THE PARTICLE ENIGMA-Restructured
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The Zig-Zag Road to Reality 1 Introduction
The zig-zag road to reality Author Colin, S, Wiseman, HM Published 2011 Journal Title Journal of Physics A: Mathematical and Theoretical DOI https://doi.org/10.1088/1751-8113/44/34/345304 Copyright Statement © 2011 Institute of Physics Publishing. This is the author-manuscript version of this paper. Reproduced in accordance with the copyright policy of the publisher.Please refer to the journal's website for access to the definitive, published version. Downloaded from http://hdl.handle.net/10072/42701 Griffith Research Online https://research-repository.griffith.edu.au The zig-zag road to reality S Colin1;2;y and H M Wiseman1;z 1 Centre for Quantum Dynamics, Griffith University, Brisbane, QLD 4111, Australia. 2 Perimeter Institute for Theoretical Physics, 31 Caroline Street North, ON N2L2Y5, Waterloo, Canada. E-mail: [email protected], [email protected] Abstract In the standard model of particle physics, all fermions are fundamentally massless and only acquire their effective bare mass when the Higgs field condenses. Therefore, in a fundamental de Broglie-Bohm pilot-wave quan- tum field theory (valid before and after the Higgs condensation), position beables should be attributed to massless fermions. In our endeavour to build a pilot-wave theory of massless fermions, which would be relevant for the study of quantum non-equilibrium in the early universe, we are naturally led to Weyl spinors and to particle trajectories which give mean- ing to the `zig-zag' picture of the electron discussed recently by Penrose. We show that a positive-energy massive Dirac electron of given helicity can be thought of as a superposition of positive and negative energy Weyl particles of the same helicity and that a single massive Dirac electron can in principle move luminally at all times. -
Some Remarks About Mass and Zitterbewegung Substructure Of
Some remarks about mass and Zitterbewegung substructure of electron P. Brovetto†, V. Maxia† and M. Salis†‡ (1) †On leave from Istituto Nazionale di Fisica della Materia - Cagliari, Italy ‡Dipartimento di Fisica - Universit`adi Cagliari, Italy Abstract - It is shown that the electron Zitterbewegung, that is, the high- frequency microscopic oscillatory motion of electron about its centre of mass, originates a spatial distribution of charge. This allows the point-like electron behave like a particle of definite size whose self-energy, that is, energy of its electromagnetic field, owns a finite value. This has implications for the electron mass, which, in principle, might be derived from Zitterbewegung physics. Key words - Elementary particle masses, Zitterbewegung theory. Introduction The nature of mass of elementary particles is one of the most intriguing top- ics in modern physics. Electron deserves a special attention because, differently from quarks which are bound in composite objects (adrons), it is a free parti- cle. Moreover, differently from neutrinos whose vanishingly small mass is still controversial, its mass is a well-known quantity. At the beginning of the past century, the question of the nature of elec- tron mass was debated on the ground of the electromagnetic theory by various authors (Abraham, Lorentz, Poincar´e). Actually, the electron charge e origi- nates in the surrounding space an electromagnetic field −→E, −→H, associated with energy density E2 + H2 /8π and momentum density −→E −→H /4πc. These × densities, when integrated over the space, account for electron self-energy and inertial mass. However, peculiar models must be introduced in order to avoid divergent results. -
1 the LOCALIZED QUANTUM VACUUM FIELD D. Dragoman
