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1.
Bohmian Mechanics at SpaceTime Singularities. I. Timelike Singularities
Open Access
Title:
Bohmian Mechanics at SpaceTime Singularities. I. Timelike Singularities
Author:
Roderich Tumulka
Roderich Tumulka
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We develop an extension of Bohmian mechanics by defining Bohmlike trajectories for (one or more) quantum particles in a curved background spacetime 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 (supercritical...
We develop an extension of Bohmian mechanics by defining Bohmlike trajectories for (one or more) quantum particles in a curved background spacetime 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 (supercritical) 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 spacetime; Reissner–Nordstrom spacetime geometry; timelike singularities; Bohmian trajectories; particle creation and annihilation; stochastic jump process. 1
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Year of Publication:
20121126
Source:
http://arxiv.org/pdf/0708.0070v1.pdf
http://arxiv.org/pdf/0708.0070v1.pdf
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en
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.248.1019
http://arxiv.org/pdf/0708.0070v1.pdf
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http://arxiv.org/pdf/0708.0070v1.pdf
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2.
Elementary proof for asymptotics of large Haardistributed unitary matrices, unpublished, www.arxiv.org
Open Access
Title:
Elementary proof for asymptotics of large Haardistributed unitary matrices, unpublished, www.arxiv.org
Author:
Christian Mastrodonato
;
Roderich Tumulka
Christian Mastrodonato
;
Roderich Tumulka
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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
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Year of Publication:
20121122
Source:
http://arxiv.org/pdf/0705.3146v2.pdf
http://arxiv.org/pdf/0705.3146v2.pdf
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.246.8632
http://arxiv.org/pdf/0705.3146v2.pdf
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http://arxiv.org/pdf/0705.3146v2.pdf
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3.
Determinate Values for Quantum Observables
Open Access
Title:
Determinate Values for Quantum Observables
Author:
Roderich Tumulka
Roderich Tumulka
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This is a comment on J. A. Barrett’s article “The PreferredBasis 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 PreferredBasis 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 spacetime, 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
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Year of Publication:
20121205
Source:
http://arxiv.org/pdf/quantph/0605130v1.pdf
http://arxiv.org/pdf/quantph/0605130v1.pdf
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DDC:
190 Modern western philosophy
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.9657
http://arxiv.org/pdf/quantph/0605130v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.252.9657
http://arxiv.org/pdf/quantph/0605130v1.pdf
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4.
Tumulka: Elementary Proof for Asymptotics of Large HaarDistributed Unitary Matrices
Open Access
Title:
Tumulka
: Elementary Proof for Asymptotics of Large HaarDistributed Unitary Matrices
Author:
Christian Mastrodonato
;
Roderich Tumulka
Christian Mastrodonato
;
Roderich Tumulka
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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
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Year of Publication:
20121121
Source:
http://arxiv.org/pdf/0705.3146v1.pdf
http://arxiv.org/pdf/0705.3146v1.pdf
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http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.9439
http://arxiv.org/pdf/0705.3146v1.pdf
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.245.9439
http://arxiv.org/pdf/0705.3146v1.pdf
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5.
Comment on the ‘Free Will Theorem
Open Access
Title:
Comment on the ‘Free Will Theorem
Author:
Roderich Tumulka
Roderich Tumulka
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In a recent paper [8], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRWtype theories have already been presented, in my recent paper [17] and by Dowker and Henson [9]. Here, I elucidate why these are not exclud...
In a recent paper [8], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRWtype theories have already been presented, in my recent paper [17] and by Dowker and Henson [9]. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen. PACS: 03.65.Ta. Key words: quantum theory without observers; Conway–Kochen “free will ” theorem; Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse; nonlocality. 1
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20121205
Source:
http://arxiv.org/pdf/quantph/0611283v2.pdf
http://arxiv.org/pdf/quantph/0611283v2.pdf
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http://arxiv.org/pdf/quantph/0611283v2.pdf
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6.
Two Arrows of Time in Nonlocal Particle Dynamics
Open Access
Title:
Two Arrows of Time in Nonlocal Particle Dynamics
Author:
Roderich Tumulka
Roderich Tumulka
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Considering what the world would be like if backwards causation were possible is usually mindbending. Here we discuss something that is easier to study, a model that incorporates a very restricted sort of backwards causation. Whereas it probably prohibits signalling to the past, it allows nonlocality while being fully covariant. And that is wha...
Considering what the world would be like if backwards causation were possible is usually mindbending. Here we discuss something that is easier to study, a model that incorporates a very restricted sort of backwards causation. Whereas it probably prohibits signalling to the past, it allows nonlocality while being fully covariant. And that is what constitutes its value: it may be a step towards 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 [4] as a toy model in Bohmian mechanics; for more about Bohmian mechanics, see Detlef Dürr’s contribution to this volume. What makes it 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 desire such a behavior of a dynamical system? Because Bell’s nonlocality theorem [1] teaches us that any dynamical system violating Bell’s inequality must be nonlocal in this sense. And Bell’s inequality, after all, is violated in Nature. Well, it is easy to come up with a nonlocal theory if one assumes that one of the Lorentz frames is preferred to the others: simply assume a mechanism of cause and effect (a sort of interaction in the widest sense) that operates instantaneously in the preferred frame. That is what nonrelativistic theories usually do. In other frames, these nonlocal effects will either travel at a
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20121205
Source:
http://arxiv.org/pdf/quantph/0210207v1.pdf
http://arxiv.org/pdf/quantph/0210207v1.pdf
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190 Modern western philosophy
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http://arxiv.org/pdf/quantph/0210207v1.pdf
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http://arxiv.org/pdf/quantph/0210207v1.pdf
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7.
