# Generally Covariant Quantum Mechanics

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 15 Generally Covariant Quantum Mechanics by Myron W. Evans, Alpha Foundation s Institutute for Advance Study (AIAS). Dedicated to the Late Jean-Pierre Vigier Abstract In order to make quantum mechanics compatible with general relativity the Heisenberg uncertainty principle is given a generally covariant (or objective) and causal interpretation. The fundamental conjugate variables are shown to be quantities such as momentum density, angular momentum density and energy density in general relativity instead of quantities such as momentum, angular momentum and energy in special relativity. The generally covariant interpretation of quantum mechanics given in this paper agrees with the repeatable and reproducible experimental data of Croca et al. and of Afshar, data which show that the conventional Heisenberg uncertainty principle is qualitatively incorrect, and with it all the arguments of the Copenhagen school throughout the twentieth century. The correctly objective interpretation of quantum mechanics is given by the deterministic school of Einstein, de Broglie, Vigier and others. This is a direct result of the Evans unified field theory. Key words: Evans unified field theory; generally covariant Heisenberg equation and Heisenberg uncertainty principle. 163

2 15.1. INTRODUCTION 15.1 Introduction Generally covariant quantum mechanics does not exist in the standard model because general relativity is causal and objective, the Copenhagen interpretation of quantum mechanics is acausal and subjective. This is the central issue of the great twentieth century debate in physics between the Copenhagen and deterministic schools of thought, an issue which is resolved conclusively in favor of the deterministic school by the Evans unified field theory [1] [19]. At the root of the debate is the Heisenberg equation of motion [20], which in its simplest form is a rewriting of the operator equivalence condition of quantum mechanics: Eq.(15.1) is an equation of special relativity where: ( ) En p µ = c, p p µ = i µ. (15.1) (15.2) is the energy momentum four vector, and: ( ) 1 µ = c t,. (15.3) Here En denotes energy, c is the vacuum speed of light, p is the linear momentum, is the reduced Planck constant, and the partial four derivative µ is defined in terms of the time derivative and the operator in Eq.(15.3). In Section 15.2 the operator equivalence (15.1) is rewritten as the Heisenberg equation of motion [20]. The Heisenberg uncertainty principle is a direct mathematical consequence of the Heisenberg equation and therefore is a direct mathematical consequence of Eq.(15.1). However, recent reproducible and repeatable experimental data [21] [23] show that the Heisenberg uncertainty principle is violated completely in several independent ways. This means that the principle as it stands is completely incorrect, i.e. by many orders of magnitude. For example in the various experiments of Croca et al. [21] the principle is incorrect by nine orders of magnitude even at moderate microscope resolution. As the resolution is increased it becomes qualitatively wrong, i.e. the conjugate variable of position and momentum appear to commute precisely within experimental precision. The uncertainty principle states that if the conjugate variables are for example the position x and the component p x of linear momentum then [20]: δxδp x 2. (15.4) This means that the δx and δp x variables cannot commute and the conventional Copenhagen interpretation is that they cannot be simultaneously observable [20] and cannot be simultaneously knowable. This subjective assertion violates causality and general relativity (i.e. objective physics) and has led to endless confusion for students. The experimental results of Croca et al [21] show that: δxδp x = (15.5) 164

3 CHAPTER 15. GENERALLY COVARIANT QUANTUM MECHANICS at moderate microscope resolution. As the latter is increased, the experimental result is: δxδp x 0 (15.6) in direct experimental contradiction of the uncertainty principle (15.4). In the independent series of experiments by Afshar [22], carried out at Harvard and elsewhere, the photon and electromagnetic wave are shown to be simultaneously observable, indicating independently that the position and momentum or time and energy conjugate variables commute precisely to within experimental precision. In a third series of independent experiments [23], on two dimensional materials near absolute zero, the Heisenberg uncertainty principle again predicts diametrically the incorrect experimental result to within instrumental precision. Each type of experiment [21] [23] is independently reproducible and repeatable to high precision. In Section 15.3 this major crisis for the standard model is resolved straightforwardly through the use of the appropriate densities of conjugate variables in general relativity. The experimentally well tested Eq.(15.1) is retained, but the fundamental conjugate variables are carefully redefined within the generally covariant Evans unified field theory, which derives generally covariant quantum mechanics from Cartans differential geometry [1] [19] for all radiated and matter fields. The result is a generally covariant quantum mechanics in agreement with the most recent experiments [21] [23] and philosophically compatible with the causal and objective Evans unified field theory. The latter denies subjectivity and acausality in natural philosophy A Simple Derivation Of The Heisenberg Equation Of Motion In its simplest form the Heisenberg equation of motion [20] is: [x, p x ] ψ = i ψ (15.7) where ψ is the wave-function. Eq.(15.7) means that the commutator: operates on the wave-function. From Eq.(15.1): [x, p x ] = xp x p x x (15.8) p x = i x (15.9) and so p x becomes a differential operator acting on ψ. The position x is interpreted as a simple multiple, i.e. x multiplies anything that follows it. Using 165

