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Title:

Bohmian Mechanics at Space-Time Singularities. I. Timelike Singularities

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We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for (one or more) quantum particles in a curved background space-time containing a singularity. Part one, the present paper, focuses on timelike singularities, part two will be devoted to spacelike singularities. We use the timelike singularity of the (super-critical...

We develop an extension of Bohmian mechanics by defining Bohm-like trajectories for (one or more) quantum particles in a curved background space-time containing a singularity. Part one, the present paper, focuses on timelike singularities, part two will be devoted to spacelike singularities. We use the timelike singularity of the (super-critical) Reissner–Nordström geometry as an example. While one could impose boundary conditions at the singularity that would prevent the particles from falling into the singularity, in the case we are interested in here particles have positive probability to hit the singularity and get annihilated. The wish for reversibility, equivariance and the Markov property then dictate that particles must also be created by the singularity, and indeed dictate the rate at which this must occur. That is, a stochastic law prescribes what comes out of the singularity. We specify explicit model equations, involving a boundary condition on the wave function at the singularity, which is applicable also to other versions of quantum theory besides Bohmian mechanics. Key words: quantum theory in curved background space-time; Reissner–Nordstrom space-time geometry; timelike singularities; Bohmian trajectories; particle creation and annihilation; stochastic jump process. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-26

Source:

http://arxiv.org/pdf/0708.0070v1.pdf

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Document Type:

text

Language:

en

DDC:

115 Time *(computed)*

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Title:

Elementary proof for asymptotics of large Haar-distributed unitary matrices, unpublished, www.arxiv.org

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We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of indepen...

We provide an elementary proof for a theorem due to Petz and Réffy which states that for a random n × n unitary matrix with distribution given by the Haar measure on the unitary group U(n), the upper left (or any other) k × k submatrix converges in distribution, after multiplying by a normalization factor √ n and as n → ∞, to a matrix of independent complex Gaussian random variables with mean Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-22

Source:

http://arxiv.org/pdf/0705.3146v2.pdf

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Document Type:

text

Language:

en

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Title:

Determinate Values for Quantum Observables

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This is a comment on J. A. Barrett’s article “The Preferred-Basis Problem and the Quantum Mechanics of Everything ” in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called “hidden”) variables. I point out that it is far from clear, f...

This is a comment on J. A. Barrett’s article “The Preferred-Basis Problem and the Quantum Mechanics of Everything ” in Brit. J. Phil. Sci. 56 (2005), which concerns theories postulating that certain quantum observables have determinate values, corresponding to additional (often called “hidden”) variables. I point out that it is far from clear, for most observables, what such a postulate is supposed to mean, unless the postulated additional variable is related to a clear ontology in space-time, such as particle world lines, string world sheets, or fields. MSC (2000): 81P05. PACS: 03.65.Ta. Key words: Bohmian mechanics, beables, observables, quantum theory without observers. In his recent article (Barrett 2005), Jeffrey A. Barrett developed an astute analysis of the problems that would arise for Bohmian mechanics if mental states did not supervene on the positions of the particles constituting the brain. My comment on his article is not so much a criticism but rather concerns a point that I think should be kept in mind in this context but that Barrett did not mention in his article. The point is that one is Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0605130v1.pdf

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Document Type:

text

Language:

en

DDC:

190 Modern western philosophy *(computed)*

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Title:

The Analogue of Bohm–Bell Processes on a Graph

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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

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0508109v2.pdf

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text

Language:

en

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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

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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

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

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

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Document Type:

text

Language:

en

DDC:

115 Time *(computed)*

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Title:

the Klein–Gordon equation”

Description:

energy-momentum and particle trajectories for

energy-momentum and particle trajectories for Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0202140v2.pdf

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text

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en

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Title:

and

Description:

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. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0105040v2.pdf

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text

Language:

en

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Title:

Response to Horton and Dewdney

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There are some points in the reply of Horton et al. [3] to my comment [2] on their paper [1] which I cannot let stand without a response. I provide here some clarification of how much I proved about the set of points where their law of motion is ill-defined. In a recent article in J. Phys. A [1], Horton et al. present what they claim is a Bohm-t...

There are some points in the reply of Horton et al. [3] to my comment [2] on their paper [1] which I cannot let stand without a response. I provide here some clarification of how much I proved about the set of points where their law of motion is ill-defined. In a recent article in J. Phys. A [1], Horton et al. present what they claim is a Bohm-type law of motion for point particles, based on a Klein–Gordon wave function and implying (unlike a similar law proposed by de Broglie) timelike world lines. Concerning this claim I pointed out in a comment [2] that the prescription they give is ill-defined in some situations, and underpinned this by a concrete example. In addition, I gave arguments to the effect that the set of “bad ” space-time points, where the law of motion is ill-defined, is a set of positive measure for many wave functions. To this Horton et al. have responded [3], ignoring my arguments, that although bad points may exist, they form a set of lesser dimension and therefore can be dealt with by a limiting procedure. I wish here to point out that the response of Horton et al. is entirely without merit. Here is why: In my comment I pointed out that those space-time points are bad where both vectors W + µ and W − µ that appear in the law of Horton et al. are spacelike, or, equivalently, where W + µ W +µ < 0 and W − µ W −µ < 0. Given that the vector fields Pµ and Sµ (on which the construction of W + µ and W − µ relies) are continuous, the functions W + µ W +µ and W − µ W −µ are continuous, too, and thus their values remain negative in an entire neighborhood of any bad space-time point. Therefore, the bad points form an open set, quite contrary to the picture of “nodal lines ” or even “isolated points ” that Horton et al. suggest in their Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0210018v1.pdf

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Document Type:

text

Language:

en

DDC:

340 Law *(computed)*

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Title:

On Spontaneous Wave Function Collapse and Quantum Field Theory

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One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini, and Weber (GRW), involving a nonlinear, stochast...

One way of obtaining a version of quantum mechanics without observers, and thus of solving the paradoxes of quantum mechanics, is to modify the Schrödinger evolution by implementing spontaneous collapses of the wave function. An explicit model of this kind was proposed in 1986 by Ghirardi, Rimini, and Weber (GRW), involving a nonlinear, stochastic evolution of the wave function. We point out how, by focussing on the essential mathematical structure of the GRW model and a clear ontology, it can be generalized to (regularized) quantum field theories in a simple and natural way. PACS numbers: 03.65.Ta; 03.70.+k. Key words: quantum field theory without observers; Ghirardi–Rimini–Weber model; identical particles; second quantization. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-12-05

Source:

http://arxiv.org/pdf/quant-ph/0508230v2.pdf

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text

Language:

en

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