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Title:

Collapse and relativity

Description:

Abstract. Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum mechanics is to devise a relativistic quantum theory without observers. One of the difficulties is to...

Abstract. Ever since we have been in the possession of quantum theories without observers, such as Bohmian mechanics or the Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse, a major challenge in the foundations of quantum mechanics is to devise a relativistic quantum theory without observers. One of the difficulties is to reconcile nonlocality with relativity. I report about recent progress in this direction based on the GRW model: A relativistic version of the model has been devised for the case of N noninteracting (but entangled) particles. A key ingredient was to focus not on the evolution of the wave function but rather on the evolution of the matter in space-time as determined by the wave function. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-01-03

Source:

http://arxiv.org/pdf/quant-ph/0602208v1.pdf

http://arxiv.org/pdf/quant-ph/0602208v1.pdf Minimize

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric, which contains two spacelike singularities, one in the past and one in the future. Since the particle world lin...

We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for quantum particles in a curved background space-time containing a spacelike singularity. As an example of such a metric we use the Schwarzschild metric, which contains two spacelike singularities, one in the past and one in the future. Since the particle world lines are everywhere timelike or lightlike, particles can be annihilated but not created at a future spacelike singularity, and created but not annihilated at a past spacelike singularity. It is argued that in the presence of future (past) spacelike singularities, there is a unique natural Bohm-like evolution law directed to the future (past). This law differs from the one in nonsingular space-times mainly in two ways: it involves Fock space since the particle number is not conserved, and the wave function is replaced by a density matrix. In particular, we determine the evolution equation for the density matrix, a pureto-mixed evolution equation of a quasi-Lindblad form. We have to leave open whether a curvature cut-off needs to be introduced for this equation to be well Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-04

Source:

http://arxiv.org/pdf/0808.3060v2.pdf

http://arxiv.org/pdf/0808.3060v2.pdf Minimize

Document Type:

text

Language:

en

DDC:

190 Modern western philosophy *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Two Arrows of Time in Nonlocal Particle Dynamics

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Considering what the world would be like if backwards causation were possible is usually mind-bending. Here I discuss something that is easier to study: a toy model that incorporates a very restricted sort of backwards causation. It defines particle world lines by means of a kind of differential delay equation with negative delay. The model pres...

Considering what the world would be like if backwards causation were possible is usually mind-bending. Here I discuss something that is easier to study: a toy model that incorporates a very restricted sort of backwards causation. It defines particle world lines by means of a kind of differential delay equation with negative delay. The model presumably prohibits signalling to the past and superluminal signalling, but allows nonlocality while being fully covariant. And that is what constitutes the model’s value: it is an explicit example of the possibility of Lorentz invariant nonlocality. That is surprising in so far as many authors thought that nonlocality, in particular nonlocal laws for particle world lines, must conflict with relativity. The development of this model was inspired by the search for a fully covariant version of Bohmian mechanics. In this paper I will introduce to you a dynamical system—a law of motion for point particles—that has been invented [5] as a toy model based on Bohmian mechanics. Bohmian mechanics is a version of quantum mechanics with particle trajectories; see [4] for an introduction and overview. What makes this toy model remarkable is that it has two arrows of time, and that precisely its having two arrows of time is what allows it to perform what it was designed for: to have effects travel faster than light from their causes (in short, nonlocality) without breaking Lorentz invariance. Why should anyone Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0210207v2.pdf

http://arxiv.org/pdf/quant-ph/0210207v2.pdf Minimize

Document Type:

text

Language:

en

DDC:

190 Modern western philosophy *(computed)*

Rights:

Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Feynman’s Path Integrals and Bohm’s Particle Paths

Description:

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman’s path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger’s equation, which is half of t...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman’s path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger’s equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0501167v2.pdf

http://arxiv.org/pdf/quant-ph/0501167v2.pdf Minimize

Document Type:

text

Language:

en

Subjects:

PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals

PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals Minimize

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Title:

Opposite arrows of time can reconcile relativity and nonlocality

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We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) ...

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time. PACS numbers 03.65.Ud; 03.65.Ta; 03.30.+p We challenge in this paper a conclusion that is almost universally accepted: that quantum phenomena, relativity, and realism are incompatible. We show that, just as in the case of the no-hidden-variables theorems, this conclusion is hasty. And, as in the hidden variables case, we do so with a counterexample. We present a relativistic toy model for nonlocal quantum phenomena that avoids the usual quantum subjectivity, or fundamental appeal to an observer, and describes instead, in a rather natural way, an objective motion of particles in Minkowski space. In contrast to that of [4], see below, our model invokes only the structure at hand: relativistic structure provided by the Lorentz metric and quantum structure provided by a wave function. It shares the conceptual framework—and forms a natural generalization—of Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0105040v4.pdf

http://arxiv.org/pdf/quant-ph/0105040v4.pdf Minimize

Document Type:

text

Language:

en

DDC:

115 Time *(computed)*

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Title:

A Relativistic Version of the Ghirardi-Rimini-Weber Model

Description:

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spontaneous wavefunction collapse. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. T...

