DOCSLIB.ORG

Electromagnetic Mass As a Superposition of Planck Masses

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Electromagnetic Mass As a Superposition of Planck Masses Open Journal of Mathematics and Physics | Volume 2, Article 84, 2020 | ISSN: 2674-5747 https://doi.org/10.31219/osf.io/cevm3 | published: 18 Feb 2020 | https://ojmp.wordpress.com DG [microresearch] Diamond Open Access Electromagnetic mass as a superposition of Planck masses Open Quantum Collaboration∗† February 24, 2020 Abstract At the Planck scale, the electromagnetic mass is composed by infinite negative Planck masses. keywords: Planck scale, quantum gravity, quantum electromagnetism Introduction 1. This work was inspired by [1–4]. 2. We use the following renormalization procedure [5,6], ∞ 1 S = Q n = 1 + 2 + 3 + 4 + 5 + 6 + ::: = − : n=1 12 ∗All authors with their affiliations appear at the end of this paper. †Corresponding author: [email protected] | Join the Open Quantum Collaboration 1 When gravity is equal to the electric force 3. GM 2 ke2 = r2 r2 4. k M 2 = e2 G 5. The fine structure constant of the relativistic quantum electromagnetism is given by ke2 1 α = ∼ : hc̵ 137 6. The Planck mass is ¾ hc̵ M = : P G 7. From (5) and (6), k e2 M 2 = P G α 8. From (4) and (7), M 2 M 2 = : P α 9. √ M = αMP 10. M M ∼ P 12 2 Renormalization scheme 1 1 11. From (2), S = −12, then −S = 12. 12. Using (11) in (10), M ∼ −SMP : 13. Using (2) in (12), ∞ M ∼ − Q nMP n=1 14. M ∼ −MP − 2MP − 3MP − 4MP − 5MP − 6MP − ::: Quantization 15. Quantizing (14), SM⟩ = − SMP ⟩ − 2 SMP ⟩ − 3 SMP ⟩ − 4 SMP ⟩ − 5 SMP ⟩ − 6 SMP ⟩ − ::: Final Remarks 16. From (3), the√ electric charge near the Planck scale is related to the mass by e = GM. 17. M = √e can be seen as an electromagnetic mass. G 18. The quantum electromagnetic mass state, SM⟩, is the superpo- sition of negative Planck masses. 19. It is believed that all the fundamental forces of nature are comparable near the Planck scale [1]. 3 Open Invitation Review, add content, and co-author this article [7, 8]. Join the Open Quantum Collaboration. Send your contribution to [email protected]. Ethical conduct of research This original work was pre-registered under the OSF Preprints [9], please cite it accordingly [10]. This will ensure that researches are con- ducted with integrity and intellectual honesty at all times and by all means. References [1] Adler, Ronald J. “Six easy roads to the Planck scale.” American Journal of Physics 78.9 (2010): 925-932. https://arxiv.org/pdf/1001.1205.pdf [2] Faraoni, Valerio. “Three new roads to the Planck scale.” American Journal of Physics 85.11 (2017): 865-869. https://aapt.scitation.org/doi/pdf/10.1119/1.4994804 [3] Adler, Ronald J., and David I. Santiago. “On gravity and the uncer- tainty principle.” Modern Physics Letters A 14.20 (1999): 1371-1381. https://arxiv.org/pdf/gr-qc/9904026.pdf [4] Lobo, Matheus P. “The Curvature of Space Due to One Photon Is Inaccessible.” OSF Preprints, 4 Sept. 2019. https://doi.org/10.31219/osf.io/wru6z [5] Lobo, Matheus P. “Sum of All Natural Numbers.” OSF Preprints, 17 Feb. 2020. https://doi.org/10.31219/osf.io/yx28b [6] Lobo, Matheus P. “The Infinity Theorem.” OSF Preprints, 4 Feb. 2020. https://doi.org/10.31219/osf.io/9zm6b 4 [7] Lobo, Matheus P. “Microarticles.” OSF Preprints, 28 Oct. 2019. https://doi.org/10.31219/osf.io/ejrct [8] Lobo, Matheus P. “Simple Guidelines for Authors: Open Jour- nal of Mathematics and Physics.” OSF Preprints, 15 Nov. 2019. https://doi.org/10.31219/osf.io/fk836 [9] COS. Open Science Framework. https://osf.io [10] Lobo, Matheus P. “Electromagnetic Mass as a Superpo- sition of Planck Masses.” OSF Preprints, 18 Feb. 2020. https://doi.org/10.31219/osf.io/cevm3 The Open Quantum Collaboration Matheus Pereira Lobo (lead author, [email protected])1,2 1Federal University of Tocantins (Brazil); 2Universidade Aberta (UAb, Portugal) 5.
