Dirac, and W.

Heisenberg advanced this view earlier, it is best exemplified by J. Conventional quantum mechanics answers this question by specifying the required mathematical properties of wavefunctions and invoking the Born postulate. The ontological question remains unanswered. There is one exception to this. A variation of the Feynman chessboard model allows a classical stochastic process to assemble a wavefunction, based solely on the geometry of spacetime paths.

A direct comparison of how a related process assembles a Probability Density Function reveals both how and why PDFs and wavefunctions differ from the perspective of an underlying kinetic theory. Many statistics problems involve predicting the joint strategy that will be chosen by the players in a noncooperative game. The relative probabilities of the joint strategies satisfying the equilibrium concept are not given, and all joint strategies that do not satisfy it are given probability zero.

Jump to Navigation. Currently there are no upcoming talks in this series. Tuesday Feb 10, Speaker s :. Hans Westman. Quantum Foundations. Scientific Areas:. Against commutators. Tuesday Jan 20, Robert Oeckl. Now, macroscopic objects are typically in interaction with a large and complex environment—they are constantly being bombarded with air molecules, photons, and the like. As a result, the reduced state of such a system quickly becomes a mixture of quasi-classical states, a phenomenon known as decoherence. A generalization of decoherence lies at the heart of an approach to the interpretation of quantum mechanics that goes by the name of decoherent histories approach see the entry on the consistent histories approach to quantum mechanics for an overview.

Decoherence plays important roles in the other approaches to quantum mechanics, though the role it plays varies with approach; see the entry on the role of decoherence in quantum mechanics for information on this. All of the above approaches take it that the goal is to provide an account of events in the world that recovers, at least in some approximation, something like our familiar world of ordinary objects behaving classically. None of the mainstream approaches accord any special physical role to conscious observers. There have, however, been proposals in that direction see the entry on quantum approaches to consciousness for discussion.

All of the above-mentioned approaches are consistent with observation. Mere consistency, however, is not enough; the rules for connecting quantum theory with experimental results typically involve nontrivial that is, not equal to zero or one probabilities assigned to experimental outcomes. These calculated probabilities are confronted with empirical evidence in the form of statistical data from repeated experiments. Extant hidden-variables theories reproduce the quantum probabilities, and collapse theories have the intriguing feature of reproducing very close approximations to quantum probabilities for all experiments that have been performed so far but departing from the quantum probabilities for other conceivable experiments.

This permits, in principle, an empirical discrimination between such theories and no-collapse theories. It has been the subject of much recent work on Everettian theories; see Saunders for an introduction and overview. If one accepts that Everettians have a solution to the evidential problem, then, among the major lines of approach, none is favored in a straightforward way by the empirical evidence.

If one is to make a decision as to which, if any, one should accept, it is to be made on other grounds. There will not be space here to give an in-depth overview of these ongoing discussions, but a few considerations can be mentioned, to give the reader a flavor of the discussions; see entries on particular approaches for more detail. Bohmians claim, in favor of the Bohmian approach, that a theory on these lines provides the most straightforward picture of events; ontological issues are less clear-cut when it comes to Everettian theories or collapse theories.

Another consideration is compatibility with relativistic causal structure. The de Broglie-Bohm theory requires a distinguished relation of distant simultaneity for its formulation, and, it can be argued, this is an ineliminable feature of any hidden-variables theory of this sort, that selects some observable to always have definite values see Berndl et al. On the other hand, there are collapse models that are fully relativistic.

On such models, collapses are localized events. Though probabilities of collapses at spacelike separation from each other are not independent, this probabilistic dependence does not require us to single one out as earlier and the other later. Thus, such theories do not require a distinguished relation of distant simultaneity. See the entry on collapse theories and references therein; see also, for some recent contributions to the discussion, Fleming , Maudlin , and Myrvold In the case of Everettian theories, one must first think about how to formulate the question of relativistic locality.

Several authors have approached this issue in somewhat different ways, with a common conclusion that Everettian quantum mechanics is, indeed, local. As mentioned, a central question of interpretation of quantum mechanics concerns whether quantum states should be regarded as representing anything in physical reality. If this is answered in the affirmative, this gives rise to new questions, namely, what sort of physical reality is represented by the quantum state, and whether a quantum state could in principle give an exhaustive account of physical reality. Harrigan and Spekkens have introduced a framework for discussing these issues.

