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Register a new userThe Two Bells Theorems of John Bell
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Howard M. Wiseman
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Many of the heated arguments about the meaning of Bells theorem arise because this phrase can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the dual assumptions of locality and determinism. His 1976 theorem is the incompatibility of quantum phenomena with the unitary property of local causality. This is contrary to Bells own later assertions, that his 1964 theorem began with that single, and indivisible, assumption of local causality (even if not by that name). While there are other forms of Bells theorems --- which I present to explain the relation between Jarrett-completeness, fragile locality, and EPR-completeness --- I maintain that Bells t
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Bells theorem can refer to two different theorems that John Bell proved, the first in 1964 and the second in 1976. His 1964 theorem is the incompatibility of quantum phenomena with the joint assumptions of Locality and Predetermination. His 1976 theorem is their incompatibility with the single property of Local Causality. This is contrary to Bells own later assertions, that his 1964 theorem began with the assumption of Local Causality, even if not by that name. Although the two Bells theorems are logically equivalent, their assumptions are not. Hence, the earlier and later theorems suggest quite different conclusions, embraced by operationalists and realists, respectively. The key issue is whether Locality or Local Causality is the appropriate notion emanating from Relativistic Causality, and this rests on ones basic notion of causation. For operationalists the appropriate notion is what is here called the Principle of Agent-Causation, while for realists it is Reichenbachs Principle of common cause. By breaking down the latter into even more basic Postulates, it is possible to obtain a version of Bells theorem in which each camp could reject one assumption, happy that the remaining assumptions reflect its weltanschauung. Formulating Bells theorem in terms of causation is fruitful not just for attempting to reconcile the two camps, but also for better describing the ontology of different quantum interpretations and for more deeply understanding the implications of Bells marvellous work.
Yes. That is my polemical reply to the titular question in Travis Norsens self-styled polemical response to Howard Wisemans recent paper. Less polemically, I am pleased to see that on two of my positions --- that Bells 1964 theorem is different from Bells 1976 theorem, and that the former does not include Bells one-paragraph heuristic presentation of the EPR argument --- Norsen has made significant concessions. In his response, Norsen admits that Bells recapitulation of the EPR argument in [the relevant] paragraph leaves something to be desired, that it disappoints and is problematic. Moreover, Norsen makes other statements that imply, on the face of it, that he should have no objections to the title of my recent paper (The Two Bells Theorems of John Bell). My principle aim in writing that paper was to try to bridge the gap between two interpretational camps, whom I call operationalists and realists, by pointing out that they use the phrase Bells theorem to mean different things: his 1964 theorem (assuming locality and determinism) and his 1976 theorem (assuming local causality), respectively. Thus, it is heartening that at least one person from one side has taken one step on my bridge. That said, there are several issues of contention with Norsen, which we (the two authors) address after discussing the extent of our agreement with Norsen. The most significant issues are: the indefiniteness of the word locality prior to 1964; and the assumptions Einstein made in the paper quoted by Bell in 1964 and their relation to Bells theorem.
Bells inequality sets a strict threshold for how strongly correlated the outcomes of measurements on two or more particles can be, if the outcomes of each measurement are independent of actions undertaken at arbitrarily distant locations. Quantum mechanics, on the other hand, predicts that measurements on particles in entangled states can be more strongly correlated than Bells inequality would allow. Whereas experimental tests conducted over the past half-century have consistently measured violations of Bells inequality---consistent with the predictions of quantum mechanics---the experiments have been subject to one or more loopholes, by means of which certain alternatives to quantum theory could remain consistent with the experimental results. This chapter reviews three of the most significant loopholes, often dubbed the locality, fair-sampling, and freedom-of-choice loopholes, and describes how recent experiments have addressed them.
Bells theorem is based on three assumptions: realism, locality, and measurement independence. The third assumption is identified by Bell as linked to the freedom of choice hypothesis. He holds that ultimately the human free will can ensure the measurement independence assumption. The incomplete experimental conditions for supporting this third assumption are known in the literature as freedom-of-choice loophole (FOCL). In a recent publication, Abellan et al [2018] address this problem and follow this same strategy embraced by Bell [2004]. Nevertheless, the possibility of human freedom of choice has been a matter of philosophical debate for more than 2000 years, and there is no consensus among philosophers on this topic. If human choice is not free, Bells solution would not be sufficient to close FOCL. Therefore, in order to support the basic assumption of this experiment, it is necessary to argue that human choice is indeed free. In this paper, we present a Kantian position on this topic and defend the view that this philosophical position is the best way to ensure that BigBell Test (Abellan et al. [2018]) can in fact close the loophole.
In addition to the regular Schwabe cycles of approximately 11 y, prolonged solar activity minima have been identified through the direct observation of sunspots and aurorae, as well as proxy data of cosmogenic isotopes. Some of these minima have been regarded as grand solar minima, which are arguably associated with the special state of the solar dynamo and have attracted significant scientific interest. In this paper, we review how these prolonged solar activity minima have been identified. In particular, we focus on the Dalton Minimum, which is named after John Dalton. We review Daltons scientific achievements, particularly in geophysics. Special emphasis is placed on his lifelong observations of auroral displays over approximately five decades in Great Britain. Daltons observations for the auroral frequency allowed him to notice the scarcity of auroral displays in the early 19th century. We analyze temporal variations in the annual frequency of such displays from a modern perspective. The contemporary geomagnetic positions of Daltons observational site make his dataset extremely valuable because his site is located in the sub-auroral zone and is relatively sensitive to minor enhancements in solar eruptions and solar wind streams. His data indicate clear solar cycles in the early 19th century and their significant depression from 1798 to 1824. Additionally, his data reveal a significant spike in auroral frequency in 1797, which chronologically coincides with the lost cycle that is believed to have occurred at the end of Solar Cycle 4. Therefore, John Daltons achievements can still benefit modern science and help us improve our understanding of the Dalton Minimum.
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