Carrying out a research program outlined by John S. Bell in 1987, we arrive at a relativistic version of the Ghirardi–Rimini–Weber (GRW) model of spontaneous wavefunction collapse. As suggested by Bell, we take the primitive ontology, or local beables, of our model to be a discrete set of space-time points, at which the collapses are centered. This set is random with distribution determined by the initial wavefunction. The model is nonlocal and violates Bell’s inequality though it does not make use of a preferred slicing of space-time or any other sort of synchronization of spacelike separated points. Like the GRW model, it reproduces the quantum probabilities in all cases presently testable, though it entails deviations from the quantum formalism that are in principle testable. Our model works in Minkowski space-time as well as in (well-behaved) curved background space-times. PACS numbers: 03.65.Ta; 03.65.Ud; 03.30.+p. Key words: spontaneous wavefunction collapse; relativity; quantum theory without observers. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0406094v1.pdf

http://arxiv.org/pdf/quant-ph/0406094v1.pdf Minimize

Document Type:

text

Language:

en

DDC:

115 Time *(computed)*

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Title:

Contents

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The Ghirardi–Rimini–Weber (GRW) theory is a physical theory that, when combined with a suitable ontology, provides an explanation of quantum mechanics. The so-called collapse of the wave function is problematic in conventional quantum theory but not in the GRW theory, in which it is governed by a stochastic law. A possible ontology is the flash ...

The Ghirardi–Rimini–Weber (GRW) theory is a physical theory that, when combined with a suitable ontology, provides an explanation of quantum mechanics. The so-called collapse of the wave function is problematic in conventional quantum theory but not in the GRW theory, in which it is governed by a stochastic law. A possible ontology is the flash ontology, according to which matter consists of random points in space-time, called flashes. The joint distribution of these points, a point process in space-time, is the topic of this work. The mathematical results concern mainly the existence and uniqueness of this distribution for several variants of the theory. Particular attention is paid to the relativistic version of the GRW theory that I developed in 2004. MSC: 81P05; 46N50; 83A05; 81Q99. Key words: quantum theory without observers; Ghirardi-Rimini-Weber (GRW) theory of spontaneous wave function collapse; relativistic Lorentz covariance; flash ontology; Dirac equation; Dirac evolution Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-05

Source:

http://arxiv.org/pdf/0711.0035v1.pdf

http://arxiv.org/pdf/0711.0035v1.pdf Minimize

Document Type:

text

Language:

en

DDC:

115 Time *(computed)*

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Title:

The Analogue of Bohm–Bell Processes on a Graph

Description:

Bohm–Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes Qt generalizing in a natural way both Bohm’s dynamical system in configuration space for nonrelativistic quantum mechanics and Bell’s jump process for lattice quantum field theories. They are such that at any time t the distribution of Q...

Bohm–Bell processes, of interest in the foundations of quantum field theory, form a class of Markov processes Qt generalizing in a natural way both Bohm’s dynamical system in configuration space for nonrelativistic quantum mechanics and Bell’s jump process for lattice quantum field theories. They are such that at any time t the distribution of Qt is |ψt | 2 with ψ the wave function of quantum theory. We extend this class here by introducing the analogous Markov process for quantum mechanics on a graph (also called a network, i.e., a space consisting of line segments glued together at their ends). It is a piecewise deterministic process whose innovations occur only when it passes through a vertex. MSC (2000): 81S99, 60J25. PACS: 02.50.Ga; 03.65.Ta. Key words: Bohmian mechanics; Bell’s jump process; quantum mechanics on a graph; equivariant Markov processes; flow on a graph. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0508109v1.pdf

http://arxiv.org/pdf/quant-ph/0508109v1.pdf Minimize

Document Type:

text

Language:

en

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Title:

The “Unromantic Pictures” of Quantum Theory

Description:

I am concerned with two views of quantum mechanics that John S. Bell called “unromantic”: spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics ...

I am concerned with two views of quantum mechanics that John S. Bell called “unromantic”: spontaneous wave function collapse and Bohmian mechanics. I discuss some of their merits and report about recent progress concerning extensions to quantum field theory and relativity. In the last section, I speculate about an extension of Bohmian mechanics to quantum gravity. PACS numbers: 03.65.Ta; 03.70.+k. Key words: quantum theory without observers; Ghirardi–Rimini–Weber model of spontaneous wave function collapse; Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0607124v1.pdf

http://arxiv.org/pdf/quant-ph/0607124v1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

1.3 The Truman Show. 6

1.3 The Truman Show. 6 Minimize

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Title:

Feynman’s Path Integrals and Bohm’s Particle Paths

Description:

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman’s path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger’s equation, which is half of t...

Both Bohmian mechanics, a version of quantum mechanics with trajectories, and Feynman’s path integral formalism have something to do with particle paths in space and time. The question thus arises how the two ideas relate to each other. In short, the answer is, path integrals provide a re-formulation of Schrödinger’s equation, which is half of the defining equations of Bohmian mechanics. I try to give a clear and concise description of the various aspects of the situation. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0501167v1.pdf

http://arxiv.org/pdf/quant-ph/0501167v1.pdf Minimize

Document Type:

text

Language:

en

Subjects:

PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals

PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals Minimize

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