In this chapter I prove that the transition probabilities, which describe the dynamics of the actually possessed properties of systems, violate the assumption of Dynamical Autonomy for composite systems. And, related to this violation, it is also proved that the dynamics of the actually possessed properties is non-local in a quite explicit way. Introduction When I introduced the assumptions of Instantaneous and Dynamical Autonomy in Section 3.3, I motivated them by making an appeal to locality. In the case of Instantaneous Autonomy, I argued that a state of a system α should codify all the information about the property ascription to that system. For if a state does not codify all the information, it may happen that a change in the state of some distant system σ (I used the example of a far-away asteroid) means that the properties of α change as well. And this would make modal property ascriptions undesirably non-local. In the case of Dynamical Autonomy one can give a similar motivation. The state of a system α, as it evolves during a time interval i , should codify all the information about the simultaneous and sequential correlations between the properties ascribed to α in that interval i . For if the evolving state does not do so, it may happen that a change in a distant system changes the correlations between the properties of α as well. Modal interpretations satisfy a number of the Autonomy assumptions. All modal interpretations satisfy Instantaneous Autonomy by construction. The transition probabilities derived in Section 8.2 prove that the bi and spectral modal interpretations satisfy Dynamical Autonomy for whole systems and that the atomic modal interpretation satisfies Dynamical Autonomy for atomic systems.
In this chapter I prove that the transition probabilities, which describe the dynamics of the actually possessed properties of systems, violate the assumption of Dynamical Autonomy for composite systems. And, related to this violation, it is also proved that the dynamics of the actually possessed properties is non-local in a quite explicit way. Introduction When I introduced the assumptions of Instantaneous and Dynamical Autonomy in Section 3.3, I motivated them by making an appeal to locality. In the case of Instantaneous Autonomy, I argued that a state of a system α should codify all the information about the property ascription to that system. For if a state does not codify all the information, it may happen that a change in the state of some distant system σ (I used the example of a far-away asteroid) means that the properties of α change as well. And this would make modal property ascriptions undesirably non-local. In the case of Dynamical Autonomy one can give a similar motivation. The state of a system α, as it evolves during a time interval i , should codify all the information about the simultaneous and sequential correlations between the properties ascribed to α in that interval i . For if the evolving state does not do so, it may happen that a change in a distant system changes the correlations between the properties of α as well. Modal interpretations satisfy a number of the Autonomy assumptions. All modal interpretations satisfy Instantaneous Autonomy by construction. The transition probabilities derived in Section 8.2 prove that the bi and spectral modal interpretations satisfy Dynamical Autonomy for whole systems and that the atomic modal interpretation satisfies Dynamical Autonomy for atomic systems.
Environmental decoherence is widely held to be the key to understanding the emergence of classicality in a quantum universe. However, in conjunction with traditional principles of interpretation, decoherence leaves unanswered a fundamental question, a version of the quantum measurement problem: Why should macroscopic objects have definite properties at all? I critically evaluate a variety of interpretive strategies intended to parlay the formal results of decoherence into the definiteness, or apparent definiteness, of familiar macroscopic properties. I argue that the crucial role of environmental decoherence in accounting for definite properties is effecting the dynamical decoupling of components of the global quantum state for which these properties are definite.This role of decoherence is most evident in the context of the Everett interpretation, where considerations regarding branch dynamics lead naturally to the conclusion that dynamical autonomy (non-interference) of branches is a restriction on any division of the global quantum state into branches. Environmental decoherence results in the requisite dynamical autonomy for branches in which familiar macroscopic observables are definite, thus providing a natural and principled way to identify an interpretation basis.The modal interpretation, with its property ascription rule based on the spectral decomposition of the reduced state, secures the right definite properties only in those cases in which it picks out properties that correspond almost exactly with the non-interfering components of the global quantum state. I argue that the non-interference of these components should be accorded interpretational significance in its own right; then the right properties can be specified without recourse to the distinctive property ascription rules of the modal interpretation.Finally, I criticize attempts of decoherence theorists to account for definite properties by appeal to effects of decoherence such as approximate diagonality of the reduced state and preservation of correlations with respect to a set of privileged states. I argue that definiteness can be accounted for by looking not to these effects but to their cause, the dynamical autonomy of the environmentally-privileged components of the global quantum state. Precisely because they are dynamically autonomous, these states can be accorded physical significance in their own right.
