Quantum Realism Glossary Brian Whitworth, May 2019

Total Page:16

File Type:pdf, Size:1020Kb

Quantum Realism Glossary Brian Whitworth, May 2019 Quantum Realism Glossary Brian Whitworth, May 2019. These definitions are based on current physics, computer science and quantum realism (QR), where the first two are accepted but the latter is a new interpretation of quantum theory. Each term links to the chapter section that discusses it in more detail. Just click on it to go there for more details. Anti-matter. Has the same mass as matter but opposite charge and magnetic momentum. In QR, it is the quantum processing of matter running in reverse. Anti-time. Feynman diagrams show anti-matter entering reactions going backwards in time. In QR, anti-matter time passes “in reverse” cycles because it is matter processing in reverse. Asynchrony. When processors cycle at their own rate with no common clock. The asynchronous quantum network is somewhat synchronized by light transfer interrupts but this method is imperfect. Bandwidth. The capacity of a transfer channel to accept information or processing. In QR, the bandwidth of one transfer channel between two nodes of the quantum network is one quantum process. Big bang. The idea that all the matter and energy of the universe expanded from a point singularity. In QR, the universe began as a small rip. Black hole. A region of space with gravity so strong that not even light can escape from it, produced when a large enough mass collapses under its own gravity to a point singularity of infinite density. In QR, a black hole represents the bandwidth of space and does not exist as a singularity. Boson. An integer spin particle, like a photon, that does not collide with itself. All the virtual particles of current physics are said to be bosons. In QR, these “force particles” are unnecessary. Breit-Wheeler process. A hypothetical process whereby photons create mass. Cartesian space. A space that is defined based on orthogonal line dimensions, so any point in it can be represented by coordinates (x, y, z, …), that are its real number extent on each dimension. Casimir effect. Two conducting plates placed close together in a vacuum experience a force pushing them together, illustrating that empty space is not empty. Channel. How a network node connects to another node. In QR, it is a quantum node’s ability to accept processing vibrating at right angles to the polarization plane of an incoming photon, where each channel has a processing bandwidth of one quantum process. Channel set. The full set of channels for any node transfer axis, that can accept a ray of light that contains photons in every possible polarization plane. Charge. An inherent property of matter that causes electrical effects. In QR, it is the constant after a processing overload creates mass, and so is a byproduct of mass. Client-server relation. A network relation that partitions work between a server resource and one or more clients, whether a server transferring a document to a client printer or a photon server transferring processing to quantum network node. Complex plane. The “imaginary” complex plane into which light vibrates, according to current physics. In QR, complex numbers represent a quantum dimension that actually exists. Consciousness. The unalloyed capacity to experience a physical observation. Conservation of photons. That the number of active photons in the universe has been constant since inflation stopped. Copenhagen interpretation of quantum theory. Bohr’s 1920 dualism that quantum waves can exist for the purpose of physics calculations but not “really” exist. It let quantum theory be a useful description of nothing. The QR interpretation of quantum theory is that it describes what actually generates physical events. Cosmic background radiation. Light from the early universe that was once white hot but is now cold by the expansion of space. In QR, it is still visible all around us because space is spherical. Cycle rate. The number of processing cycles per second, e.g. a gigahertz processor runs a billion cycles/second. The quantum network cycle rate is about ten million, trillion, trillion, trillion cycles per second. Dark energy. An unknown negative energy that pushes the universe apart. In QR, it arises because new nodes of space receive but don’t transmit processing for their first cycle . Dark matter. Gives galaxies more gravity than their stars and planets allow, to stop them flying apart. In QR, the black hole at the center of most galaxies traps light in a halo around it to create mass that is not visible as particles are. Delayed choice two-slit experiment. A two-slit experiment where the measurement method decided after the light has passed through the slits determines whether it travels as a particle or a wave. Distributed processing. A constant amount of processing that when shared runs slower not less. Down quark. A first-generation quark