Feynman’s Path Integrals and Bohm’s Particle Paths
Open Access
Title:
Feynman’s Path Integrals and Bohm’s Particle Paths
Author:
Roderich Tumulka
Roderich Tumulka
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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 reformulation 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 reformulation 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.
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20121205
Source:
http://arxiv.org/pdf/quantph/0501167v2.pdf
http://arxiv.org/pdf/quantph/0501167v2.pdf
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Subjects:
PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals
PACS. 03.65.Ta. Key words ; Bohmian mechanics ; Feynman path integrals
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http://arxiv.org/pdf/quantph/0501167v2.pdf
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8.
Contents
Open Access
Title:
Contents
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Roderich Tumulka
Roderich Tumulka
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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 socalled 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 socalled 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 spacetime, called flashes. The joint distribution of these points, a point process in spacetime, 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; GhirardiRiminiWeber (GRW) theory of spontaneous wave function collapse; relativistic Lorentz covariance; flash ontology; Dirac equation; Dirac evolution
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Year of Publication:
20130805
Source:
http://arxiv.org/pdf/0711.0035v1.pdf
http://arxiv.org/pdf/0711.0035v1.pdf
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http://arxiv.org/pdf/0711.0035v1.pdf
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9.
On Spontaneous Wave Function Collapse and Quantum Field Theory
Open Access
Title:
On Spontaneous Wave Function Collapse and Quantum Field Theory
Author:
Roderich Tumulka
Roderich Tumulka
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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
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20121205
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http://arxiv.org/pdf/quantph/0508230v1.pdf
http://arxiv.org/pdf/quantph/0508230v1.pdf
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10.
Comment on “The Free Will Theorem
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Title:
Comment on “The Free Will Theorem
Author:
Roderich Tumulka
Roderich Tumulka
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In a recent paper [7], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRWtype theories have already been presented, in my recent paper [16] and by Dowker and Henson [8]. Here, I elucidate why these are not exclud...
In a recent paper [7], Conway and Kochen claim to have established that theories of the GRW type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRWtype theories have already been presented, in my recent paper [16] and by Dowker and Henson [8]. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen. PACS: 03.65.Ta. Key words: quantum theory without observers; Conway–Kochen “free will ” theorem; Ghirardi–Rimini–Weber (GRW) theory of spontaneous wave function collapse; nonlocality. 1
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http://arxiv.org/pdf/quantph/0611283v1.pdf
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(1) Sheldon Goldstein Department
(1) Struyve, Ward
(1) T Hψt
(1) TAUSK, Daniel V.
(1) TUMULKA, Roderich
(1) Teufel, Stefan
(1) Tumulka, Roderich (internal member)
(1) University of Helsinki, Department of...
(1) tumulka, roderich
Author:
Subject
(67) quantum physics
(10) mathematical physics
(7) bohmian mechanics
(6) quantum mechanics
(5) key words
(4) articles
(4) condensed matter statistical mechanics
(4) empirical equivalence
(4) fundamental
(4) mathematics probability
(4) ontology
(3) contents
(2) 03 65 ta
(2) 46n50
(2) 60j75
(2) 81p99
(2) 81q99
(2) 81t25
(2) feynman path integrals
(2) pacs 03 65 ta key words
(1) 020602
(1) 020699
(1) 03 65 vf
(1) 1 3 the truman show 6
(1) 111 mathematics
(1) 114 physical sciences
(1) 15a52
(1) 240201
(1) 34a12
(1) 60b10
(1) 60g15
(1) 60g17
(1) 81p05
(1) 81q70 pacs
(1) 81s99
(1) 82b10
(1) 83a05
(1) conditional wave function
(1) ddc 510
(1) discussions
(1) engineering and technology
(1) environment
(1) faculty of science
(1) fakultät für mathematik
(1) field theory and string theory
(1) general relativity and quantum cosmology
(1) hamiltonian operator
(1) high energy physics theory
(1) informatik und statistik
(1) it plays a role similar to that of bohm s...
(1) multiply connected configuration spaces
(1) original article
(1) pacs
(1) physics and astronomy
(1) physics classical physics
(1) physics history and philosophy of physics
(1) pre2009 theoretical physics
(1) relativistic mechanics
(1) research articles
(1) schrödinger equation
(1) spontaneous wave function collapse · empirical...
(1) theorems
(1) these two
(1) topological phases
(1) typical wave function
(1) universal covering space msc 2000
Subject:
Dewey Decimal Classification (DDC)
(53) Modern western philosophy [19*]
(14) Mathematics [51*]
(10) Metaphysics [11*]
(7) Physics [53*]
(4) Chemistry [54*]
(1) Social sciences, sociology & anthropology...
(1) Law [34*]
Dewey Decimal Classification (DDC):
Year of Publication
(70) 2012
(33) 2013
(16) 2008
(16) 2009
(11) 2006
(9) 2010
(8) 2005
(8) 2011
(7) 2003
(7) 2004
(7) 2007
(5) 2014
(4) 2002
(2) 2001
(1) 1998
(1) 2015
Year of Publication:
Content Provider
(119) CiteSeerX
(67) ArXiv.org
(6) HighWire Press
(6) Pittsburgh Univ.: PhilSci Archive
(1) Griffith Univ.
(1) Munich LMU: Digital theses
(1) PubMed Central
(1) Rutgers Univ.: RUcore
(1) São Paulo Univ.: Intellectual Production
(1) Frankfurt/Main Univ.: Publications
(1) Helsingfors Univ.: HELDA
Content Provider:
Language
(130) English
(74) Unknown
(1) German
Language:
Document Type
(194) Text
(9) Article, Journals
(1) Theses
(1) Unknown
Document Type:
Access
(194) Open Access
(11) Unknown
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