The world of quantum theory is not deterministic; however, the quantum theory of an isolated system describes its state as evolving deterministically.How can these two points be reconciled? The modal interpretation (of which a number of variants have been developed) answers this as follows. An observable may have a value even if the system is not in the corresponding eigenstate of that observable. The state of the system only constrains the possible values the observable can have, and (at least under certain conditions) the probabilities that it has those values. Hence, the eigenvalue–eigenstate link is violated. There is no collapse; the state of an isolated system always evolves in accordance with the Schroedinger equation. Hence the values of observables can change indeterministically, though this stochastic process is constrained by the deterministically evolving quantum state. Terminology varies but in this book the quantum state is then called the dynamical state, and a summary of the values of the observables pertaining to the system is called the value state. Since not all observables are mutually compatible, they will not all have simultaneous sharp values, but for each there is a minimum Borel set of values as its current range. The specific modal interpretation developed here is the Copenhagen Variant of the Modal Interpretation, which places holistic constraints on values of observables pertaining to parts of composite systems.
With an interpretation of quantum mechanics one can not only predict probabilities for outcomes of measurements performed on quantum systems but also ascribe properties to these systems themselves. I consider interpretations (notably modal interpretations) that ascribe at least those properties to a system which are represented by the eigenprojections of the reduced state. Such interpretations solve the measurement problem for ideal measurements. Here, however, I prove that these interpretations cannot define joint property ascriptions to three or more systems.
Starting from the late 60’s many experiments have been performed to verify the violation Bell’s inequality by Einstein-Podolsky-Rosen (EPR) type correlations. The idea of these experiments being that: (i) Bell’s inequality is a consequence of locality, hence its experimental violation is an indication of non locality; (ii) this violation is a typical quantum phenomenon because any classical system making local choices (either deterministic or random) will produce correlations satisfying this inequality. Both statements (i) and (ii) have been criticized by quantum probability on theoretical grounds (not discussed in the present paper) and the experiment discussed below has been devised to support these theoretical arguments. We emphasize that the goal of our experiment is not to reproduce classically the EPR correlations but to prove that there exist perfectly local classical dynamical systems violating Bell’s inequality. The conclusions of the present experiment are: no contradiction between quantum theory and locality can be deduced from the violation of Bell’s inequality. The Copenhagen interpretation of quantum theory becomes quite reasonable and not metaphyisic if interpreted at the light of the chameleon effect. One can realize quantum entanglement by classical computers. In section (7) we prove that our experiment also provides a classical analogue of the type of logical (i.e. independent of statistics) incompatibilities pointed out by Greenberger, Home and Zeilinger. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
It has been suggested that the Modal Interpretation of Quantum Mechanics (QM) is "incomplete" if it lacks a dynamics for possessed values. I argue that this is only one of two possible attitudes one might adopt toward a Modal Interpretation without dynamics. According to the other attitude, such an interpretation is a complete interpretation of QM as standardly formulated, an interpretation whose innovation is to attempt to make sense of the quantum realm without the expedient of novel physics. Then I explain why this attitude, though available, is unattractive. Without dynamics, the Modal Interpretation vanquishes the measurement problem only, it seems, to succumb to the problem of state preparation. On this view, the Modal Interpretation needs dynamics not to be an interpretation at all, but to be an adequate one. I review reasons to suspect that the dynamics which would best suit the Modal Interpretation--a dynamics equivalent to a set of two time transition probabilities of the sort used to solve the preparation problem--is not a dynamics the interpretation can have. I close with a brief discussion of versions of the Modal Interpretation that may not succumb to the considerations presented here.
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.