with a strange -⅓rd charge. In QR, it is a head-head-tail three-way collision of extreme light that almost fills the channels of a node plane and has a negative remainder. Dualism. The belief that two distinct and different realities co-exist, such as mind and body. Einstein’s equation. E=mc2 states that the energy of matter is its mass times the speed of light squared. In QR, it can be derived from the definition of matter as trapped light. Electric field. A field that surrounds a charge to attract or repel other charges. In QR, charges spread processing remainders on the quantum network that interact to bias the random movement of their matter. Electromagnetic field. In current physics, a field with electrical and magnetic aspects that cause each other, although that is illogical. In QR, electricity and magnetism are caused by one quantum field. Electromagnetic spectrum. All the frequencies of light as a sine wave vibrating in an imaginary dimension. In QR, it is the same quantum process distributed more or less on the surface of space. Electron. A simple elementary matter particle with a negative charge. In QR, it is a head-head collision of extreme light that fills the channels of a node axis leaving a negative processing remainder. Electron shell. Electrons in an atom occupy shells and sub-shells as waves not particles. In QR, they do so based on distance from the nucleus, harmonic and wave orientation. Electron spin. In current physics, an electron is said to “half-spin”. In QR, this is because only half the photons of an electron are visible from any direction. Empty space. Space that has nothing in it. In QR, empty space isn't empty because null processing isn't “nothing”. Energy. A physical system’s capacity to perform work. In QR, it is the quantum processing transfer rate at the node. Entanglement. When entangled photons leave in opposite directions, measuring the random spin of either instantly gives the other the opposite spin no matter how far apart they are. In QR, the entangling event merges two opposite spin servers, so when a new event links one server's spin to one photon, the opposite spin server instantly runs the other wherever it is on the screen of space. Entropy. The amount of disorder in a closed system. Evolution. An iterative process that lets entities survive by trial and error to pass on properties to their descendants. Existence. Physical realism defines it as having a physical reality. Quantum realism defines it as having a quantum reality. Extreme light. The highest frequency of light, with a wavelength of two Planck lengths. Family generations. Electrons, neutrinos and quarks have three generations, each like the last but heavier, then no more. In QR, this is because the three dimensions of space let their photon structures repeat. Field. A mathematical method that assigns a value to every point in space, equivalent to a new dimension. Field theory. A theory where invisible fields spawn virtual particles to cause forces like gravity, thus avoiding action at a distance. Fundamental particle. A particle that can’t be broken down further by particle accelerators, that is assumed to have no size or substructure. In QR, fundamental particles are neither fundamental nor particles. Gauss’s flux law. That a flux spreading in three dimensions decreases as the inverse square of its radius. General relativity. Einstein’s theory that the force of gravity is equivalent to the force of an acceleration. Gluons. Virtual particles that bind quarks in the atomic nucleus. In QR, photon sharing explains this so gluons are unnecessary. Goldilocks effect. That our universe has an unreasonable number of parameters set “just right” for life, without which we couldn’t exist. QR attributes it to life evolving as best it can, given the limits of the originating quantum reality. Graviton. A virtual particle invented to explain gravity based on no evidence whatsoever. QR attributes gravity to the quantum field gradient around matter, so gravitons are unnecessary agents. Gravity. The force that draws matter together at a distance. In QR, the quantum field gradient around a large mass makes other matter more likely to reboot towards it. Grounded theory. A scientific method that iteratively acquires data then forms predictive theories. Quantum realism applies grounded theory to physics. Just-in-time computing. The strategy of leaving processing decisions until the last possible moment. In QR, light uses this strategy to define a photon’s path after it arrives. Kinetic energy. Energy associated with the movement of matter. QR attributes it to matter acquiring photons that bias its movement in a particular direction. Hidden variables. The idea that hidden physical causes explain what quantum theory describes. In QR, the hidden variable is quantum reality. Higgs particle. A virtual particle invoked to explain another virtual particle that explains neutron decay.
