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Locality has always been held a sacred principle of fundamental physical theories. Non-local theories have often been regarded as provisional, phenomenological accounts, waiting to be replaced by more fundamental local theories. For example, Newton's theory of gravity is a non-local theory. It describes particles that attract each other with certain forces that act instantaneously. If one of the particles were to be displaced, this would have an instantaneous albeit possibly very small effect on the other particles.
Newton himself saw this as an unacceptable feature of the theory, stating [1]:. Gravity must be caused by an Agent acting constantly according to certain laws. Coulomb's law, which describes the force between static charged particles, is analogous to Newton's gravitational force and is also non-local. However, the work of Maxwell and others made clear that electromagnetism given by Maxwell's equations and the Lorentz force law, from which Coulomb's law can be derived can be understood as a completely local theory, with interactions between the charges being mediated by the electromagnetic field.
Such a local account for gravity had to wait a bit longer until the advent of Einstein's theory of general relativity. According to Einstein's theory, which subsumes Newton's theory in the non-relativistic limit, gravity acts not by non-local forces but by the geometry of why mobile hotspot is not connecting to pc whose changes propagate locally.
However, the world is not classical but quantum mechanical. Quantum mechanics is non-local, in the same way as Newtonian gravity, in the sense that there exist interactions what is general theory of relativity non examples events in space-time that can only be connected by signals moving faster than the speed of light.
However, unlike What is general theory of relativity non examples gravity, the non-locality of quantum mechanics is not an artifact of the provisional nature of the theory. Rather, any possible alternative for quantum mechanics must be non-local, at least if it is to agree with certain predictions of quantum mechanics. Since these predictions seem to be well confirmed by experiments, the non-locality is inescapable. This striking conclusion follows from John Bell's theorem.
To celebrate its 50 th anniversary, Mary Bell John's wife and Shan Gao collected a broad selection of papers on Bell and his work on the foundations of quantum mechanics. The book has four parts. The first focuses on Bell. The second part deals with Bell's theorem, gving a detailed exposition of the theorem and the experimental results. The third concerns the which command is used to display variable values of non-locality and the last part concerns "non-local realistic theories".
These are theories that provide a clear ontology, -- e. The attention to such theories is quite appropriate since Bell's preoccupation was not only with the non-local nature of quantum mechanics. Even though he was employing the theory on a daily basis as a high energy physicist working in CERN, he was deeply troubled with the formulation of the theory. He found it unprofessionally vague and ambiguous. He demanded a precise mathematical and conceptual formulation of quantum mechanics.
In particular, this implies being precise about the ontology of the theory. Or to use the terminology he introduced, it is important to be clear about what are the "beables" in the theory, i. Therefore he was a great supporter of theories what is general theory of relativity non examples as Bohmian mechanics also called de Broglie-Bohm theory and spontaneous collapse theories, which meet those demands.
Actually, it was his appreciation of Bohmian mechanics with its explicit non-locality that got him to start thinking about whether it was possible to formulate a theory that is as precise as this one, yet is local. His theorem beautiful couple meaning in telugu that this was impossible.
Even though the book's four parts cover different topics, there is quite naturally no strict division of the papers. Many of the other papers contain recollections as well. In addition, discussions on the nature of non-locality often go together with consideration of precise versions of quantum mechanics. In reviewing the book, we will not strictly follow the chapter order. Part II starts with contributions by Jean Bricmont and Roderich Tumulka, who carefully examine what Bell's theorem actually proves and and what, exactly, it assumes.
While the theorem is technically easy, its implications have -- to this day -- often been misunderstood. The non-locality is unacceptable to manyand unwarranted claims are often made about assumptions underlying Bell's theorem. Rather than giving up locality we could give up one of these assumptions. For example, it is often claimed that Bell's theorem requires assumptions like realism or determinism.
In this context it is often stated that Bell's theorem disproves local what is general theory of relativity non examples as, unfortunately, in the book's preface, which suggests the assumptions of both locality and realism, whatever the latter may exactly mean. However, this is mistaken; Bricmont and Tumulka do a great job in rectifying these and other misconceptions. These contributions are good additions to previous discussions, e.
The misconception that realism is an assumption made by Bell unfortunately features in Marco Genovese's well-presented chapter on experimental tests of Bell's inequalities. Genovese discusses the very recent and important loophole-free experiments of the Delft group in an appendix added after submission. But there are problems with Genovese's introduction to Bell's theorem and and his discussion of its conclusions. Genovese states that Bell's theorem assumes "realism" in addition to locality.
