Relativistic dynamical reduction models: General framework and examples

Ghirardi, GianCarlo; Grassi, R.; Pearle, Philip

doi:10.1007/bf01883487

Cited by 220 publications

(97 citation statements)

References 21 publications

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“…The problem in this case is that, as the ϕ(x)-state becomes more certain, the scalar field momentum state becomes more uncertain. The result is a divergent increase in the energy density [5,6]. …”

Section: Energy Processmentioning

confidence: 99%

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Relativistic State Reduction Dynamics

2010

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A mechanism describing state reduction dynamics in relativistic quantum field theory is outlined. The mechanism involves nonlinear stochastic modifications to the standard description of unitary state evolution and the introduction of a relativistic field in which a quantized degree of freedom is associated to each point in spacetime. The purpose of this field is to mediate in the interaction between classical stochastic influences and conventional quantum fields. The equations of motion are Lorentz covariant, frame independent, and do not result in divergent behavior. It is shown that the mathematical framework permits the specification of unambiguous local properties providing a connection between the model and evidence of real world phenomena. The collapse process is demonstrated for an idealized example.

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Section: Energy Processmentioning

confidence: 99%

“…The formulation of CSL, in terms of a stochastic differential equation, invites a straightforward generalization to relativistic quantum field theory (QFT), but it is well known that this results in physically unacceptable divergent behavior [5,6]. Here we shall address the question of how these infinities can be avoided.…”

Section: Introductionmentioning

confidence: 99%

Relativistic State Reduction Dynamics

2010

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“…[19][20][21]), the coefficient of δ 3 ( 0) is a nontrivial operator and not a constant. The δ 3 ( 0) singularity is a direct result of the local derivative structure of the drift term, and we have not found a mechanism to cancel it within the standard stochastic differential equation and quantum field theory framework discussed here.…”

Section: Iii4 Energy Nonconservationmentioning

confidence: 99%

“…(For previous related approaches to this problem, see e.g. [19][20][21][22][23].) The generalized equation, like its nonrelativistic counterparts,…”

Section: Introductionmentioning

confidence: 99%

Generalized stochastic Schrödinger equations for state vector collapse

Adler

Brun

2001

J. Phys. A: Math. Gen.

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A number of authors have proposed stochastic versions of the Schrödinger equation, either as effective evolution equations for open quantum systems or as alternative theories with an intrinsic collapse mechanism. We discuss here two directions for generalization of these equations. First, we study a general class of norm preserving stochastic evolution equations, and show that even after making several specializations, there is an infinity of possible stochastic Schrödinger equations for which state vector collapse is provable. Second, we explore the problem of formulating a relativistic stochastic Schrödinger equation, using a manifestly covariant equation for a quantum field system based on the interaction picture of Tomonaga and Schwinger. The stochastic noise term in this equation can couple to any local scalar density that commutes with the interaction energy density, and leads to collapse onto spatially localized eigenstates. However, as found in a similar model by Pearle, the equation predicts an infinite rate of energy nonconservation proportional to δ 3 ( 0), arising from the local double commutator in the drift term.1

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“…The fact that we can't expect a collapse theory to produce eigenstates of local observables led Ghirardi et al (1990) to propose, as a criterion for attribution of local objective properties to systems, one based one approximations to eigenstates. 8 We think that the appropriate attitude is the following: when considering a local observable A with its associated support we say that an individual system has the objective property a (a being an eigenvalue of A), only when the mean value of P a is extremely close to one, when evaluated on all spacelike hypersurfaces containing the support of A (p. 1310).…”

Section: Quantum State Evolution In a Relativistic Spacetimementioning

confidence: 99%

Lessons of Bell's Theorem: Nonlocality, Yes; Action at a Distance, Not Necessarily

Myrvold

2016

Quantum Nonlocality and Reality

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Relativistic dynamical reduction models: General framework and examples

Cited by 220 publications

References 21 publications

Relativistic State Reduction Dynamics

Relativistic State Reduction Dynamics

Generalized stochastic Schrödinger equations for state vector collapse

Lessons of Bell's Theorem: Nonlocality, Yes; Action at a Distance, Not Necessarily

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