Intrinsic quantum dynamics of particles in brane gravity - INSPIRE

DataBETA

Intrinsic quantum dynamics of particles in brane gravity

Shahram Jalalzadeh
(
- Pernambuco U.
)

Mar 20, 2023

17 pages

Published in:

Annals Phys. 452 (2023) 169291

Published: Mar 24, 2023
and
Published: May, 2023

e-Print:

2303.11104 [gr-qc]

DOI:

10.1016/j.aop.2023.169291 (publication)

View in:

ADS Abstract Service

reference search1 citation

Citations per year

Abstract: (Elsevier Inc.)

The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles’ energy–momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We demonstrate that the frequency of these oscillations is proportional to the kinetic energy of the particle in the brane. We show that the classical stability of particle trajectories on the brane gives us the Bohr–Sommerfeld quantization condition. The particle’s motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. Furthermore, we exhibited that the particle’s motion along the extra dimension is identical to the time-independent Schrödinger equation. The dynamics of a free particle, particles in a box, a harmonic oscillator, a bouncing particle, and tunneling are re-examined. We show that the particle’s motion along the extra dimension yields a quantized energy spectrum for bound states. •The particle’s motion along the extra dimension helps explain quantum behavior.•Planck’s constant can be calculated in terms of other fundamental constants.•Motion along the extra dimension leads to the Schrodinger equation.•Particle jumps in the extra dimension can be used to explain quantum tunneling.

Note:

17 pages, 4 figures, to appear in Annal of Physics

Brane gravity
Geodesic equation
Bohr–Sommerfeld quantization
Extra dimension
Schrödinger equation
tensor: energy-momentum
particle: stability
stability: classical
membrane model: tension
energy: kinetic

References(67)

Figures(4)

[1]

Does gravity come from quantum information?

Xiao-Liang Qi
(
- Stanford U., Phys. Dept.
)

- Nature Phys. 14 (2018) 10, 984-987
•
DOI:
- 10.1038/s41567-018-0297-3

[2]

Gravity as a quantum effect on quantum space-time

Harold C. Steinacker
(
- Vienna U.
)

- Phys.Lett.B 827 (2022) 136946
•
e-Print:
- 2110.03936
•
DOI:
- 10.1016/j.physletb.2022.136946

[3]

Emergent Geometry and Gravity from Matrix Models: an Introduction

Harold Steinacker
(
- Vienna U.
)

- Class.Quant.Grav. 27 (2010) 133001
•
e-Print:
- 1003.4134
•
DOI:
- 10.1088/0264-9381/27/13/133001

[4]

Analogue gravity

Carlos Barcelo
(
- IAA, Granada
)
,
Stefano Liberati
(
- INFN, Trieste and
- SISSA, Trieste
)
,
Matt Visser
(
- Victoria U., Wellington
)

- Living Rev.Rel. 8 (2005) 12,
- Living Rev.Rel. 14 (2011) 3
•
e-Print:
- gr-qc/0505065
•
DOI:
- 10.12942/lrr-2005-12

[5]

Vacuum Quantum Fluctuations in Curved Space and the Theory of Gravitation

A.D. Sakharov
(
- Unlisted
)

- Gen.Rel.Grav. 32 (2000) 2, 365-367,
- Dokl.Akad.Nauk SSSR 177 (1967) 1, 70-71
•
DOI:
- 10.1023/A:1001947813563

[6]

Thermodynamics of space-time: The Einstein equation of state

Ted Jacobson
(
- Maryland U.
)

- Phys.Rev.Lett. 75 (1995) 1260-1263
•
e-Print:
- gr-qc/9504004
•
DOI:
- 10.1103/PhysRevLett.75.1260

[7]

On the Origin of Gravity and the Laws of Newton

Erik P. Verlinde
(
- Amsterdam U.
)

- JHEP 04 (2011) 029
•
e-Print:
- 1001.0785
•
DOI:
- 10.1007/JHEP04(2011)029

[8]

H. Reichenbach

[9]

fourth ed

P.A.M. Dirac

- The International series of monographs in physics (1947)

[10]

