different from a. A similar setup is constructed at station 2, with the alternative polarizer axes now b and b′. It is important that the “events” not only of the arrival of the photons at S₁ and S₂ but of the activation of the two switches, i.e. of the “choice” of which of the two alternative measurements to make at each station, be spacelike separated.