Remarks on Causality in Relativistic Quantum Field Theory

Rédei, Miklós; Summers, Stephen J.

doi:10.1007/s10773-006-9299-5

Cited by 18 publications

(18 citation statements)

References 30 publications

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“…Since von Neumann's work on quantum logic and operator algebras [3,4], it has been known that quantum theory can be viewed as a generalization of probability theory [5,6]. If we want to understand what this tells us about the nature of reality then we will need to adopt a concrete theory of how probabilities relate to the world, which is the job of an interpretation of probability theory 1 .…”

Section: The Interpretation Of Probabilitymentioning

confidence: 99%

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“It from Bit” and the Quantum Probability Rule

Leifer

2015

The Frontiers Collection

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I argue that, on the subjective Bayesian interpretation of probability, "it from bit" requires a generalization of probability theory. This does not get us all the way to the quantum probability rule because an extra constraint, known as noncontextuality, is required. I outline the prospects for a derivation of noncontextuality within this approach and argue that it requires a realist approach to physics, or "bit from it". I then explain why this does not conflict with "it from bit". This version of the essay includes an addendum responding to the open discussion that occurred on the FQXi website. It is otherwise identical to the version submitted to the contest.

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Section: The Interpretation Of Probabilitymentioning

confidence: 99%

“…Based on this kind of argument, many subjective Bayesians regard probability theory as akin to propositional logic 5 . In logic, you start with a set of premises that you regard as true, and then you use the rules of logic to figure out what other propositions must be true or false as a consequence.…”

Section: Is Probability Theory Normative?mentioning

confidence: 99%

“It from Bit” and the Quantum Probability Rule

Leifer

2015

The Frontiers Collection

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“…Note finally that one can raise the problem of common cause completability and common cause closedness of non-classical probability spaces [15], [23], [24] where the Boolean algebra is replaced by a more general orthocomplemented lattice and the classical probability measure by a general countably additive bounded measure. It would be interesting to see if the product construction described in this paper for classical probability spaces is extendible to general probability spaces and whether common cause closedness of nonclassical probability spaces can be established along the lines presented in this paper.…”

Section: Arguments Showing That the Epr Correlations Cannot Be Explaimentioning

confidence: 99%

Characterizing Common Cause Closed Probability Spaces

Gyenis

Rédei²

2011

Philos. of Sci.

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A classical probability measure space was defined in earlier papers [14], [9] to be common cause closed if it contains a Reichenbachian common cause of every correlation in it, and common cause incomplete otherwise. It is shown that a classical probability measure space is common cause incomplete if and only if it contains more than one atom. Furthermore, it is shown that every probability space can be embedded into a common cause closed one; which entails that every classical probability space is common cause completable with respect to any set of correlated events. The implications of these results for Reichenbach's Common Cause Principle are discussed, and it is argued that the Principle is only falsifiable if conditions on the common cause are imposed that go beyond the requirements formulated by Reichenbach in the definition of common cause.

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“…on this von Neumann algebra. Therefore, the pair (M, ϕ) is also a "probabilistic object" in our model (see [10][11][12]). In this sense, probability and dynamics are fully unified.…”

Section: Noncommutative Geometry Of the Closed Friedman Modelmentioning

confidence: 99%

A noncommutative Friedman cosmological model

Heller

2010

Ann. Phys.

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The closed Friedman cosmological model, based on noncommutative geometry, is presented. Two global effects exhibited by the model are discussed. The first effect is the "generation of matter out of geometry". Gravitational field equation in this model has the form of the eigenvalue equation for the Einstein operator. It turns out that the eigenvalues of this operator reproduce components of the energy-momentum tensor. The second effect concerns the existence of the initial and final singularities. Because of the strongly probabilistic character of the noncommutative dynamics on the fundamental level, although singularities do exist, they are probabilistically irrelevant.

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Remarks on Causality in Relativistic Quantum Field Theory

Cited by 18 publications

References 30 publications

“It from Bit” and the Quantum Probability Rule

“It from Bit” and the Quantum Probability Rule

Characterizing Common Cause Closed Probability Spaces

A noncommutative Friedman cosmological model

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