I. Fényes

- Z.Phys. 132 (1952) 1, 81-106

[11]

Derivation of the Schrodinger equation from Newtonian mechanics

Edward Nelson
(
- Princeton U.
)

- Phys.Rev. 150 (1966) 1079-1085
•
DOI:
- 10.1103/PhysRev.150.1079

[12]

Cosmic origin of quantization

F. Calogero
(
- Rome U. and
- INFN, Rome
)

- Phys.Lett.A 228 (1997) 335-346,
- Int.J.Mod.Phys.B 18 (2004) 519-526
•
DOI:
- 10.1016/S0375-9601(97)00107-2

[13]

On a Geometrical Description of Quantum Mechanics

M. Novello
(
- Rio de Janeiro, CBPF
)
,
J.M. Salim
(
- Rio de Janeiro, CBPF
)
,
F.T. Falciano
(
- Rio de Janeiro, CBPF
)

- Int.J.Geom.Meth.Mod.Phys. 8 (2011) 87-98
•
e-Print:
- 0901.3741
•
DOI:
- 10.1142/S0219887811004987

[14]

Quantum mechanics from cosmic fluctuations

B.G. Sidharth
(
- Birla Sci. Ctr., Hyderabad
)

- Chaos Solitons Fractals 15 (2003) 25-27
•
DOI:
- 10.1016/S0960-0779(02)00113-3

[15]

Derivation of the postulates of quantum mechanics from the first principles of scale relativity

Laurent Nottale
(
- Paris Observ. and
- Diderot U., Paris
)
,
Marie-Noelle Celerier
(
- Paris Observ. and
- Diderot U., Paris
)

- J.Phys.A 40 (2007) 14471-14498
•
e-Print:
- 0711.2418
•
DOI:
- 10.1088/1751-8113/40/48/012

[16]

H.T. Flint

- Proc.Phys.Soc. 48 (1936) 3, 433-443
•
DOI:
- 10.1088/0959-5309/48/3/310

[17]

STATISTICAL INTERPRETATION OF THE KLEIN-GORDON EQUATION IN TERMS OF THE SPACE-TIME WEYL CURVATURE

E. Santamato
(
- Naples U.
)

- J.Math.Phys. 25 (1984) 2477-2480,
- J. Math. Phys. 25 ( 1984) 2477-2480
•
DOI:
- 10.1063/1.526467

[18]

C. Castro

- Found.Phys. 22 (1992) 4, 569-615
•
DOI:
- 10.1007/BF00732924

[19]

W.R. Wood
,
G. Papini

- Found.Phys.Lett. 6 (1993) 3, 207-223
•
DOI:
- 10.1007/BF00665726

[20]

Geometric derivation of the Schrödinger equation from classical mechanics in curved Weyl spaces

E. Santamato
(
- Naples U.
)

- Phys.Rev.D 29 (1984) 2, 216
•
DOI:
- 10.1103/PhysRevD.29.216

[21]

QUANTUM MECHANICS IN THE FORMALISM OF LONDON AND WEYL

J. Godfrey
(
- Notre Dame U.
)

- Phys.Rev.Lett. 52 (1984) 1365-1368
•
DOI:
- 10.1103/PhysRevLett.52.1365

[22]

Geometrizing relativistic quantum mechanics

- Found.Phys. 40 (2010) 1885-1901
•
DOI:
- 10.1007/s10701-010-9496-1

[23]

Quantum Measurement and Geometry

James T. Wheeler
(
- Swarthmore Coll.
)

- Phys.Rev.D 41 (1990) 431
•
DOI:
- 10.1103/PhysRevD.41.431

[24]

Geometric description of Schrödinger equation in Finsler and Funk geometry

- Int.J.Geom.Meth.Mod.Phys. 16 (2019) 07, 1950098
•
e-Print:
- 1904.12153
•
DOI:
- 10.1142/S0219887819500981

[25]

I. Tavernelli

- Annals Phys. 371 (2016) 239-253
•
e-Print:
- 1510.06330
•
DOI:
- 10.1016/j.aop.2016.04.020

1-25 of 67
1
2
3
25 / page