Load more

Recommended publications
  • Hendrik Antoon Lorentz's Struggle with Quantum Theory A. J
    Hendrik Antoon Lorentz’s struggle with quantum theory A. J. Kox Archive for History of Exact Sciences ISSN 0003-9519 Volume 67 Number 2 Arch. Hist. Exact Sci. (2013) 67:149-170 DOI 10.1007/s00407-012-0107-8 1 23 Your article is published under the Creative Commons Attribution license which allows users to read, copy, distribute and make derivative works, as long as the author of the original work is cited. You may self- archive this article on your own website, an institutional repository or funder’s repository and make it publicly available immediately. 1 23 Arch. Hist. Exact Sci. (2013) 67:149–170 DOI 10.1007/s00407-012-0107-8 Hendrik Antoon Lorentz’s struggle with quantum theory A. J. Kox Received: 15 June 2012 / Published online: 24 July 2012 © The Author(s) 2012. This article is published with open access at Springerlink.com Abstract A historical overview is given of the contributions of Hendrik Antoon Lorentz in quantum theory. Although especially his early work is valuable, the main importance of Lorentz’s work lies in the conceptual clarifications he provided and in his critique of the foundations of quantum theory. 1 Introduction The Dutch physicist Hendrik Antoon Lorentz (1853–1928) is generally viewed as an icon of classical, nineteenth-century physics—indeed, as one of the last masters of that era. Thus, it may come as a bit of a surprise that he also made important contribu- tions to quantum theory, the quintessential non-classical twentieth-century develop- ment in physics. The importance of Lorentz’s work lies not so much in his concrete contributions to the actual physics—although some of his early work was ground- breaking—but rather in the conceptual clarifications he provided and his critique of the foundations and interpretations of the new ideas.
    [Show full text]
  • Unification of the Maxwell- Einstein-Dirac Correspondence
    Unification of the Maxwell- Einstein-Dirac Correspondence The Origin of Mass, Electric Charge and Magnetic Spin Author: Wim Vegt Country: The Netherlands Website: http://wimvegt.topworld.center Email: [email protected] Calculations: All Calculations in Mathematica 11.0 have been printed in a PDF File Index 1 “Unified 4-Dimensional Hyperspace 5 Equilibrium” beyond Einstein 4-Dimensional, Kaluza-Klein 5-Dimensional and Superstring 10- and 11 Dimensional Curved Hyperspaces 1.2 The 4th term in the Unified 4-Dimensional 12 Hyperspace Equilibrium Equation 1.3 The Impact of Gravity on Light 15 2.1 EM Radiation within a Cartesian Coordinate 23 System in the absence of Gravity 2.1.1 Laser Beam with a Gaussian division in the x-y 25 plane within a Cartesian Coordinate System in the absence of Gravity 2.2 EM Radiation within a Cartesian Coordinate 27 System under the influence of a Longitudinal Gravitational Field g 2.3 The Real Light Intensity of the Sun, measured in 31 our Solar System, including Electromagnetic Gravitational Conversion (EMGC) 2.4 The Boundaries of our Universe 35 2.5 The Origin of Dark Matter 37 3 Electromagnetic Radiation within a Spherical 40 Coordinate System 4 Confined Electromagnetic Radiation within a 42 Spherical Coordinate System through Electromagnetic-Gravitational Interaction 5 The fundamental conflict between Causality and 48 Probability 6 Confined Electromagnetic Radiation within a 51 Toroidal Coordinate System 7 Confined Electromagnetic Radiation within a 54 Toroidal Coordinate System through Electromagnetic-Gravitational
    [Show full text]
  • Ether and Electrons in Relativity Theory (1900-1911) Scott Walter
    Ether and electrons in relativity theory (1900-1911) Scott Walter To cite this version: Scott Walter. Ether and electrons in relativity theory (1900-1911). Jaume Navarro. Ether and Moder- nity: The Recalcitrance of an Epistemic Object in the Early Twentieth Century, Oxford University Press, 2018, 9780198797258. hal-01879022 HAL Id: hal-01879022 https://hal.archives-ouvertes.fr/hal-01879022 Submitted on 21 Sep 2018 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. Ether and electrons in relativity theory (1900–1911) Scott A. Walter∗ To appear in J. Navarro, ed, Ether and Modernity, 67–87. Oxford: Oxford University Press, 2018 Abstract This chapter discusses the roles of ether and electrons in