1 THE LOCALIZED QUANTUM VACUUM FIELD D. Dragoman – Univ. Bucharest, Physics Dept., P.O. Box MG-11, 077125 Bucharest, Romania, e-mail: [email protected] ABSTRACT A model for the localized quantum vacuum is proposed in which the zero-point energy of the quantum electromagnetic field originates in energy- and momentum-conserving transitions of material systems from their ground state to an unstable state with negative energy. These transitions are accompanied by emissions and re-absorptions of real photons, which generate a localized quantum vacuum in the neighborhood of material systems. The model could help resolve the cosmological paradox associated to the zero-point energy of electromagnetic fields, while reclaiming quantum effects associated with quantum vacuum such as the Casimir effect and the Lamb shift; it also offers a new insight into the Zitterbewegung of material particles. 2 INTRODUCTION The zero-point energy (ZPE) of the quantum electromagnetic field is at the same time an indispensable concept of quantum field theory and a controversial issue (see [1] for an excellent review of the subject). The need of the ZPE has been recognized from the beginning of quantum theory of radiation, since only the inclusion of this term assures no first-order temperature-independent correction to the average energy of an oscillator in thermal equilibrium with blackbody radiation in the classical limit of high temperatures. A more rigorous introduction of the ZPE stems from the treatment of the electromagnetic radiation as an ensemble of harmonic quantum oscillators. Then, the total energy of the quantum electromagnetic field is given by E = åk,s hwk (nks +1/ 2) , where nks is the number of quantum oscillators (photons) in the (k,s) mode that propagate with wavevector k and frequency wk =| k | c = kc , and are characterized by the polarization index s. -
Zitterbewegung and a Formulation for Quantum Mechanics
Zitterbewegung and a formulation for quantum mechanics B. G. Sidharth∗ and Abhishek Das† B.M. Birla Science Centre, Adarsh Nagar, Hyderabad - 500 063, India Abstract In this short note, we try to show that inside a vortex like region, like a black hole one cane observe superluminosity which yields some interesting results. Also, we consider the zitterbewegung fluctuations to obtain an interpretation of quantum mechanics. 1 Introduction As is well known, the phenomenon of zitterbewegung has been studied by many eminent authors like Schrodinger [1] and Dirac [2]. Zitterbewegung is a type of rapid fluctuation that is attributed to the interference between positive and negative energy states. Dirac pointed out that the rapidly oscillating terms that arise on account of zitterbewegung is averaged out when we take a measurement remembering that no measurement is instanta- neous. Interestingly, Hestenes [3, 4] too sought to explain quantum mechanics through the phe- nomenon of zitterbewegung. Besides, the authors of this paper have also studied the afore- said phenomenon quite extensively in the past few years [5, 6, 7, 8, 9, 10]. However, in this paper we shall derive some interesting results that substantiate that the Compton scale and zitterbewegung can delineate several phenomena. 2 Theory arXiv:2002.11463v1 [physics.gen-ph] 8 Feb 2020 Let us consider an object, such as a black hole or some particle, that is spiralling like a vortex. In that case, we know that the circulation is given by 2π~n Γ = vdr = ¼C m ∗Email: [email protected] †Email: [email protected] 1 where, C denotes the contour of the vortex, n is the number of turns and m is the mass of the circulating particle. -
Quantum Trajectories: Real Or Surreal?
entropy Article Quantum Trajectories: Real or Surreal? Basil J. Hiley * and Peter Van Reeth * Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK * Correspondence: [email protected] (B.J.H.); [email protected] (P.V.R.) Received: 8 April 2018; Accepted: 2 May 2018; Published: 8 May 2018 Abstract: The claim of Kocsis et al. to have experimentally determined “photon trajectories” calls for a re-examination of the meaning of “quantum trajectories”. We will review the arguments that have been assumed to have established that a trajectory has no meaning in the context of quantum mechanics. We show that the conclusion that the Bohm trajectories should be called “surreal” because they are at “variance with the actual observed track” of a particle is wrong as it is based on a false argument. We also present the results of a numerical investigation of a double Stern-Gerlach experiment which shows clearly the role of the spin within the Bohm formalism and discuss situations where the appearance of the quantum potential is open to direct experimental exploration. Keywords: Stern-Gerlach; trajectories; spin 1. Introduction The recent claims to have observed “photon trajectories” [1–3] calls for a re-examination of what we precisely mean by a “particle trajectory” in the quantum domain. Mahler et al. [2] applied the Bohm approach [4] based on the non-relativistic Schrödinger equation to interpret their results, claiming their empirical evidence supported this approach producing “trajectories” remarkably similar to those presented in Philippidis, Dewdney and Hiley [5]. However, the Schrödinger equation cannot be applied to photons because photons have zero rest mass and are relativistic “particles” which must be treated differently. -