Recommended publications
  • Elementary Particles: an Introduction
    Elementary Particles: An Introduction By Dr. Mahendra Singh Deptt. of Physics Brahmanand College, Kanpur What is Particle Physics? • Study the fundamental interactions and constituents of matter? • The Big Questions: – Where does mass come from? – Why is the universe made mostly of matter? – What is the missing mass in the Universe? – How did the Universe begin? Fundamental building blocks of which all matter is composed: Elementary Particles *Pre-1930s it was thought there were just four elementary particles electron proton neutron photon 1932 positron or anti-electron discovered, followed by many other particles (muon, pion etc) We will discover that the electron and photon are indeed fundamental, elementary particles, but protons and neutrons are made of even smaller elementary particles called quarks Four Fundamental Interactions Gravitational Electromagnetic Strong Weak Infinite Range Forces Finite Range Forces Exchange theory of forces suggests that to every force there will be a mediating particle(or exchange particle) Force Exchange Particle Gravitational Graviton Not detected so for EM Photon Strong Pi mesons Weak Intermediate vector bosons Range of a Force R = c Δt c: velocity of light Δt: life time of mediating particle Uncertainity relation: ΔE Δt=h/2p mc2 Δt=h/2p R=h/2pmc So R α 1/m If m=0, R→∞ As masses of graviton and photon are zero, range is infinite for gravitational and EM interactions Since pions and vector bosons have finite mass, strong and weak forces have finite range. Properties of Fundamental Interactions Interaction
    [Show full text]
  • Chapter 5 the Relativistic Point Particle
    Chapter 5 The Relativistic Point Particle To formulate the dynamics of a system we can write either the equations of motion, or alternatively, an action. In the case of the relativistic point par- ticle, it is rather easy to write the equations of motion. But the action is so physical and geometrical that it is worth pursuing in its own right. More importantly, while it is difficult to guess the equations of motion for the rela- tivistic string, the action is a natural generalization of the relativistic particle action that we will study in this chapter. We conclude with a discussion of the charged relativistic particle. 5.1 Action for a relativistic point particle How can we find the action S that governs the dynamics of a free relativis- tic particle? To get started we first think about units. The action is the Lagrangian integrated over time, so the units of action are just the units of the Lagrangian multiplied by the units of time. The Lagrangian has units of energy, so the units of action are L2 ML2 [S]=M T = . (5.1.1) T 2 T Recall that the action Snr for a free non-relativistic particle is given by the time integral of the kinetic energy: 1 dx S = mv2(t) dt , v2 ≡ v · v, v = . (5.1.2) nr 2 dt 105 106 CHAPTER 5. THE RELATIVISTIC POINT PARTICLE The equation of motion following by Hamilton’s principle is dv =0. (5.1.3) dt The free particle moves with constant velocity and that is the end of the story.
    [Show full text]
  • Theory of More Than Everything1
    Universally of Marineland Alimentary Gastronomy Universe of Murray Gell-Mann Elementary My Dear Watson Unified Theory of My Elementary Participles .. ^ n THEORY OF MORE THAN EVERYTHING1 V. Gates, Empty Kangaroo, M. Roachcock, and W.C. Gall 2 Compartment of Physiques and Astrology Universally of Marineland, Alleged kraP, MD ABSTRACT We derive a theory which, after spontaneous, dynamical, and ad hoc symmetry breaking, and after elimination of all fields except a set of zero measure, produces 10-dimensional superstring theory. Since the latter is a theory of only everything, our theory describes much more than everything, and includes also anything, something, and nothing. (More text should go here. So sue me.) 1Work supported by little or no evidence. 2Address after September 1, 1988: ITP, SHIITE, Roc(e)ky Brook, NY Uniformity of Modern Elementary Particle Physics Unintelligibility of Many Elementary Particle Physicists Universal City of Movieland Alimony Parties You Truth is funnier than fiction | A no-name moose1] Publish or parish | J.C. Polkinghorne Gimme that old minimal supergravity. Gimme that old minimal supergravity. It was good enough for superstrings. 1 It's good enough for me. ||||| Christian Physicist hymn1 2 ] 2. CONCLUSIONS The standard model has by now become almost standard. However, there are at least 42 constants which it doesn't explain. As is well known, this requires a 42 theory with at least @0 times more particles in its spectrum. Unfortunately, so far not all of these 42 new levels of complexity have been discovered; those now known are: (1) grandiose unification | SU(5), SO(10), E6,E7,E8,B12, and Niacin; (2) supersummitry2]; (3) supergravy2]; (4) supursestrings3−5].