relativity the- ory. One of the most radical moves made by Albert Einstein was to dismiss the ether from electrodynamics. His fellow physicists felt challenged by Einstein’s view, and they came up with a variety of responses, ranging from enthusiastic approval, to dismissive rejection. Among the naysayers were the electron theorists, who were unanimous in their affirmation of the ether, even if they agreed with other aspects of Einstein’s theory of relativity. The eventual success of the latter theory (circa 1911) owed much to Hermann Minkowski’s idea of four-dimensional spacetime, which was portrayed as a conceptual substitute of sorts for the ether.
    [Show full text]
  • Lorentz's Electromagnetic Mass: a Clue for Unification?
    Lorentz’s Electromagnetic Mass: A Clue for Unification? Saibal Ray Department of Physics, Barasat Government College, Kolkata 700 124, India; Inter-University Centre for Astronomy and Astrophysics, Pune 411 007, India; e-mail: [email protected] Abstract We briefly review in the present article the conjecture of electromagnetic mass by Lorentz. The philosophical perspectives and historical accounts of this idea are described, especially, in the light of Einstein’s special relativistic formula E = mc2. It is shown that the Lorentz’s elec- tromagnetic mass model has taken various shapes through its journey and the goal is not yet reached. Keywords: Lorentz conjecture, Electromagnetic mass, World view of mass. 1. Introduction The Nobel Prize in Physics 2004 has been awarded to D. J. Gross, F. Wilczek and H. D. Politzer [1,2] “for the discovery of asymptotic freedom in the theory of the strong interaction” which was published three decades ago in 1973. This is commonly known as the Standard Model of mi- crophysics (must not be confused with the other Standard Model of macrophysics - the Hot Big Bang!). In this Standard Model of quarks, the coupling strength of forces depends upon distances. Hence it is possible to show that, at distances below 10−32 m, the strong, weak and electromagnetic interactions are “different facets of one universal interaction”[3,4]. This instantly reminds us about another Nobel Prize award in 1979 when S. Glashow, A. Salam and S. Weinberg received it “for their contributions to the theory of the unified weak and electro- magnetic interaction between elementary particles, including, inter alia, the prediction of the arXiv:physics/0411127v4 [physics.hist-ph] 31 Jul 2007 weak neutral current”.
    [Show full text]
  • Electron Electromagnetic-Mass Melting in Strong Fields
    PHYSICAL REVIEW D 102, 036014 (2020) Electron electromagnetic-mass melting in strong fields Stefan Evans and Johann Rafelski Department of Physics, The University of Arizona, Tucson, Arizona 85721, USA (Received 21 November 2019; accepted 29 July 2020; published 14 August 2020) We study the response of the electron mass to an externally applied electrical field. As a consequence of nonlinear electromagnetic (EM) effective action, the mass of a particle diminishes in the presence of an externally applied electric field. We consider modification of the muon anomalous magnetic moment g − 2 due to electron loop insert in higher order. Since the virtual electron pair is in close proximity to the muon, it experiences strong field phenomena. We show that the current theory-experiment muon g − 2 discrepancy could originate in the (virtual) electron mass nonperturbative modification by the strong muon EM field. The magnitude of the electron mass modification can be also assessed via enhancement of eþe−-pair production in strong fields. DOI: 10.1103/PhysRevD.102.036014 I. INTRODUCTION The electron mass response to external EM fields has – The Higgs minimal coupling mass generating mecha- been studied before [2 4]. We revisit the topic with the aim nism of heavy, beyond GeV mass scale, elementary to better understand the relation between the two dominant particles is well established. The origin of the lightest contributions to electron mass, the EM and Higgs portions. standard model (SM) electron mass is not expected to be The EM mass in external fields can be studied in QED resolved experimentally in the near future: the LHC pp- either as EM-self-energy or in the EM-energy-momentum collider is capable of constraining the minimal coupling to tensor analysis: We show this in Sec.
