Stochastic motion of an open bosonic string

Santos, L. F.; Escobar, C.

doi:10.1016/s0375-9601(99)00231-5

Cited by 5 publications

(4 citation statements)

References 13 publications

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“…Finally, as we will explain in section 7.4, stochastic mechanics provides a mathematically clean description of the quantum foam that is hypothesized in quantum gravity. It is, therefore, not surprising that the tools from stochastic mechanics have also found their way into quantum gravity models [98][99][100][101][102].…”

Section: Stochastic Mechanicsmentioning

confidence: 99%

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

Kuipers¹

2023

Preprint

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We unify Brownian motion and quantum mechanics in a single mathematical framework. In particular, we show that non-relativistic quantum mechanics of a single spinless particle on a flat space can be described by a Wiener process that is rotated in the complex plane. We then extend this theory to relativistic stochastic theories on manifolds using the framework of second order geometry. As a byproduct, our results suggest that a consistent path integral based formulation of a quantum theory on a Lorentzian (Riemannian) manifold requires an Itô deformation of the Poincaré (Galilean) symmetry, arising due to the coupling of the quadratic variation to the affine connection.

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Section: Stochastic Mechanicsmentioning

confidence: 99%

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

Kuipers¹

2023

Preprint

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“…If one insists on adding beables for the bosons, perhaps one could adapt the approach of Nielsen et al [59,60], who show how to introduce a Dirac sea for bosons in second-quantized field theory based on massive hypermultiplets. Finally, it seems plausible that one could make a ZSM generalization of bosonic string theory by constructing a Nelson-Yasue version of the model of Santos and Escobar [61], who use the Guerra-Morato variational principle to construct a stochastic mechanics of the open bosonic string (the idea being that the open bosonic string's IRF oscillations would play the role of the zbw, and would be hypothesized to be dynamically driven by resonant coupling to the ZSM version of Nelson's ether). All this remains for future work.…”

Section: Plausibility Of the Zitterbewegung Hypothesismentioning

confidence: 99%

A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics II

Derakhshani

2016

Preprint

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The "zitterbewegung stochastic mechanics" (ZSM) answer to Wallstrom's criticism, introduced in the companion paper [1], is extended to many particles. We first formulate the many-particle generalization of Nelson-Yasue stochastic mechanics (NYSM), incorporating external and classical interaction potentials. Then we formulate the many-particle generalization of the classical zitterbewegung zbw model introduced in Part I, for the cases of free particles, particles interacting with external fields, and classically interacting particles. On the basis of these developments, ZSM is constructed for classically free particles, as well as for particles interacting both with external fields and through inter-particle scalar potentials. Throughout, the beables of ZSM (based on the many-particle formulation) are made explicit. Subsequently, we assess the plausibility and generalizability of the zbw hypothesis. We close with an appraisal of other proposed answers, and compare them to ZSM.

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“…A non-relativistic theory of single-time and multi-time measurements has also been developed [36,37,38,39,40], as have extensions of non-relativistic stochastic mechanics to finite temperature and non-equilibrium open systems [5,41,42,19,43]. Field theoretic generalizations also exist, for the cases of scalar fields [44,45,46,10,47], Maxwell fields [48,49], vector-meson fields [50], the linearized gravitational field [51], coupling to dissipative environments [45,52], non-Abelian gauge theory [6], bosonic string theory [53], M-theory [25], and backgroundindependent quantum gravity [26]. However, Wallstrom [54,55] pointed out that extant formulations of stochastic mechanics ultimately fail to derive quantum mechanics because they require an "ad hoc" quantization condition on the postulated velocity potential, S, in order to recover single-valued Schrödinger wave functions.…”

Section: Introductionmentioning

confidence: 99%

A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics I

Derakhshani

2015

Preprint

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Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity potential, S, in order to derive Schrödinger wave functions. We propose an answer to this criticism by modifying the Nelson-Yasue formulation of non-relativistic stochastic mechanics for a spinless particle with the following hypothesis: a spinless Nelson-Yasue particle of rest mass m continuously undergoes a driven steady-state oscillation of 'zitterbewegung' (zbw ) frequency, ωc = (1/ ) mc 2 , in its instantaneous mean forward (and backward) translational rest frame. With this hypothesis we show that, in the lab frame, S arises from imposing the constraint of conservative diffusions on the time-symmetrized steady-state phase of the zbw particle, satisfies the required quantization condition, and evolves in time by the Hamilton-Jacobi-Madelung equations (when generalized to describe a statistical ensemble of zbw particles). From the mathematical equivalence of Schrödinger's equation with the Hamilton-Jacobi-Madelung equations plus the quantization condition, Schrödinger wave functions for a spinless particle (in and excluding external fields) are thereby recovered. We also apply this 'zitterbewegung stochastic mechanics' (ZSM) to the case of a central potential and show that it predicts angular momentum quantization. This paper sets the foundation for Part II, which will (primarily) work out the many-particle version of ZSM.

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Stochastic motion of an open bosonic string

Cited by 5 publications

References 13 publications

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

Stochastic Mechanics and the Unification of Quantum Mechanics with Brownian Motion

A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics II

A Suggested Answer To Wallstrom's Criticism: Zitterbewegung Stochastic Mechanics I

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