    [Show full text]
  • Gravitational Field of Massive Point Particle in General Relativity
    Gravitational Field of Massive Point Particle in General Relativity P. P. Fiziev∗ Department of Theoretical Physics, Faculty of Physics, Sofia University, 5 James Bourchier Boulevard, Sofia 1164, Bulgaria. and The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34014 Trieste, Italy. Utilizing various gauges of the radial coordinate we give a description of static spherically sym- metric space-times with point singularity at the center and vacuum outside the singularity. We show that in general relativity (GR) there exist a two-parameters family of such solutions to the Einstein equations which are physically distinguishable but only some of them describe the gravitational field of a single massive point particle with nonzero bare mass M0. In particular, we show that the widespread Hilbert’s form of Schwarzschild solution, which depends only on the Keplerian mass M < M0, does not solve the Einstein equations with a massive point particle’s stress-energy tensor as a source. Novel normal coordinates for the field and a new physical class of gauges are proposed, in this way achieving a correct description of a point mass source in GR. We also introduce a gravi- tational mass defect of a point particle and determine the dependence of the solutions on this mass − defect. The result can be described as a change of the Newton potential ϕN = GN M/r to a modi- M − 2 0 fied one: ϕG = GN M/ r + GN M/c ln M and a corresponding modification of the four-interval. In addition we give invariant characteristics of the physically and geometrically different classes of spherically symmetric static space-times created by one point mass.
    [Show full text]
  • Fall 2009 PHYS 172: Modern Mechanics
    PHYS 172: Modern Mechanics Fall 2009 Lecture 16 - Multiparticle Systems; Friction in Depth Read 8.6 Exam #2: Multiple Choice: average was 56/70 Handwritten: average was 15/30 Total average was 71/100 Remember, we are using an absolute grading scale where the values for each grade are listed on the syllabus Typically, exam grades (500/820 points) are lower than homework, recitation, clicker, & labs grades Clicker Question #1 You get in a parked car and start driving. Assume that you travel a distance D in 10 seconds, with a constant acceleration a. Define the system to be the car plus the driver (you), whose total mass is M and acceleration a. Choose the correct statement for this system: A. The final total kinetic energy is Ktotal= MaD. B. The final translational kinetic energy is Ktrans= MaD. C. The total energy of the system changes by +MaD. D. The total energy of the system changes by -MaD.. E. The total energy of the system does not change. Clicker Question Discussion You get in a parked car and start driving. Assume that you travel a distance D in 10 seconds, with a constant acceleration a. Define the system to be the car plus the driver (you), whose total mass is M and acceleration a. Choose the correct statement for this system: A. The final total kinetic energy is Ktotal= MaD.No, this is just the translational K. There is also relative K (wheels, etc.) B. The final translational kinetic energy is Ktrans= MaD. Correct, use point particle system; force is friction applied by the road on the tires.
    [Show full text]
  • “WHAT IS an ELECTRON?” Contents 1. Quantum Mechanics in A
    \WHAT IS AN ELECTRON?" OR PARTICLES AS REPRESENTATIONS ROK GREGORIC Abstract. In these informal notes, we attempt to offer some justification for the math- ematical physicist's answer: \A certain kind of representation.". This requires going through some reasonably basic physical ideas, such as the barest basics of quantum mechanics and special relativity. Contents 1. Quantum Mechanics in a Nutshell2 2. Symmetry7 3. Toward Particles 11 4. Special Relativity in a Nutshell 14 5. Spin 21 6. Particles in Relativistic Quantum Mechaniscs 25 0.1. What these notes are. This are higly informal notes on basic physics. Being a mathematician-in-training myself, I am afraid I am incapable of writing for any other audience. Thus these notes must fall into the unfortunate genre of \physics for math- ematicians", an idiosyncracy on the level of \music for the deaf" or \visual art for the blind" - surely possible in some fashion, but only after overcoming substantial technical obstacles, and even then likely to be accussed by the cognoscenti of \missing the point" of the original. And yet we beat on, boats against the current, . 0.2. How they came about. As usual, this write-up began its life in the form of a series of emails to my good friend Tom Gannon. Allow me to recount, only a tinge apocryphally, one major impetus for its existence: the 2020 New Year's party. Hosted at Tom's apartment, it featured a decent contingent of UT math department's grad student compartment. Among others in attendence were Ivan Tulli, a senior UT grad student working on mathematics inperceptably close to theoretical physics, and his wife Anabel, a genuine experimental physicist from another department, in town to visit her husband.