    [Show full text]
  • A Simple Derivation of Lorentz Self Force
    A Simple Derivation of Lorentz Self-Force Asrarul Haque∗ Department of Physics, BITS Pilani Hyderabad Campus, Hyderabad-500078, AP, India. (Dated: September 23, 2018) Abstract We derive the Lorentz self-force for a charged particle in arbitrary non-relativistic motion via averaging the retarded fields. The derivation is simple and at the same time pedagogically acces- sible. We obtain the radiation reaction for a charged particle moving in a circle. We pin down the underlying concept of mass renormalization. arXiv:1403.5622v2 [physics.class-ph] 22 Aug 2014 1 I. INTRODUCTION The electromagnetic field goes to infinity at the position of a point charge. The electro- static field at the position of the charged particle ~ 1 q r→0 E(~r)= 3 ~r −−→∞ (1) 4πε0 r and the self-energy of the point charge in the rest frame of the charged particle π 2π ∞ 2 2 r=∞ ε0 2 3 1 q q 1 U = E d r = 2 sin θdθ dφ 2 dr = − →∞ (2) 2 Z 32π ε0 Z Z Z r 8πε0 r r=0 0 0 0 turn out divergent. The concept of the point-like (structureless or dimensionless object) charge may be an idealization. The measurement of the anomalous magnetic moment of an electron based on the quantum field theoretic calculations leads to the following upper bound on the size of the electron1 l : l ≤ 10−17cm. Thus, a charged particle might be considered as an extended object with a finite size. In order to circumvent the problem of divergence of the field at the point charge, it is plau- sible either: (1) to consider the averaged value of the field in the suitably small closed region surrounding the point charge as the value of the field under consideration at the position of the point charge or (2) to think a charged particle as an extended object having small dimension with a charge distribution.
    [Show full text]
  • Conceptual Development of Einstein's Mass-Energy Relationship
    New Horizons in Education, No 51, May 2005 Conceptual Development of Einstein’s Mass-Energy Relationship Wong Chee Leong & Yap Kueh Chin National Institute of Education, Nanyang Technological University Einstein's special theory of relativity was concepts of Einstein’s mass-energy relationship published in 1905. It stands as one of the greatest during these 100 years. Challenges, issues and intellectual achievements in the history of human implications for curriculum development, thought. Einstein described the equivalence of instruction and assessment are also discussed. mass and energy as "the most important upshot Keywords: Einstein, Mass-Energy of the special theory of relativity" (Einstein, 1919). relationship, E = mc2 In this paper, we will discuss the evolution of the !"#$ J !"#$%& !"#$%&'()* NVMR !"#$%&'()*+,-./0 !"#$%&'()*+,-./ !"#$%&'()*+),-./0 NVNV !"#!$%&'()$*+ !" !"#$%&'() *+,- . ! !"#$ J bZãÅO !"#$%&'()*+, Introduction The vast impact of E = mc2 can be justified by how it is coined as the “most famous equation in Science”. Are not gross Bodies and Light convertible into Harald Fritzsch (1997) described this impact in his book one another, and may not Bodies receive much of their “An Equation that changed the world”. In addition, there Activity from the Particles of Light which enter their is a large amount of published work, both in books and Composition? journals, which look at this equation from many Newton, Opticks (4 ed. , 1730) different perspectives. One disturbing fact, according 56 Conceptual Development of Einstein’s Mass-Energy Relationship to Warren (1976), is that many of the authors who velocity-dependent mass. In our recent survey of more misrepresent mass-energy were trained in the period than 30 textbooks, and more than 100 “popular” books when the available textbooks were mostly correct and from UK and USA (published after Okun’s paper in clear.
