On Bell’s Everett (?) Theory

Yoav Ben-Dov

Aurélien Drezet, CNRS-University Joseph Fourier

Shan Gao

Bell's Everett (?) theory, or the pilot-wave theory without trajectories, is Bell's interpretation of Everett's theory, aiming to remove the picture of many worlds from the theory. In this paper, I argue that Bell's attempt is not successful, since his Everett (?) theory contradicts quantum mechanics and experiments.

Aurélien Drezet

Everett’s many-worlds or multiverse theory is an attempt to find an alternative to the standard Copenhagen interpretation of quantum mechanics. Everett’s theory is often claimed to be local in the Bell sense. Here, we show that this is not the case and debunk the contradictions by analyzing in detail the Greenberger–Horne–Zeilinger (GHZ) nonlocality theorem. We discuss and compare different notions of locality often mixed in the Everettian literature and try to explain the nature of the confusion. We conclude with a discussion of probability and statistics in the many-worlds theory and stress that the strong symmetry existing between branches in the theory prohibits the definition of probability and that the theory cannot recover statistics. The only way out from this contradiction is to modify the theory by adding hidden variables à la Bohm and, as a consequence, the new theory is explicitly Bell-nonlocal.

Simon Saunders

I define a notion of local causality LOC closely modelled on the Bell principle, construed as the condition that single case probabilities cannot be modified by actions at spacelike separation. The new principle, like that of Bell, forces Bell inequalities, but with two loopholes: one is retrocausation, known to Bell, but the other is nonuniqueness of remote outcomes, a loophole only for LOC, not for the Bell principle. I also set out a theory of physical probability, applicable to the Everett interpretation, in agreement with the Born rule, and therefore violating Bell inequalities. I show it is consistent with LOC. Surprisingly, both loopholes are exploited. I conclude not only that probability in the Everett interpretation involves no action at a distance, but that the observed violations of Bell inequalities is powerful evidence for many worlds.

Foad Dizadji-Bahmani