John Bell’s Ultimate Observer

Yuri Barzov
3 min readApr 17, 2024
Picture by Dmitry Buterin

John Stewart Bell became famous due to Bell’s theorem with which he proved that quantum mechanics and the non-local information exchange between entangled systems in particular cannot be duplicated by any deterministic classical theory (explained by hidden classical variables).

In 2022, the Nobel Prize in Physics was awarded to Alain Aspect, John Clauser, and Anton Zeilinger for the experimental validation of Bell’s theorem.

Bell’s work on interpretations of quantum mechanics are less known than his theorem but they contain some very interesting ideas. The introduction of the ultimate observer to the Copenhagen interpretation of quantum mechanics is one of them. Bell was not an orthodox proponent of the Copenhagen interpretation. Therefore he treated it somewhat frivolously when he introduced the ultimate observer into it as a device for comparing it with the pilot-wave interpretation. I think the best way now is to give him an opportunity to explain this idea himself.

“It remains to compare the pilot-wave theory with the orthodox quantum mechanics at a practical level, which is that of the xs (exposed variables as the opposite to the wave function as a hidden variable). A convenient device for this purpose is to imagine, in the context of the orthodox approach, a sort of ultimate observer, outside the world and from time to time observing its macroscopic aspects. He will see in particular other, internal observers at work, will see what their instruments read, what their computers print out, and so on. In so far as ordinary quantum mechanics yields at the appropriate level a classical world, in which the boundary between system and observer can be rather freely moved, it will be sufficient to account for what such an ultimate observer would see. If he were to observe at time t the whole ensemble of worlds corresponding to an initial state

he would see, according to the usual theory, the distribution of Xs given closely by


obtained by solving the world Schrödinger equation. It would not be exactly this, for his own activities cause wave-packet reduction and spoil the Schrödinger equation. But macroscopic observations are supposed to have not much effect on subsequent macroscopic statistics. Thus (4) is closely the distribution implied by the usual theory.

Moreover, it is easy to construct in the pilot-wave theory an ensemble of worlds that will give the distribution (9) exactly.”

Bell, John S. Quantum Mechanics For Cosmologists, Speakable And Unspeakable In Quantum Mechanics, Cambridge University Press, 1987, pp. 128–129