    [Show full text]
  • The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics?
    applied sciences Article The Enigma of the Muon and Tau Solved by Emergent Quantum Mechanics? Theo van Holten Aerospace Engineering, Delft University of Technology, Utrechtseweg 43, 1213 TL Hilversum, The Netherlands; [email protected]; Tel.: +31-(0)357721155 Received: 1 February 2019; Accepted: 3 April 2019; Published: 8 April 2019 Abstract: This paper addresses the long-standing question of how it may be explained that the three charged leptons (the electron, muon and tau particle) have different masses, despite their conformity in other respects. In the field of Emergent Quantum Mechanics non-singular electron models are being revisited, and from this exploration has come a possible answer. In this paper a deformable droplet model is considered. It is shown how the model can be made self-consistent, whilst obeying the laws of momentum and energy conservation as well as Larmor’s radiation law. The droplet appears to have three different static equilibrium configurations, each with a different mass. Tentatively, these three equilibrium masses were assumed to correspond with the measured masses of the charged leptons. The droplet model was tuned accordingly, and was thereby completely quantified. The dynamics of the droplet then showed a “De Broglie-like” relation p = K/l. Beat patterns in the vibrations of the droplet play the role of the matter waves of usual quantum mechanics. The value of K, calculated by the droplet theory, practically equals Planck’s constant: K =∼ h. This fact seems to confirm the correctness of identifying the three types of charged leptons with the equilibria of a droplet of charge.
    [Show full text]
  • The Renormalization of Charge and Temporality in Quantum Electrodynamics
    The renormalization of charge and temporality in quantum electrodynamics Mario Bacelar Valente abstract In this article it is intended a closer look at the renormalization procedure used in quantum electrodynamics to cope with the divergent integrals that appear in higher-order calculations within the theory. The main focus will be the charge renormalization that reveals, in a clearer way than the mass renormalization, structural limitations present in quantum electrodynamics that are even more aggravating than the ones usually pointed at when considering the renormalization procedure. In this way we see that the possibility of charge renormalization is due to limitations of the theory in the temporal description of the interactions. 1 Introduction The appearance of divergent integrals in higher-order calculations in quantum electrodynamics where the so-called radiative corrections are taken into account has been seen as, at least, indicating that the theory fails for high energies. As J. Schwinger stated, “electrodynamics unquestionably requires revision at ultra-relativistic energies” (Aramaki 1989, 93). Even considering the accuracy of the theory at lower energies, Schwinger considered that the renormalization procedure, that permits avoiding the infinites in the results of the calculations, ultimately has to be excluded from physics (Cao 1993, 50). Regarding this problem the position of P. Dirac was even less sympathetic: “I am very dissatisfied with the situation, because this so-called “good theory” does involve neglecting infinities which appear in its equations” (Kragh 1990, 184). In general the position of leading physicists was very critical regarding quantum electrodynamics, and some pinpointed to structural problems that go beyond the high energy behaviour of quantum electrodynamics.
    [Show full text]
  • On the Definition of “Hidden” Momentum
    On the Definition of “Hidden” Momentum Kirk T. McDonald Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 (July 9, 2012; updated February 14, 2020) In 1822 [1, 2], Amp`ere argued that the magnetic interaction between two electrical circuits could be written as a double integral over the current elements in the two circuits, with the vector integrand being along the line of centers of pairs of current elements. This insured that the total force on each circuit obeyed Newton’s third law, i.e., that mechanical momentum is conserved. Amp`ere hesitated to interpret the integrand as the force law between isolated current elements, perhaps because the integrand did not factorize. In 1845, Grassmann [5] gave an alternate form of the integrand which did factorize (into what is now called the Biot-Savart form), such that the force on each circuit had the same value as in Amp`ere’s calculation, but the forces on a pair of isolated current elements did not obey Newton’s third law, i.e., such that mechanical momentum would not be conserved in the interaction of isolated current elements. Maxwell (sec. 527 of [7]) favored Amp`ere over Grassmann (and the school of Neumann and Weber) in this matter, and was skeptical of the notion of free moving charges.1 The concept of free moving charges was revived by J.J. Thomson beginning with speculations as to electromagnetic mass/momentum (1881) [8], and continuing with a concept of momentum stored in the electromagnetic field (1891) [10, 11], with the field- 2 2 momentum density being the Poynting vector [9] divided by c , pEM = S/c ,wherec is the speed of light in vacuum.2,3 Thomson was also the first to consider (1904) [17, 18, 19] an example in which an elec- tromechanical system initially “at rest” leads to motion of part of the system if the magnetic field later drops to zero.
