EJTP ELECTRONIC JOURNAL OFTHEORETICAL PHYSICS

Volume 12 Number 35May, 2016

http://www.ejtp.com E-mail:info@ejtp.com

editorsIgnazio LicataAmmar Sakaji

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Ist edition: May 2016

Table of Contents

1. Preface ............................................................................................ iL. LICATA, A.SAKAJI

2. Deficiencies of Bohm Trajectories in View of Basic Quantum Principles 1P. CHEN, H. KLEINERT

3. What is the Actual Behaviour of the Electron? From Bohm's Approach

to the Transactional Interpretation to A Three-Dimensional Timeless Non-Local Quantum Vacuum................................................................. 13D. FISCALETTI

4. Dynamical R-parity Violations from Exotic Instantons ......................... 39A. ADDAZI

5. A Proof for Poisson Bracket in Noncommutative Algebra of Quantum Mechanics.............................................................................................. 57S. KHORASANI

6. Feynman Amplitude for Dirac and Majorana Neutrinos ............................ 73A. DAMANIK

7. Quantum Modification of General Relativity ......................................... 79E.A.NOVIKOV

8. Black Holes - Anybody out there?............................................................... 91J. HANSSON

9. Application of Covariant Analytic Mechanics with Differential Forms toGravity with Dirac Field ....................................................................... 95S. NAKAJIMA

10. Mirror Mesons at the Large Hadron Collider (LHC) ............................... 115G. TRIANTAPHYLLOU

11. The DKP Equation in the Woods-Saxon Potential Well: Bound States... 145B. BOUTABIA-CHÉRAITIA, A. MAKHLOUF

12. Spatially Homogeneous Bianchi Type-I Perfect Fluid Cosmological Models in f(R) Gravity Theory ............................................................... 155P. SHRI RAM

13. Surface waveguide States and Nanocatalyst Activity .......................... 173V.M. ADAMYAN, I.Y. POPOV, I.V. BLINOVA

14. Isotropic Robertson-Walker Universe with Van der Waals Equation ofState in Brans-Dicke Theory of Gravitation .......................................... 191K. PRIYOKURAM, M. DEWRI

15. Earth Matter Effect on Democratic Neutrinos ....................................... 199D. ZHURIDOV

16. Treatment of N-dimensional Schrödinger Equation for Anharmonic Potential via Laplace Transform............................................................ 207T. DAS

Editor in Chief

Ignazio Licata

Foundations of Quantum Mechanics, Complex System & Computation in Physics and Biology, IxtuCyber for Complex Systems , and ISEM, Institute for Scientific Methodology, Palermo, Sicily – Italy

editor[AT]ejtp.info Email: ignazio.licata[AT]ejtp.info

ignazio.licata[AT]ixtucyber.org

Co-Editor

Ammar Sakaji

Theoretical Condensed Matter, Mathematical Physics International Institute for Theoretical Physics and Mathematics (IITPM), Prato, Italy. Amman-Jordan Tel:+962778195003 :+971557967946 Email: info[AT]ejtp.com info[AT]ejtp.info

Editorial Board

Gerardo F. Torres del Castillo

Mathematical Physics, Classical Mechanics, General Relativity, Universidad Autónoma de Puebla, México, Email:gtorres[AT]fcfm.buap.mx Torresdelcastillo[AT]gmail.com

Leonardo Chiatti

Medical Physics Laboratory AUSL VT Via Enrico Fermi 15, 01100 Viterbo (Italy) Tel : (0039) 0761 1711055 Fax (0039) 0761 1711055 Email: fisica1.san[AT]asl.vt.it chiatti[AT]ejtp.info

Francisco Javier Chinea

Differential Geometry & General Relativity, Facultad de Ciencias Físicas, Universidad Complutense de Madrid, Spain, E-mail: chinea[AT]fis.ucm.es

Maurizio Consoli

Non Perturbative Description of Spontaneous Symmetry Breaking as a Condensation Phenomenon, Emerging Gravity and Higgs Mechanism, Dip. Phys., Univ. CT, INFN,Italy