4 15.3. THE GENERALLY COVARIANT HEISENBERG EQUATION the Leibnitz Theorem and these operator rules it follows that: [x, p x ] ψ = (xp x p x x) ψ = x (p x ψ) p x (xψ) = x (p x ψ) (p x x) ψ x (p x ψ) = (p x x) ψ ( = i x ) ψ x = i ψ (15.10) and it is seen that the Heisenberg equation is a rewriting of Eq.(15.1), a component of which is Eq.(15.9). Using standard methods [20] we obtain the famous Heisenberg uncertainty principle δxδp x 2 (15.11) from Eq.(15.9) and thus from Eq.(15.1), the famous wave particle duality of de Broglie. This derivation is given to show that the uncertainty principle, which has dominated thought in physics for nearly a century, is another statement of the de Broglie wave particle duality. The subjective and acausal interpretations inherent in the Heisenberg uncertainty principle were rejected immediately by Einstein and his followers, as is well known, and later also rejected by de Broglie and his follower Vigier. These are the acknowledged masters of the deterministic school of physics in the twentieth century. The data [21] [23] now show with pristine clarity that the deterministic school is right, the Copenhagen school is wrong. It is important to realize that the deterministic school accepts quantum mechanics, i.e accepts Eq.(15.1) but rejects the INTERPRETATION of Eq.(15.7) by the Copenhagen school. The ensuing debate became protracted due to a lack of a unified field theory and a lack of experimental data. Both are now available The Generally Covariant Heisenberg Equation Neither school discovered the reason why Eq.(15.11) is so wildly incorrect. With the emergence of the Evans unified field theory (2003 to present), more than a hundred years after special relativity ( ), we now know why the experiments [21] [23] give the results they do. The error in the Copenhagen school s philosophy is the obvious one - the subjective reliance on conjugate variables which are not correctly objective (generally covariant). They are not DENSITIES, as required by the fundamentals of general relativity and the Evans unified field theory. In order to develop a correctly objective quantum mechanics the momentum p x has to be replaced by a momentum density p x and the angular 166

5 CHAPTER 15. GENERALLY COVARIANT QUANTUM MECHANICS momentum by an angular momentum density. fundamental law of general relativity [1] [19] is: The reason is that the R = kt (15.12) where T is the scalar valued canonical energy-momentum density, R is a well defined scalar curvature, and k is Einstein s constant. In the rest frame T reduces to the mass density of an elementary particle: and within a factor c 2 this is the rest energy density: Here V 0 is the Evans rest volume T m V 0 (15.13) En 0 = mc2 V 0. (15.14) V 0 = 2 k mc 2 (15.15) where m is the elementary particle mass. Define the experimental momentum density for a given instrument by: p x = p x V and define the fundamental angular momentum or action density by: (15.16) = V 0. (15.17) Here V is a macroscopic volume defined by the apparatus being used, or the volume occupied by the momentum component p x. The quantum is the fundamental density of the reduced Planck constant: = mc2 k (15.18) i.e. the rest energy divided by the product of and k. Eq(15.18) means that the quantum of action occupies the Evans rest volume V 0. For any particle, including the six quarks, the photon and the neutrinos, the graviton and the gravitino. This deduction follows from the special relativistic limit of the Evans wave equation for one particle is [1] [19]: In general relativity therefore Eq.(15.9) becomes: kt = km V 0 = m2 c 2 2. (15.19) p x = i x (15.20) 167

6 15.3. THE GENERALLY COVARIANT HEISENBERG EQUATION i.e.: p x ψ = i ψ x. (15.21) Eq.(15.9), which is precisely verified experimentally in quantum mechanics, is therefore the same as: p x = i V 0 V (15.22) x which is a special case of the fundamental wave particle duality in general relativity: p µ = i V 0 V µ. (15.23) The generally covariant Heisenberg equation is therefore: [x, p x ] = i V 0 V (15.24) and the fundamental conjugate variables of generally covariant quantum mechanics are x and p x. The fundamental quantum is. Experimentally for a macroscopic volume V : V 0 V (15.25) and so which implies [x, p x ] 0 (15.26) δx 0, δp x 0 (15.27) is quite possible experimentally. Therefore what is being observed experimentally in the Croca and Afshar experiments is p x and not p x, and and not. This deduction means that a particle coexists with its matter wave, as inferred by de Broglie. For electromagnetism this coexistence has been clearly observed by Afshar [22] in modified Young experiments which are precise, reproducible and repeatable. The fundamental conjugate variables are therefore position and momentum density, or time and energy density, and not position and momentum, or time and energy as in the conventional theory [20] and as in the Copenhagen interpretation. The wave function is always the tetrad, and this is always defined causally and objectively by Cartans differential geometry [1] [19]. There is no uncertainty or acausality in geometry and none in physics. The fundamental wave equation of generally covariant quantum mechanics is the Evans wave equation [1] [19]: ( + kt ) q a µ = 0 (15.28) which reduces to all other wave equations of physics, and thence to other equations of physics in well defined limits. 168

