Abstract After forty years of EPR experiments, it appears on the face of the experimental facts that one of the oldest ideas in Physics has been falsified, namely the retarded interaction paradigm, the notion that long range interactions between quanta, or equivalently causal influences between point events, are mediated by physical entities - fields, particles or “causal influences” in general - that travel through space from one point to the other at or below the characteristic velocity, c. A critical examination of this basic idea shows it to be unsatisfactory in all respects. An alternative is then proposed that satisfies both causality and local action, “distributed action”, which is germane to local realist field models of the quanta, where matter and energy extend in space and interact locally and causally at all locations where they overlap. Bell Inequalities cannot be derived in this context because, with distributed fieldfield interactions, spacelike separation of events does not guarantee the fundamental “no influence” assumption from which all the various Bell Inequalities are derived. Distributed action thus explains what appears to us as instantaneous action at a distance. PACS: 03.65.Ud 03.75.-b
Abstract After forty years of EPR experiments, it appears on the face of the experimental facts that one of the oldest ideas in Physics has been falsified, namely the retarded interaction paradigm, the notion that long range interactions between quanta, or equivalently causal influences between point events, are mediated by physical entities - fields, particles or “causal influences” in general - that travel through space from one point to the other at or below the characteristic velocity, c. A critical examination of this basic idea shows it to be unsatisfactory in all respects. An alternative is then proposed that satisfies both causality and local action, “distributed action”, which is germane to local realist field models of the quanta, where matter and energy extend in space and interact locally and causally at all locations where they overlap. Bell Inequalities cannot be derived in this context because, with distributed fieldfield interactions, spacelike separation of events does not guarantee the fundamental “no influence” assumption from which all the various Bell Inequalities are derived. Distributed action thus explains what appears to us as instantaneous action at a distance. PACS: 03.65.Ud 03.75.-b
Introduction: Bell’s concept of local causality assumes more than local action. It also presumes an ontology of point particles. Bell correlations are feasible in nonlinear field ontologies with quantised interactions between suitably correlated participants. Materials and methods: Local causality is unsatisfactory for many reasons, not just Bell’s Theorem. The EPR paradox is due to metaphysical overcommitment to point models. An alternative, distributed concept of long-range interaction is appropriate for field ontologies. Inherently distributed field interaction quanta modify the causal structure of relations between observables. Results: Causal structure of Bell measurements in de Broglie–Bohm EPR experiments: Causal analysis of local realist field models violates Bell Inequalities without violating local action. Experimental Tests: Testable consequences include an observable range dependence of the coherence time of Bell states. Conclusions: Local realist field ontologies are not ruled out by the existence of Bell correlations in nature. The only “conflict” between quantum mechanics and relativity is because lightcone causal analysis effectively presumes a particle ontology.
Introduction Fifty years after the publication of Bell's theorem, there remains some controversy regarding what the theorem is telling us about quantum mechanics, and what the experimental violations of Bell inequalities are telling us about the world. This chapter represents my best attempt to be clear about what I think the lessons are. In brief: There is some sort of nonlocality inherent in any quantum theory, and, moreover, in any theory that reproduces, even approximately, the quantum probabilities for the outcomes of experiments. But not all forms of nonlocality are the same; there is a distinction to be made between action at a distance and other forms of nonlocality, and I will argue that the nonlocality needed to violate the Bell inequalities need not involve action at a distance. Furthermore, the distinction between forms of nonlocality makes a difference when it comes to compatibility with relativistic causal structure. The Bell locality condition is a condition which, if satisfied, renders possible a completely local account of the correlations between outcomes of spatially separated experiments. Bell's theorem tells us that the probabilities that we compute from quantum mechanics do not admit of such an account. Modulo auxiliary assumptions that, in my opinion, should be noncontroversial, this yields the conclusion that there must be something nonlocal about any theory that yields the quantum mechanical probabilities or anything close to them. One way to violate the Bell locality condition – and this is the way that any deterministic theory must do it – is via straightforward action at a distance. However, we should also consider the possibility of a stochastic theorywith probabilistic laws that involve irreducible correlations. The sort of nonlocality inherent in such a theory involves relations between events that are significantly different from causal relations as usually conceived. Perhaps surprisingly, such a theory, unlike its deterministic cousins, need not invoke a distinguished relation of distant simultaneity. This makes a difference for the situation of the two sorts of theories vis-a-vis relativity. Though a deterministic theory can achieve the appearance of being relativistic, at the level of observable phenomena, it can do so only by introducing a preferred foliation and with it a causal structure at odds with relativistic causal structures. Things are otherwise with dynamical collapse theories.