Email: Maurizio.Consoli[AT]ct.infn.it

Avshalom Elitzur

Foundations of Quantum Physics ISEM, Institute for Scientific Methodology, Palermo, Italy Email: Avshalom.Elitzur[AT]ejtp.info

Elvira Fortunato

Quantum Devices and Nanotechnology:

Departamento de Ciência dos Materiais CENIMAT, Centro de Investigação de Materiais I3N, Instituto de Nanoestruturas, Nanomodelação e Nanofabricação FCT-UNL Campus de Caparica 2829-516 Caparica Portugal

Tel: +351 212948562; Directo:+351 212949630 Fax: +351 212948558 Email:emf[AT]fct.unl.pt elvira.fortunato[AT]fct.unl.pt

Tepper L. Gill

Mathematical Physics, Quantum Field Theory Department of Electrical and Computer Engineering Howard University, Washington, DC, USA

Email: tgill[AT]Howard.edu tgill[AT]ejtp.info

Alessandro Giuliani

Mathematical Models for Molecular Biology Senior Scientist at Istituto Superiore di Sanità Roma-Italy

Email: alessandro.giuliani[AT]iss.it

Vitiello Giuseppe

Quantum Field Theories, Neutrino Oscillations, Biological Systems Dipartimento di Fisica Università di Salerno Baronissi (SA) - 84081 Italy Phone: +39 (0)89 965311 Fax : +39 (0)89 953804 Email: vitiello@sa.infn.it

Richard Hammond

General Relativity High energy laser interactions with charged particles Classical equation of motion with radiation reaction Electromagnetic radiation reaction forces Department of Physics University of North Carolina at Chapel Hill, USA Email: rhammond[AT]email.unc.edu

Arbab Ibrahim

Theoretical Astrophysics and Cosmology Department of Physics, Faculty of Science, University of Khartoum, P.O. Box 321, Khartoum 11115, Sudan

Email: aiarbab[AT]uofk.edu arbab_ibrahim[AT]ejtp.info

Kirsty Kitto

Quantum Theory and Complexity Information Systems | Faculty of Science and Technology Queensland University of Technology Brisbane 4001 Australia

Email: kirsty.kitto[AT]qut.edu.au

Hagen Kleinert

Quantum Field Theory Institut für Theoretische Physik, Freie Universit¨at Berlin, 14195 Berlin, Germany

Email: h.k[AT]fu-berlin.de

Wai-ning Mei

Condensed matter Theory Physics Department University of Nebraska at Omaha,

Omaha, Nebraska, USA Email: wmei[AT]mail.unomaha.edu physmei[AT]unomaha.edu

Beny Neta

Applied Mathematics Department of Mathematics Naval Postgraduate School 1141 Cunningham Road Monterey, CA 93943, USA Email: byneta[AT]gmail.com

Peter O'Donnell

General Relativity & Mathematical Physics, Homerton College, University of Cambridge, Hills Road, Cambridge CB2 8PH, UK E-mail: po242[AT]cam.ac.uk

Rajeev Kumar Puri

Theoretical Nuclear Physics, Physics Department, Panjab University Chandigarh -160014, India Email: drrkpuri[AT]gmail.com rkpuri[AT]pu.ac.in

Haret C. Rosu

Advanced Materials Division Institute for Scientific and Technological Research (IPICyT) Camino a la Presa San José 2055 Col. Lomas 4a. sección, C.P. 78216 San Luis Potosí, San Luis Potosí, México Email: hcr[AT]titan.ipicyt.edu.mx

Zdenek Stuchlik

Relativistic Astrophysics Department of Physics, Faculty of Philosophy and Science, Silesian University, Bezru covo n´am. 13, 746 01 Opava, Czech Republic Email: Zdenek.Stuchlik[AT]fpf.slu.cz