In their terminology, a complete specification of the physical properties is given by the ontic state of a system. An ontological model posits a space of ontic states and associates, with any preparation procedure, a probability distribution over ontic states. This gives a nice way of posing the question of quantum state realism: are there preparations corresponding to distinct pure quantum states that can give rise to the same ontic state, or, conversely, are there ontic states compatible with distinct quantum states?

## Information insights

The Pusey, Barrett and Rudolph PBR theorem does not close off all options for anti-realism about quantum states; an anti-realist about quantum states could reject the Preparation Independence assumption, or reject the framework within which the theorem is set; see discussion in Spekkens 92— See also Leifer for a careful and thorough overview of theorems relevant to quantum state realism.

The major realist approaches to the measurement problem are all, in some sense, realist about quantum states. Merely saying this is insufficient to give an account of the ontology of a given interpretation. Among the questions to be addressed are: if quantum states represent something physically real, what sort of thing is it? This is the question of the ontological construal of quantum states. Another question is the EPR question, whether a description in terms of quantum states can be taken as, in principle, complete, or whether it must be supplemented by different ontology.

The original conception was that each particle would have its own guiding wave. If quantum states represent something in physical reality, they are unlike anything familiar in classical physics.

On this view, this high-dimensional space is thought of as more fundamental than the familiar three-dimensional space or four-dimensional spacetime that is usually taken to be the arena of physical events. See Albert , , for the classic statement of the view; other proponents include Loewer , Lewis , Ney , a,b, , and North Most of the discussion of this proposal has taken place within the context of nonrelativistic quantum mechanics, which is not a fundamental theory.

It has been argued that considerations of how the wave functions of nonrelativistic quantum mechanics arise from a quantum field theory undermines the idea that wave functions are relevantly like fields on configuration space, and also the idea that configuration spaces can be thought of as more fundamental than ordinary spacetime Myrvold Taking a wave function to be a multi-field, on the other hand, involves accepting nonseparability.

Another difference between taking wave-functions as multi-fields on ordinary space and taking them to be fields on a high-dimensional space is that, on the multi-field view, there is no question about the relation of ordinary three-dimensional space to some more fundamental space. It has been argued that, on the de Broglie-Bohm pilot wave theory and related pilot wave theories, the quantum state plays a role more similar to that of a law in classical mechanics; its role is to provide dynamics for the Bohmian corpuscles, which, according to the theory, compose ordinary objects.

The conception is extended to interpretations of collapse theories by Allori et al. Primitive ontology is to be distinguished from other ontology, such as the quantum state, that is introduced into the theory to account for the behavior of the primitive ontology.

The distinction is meant to be a guide as to how to conceive of the nonprimitive ontology of the theory. Quantum mechanics has not only given rise to interpretational conundrums; it has given rise to new concepts in computing and in information theory. Quantum information theory is the study of the possibilities for information processing and transmission opened up by quantum theory. Another area of active research in the foundations of quantum mechanics is the attempt to gain deeper insight into the structure of the theory, and the ways in which it differs from both classical physics and other theories that one might construct, by characterizing the structure of the theory in terms of very general principles, often with an information-theoretic flavour.

This project has its roots in early work of Mackey , , Ludwig , and Piron aiming to characterize quantum mechanics in operational terms. This has led to the development of a framework of generalized probabilistic model. It also has connections with the investigations into quantum logic initiated by Birkhoff and von Neumann see the entry quantum logic and probability theory for an overview. Interest in the project of deriving quantum theory from axioms with clear operational content was revived by the work of Hardy [], Other Internet Resources.

See Chiribella and Spekkens for a snapshot of the state of the art of this endeavour. Introduction 2. Quantum theory 2. Entanglement, nonlocality, and nonseparability 4. The measurement problem 4. Ontological Issues 5. Quantum computing and quantum information theory 7. Bibliography Albert, David Z. Cushing, A.

### 1. Introduction

Goldstein eds. Placzek and J. Butterfield eds. Bell, J. Reprinted in Bell 1— Masanes and M. New J.

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Brukner, The classical limit of a physical theory and the dimensionality of space. Springer, , arXiv Wever, Quantum theory from questions. A, 95 , Toggle navigation.

## Quantum correlations which imply causation

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## Quantum correlations which imply causation

Operational reconstruction of quantum theory. The origin of Hilbert space State spaces of a two-dimensional system in the generalized probabilistic theories [DB09]. The dimensionality of space Dynamics of the generalized spin as generated by its interaction with a single coherent macroscopic state in three-dimensional space left or with a pair of coherent states in four-dimensional space right [DB16].