On the Geometrization of Bohmian Mechanics: A New Approach to Quantum Gravity

Shojai, Fatimah; Golshani, Mohammad

doi:10.1142/s0217751x98000305

Cited by 49 publications

(101 citation statements)

References 5 publications

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“…In a previous paper [1] it was shown that the application of an idea of de-Broglie leads to the fact that the quantum effects of matter are equivalent to a specific conformal factor of the space-time metric. In the de-Broglie-Bohm relativistic quantum theory [3], the Klein-Gordon equation…”

Section: Quantum Effects Scale and Conformal Transformationsmentioning

confidence: 99%

“…This new metric is called the physical metric because it has physical interpretation. For example the singularities of FRW universe would be removed in g µν [1].…”

Section: Qmentioning

confidence: 99%

“…In our previous work [1], the conformal transformation was applied only to the spacetime metric. Other quantities like mass, density and so on were assumed to posses no transformation.…”

Section: Qmentioning

confidence: 99%

“…

AbstractRecently [1], it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can * Email: FATIMAH@NETWARE2.IPM.AC.IR † Email: SHOJAI@NETWARE2.IPM.AC.IR

…”

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confidence: 99%

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Conformal Transformations and Quantum Gravity

Shojai

Golshani

1998

Mod. Phys. Lett. A

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Section: Quantum Effects Scale and Conformal Transformationsmentioning

confidence: 99%

“…This new metric is called the physical metric because it has physical interpretation. For example the singularities of FRW universe would be removed in g µν [1].…”

Section: Qmentioning

confidence: 99%

“…In our previous work [1], the conformal transformation was applied only to the spacetime metric. Other quantities like mass, density and so on were assumed to posses no transformation.…”

Section: Qmentioning

confidence: 99%

“…

…”

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confidence: 99%

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Conformal Transformations and Quantum Gravity

Shojai

Golshani

1998

Mod. Phys. Lett. A

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“…Then, as was already shown by Shojai et al in [3], the quantum potential modifies the background geometry giving a curved space-time with the metric given by eq. (13).…”

Section: Epr Correlations Via a Wormholementioning

confidence: 59%

Might EPR particles communicate through a wormhole?

Santini¹

2007

Europhys. Lett.

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PACS 03.65.Ta -Foundations of quantum mechanics PACS 03.65.Ud -Entanglement and quantum nonlocality PACS 03.70.+k -Theory of quantized fieldsAbstract. -We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.Introduction. -There is an increasing interest in the application of the Bohm -de Broglie (BdB) interpretation of quantum mechanics to several areas, such as quantum cosmology, quantum gravity and quantum field theory, see for example. In this work, we develop a causal approach to the Einstein-Podolsky-Rosen (EPR) problem i.e. a two-particle correlated system. We attack the problem from the point of view of quantum field theory, considering the two-particle function for a scalar field. In the BdB approach, it is possible to interpret the quantum effects as modifying the geometry in such a way that the scalar particles see an effective geometry. As a first example, we show that a two dimensional EPR model, in a particular quantum state and under a non-tachyonic approximating condition, can exhibit an effective metric that is analogous to a two dimensional black hole (BH) in some region (which is limited by the approximations we made). In a second example, for a two-dimensional static EPR model we are able to show that quantum effects produce an effective geometry with singularities in the metric, a key ingredient of a bridge construction or wormhole. In this way, and following a suggestion by Holland [6], we can envisage the possibility of interpreting the EPR correlations as driven by an effective wormhole, through which physical signals can propagate. This letter is organized as follows: in the next section we recall the basic features of a relativistic scalar field and write the two-particle wave equation. Then, we apply the BdB interpretation to it and, from the generalized Hamilton-Jacobi equation, we visualize the quantum potential as generating an

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Fluctuations, Information, Gravity and the Quantum Potential

Carroll¹

2006

144

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We show how the quantum potential arises in various ways and trace its connection to quantum fluctuations and Fisher information along with its realization in terms of Weyl curvature. It represents a genuine quantization factor for certain classical systems as well as an expression for quantum matter in gravity theories of Weyl-Dirac type. Many of the facts and examples are extracted from the literature (with references cited) and we mainly provide connections and interpretation, with a few new observations. We deliberately avoid ontological and epistemological discussion and resort to a collection of contexts where the quantum potential plays a visibly significant role. In particular we sketch some recent results of F. and A. Shojai on Dirac-Weyl action and Bohmian mechanics which connects quantum mass to the Weyl geometry. Connections a la Santamato of the quantum potential with Weyl curvature arising from a stochastic geometry, are also indicated for the Schrödinger equation (SE) and Klein-Gordon (KG) equation. Quantum fluctuations and quantum geometry are linked with the quantum potential via Fisher information. Derivations of SE and KG from Nottale's scale relativity are sketched along with a variety of approaches to the KG equation. Finally connections of geometry and mass generation via Weyl-Dirac geometry with many cosmological implications are indicated, following M. Israelit and N. Rosen.

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On the Geometrization of Bohmian Mechanics: A New Approach to Quantum Gravity

Cited by 49 publications

References 5 publications

Conformal Transformations and Quantum Gravity

Conformal Transformations and Quantum Gravity

Might EPR particles communicate through a wormhole?

Fluctuations, Information, Gravity and the Quantum Potential

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