S.I. Themelis

Atomic, Molecular & Optical Physics Foundation for Research and Technology - Hellas P.O. Box 1527, GR-711 10 Heraklion, Greece Email: stheme[AT]iesl.forth.gr

Yurij Yaremko

Special and General Relativity, Electrodynamics of classical charged particles, Mathematical Physics, Institute for Condensed Matter Physics of Ukrainian National Academy of Sciences 79011 Lviv, Svientsytskii Str. 1 Ukraine Email: yu.yaremko[AT]gmail.com yar[AT]icmp.lviv.ua

yar[AT]ph.icmp.lviv.ua

Nicola Yordanov

Physical Chemistry Bulgarian Academy of Sciences, BG-1113 Sofia, Bulgaria Telephone: (+359 2) 724917 , (+359 2) 9792546

Email: ndyepr[AT]ic.bas.bg ndyepr[AT]bas.bg

Former Editors:

Ignazio Licata, Editor in Chief (August 2015-)

Ignazio Licata, Editor in Chief (October 2009- August 2012)

Losé Luis López-Bonilla, Co-Editor (2008-2012)

Ammar Sakaji, Founder and Editor in Chief (2003- October 2009) and (August 2012- August2015).

Electronic Journal of Theoretical Physics 13, No. 35 (2016) i

EJTP V12, No 35. Breaking Bad ( News)

EJTP returns to its readers with a new load of good Physics choice after careful debate.

We believe in science as an intellectual craft, and willingly pay the price of our freedom.

I will not focus here on every single contribution, but, for personal reasons, I want

to signal the opening paper of Pisin Chen and Hagen Kleinert on foundational issues of

Quantum Mechanics. The interest of the two scholars so committed on the edge at ad-

vanced astrophysics and particle physics reminds all of us the importance of not forgetting

the foundational work, where the feet of our theories are based. It will be necessary to

go beyond the standard model in the direction of quantum gravity. On this side we also

find Khorasani, Fiscaletti, Novikov and Hansson, The latter two from the perspective of

General Relativity, whereas Addazi, Damanik and Triantaphyllou take a look beyond the

Standard Model.

Our cover is not only a tribute to a enormously successful TV series, “Breaking Bad”

by Vince Gilligan. As is known, the nickname of the protagonist, the chemist Walter

White, is “Heisenberg”. This indicates how much science has penetrated deeply in the

collective imagination, until a few years ago, the spectator reaction would be: “Heisen-

berg who?”.However, this provides a starting point for further reflections. In the story

Walter is forced to use its sophisticated chemistry to survive, becoming a cog in the

criminal system.

How much actual freedom is given to the individual scientist in the production system,

today? We do not just talk about technology, but also of science entertainment, media

science, made of few dominant theories “not even wrong”? Science is still a collective

enterprise, slow and difficult, critical and speculative, or is it the new met?

Ignazio Licata, EJTP Editor

Ammar Sakaji, EJTP Co-Editor

EJTP 13, No. 35 (2016) 1–12 Electronic Journal of Theoretical Physics

Deficiencies of Bohm Trajectories in View of BasicQuantum Principles

Pisin Chen1∗ and Hagen Kleinert2†

1Department of Physics and Leung Center for Cosmology and Particle Astrophysics(LeCosPA), National Taiwan University, Taipei, Taiwan, 10617

2Institut fur Theoretische Physik, Freie Universitat Berlin, 14195 Berlin, Germany

Received 3 April 2016, Accepted 11 April 2016, Published 25 May 2016

Abstract: Quantum mechanics has been one of the most successful theories in physics, yet its

foundation has remained a subject of discussion ever since it was incepted in the 1920s. While

the Copenhagen interpretation represents the main-stream view, recent years have witnessed

revived interest in the alternative deterministic, or pilot-wave, interpretation, pioneered by

Madelung, de Broglie, and Bohm. It has been argued that these two interpretations are basically

equivalent. In this article we show that this is not true. We exhibit the approximate nature of

particle trajectories in Bohm’s quantum mechanics. They follow the streamlines of a superfluid

in Madelung’s reformulation of the Schrodinger wave function, around which the proper particle

trajectories perform their quantum mechanical fluctuations that ensure Heisenberg’s uncertainty

relation between position and momentum. These fluctuations explain the apparent discrepancy

in the double-slit interference intensities between Bohmian mechanics and observations. They

are also the reason for the non-existence of a possible radiation that would be emitted by an

electron if its physical trajectory were deflected by the Bohmian quantum potential.c© Electronic Journal of Theoretical Physics. All rights reserved.

