Reformulating Bell's theorem: The search for a truly local quantum theory

Abstract

The apparent nonlocality of quantum theory has been a persistent concern. Einstein et. al. (1935) and Bell (1964) emphasized the apparent nonlocality arising from entanglement correlations. While some interpretations embrace this nonlocality, modern variations of the Everett-inspired many worlds interpretation try to circumvent it. In this paper, we review Bell's "no-go" theorem and explain how it rests on three axioms, local causality, no superdeterminism, and one world. Although Bell is often taken to have shown that local causality is ruled out by the experimentally confirmed entanglement correlations, we make clear that it is the conjunction of the three axioms that is ruled out by these correlations. We then show that by assuming local causality and no superdeterminism, we can give a direct proof of many worlds. The remainder of the paper searches for a consistent, local, formulation of many worlds. We show that prominent formulations whose ontology is given by the wave function violate local causality, and we critically evaluate claims in the literature to the contrary. We ultimately identify a local many worlds interpretation that replaces the wave function with a separable Lorentz-invariant wave-field. We conclude with discussions of the Born rule, and other interpretations of quantum mechanics. * This is a preprint. The final and definitive version of this paper will be published in Studies in History and Philosophy of Modern Physics.

An Elementary Proof That Everett’s Quantum Multiverse Is Nonlocal: Bell-Locality and Branch-Symmetry in the Many-Worlds Interpretation

“…The claim goes back to Everett's work [1,2] where he mentioned that his theory solves the Einstein-Podolsky-Rosen (EPR) contradiction [3] in a local way. In the same vein, locality claims involving Bell's theorem [4] and Greenberger-Horne-Zeilinger (GHZ) states [5] have been discussed by Page [6], Blaylock [7], Vaidman [8,9], Tipler [10], Timpson and Brown [11,12], and many others [13][14][15][16][17][18][19][20][21], including popular science books [22,23]. Unfortunately, these claims are based on a misunderstanding of EPR and Bell works [3,4], and it is the purpose of this article to explain why it is so.…”

“…The question that we want to answer now is why advocates of Everett's theory strongly believe that the Bell-GHZ theorem does not prove nonlocality in their approach? We can find at least two arguments or reasons in the literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

“…Indeed, there is a different, more sophisticated version of the same reasoning, which is even more often given by proponents of locality in Everett's theory. The point is that Everett's theory relaxes the 'single/unique outcome assumption', which is claimed to be an hidden assumption of Bell-GHZ theorems [9][10][11][12]17,20,21]. Since there is more than one outcome existing in different 'parallel' independent worlds (contributing to the whole universal wave-function), Bell-GHZ theorems based on beables λ do not apply, and there is no sense in speaking about Bell's nonlocality in Everett's theory-the notion cannot even be clearly formulated.…”

Wigner Friend scenarios with non-invasive weak measurements

“…Purely unitary approaches (such as the Many-Worlds Interpretation) uphold that the projection postulate makes quantum theory non-universal and logically inconsistent [2]. In such approaches, whether the Friends and the agents W evolve or not in different worlds, observing or not different facts and how different facts can be reconciled when all the agents meet depends on subtle assumptions concerning the branching mechanism (for a recent discussion detailing on how branching issues in EPR or GHZ setups might lead agents evolving independently to reconcile their viewpoints, see [30]).…”

Local Quantum Theory with Fluids in Space-Time

“…This model is consistent with the Lorentz covariant Heisenberg-Schrödinger model proposed by Schwinger in 1948 [3], and restores the equivalence between the local Heisenberg and Schrödinger pictures. However, we now know from Bell's theorem [4,5,6,7,8] that if we wish to maintain independence of measurement settings, then this is unavoidably a theory of many local worlds [9].…”