Spooky Action at a Distance In the context of correlation experiments involving pairs of experiments performed at very nearly the same time in very far-apart experimental regions, Einstein famously said [1], But on one supposition we should in my opinion hold absolutely fast: “The real factual situation of the system S2 is independent of what is done with system S1 which is spatially separated from the former.” This demand is incompatible with the basic ideas of standard (Copenhagen/orthodox) quantum mechanics, which makes two relevant claims: (1) Experimenters in the two labs make “local free choices” that determine which experiments will be performed in their respective labs. These choices are free in the sense of not being predetermined by the prior history of the physically described aspects of the universe, and they are localized in the sense that the physical effects of these free choices are inserted into the physically described aspects of the universe only within the laboratory in which the associated experiment is being performed. (2) These choices of what is done with the system being measured in one lab can (because of a measurement-induced global collapse of the quantum state) influence the outcome of the experiment performed at very close to the same time in the very faraway lab. This influence of what is done with the system being measured in one region upon the outcome appearing at very nearly the same time in a very faraway lab was called “spooky action at a distance” by Einstein, and was rejected by him as a possible feature of “reality.” John Bell's Quasi-classical Statistical Theory Responding to the seeming existence in the quantum world of “spooky actions,” John Bell [2] proposed a possible alternative to the standard approach that might conceivably be able to reconcile quantum spookiness with “reality.” This alternative approach rests on the fact that quantum mechanics is a statistical theory.We already have in physics a statistical theory called “classical statistical mechanics.”
By moving to the context of relativistic space-time structure, this chapter completes the argument of Chapter 4 that we can use quantum theory locally to explain correlations that violate Bell inequalities with no instantaneous action at a distance. Chance here must be relativized not just to time but to a space-time point, so that an event may have more than one chance at the same time—it may even be certain relative to one space-time point but ‘at the same time’ completely uncertain relative to another. This renders Bell’s principle of Local Causality either inapplicable or intuitively unmotivated. Counterfactual dependence between the outcomes of measurements on systems assigned an entangled state is not causal since neither outcome is subject to intervention: but it may still be appealed to in a non-causal explanation of one in terms of the other.
Abstract The Einstein‐Podolsky‐Rosen “gedanken‐experiment” does not imply non‐local interactions or an “action‐at‐a‐distance”. Contrary, the EPR proves the measurements at one particle does not have influences at canonical variables of the other particles if the quantum‐mechanical commutation relations are true. But, the EPR implices correlations between the particles which come in by “subjective knowledge”. These correlations are a priori informations about the relative motion or, complementarily, about the motion of the center of mass. The impression of an action‐at‐a‐distance is produced by the use of usual particle coordinates in the EPR‐arrangements. The discussion of the Einstein‐Podolsky‐Rosen “gedanken‐experiment” (EPR) has been going on over fifty years. EINSTEIN, PODOLSKY, and ROSEN formulated their famous paradox in 1935, and in the discussion between N. BOHR (1935, 1949) and A. EINSTEIN (1936, 1948); A. EINSTEIN (1948) made his point that the EPR implied an “action‐at‐a‐distance” for quantum‐mechanical particles (without obvious classical interactions). His argument is the starting point for the recent discussion about EPR and causality (see A. Aspect, 1981).
The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B , either A is in the causal past of B , B is in the causal past of A , or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B , an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A ’s future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. We show that the processes realizable by classically controlled quantum circuits are ECS and conjecture that the reverse also holds.