The Stueckelberg Wave Equation and the Anomalous Magnetic Moment of the Electron
The Stueckelberg wave equation and the anomalous magnetic moment of the electron A. F. Bennett College of Earth, Ocean and Atmospheric Sciences Oregon State University 104 CEOAS Administration Building Corvallis, OR 97331-5503, USA E-mail: [email protected] Abstract. The parametrized relativistic quantum mechanics of Stueckelberg [Helv. Phys. Acta 15, 23 (1942)] represents time as an operator, and has been shown elsewhere to yield the recently observed phenomena of quantum interference in time, quantum diffraction in time and quantum entanglement in time. The Stueckelberg wave equation as extended to a spin–1/2 particle by Horwitz and Arshansky [J. Phys. A: Math. Gen. 15, L659 (1982)] is shown here to yield the electron g–factor g = 2(1+ α/2π), to leading order in the renormalized fine structure constant α, in agreement with the quantum electrodynamics of Schwinger [Phys. Rev., 73, 416L (1948)]. PACS numbers: 03.65.Nk, 03.65.Pm, 03.65.Sq Keywords: relativistic quantum mechanics, quantum coherence in time, anomalous magnetic moment 1. Introduction The relativistic quantum mechanics of Dirac [1, 2] represents position as an operator and time as a parameter. The Dirac wave functions can be normalized over space with respect to a Lorentz–invariant measure of volume [2, Ch 3], but cannot be meaningfully normalized over time. Thus the Dirac formalism offers no precise meaning for the expectation of time [3, 9.5], and offers no representations for the recently– § observed phenomena of quantum interference in time [4, 5], quantum diffraction in time [6, 7] and quantum entanglement in time [8]. Quantum interference patterns and diffraction patterns [9, Chs 1–3] are multi–lobed probability distribution functions for the eigenvalues of an Hermitian operator, which is typically position. -
Bohmian Mechanics Versus Madelung Quantum Hydrodynamics
Ann. Univ. Sofia, Fac. Phys. Special Edition (2012) 112-119 [arXiv 0904.0723] Bohmian mechanics versus Madelung quantum hydrodynamics Roumen Tsekov Department of Physical Chemistry, University of Sofia, 1164 Sofia, Bulgaria It is shown that the Bohmian mechanics and the Madelung quantum hy- drodynamics are different theories and the latter is a better ontological interpre- tation of quantum mechanics. A new stochastic interpretation of quantum me- chanics is proposed, which is the background of the Madelung quantum hydro- dynamics. Its relation to the complex mechanics is also explored. A new complex hydrodynamics is proposed, which eliminates completely the Bohm quantum po- tential. It describes the quantum evolution of the probability density by a con- vective diffusion with imaginary transport coefficients. The Copenhagen interpretation of quantum mechanics is guilty for the quantum mys- tery and many strange phenomena such as the Schrödinger cat, parallel quantum and classical worlds, wave-particle duality, decoherence, etc. Many scientists have tried, however, to put the quantum mechanics back on ontological foundations. For instance, Bohm [1] proposed an al- ternative interpretation of quantum mechanics, which is able to overcome some puzzles of the Copenhagen interpretation. He developed further the de Broglie pilot-wave theory and, for this reason, the Bohmian mechanics is also known as the de Broglie-Bohm theory. At the time of inception of quantum mechanics Madelung [2] has demonstrated that the Schrödinger equa- tion can be transformed in hydrodynamic form. This so-called Madelung quantum hydrodynam- ics is a less elaborated theory and usually considered as a precursor of the Bohmian mechanics. The scope of the present paper is to show that these two theories are different and the Made- lung hydrodynamics is a better interpretation of quantum mechanics than the Bohmian me- chanics. -