    [Show full text]
  • A Comparison Between Lorentz's Ether Theory And
    A COMPARISON BETWEEN LORENTZ’S ETHER THEORY AND SPECIAL RELATIVITY IN THE LIGHT OF THE EXPERIMENTS OF TROUTON AND NOBLE by Michael Heinrich Paul Janssen Kandidaats (≈ B.A.) Philosophy, Universiteit van Amsterdam, 1982 Doctoraal (≈ M.S.) Theoretical Physics, Universiteit van Amsterdam, 1988 Submitted to the Graduate Faculty of Arts and Sciences in partial fulfillment of the requirements for the degree of Doctor of Philosophy University of Pittsburgh 1995 Copyright by Michel Janssen 1995 ii (committee signature page) iii For Suzy I was just getting up Hit the road before it’s light Trying to catch an hour on the sun When I saw those thrashers rolling by Looking more than two lanes wide I was feeling like my day had just begun —Neil Young iv A COMPARISON BETWEEN LORENTZ’S ETHER THEORY AND SPECIAL RELATIVITY IN THE LIGHT OF THE EXPERIMENTS OF TROUTON AND NOBLE Michel Janssen, PhD University of Pittsburgh, 1995 In Part One of this dissertation, I analyze various accounts of two etherdrift experiments, the Trouton-Noble experiment and an earlier experiment by Trouton. Both aimed at detecting etherdrift with the help of a condenser in a torsion balance. I argue that the difficulties ether- theorists Lorentz and Larmor had in accounting for the negative results of these experiments stem from the fact that they did not (properly) take into account that, if we charge a moving condenser, we not only change its energy, but also its momentum and its mass. I establish two additional results. (1) The Trouton experiment can be seen as a physical realization of a thought experiment used by Einstein to argue for the inertia of energy.
    [Show full text]
  • Electromagnetic Mass and Violation of Newton's Law Shreeram Acharya =
    The Himalayan Physics, Vol.1, No.1, May 2010 Electromagnetic Mass and Violation of Newton’s Law Shreeram Acharya Department of Physic, PN Campus, Pokhara, Email: [email protected] When an electron having all charge (q) distributed which is proportional to its velocity just form the uniformly on its surface of sphere of radius (a) , is at electromagnetic infl uence. The coeffi cient of rest, no magnetic fi eld is associated with it. Then the velocity in the expression of momentum is called energy per unit volume of the fi eld is given mass, so the coeffi cient of v on right side should indicate the mass which arises only due to the effect 2 u= εo E of electrodynamics and is called electromagnetic mass i.e. = 2 = = This implies that the total mass of a charged particle in Total energy = U motion with small velocity is sum of the mechanical electrica l = and the electromagnetic masses. = 4 = = For the total mass to be electromagnetic, Which becomes infi nite if a=0(point charge) = indicating that there is infi nite amount of energy in the fi eld surrounding a point charge at rest, which is a matter of trouble. To analyze the problem, it is necessary to calculate the change in energy when the charged particle is moved with v<c. According to the theory of electrodynamics, momentum must be same as the energy multiplied by . The momentum density is given by Where is classical electron radius = When the electron has very high velocity, then the = momentum of electron is found to be This on intregating over volume gives momentum having value It shows that a charged particle carries a momentum 97 Acharya/Electromagnetic..
    [Show full text]