    [Show full text]
  • Chapter 11 the Relativistic Quantum Point Particle
    Chapter 11 The Relativistic Quantum Point Particle To prepare ourselves for quantizing the string, we study the light-cone gauge quantization of the relativistic point particle. We set up the quantum theory by requiring that the Heisenberg operators satisfy the classical equations of motion. We show that the quantum states of the relativistic point particle coincide with the one-particle states of the quantum scalar field. Moreover, the Schr¨odinger equation for the particle wavefunctions coincides with the classical scalar field equations. Finally, we set up light-cone gauge Lorentz generators. 11.1 Light-cone point particle In this section we study the classical relativistic point particle using the light-cone gauge. This is, in fact, a much easier task than the one we faced in Chapter 9, where we examined the classical relativistic string in the light- cone gauge. Our present discussion will allow us to face the complications of quantization in the simpler context of the particle. Many of the ideas needed to quantize the string are also needed to quantize the point particle. The action for the relativistic point particle was studied in Chapter 5. Let’s begin our analysis with the expression given in equation (5.2.4), where an arbitrary parameter τ is used to parameterize the motion of the particle: τf dxµ dxν S = −m −ηµν dτ . (11.1.1) τi dτ dτ 249 250 CHAPTER 11. RELATIVISTIC QUANTUM PARTICLE In writing the above action, we have set c =1.Wewill also set =1when appropriate. Finally, the time parameter τ will be dimensionless, just as it was for the relativistic string.
    [Show full text]
  • Neutron Star Equation of State Via Gravitational Wave Observations
    Neutron star equation of state via gravitational wave observations C Markakis1, J S Read2, M Shibata3, K Uryu¯ 4, J D E Creighton1, J L Friedman1, and B D Lackey1 1 Department of Physics, University of Wisconsin–Milwaukee, P.O. Box 413, Milwaukee, WI 53201, USA 2 Max-Planck-Institut fur¨ Gravitationsphysik, Albert-Einstein-Institut, Golm, Germany 3 Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan 4 Department of Physics, University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213, Japan Abstract. Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence. 1. Introduction In numerical simulations of the late inspiral and merger of binary neutron-star systems, one commonly specifies an equation of state for the matter, perform a numerical simulation and extract the gravitational waveforms produced in the inspiral.
    [Show full text]
  • What Is a Photon? Foundations of Quantum Field Theory
    What is a Photon? Foundations of Quantum Field Theory C. G. Torre June 16, 2018 2 What is a Photon? Foundations of Quantum Field Theory Version 1.0 Copyright c 2018. Charles Torre, Utah State University. PDF created June 16, 2018 Contents 1 Introduction 5 1.1 Why do we need this course? . 5 1.2 Why do we need quantum fields? . 5 1.3 Problems . 6 2 The Harmonic Oscillator 7 2.1 Classical mechanics: Lagrangian, Hamiltonian, and equations of motion . 7 2.2 Classical mechanics: coupled oscillations . 8 2.3 The postulates of quantum mechanics . 10 2.4 The quantum oscillator . 11 2.5 Energy spectrum . 12 2.6 Position, momentum, and their continuous spectra . 15 2.6.1 Position . 15 2.6.2 Momentum . 18 2.6.3 General formalism . 19 2.7 Time evolution . 20 2.8 Coherent States . 23 2.9 Problems . 24 3 Tensor Products and Identical Particles 27 3.1 Definition of the tensor product . 27 3.2 Observables and the tensor product . 31 3.3 Symmetric and antisymmetric tensors. Identical particles. 32 3.4 Symmetrization and anti-symmetrization for any number of particles . 35 3.5 Problems . 36 4 Fock Space 38 4.1 Definitions . 38 4.2 Occupation numbers. Creation and annihilation operators. 40 4.3 Observables. Field operators. 43 4.3.1 1-particle observables . 43 4.3.2 2-particle observables . 46 4.3.3 Field operators and wave functions . 47 4.4 Time evolution of the field operators . 49 4.5 General formalism . 51 3 4 CONTENTS 4.6 Relation to the Hilbert space of quantum normal modes .