Pilot-Wave Hydrodynamics
FL47CH12-Bush ARI 1 December 2014 20:26 Pilot-Wave Hydrodynamics John W.M. Bush Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139; email: [email protected] Annu. Rev. Fluid Mech. 2015. 47:269–92 Keywords First published online as a Review in Advance on walking drops, Faraday waves, quantum analogs September 10, 2014 The Annual Review of Fluid Mechanics is online at Abstract fluid.annualreviews.org Yves Couder, Emmanuel Fort, and coworkers recently discovered that a This article’s doi: millimetric droplet sustained on the surface of a vibrating fluid bath may 10.1146/annurev-fluid-010814-014506 self-propel through a resonant interaction with its own wave field. This ar- Copyright c 2015 by Annual Reviews. ticle reviews experimental evidence indicating that the walking droplets ex- All rights reserved hibit certain features previously thought to be exclusive to the microscopic, Annu. Rev. Fluid Mech. 2015.47:269-292. Downloaded from www.annualreviews.org quantum realm. It then reviews theoretical descriptions of this hydrody- namic pilot-wave system that yield insight into the origins of its quantum- Access provided by Massachusetts Institute of Technology (MIT) on 01/07/15. For personal use only. like behavior. Quantization arises from the dynamic constraint imposed on the droplet by its pilot-wave field, and multimodal statistics appear to be a feature of chaotic pilot-wave dynamics. I attempt to assess the po- tential and limitations of this hydrodynamic system as a quantum analog. This fluid system is compared to quantum pilot-wave theories, shown to be markedly different from Bohmian mechanics and more closely related to de Broglie’s original conception of quantum dynamics, his double-solution theory, and its relatively recent extensions through researchers in stochastic electrodynamics. -
Can Gravitons Be Effectively Massive Due to Their Zitterbewegung Motion? Elias Koorambas
Can gravitons be effectively massive due to their zitterbewegung motion? Elias Koorambas To cite this version: Elias Koorambas. Can gravitons be effectively massive due to their zitterbewegung motion?. 2014. hal-00990723 HAL Id: hal-00990723 https://hal.archives-ouvertes.fr/hal-00990723 Preprint submitted on 14 May 2014 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Can gravitons be effectively massive due to their zitterbewegung motion? E.Koorambas 8A Chatzikosta, 11521 Ampelokipi, Athens, Greece E-mail:[email protected] Submission Date: May 14, 2014 Abstract: Following up on an earlier, De Broglie-Bohm approach within the framework of quantum gauge theory of gravity, and based on the Schrödinger-Dirac equation for gravitons, we argue that gravitons are effectively massive due to their localized circulatory motion. This motion is analogous to the proposed zitterbewegung (ZB) motion of electrons. PACS numbers: 04.60.-m, 11.15.-q, 03.65.Ta Keywords: Quantum Gravity, Gauge Field, Bohm Potential, Zitterbewegung Model 1. Introduction Following, D. Hestenes, the idea that the The ZB of photons is studied via the electron spin and magnetic moment are momentum vector of the electromagnetic generated by a localized circulatory motion of field. -
The Quantum Potential And''causal''trajectories For
REFERENCE IC/88/161 \ ^' I 6 AUG INTERNATIONAL CENTRE FOR / Co THEORETICAL PHYSICS THE QUANTUM POTENTIAL AND "CAUSAL" TRAJECTORIES FOR STATIONARY STATES AND FOR COHERENT STATES A.O. Barut and M. Bo2ic INTERNATIONAL ATOMIC ENERGY AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION IC/88/161 I. Introduction International Atomic Energy Agency During the last decade Bohm's causal trajectories based on the and concept of the so called "quantum potential" /I/ have been evaluated United Nations Educational Scientific and Cultural Organization in a number of cases, the double slit /2,3/, tunnelling through the INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS barrier /4,5/, the Stern-Gerlach magnet /6/, neutron interferometer /8,9/, EPRB experiment /10/. In all these works the trajectories have been evaluated numerically for the time dependent wave packet of the Schrodinger equation. THE QUANTUM POTENTIAL AND "CAUSAL" TRAJECTORIES