Keywords: Quantum Mechanics; Bohmian Quantum Mechanics; Bohm Trajectories; Pilot-wave,

Interpretation; Madelung; de Broglie; Bohm

PACS (2010): 03.65.-w; 03.65.Ta; 03.75.Nt

1 Introduction

In modern work on quantum mechanics (QM), one often reads, as justification of the

effort, remark made by Richard Feynman in a 1964 lecture [1] that he thinks “it is safe

to say that no one understands quantum mechanics”. Similarly, Murray Gell-Mann in

∗ Email: pisinchen@phys.ntu.edu.tw† Email: h.k@fu-berlin.de

2 Electronic Journal of Theoretical Physics 13, No. 35 (2016) 1–12

his lecture at the 1976 Nobel Conference regrets that “Niels Bohr brainwashed the whole

generation of theorists into thinking that the job (of finding an adequate presentation

of quantum mechanics) was done 50 years ago” [2]. Thus there is no wonder that even

now reputable scientists are trying to get our deterministic thinking in line with quantum

theory [3].

A theory of this type has been proposed a long time ago. It is based on an observation

made as early as 1926, during the inceptive days of QM, by Madelung [4, 5]. He demon-

strated that the Schrodinger equation can be transcribed into a hydrodynamic form, in

which the Schrodinger field becomes the probability amplitude of the fluid. This was

later referred to as the “Madelung quantum hydrodynamic” interpretation. Around the

same time, de Broglie presented a deterministic interpretation of QM at the 1927 Solvay

Conference, which was further developed by Bohm in 1952 to its present form [6].

It has been long believed by the experts on foundations of quantum mechanics that

Bohmian mechanics and standard quantum mechanics are observationally equivalent [6,

7, 8, 10, 9]. They are merely different ontological interpretations on what exactly happens

to a quantum particle, say electron, in a physical process. There are two salient features in

Bohmian mechanics. One, quantum processes are inherently nonlocal, manifested by the

quantum potential that permeates the entire space-time. Two, guided by this quantum

potential, a test particle will execute deterministic motion (which Bohm called causal).

That is, the particle’s position and momentum are simultaneously specified throughout

space-time. This is in drastic contrast to the basic notion of Heisenberg’s uncertainty

principle. It therefore appears meaningful to investigate the equivalence of these two

formulations of QM in some details.

In this note we want to demonstrate that Bohmian way of doing QM is not equivalent,

but a certain semiclassical approximation to proper Schrodinger QM. To do this, we

invoke the second quantization reformulation of the Schrodinger equation as an N-body

system. Following Madelung’s original philosophy, we identify this N-body system as

a superfluid and characterize its physical properties by its particle current density Jkand its superfluid velocity Vs

k. This superfluid embodies de Broglie’s pilot wave that

guides the motion of a single particle. Under this setting, single-particle movements will

be found from fluctuating paths around the superfluid streamlines in a semi-classical

approximation. The fluctuations explain the discrepancy in the double-slit interference

intensities between that derived from Bohmian mechanics and quantum mechanics. They

are also the reason for the non-existence of a radiation that would have to be emitted by

an electron if its physical trajectory is deflected by the Bohmian quantum potential.

2 Pilot Wave

In order to elucidate our point, it is useful to invoke the second-quantized reformulation

of Schrodinger QM [12] as a functional integral over a Schrodinger field ψ(x, t) via the