What is meant in this case by "realism" is just determinism. But as explained in the contributions by Bricmont and Tumulka, Bell never assumed determinism. He explicitly warned against it. In the first version of his theorem Bell derived determinism from locality using the EPR argument, while in a later version which avoids the assumption of perfect anti-correlation for the singlet state in the EPR argument the variables in the theory determine the outcomes probabilistically.
So Genovese's conclusion that the experimental tests make "it possible to exclude any possible deterministic extension of quantum mechanics" is just wrong. Even stated as such, Bohmian mechanics would be a counterexample because it is deterministic and reproduces the predictions of quantum mechanics. The conclusion should be that the test makes it possible to exclude any local theory, whether it be deterministic or stochastic.
It is correct that Bell's theorem has assumptions other than locality. Locality might be preserved if one of these other assumptions is given up. But these assumptions are quite natural and are usually taken for granted. For example, it is assumed that settings for measurements can be chosen independently of the system on which the measurement is performed also called the "free will assumption" or perhaps better the "no conspiracy assumption".
However, giving up this assumption in order to save locality what is ideology in international relations make the theory incredibly conspiratorial, making any kind of scientific inquiry impossible [2]. Another example is described in Trevor Norsen's contribution. One may think our experience of the world is merely an illusion and that what happens in the actual world is completely local.
However, our experiences, which what is general theory of relativity non examples this case are brain-in-a-vat-like, give the impression of non-locality. Another possibility is that the structure of space-time is different than assumed. For example, in his theorem Bell tacitly assumed that the topology of space-time is simply connected. If space-time is multiply connected it may be that systems that appear widely separated are actually close by, perhaps connected by something like a wormhole [3].
The non-locality could be merely apparent if entangled systems are connected like this. But, of course, whether such an idea can be further developed remains to be seen. Another assumption in Bell's theorem is that experiments have definite outcomes. In the Many Worlds theory also called the Everett theory this assumption is violated. But this does not necessarily mean that the theory is local. One can still check directly whether a particular theory is local or not.
In the usual version of the theory, the wave function is the only beable. It is not a local beable, i. As explained in detail by Norsen, the fact that there are no local beables means that the theory is neither local or what is a good cash conversion percentage, because the theory lacks the kind of structure necessary for an analysis.
Norsen goes on to discuss versions of the Many Worlds theory that do include local beables. While the situation is not so clear in that case, he argues that such theories seem non-local. On the other hand, Harvey R. Brown and Christopher G. Timpson claim that the Many Worlds theory does violate locality, without specifying any local beables. They talk about systems localized in certain regions in space and localized measurements, but it is unclear to what extent we should understand this literally.
If the wave function is all there is, then the physical arena does not seem to be physical space or space-time but rather configuration space or perhaps some Hilbert space. As is convincingly argued by Norsen, this means that one cannot meaningfully discuss the possibility of locality in that case. Lev Vaidman is explicit in stating that in the Many Worlds theory, the wave function in configuration space is all that exists, but also claims that there is non-locality.
However, this is not Brown and Timpson's main point. They also claim that while the theory is non-local meaning of injured in spanish refer to "local-causality" instead of "locality"the theory does not have action-at-a-distance and therefore is not at variance with relativity. A similar stance is taken by Vaidman and Wayne Myrvold. Myrvold not only considers the Many Worlds theory, but makes the case in general that non-locality can be violated in two ways, namely, parameter dependence and outcome dependence.
The former means dependence on the choice of experiment e. For example, Bohmian mechanics violates the former, while spontaneous collapse theories violate the latter. It is argued as, e. These are interesting considerations. Indeed an interesting question is what should be demanded of a proper relativistic theory in the light of the violation of locality. At least, it seems that, just as in the case of the discussion on locality, space-time itself and local beables should figure in a proper relativistic theory.
Bernard D'Espagnat argues that locality may be maintained if somehow the notion of reality depends on the observer, as in a theory such as Rovelli's Relational Quantum Mechanics. I am not sure what exactly exists in the world according to such a theory, i. If this means that there are no local beables, then again Norsen's arguments apply.
This is unfortunately not addressed in this contribution. Henry P.
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