FOR STATIONARY STATES AND FOR COHERENT STATES * In the present paper we study explicitly the quantum potential and the associated trajectories for stationary states and for coherent states. We show how the quantum potential arises from the classical A.O. Barut ** and M. totii *** action. The classical action is a sum of two parts S ,= S^ + Sz> one International Centre for Theoretical Physics, Trieste, Italy. part Sj becomes the quantum action, the other part S2 is shifted to the quantum potential. We also show that the two definitions of causal ABSTRACT trajectories do not coincide for stationary states. We show for stationary states in a central potential that the quantum The content of our paper is as follows. Section II is devoted to action S is only a part of the classical action W and derive an expression for the "quantum potential" IL in terms of the other part. -
Photon Wave Mechanics: a De Broglie - Bohm Approach
PHOTON WAVE MECHANICS: A DE BROGLIE - BOHM APPROACH S. ESPOSITO Dipartimento di Scienze Fisiche, Universit`adi Napoli “Federico II” and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli Mostra d’Oltremare Pad. 20, I-80125 Napoli Italy e-mail: [email protected] Abstract. We compare the de Broglie - Bohm theory for non-relativistic, scalar matter particles with the Majorana-R¨omer theory of electrodynamics, pointing out the impressive common pecu- liarities and the role of the spin in both theories. A novel insight into photon wave mechanics is envisaged. 1. Introduction Modern Quantum Mechanics was born with the observation of Heisenberg [1] that in atomic (and subatomic) systems there are directly observable quantities, such as emission frequencies, intensities and so on, as well as non directly observable quantities such as, for example, the position coordinates of an electron in an atom at a given time instant. The later fruitful developments of the quantum formalism was then devoted to connect observable quantities between them without the use of a model, differently to what happened in the framework of old quantum mechanics where specific geometrical and mechanical models were investigated to deduce the values of the observable quantities from a substantially non observable underlying structure. We now know that quantum phenomena are completely described by a complex- valued state function ψ satisfying the Schr¨odinger equation. The probabilistic in- terpretation of it was first suggested by Born [2] and, in the light of Heisenberg uncertainty principle, is a pillar of quantum mechanics itself. All the known experiments show that the probabilistic interpretation of the wave function is indeed the correct one (see any textbook on quantum mechanics, for 2 S. -
Wave Equations Greiner Greiner Quantum Mechanics Mechanics I an Introduction 3Rd Edition (In Preparation)
W Greiner RELATIVISTIC QUANTUM MECHANICS Wave Equations Greiner Greiner Quantum Mechanics Mechanics I An Introduction 3rd Edition (in preparation) Greiner Greiner Quantum Theory Mechanics II Special Chapters (in preparation) (in preparation) Greiner Greiner· Muller Electrodynamics Quantum Mechanics (in preparation) Symmetries 2nd Edition Greiner· Neise . StOcker Greiner Thermodynamics Relativistic Quantum Mechanics and Statistical Mechanics Wave Equations Greiner· Reinhardt Field Quantization (in preparation) Greiner . Reinhardt Quantum Electrodynamics 2nd Edition Greiner· Schafer Quantum Chromodynamics Greiner· Maruhn Nuclear Models (in preparation) Greiner· MUller Gauge Theory of Weak Interactions Walter Greiner RELATIVISTIC QUANTUM MECHANICS Wave Equations With a Foreword by D. A. Bromley With 62 Figures, and 89 Worked Examples and Exercises Springer Professor Dr. Walter Greiner Institut fiir Theoretische Physik der Johann Wolfgang Goethe-Universitat Frankfurt Postfach 111932 D-60054 Frankfurt am Main Germany Street address: Robert-Mayer-Strasse 8-\ 0 D-60325 Frankfurt am Main Germany ISBN 978-3-540-99535-7 ISBN 978-3-642-88082-7 (eBook) DOl 10.1007/978-3-642-88082-7 Title of the original German edition: Theoretische Physik, Band 6: Relativistische Quantenmechanik, 2., iiberarbeitete und erweiterte Auflage 1987 © Verlag Harri Deutsch, Thun 1981 1st Edition 1990 3rd printing 1995 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer Verlag.