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.
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.
J.S. Bell's remarkable 1964 theorem showed that any theory sharing the empirical predictions of orthodox quantum mechanics would have to exhibit a surprising – and, from the point of view of relativity theory, very troubling – kind of nonlocality. Unfortunately, even still on this 50th anniversary, many commentators and textbook authors continue to misrepresent Bell's theorem. In particular, one continues to hear the claim that Bell's result leaves open the option of concluding either nonlocality or the failure of some unorthodox “hidden variable” (or “determinism” or “realism”) premise. This mistaken claim is often based on a failure to appreciate the role of the earlier 1935 argument of Einstein, Podolsky, and Rosen in Bell's reasoning. After briefly reviewing this situation, I turn to two alternative versions of quantum theory – the “many worlds” theory of Everett and the quantum Bayesian interpretation of Fuchs, Schack, Caves, and Mermin – that purport to provide actual counterexamples to Bell's claim that nonlocality is required to account for the empirically verified quantum predictions. After analyzing each theory's grounds for claiming to explain the EPR–Bell correlations locally, however, one can see that (despite a number of fundamental differences) the two theories share a common for-all-practical-purposes (FAPP) solipsistic character. This dramatically undermines such theories’ claims to provide a local explanation of the correlations and thus, by concretizing the ridiculous philosophical lengths to which one must go to elude Bell's own conclusion, reinforces the assertion that nonlocality really is required to coherently explain the empirical data. Introduction Fifty years ago, in 1964 [1], John Stewart Bell first proved the theorem that has become widely known as “Bell's Theorem” but that Bell himself instead referred to as the “locality inequality theorem” [2]. In Bell's own view, the theorem showed that the empirical predictions of local theories will be constrained by Bell's inequality (or as Bell himself preferred to call it, the “locality inequality”). Hence, nonlocality is a necessary feature of any theory that shares the empirical predictions of standard quantum mechanics.
The nature of branching in the many-worlds interpretation (MWI) of quantum mechanics remains an open question, particularly regarding its locality and compatibility with special relativity. This paper challenges the conventional view that branching is either global or local, demonstrating instead that it is nonlocal for entangled systems. Through a new analysis of the EPR-Bohm experiment, I argue that global branching has several potential issues and can hardly be justified. At the same time, I argue that branching cannot be entirely local, as entangled particles exhibit simultaneous, spacelike-separated branching, manifesting an apparent action at a distance within individual worlds. However, while nonlocal branching suggests the emergence of a preferred Lorentz frame within each world, the multiverse as a whole retains full Lorentz invariance, ensuring no superluminal signaling. By refining the ontology of branching and resolving tensions between MWI and relativistic constraints, this analysis may help advance our understanding of quantum nonlocality and also strengthen MWI's standing as a viable interpretation of quantum mechanics.
The hidden variable theories are, more cumbersome and artificial—while the Copenhagen interpretation is hopelessly incomplete because of its a priori reliance on classical physics, as well as a philosophic monstrosity with a “reality” concept for the macroscopic world and denial of the same for microcosm. In recent work on the Everett (Many-Worlds) interpretation of quantum mechanics, it has increasingly been recognized that any version of the interpretation worth defending will be one in which the basic formalism of quantum mechanics is left unchanged. Properties such as the interpretation of wave-function as describing a multiverse of branching worlds, or the ascription of probabilities to the branching events, must be emergent from the unitary quantum mechanics rather than added explicitly to the mathematics. Deutsch’s strategy was to introduce a few assumptions from decision theory into the Everett interpretation and then to show how they work with quantum theory to create a natural value measure that is the same as the expectation value.
It is argued that the lesson we should learn from Bell's inequalities is not that quantum mechanics requires some kind of action at a distance, but that it leads us to believe in parallel worlds. Introduction Bell's work [1] led to a revolution in our understanding of nature. I remember attending my first physics conference, on “Microphysical Reality and Quantum Formalism,” in Urbino, 1985. Most of the talks were about Aspect's experiment [2] confirming the nonlocality of quantum mechanics based on experimental violations of Bell's inequalities. Although I did not share the skepticism of many speakers regarding the results of Aspect, I was not ready to accept that a local action in one place can instantaneously change anything at another place. So, while for the majority the lesson from Bell was that quantum mechanics requires some “spooky action at a distance”, I was led by Bell's result to an alternative revolutionary change in our view of nature. I saw no other way than accepting the manyworlds interpretation (MWI) of quantum mechanics [3, 4]. I shall start by presenting the Einstein–Podolsky–Rosen (EPR) [5] argument. Then I will present Bell's presented using the Greenberger–Horne–Zeilinger setup [6] in the form proposed by Mermin [7, 8]. The discussion of nonlocality will suggest that Bell's inequalities are the only manifestation of action at a distance in nature. The demonstration of the necessity of action at a distance will be done through a detailed analysis of the GHZ experiment. Then I shall show how multiple worlds resolve the problem of action at a distance. After discussing the issue of nonlocality in the MWI, I shall conclude by citing Bell's views on the MWI. EPR–Bell–GHZ The story of Bell cannot be told without first describing the EPR argument. Instead of following the historical route, I shall use the GHZ setup, which, in my view, is the clearest way to explain the EPR and Bell's discovery.
Abstract Much of the evidence for quantum mechanics is statistical in nature. Relative frequency data summarizing the results of repeated experiments is compared to probabilities calculated from the theory; close agreement between the observed relative frequencies and calculated probabilities is taken as evidence in favour of the theory. The Everett interpretation, if it is to be a candidate for serious consideration, must be capable of doing justice to this sort of reasoning. Since, on the Everett interpretation, all outcomes with non-zero amplitude are actualized on different branches, it is not obvious that sense can be made of ascribing probabilities to outcomes of experiments, and this poses a prima facie problem for statistical inference. It is incumbent on the Everettian either to make sense of ascribing probabilities to outcomes of experiments in the Everett interpretation, or to find a substitute on which the usual statistical analysis of experimental results continues to count as evidence for quantum mechanics, and, since it is the very evidence for quantum mechanics that is at stake, this must be done in a way that does not presuppose the correctness of Everettian quantum mechanics. This requires an account of theory confirmation that applies to branching-universe theories but does not presuppose the correctness of any such theory. This chapter supplies and defends such an account. The account has the consequence that statistical evidence can confirm a branching-universe theory such as Everettian quantum mechanics in the same way in which it can confirm a non-branching probabilistic theory.
Bell's theorem is 50 years old. Still there is a controversy about its implications. Much of it has its roots in confusion regarding the premises from which the theorem can be derived. Some claim that a derivation of Bell's inequalities requires just locality assumption, and nothing more. Violations of the inequalities are then interpreted as ``nonlocality'' or ``quantum nonlocality''. We show that such claims are unfounded and that every derivation of Bell's inequalities requires a premise -- in addition to locality and freedom of choice -- which is either assumed tacitly, or unconsciously, or is embedded in a single compound condition (like Bell's ``local causality''). The premise is equivalent to the assumption of existence of additional variables which do not appear in the quantum formalism (in form of determinism, or joint probability for outcomes of all conceivable measurements, or ``additional causes`'', or ``hidden variables'', ``complete description of the state'' or counterfactual definiteness, etc.). A certain irony is that perhaps the main message of violation of Bell's inequalities is that our notion of locality should be based on an operationally well-defined no-signalling condition, rather than on local causality.