    [Show full text]
  • Neutron Physics a Revision of I. Halpern's Notes on E. Fermi's Lectures in 1945
    , ‘.. iJNCLASSIFIED . x COMMISSION UNITED STATES ATOMIC ENERGY . 1 I~,., ,#AECD-2664 NEUTRON PHYSICS A Revision of I. Halpern’s Notes on E. Fermi’s Lectures in 1945 BY J. G. Beckerley October 16, 1951 [TIS Issuance Date] Atomic Energy Commission New York Operations : ‘t to TIC ;iiiii *=c; :LTechnical Information Service, Oak Ridge, Tennessee . _ .._ U,NCLASSlFIEB DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. l auaum3op leu!Spo alqel!ene waq aqi LLIOJJpa%IpoJd we sa6euq l S$anpOJd a6euy y.~o~$aala u! alq!6all! aq Aeur Umunaop !+!I.@JO suo!~od tfmmmsia Issuance of this document does not constitute authority for declassification of classified copies of the same or similar content and title and by the same author. PRINTEDINUSA PRICE 35 CENTS AEC,Oak Ridge,Tenn.,g-l-49--2500-A2327 Reprlnted,AEC,Oak Ridge,Tenn.,l.o-16-51--300~WI4541 a-934 PREFACE In the Fall of 1945 a course in Neutron Physics was given by Professor Fermi as part of the program of the Los Alamos University.
    [Show full text]
  • ELEMENTARY PARTICLES in PHYSICS 1 Elementary Particles in Physics S
    ELEMENTARY PARTICLES IN PHYSICS 1 Elementary Particles in Physics S. Gasiorowicz and P. Langacker Elementary-particle physics deals with the fundamental constituents of mat- ter and their interactions. In the past several decades an enormous amount of experimental information has been accumulated, and many patterns and sys- tematic features have been observed. Highly successful mathematical theories of the electromagnetic, weak, and strong interactions have been devised and tested. These theories, which are collectively known as the standard model, are almost certainly the correct description of Nature, to first approximation, down to a distance scale 1/1000th the size of the atomic nucleus. There are also spec- ulative but encouraging developments in the attempt to unify these interactions into a simple underlying framework, and even to incorporate quantum gravity in a parameter-free “theory of everything.” In this article we shall attempt to highlight the ways in which information has been organized, and to sketch the outlines of the standard model and its possible extensions. Classification of Particles The particles that have been identified in high-energy experiments fall into dis- tinct classes. There are the leptons (see Electron, Leptons, Neutrino, Muonium), 1 all of which have spin 2 . They may be charged or neutral. The charged lep- tons have electromagnetic as well as weak interactions; the neutral ones only interact weakly. There are three well-defined lepton pairs, the electron (e−) and − the electron neutrino (νe), the muon (µ ) and the muon neutrino (νµ), and the (much heavier) charged lepton, the tau (τ), and its tau neutrino (ντ ). These particles all have antiparticles, in accordance with the predictions of relativistic quantum mechanics (see CPT Theorem).
    [Show full text]
  • Arxiv:1908.06423V4 [Hep-Th] 4 Sep 2020 Dimensional Space
    QUANTUM MECHANICS OF PARTICLE ON A TORUS KNOT: CURVATURE AND TORSION EFFECTS APREPRINT Dripto Biswas Subir Ghosh School of Physical Sciences Physics and Applied Mathematics Unit National Institute of Science Education and Research Indian Statistical Institute, Kolkata Odisha, India West Bengal, India [email protected] [email protected] September 7, 2020 ABSTRACT Constraints play an important role in dynamical systems. However, the subtle effect of constraints in quantum mechanics is not very well studied. In the present work we concentrate on the quantum dynamics of a spin-less, point particle moving on a non-trivial torus knot. We explicitly take into account the role of curvature and torsion, generated by the constraints that keep the particle on the knot. We exploit the "Geometry Induced Potential (GIP) approach" to construct the Schrodinger equation for the dynamical system, obtaining thereby new results in terms of particle energy eigenvalues and eigenfunctions. We compare our results with existing literature that completely ignored the contributions of curvature and torsion. In particular, we explicitly show how the "knottedness" of the path influences the results. In the process we have revealed a (possibly un-noticed) "topological invariant". Keywords Torus Knot · Geometry-Induced Potential(GIP) · Curvature · Torsion · Winding Number · Hill Equation · Mathieu Equation 1 Introduction In recent times, theoretical development in quantum physics on curved low-dimensional spaces has attracted a lot attention mainly due to the improved expertise in synthesizing low-dimensional nanostructures with curved geometries [1–5]. The approach of De Witt [6] was to directly consider the quantum particle motion in curved n- arXiv:1908.06423v4 [hep-th] 4 Sep 2020 dimensional space.
    [Show full text]