7 CHAPTER 15. GENERALLY COVARIANT QUANTUM MECHANICS Acknowledgments The British Government is thanked for a Civil List Pension. Franklin Amador is thanked for meticulous typesetting. Sean MacLachlan and Bob Gray are thanked for setting up the websites and The Ted Annis Foundation, Craddock Inc, Prof. John B. Hart and several others are thanked for funding. The staff of AIAS and many others are thanked for many interesting discussions, 2003 to present. 169

8 15.3. THE GENERALLY COVARIANT HEISENBERG EQUATION 170

9 Bibliography [1] M. W. Evans, Found. Phys. Lett., 16, 367, 507 (2003). [2] M. W. Evans, Found. Phys. Lett., 17, 25, 149, 267, 301, 393, 433, 535, 663 (2004). [3] M. W. Evans, Found. Phys. Lett., 18, 259 (2005). [4] M. W. Evans, Generally Covariant Unified Field Theory: the Geometrization of Physics (in press 2005, preprints on and [5] L. Felker, The Evans Equations of Unified Field Theory (in press 2005, preprints on and [6] M. W. Evans, The Objective Laws of Classical Electrodynamics, the Effect of Gravitation on Electromagnetism, J. New Energy Special Issue (2005, preprint on and [7] M. W. Evans, First and Second Order Aharonov Bohm Effects in the Evans Unified Field Theory, J. New Energy Special Issue (2005, preprint on and [8] M. W. Evans, The Spinning of Spacetime as Seen in the Inverse Faraday Effect, J. New Energy Special Issue (2005, preprint on and [9] M. W. Evans, On the Origin of Polarization and Magnetization, J. New Energy Special Issue (2005, preprint on and [10] M. W. Evans, Explanation of the Eddington Experiment in the Evans Unified Field Theory, J. New Energy Special Issue (2005, preprint on and [11] M. W. Evans, The Coulomb and Ampère Maxwell Laws in the Schwarzschild Metric: A Classical Calculation of the Eddington Effect from the Evans Field Theory, J. New Energy Special Issue (2005, preprint on and 171

10 BIBLIOGRAPHY [12] M. W. Evans, Generally Covariant Heisenberg Equation from the Evans Unified Field Theory, J. New Energy Special Issue (2005, preprint on and [13] M. W. Evans, Metric Compatibility and the Tetrad Postulate, J. New Energy Special Issue (2005, preprint on and [14] M. W. Evans. Derivation of the Evans Lemma and Wave Equation from the First Cartan Structure Equation, J. New Energy Special Issue (2005, preprint on and [15] M. W. Evans, Proof of the Evans Lemma from the Tetrad Postulate, J. New Energy Special Issue (2005, preprint on and [16] M. W. Evans, Self-Consistent Derivation of the Evans Lemma and Application to the Generally Covariant Dirac Equation, J. New Energy Special Issue (2005, preprint on and [17] M. W. Evans, Quark Gluon Model in the Evans Unified Field Theory, J. New Energy Special Issue (2005, preprint on and [18] M. W. Evans, The Origin of Intrinsic Spin and the Pauli Exclusion Principle in the Evans Unified Field Theory, J. New Energy Special Issue (2005, preprint on and [19] M. W. Evans, On the Origin of Dark Matter as Spacetime Torsion, J. New Energy Special Issue (2005, preprint on and [20] P. W. Atkins, Molecular Quantum Mechanics (Oxford Univ Press, 2nd ed., 1983). [21] J. R. Croca, Towards a Non-Linear Quantum Physics (World Scientific, 2003). [22] M. Chown, New Scientist, 183, 30 (2004). [23] B. Schechter, New Scientist, pp.38 ff (2004). 172

### Orbital Dynamics in Terms of Spacetime Angular Momentum

Chapter 4 Orbital Dynamics in Terms of Spacetime Angular Momentum by Myron W. Evans 1 and H. Eckardt 2 Alpha Institute for Advanced Study (AIAS) (www.aias.us, www.atomicprecision.com) Abstract Planar orbital

### The force equation of quantum mechanics.

The force equation of quantum mechanics. by M. W. Evans, Civil List and Guild of Graduates, University of Wales, (www.webarchive.org.uk, www.aias.us,, www.atomicprecision.com, www.upitec.org, www.et3m.net)

### MASTER OF SCIENCE IN PHYSICS MASTER OF SCIENCES IN PHYSICS (MS PHYS) (LIST OF COURSES BY SEMESTER, THESIS OPTION)

MASTER OF SCIENCE IN PHYSICS Admission Requirements 1. Possession of a BS degree from a reputable institution or, for non-physics majors, a GPA of 2.5 or better in at least 15 units in the following advanced

### Einstein, Cartan and Evans Start of a New Age in Physics?

Albert Einstein Elie Cartan Myron W. Evans 1 Einstein, Cartan and Evans Start of a New Age in Physics? Horst Eckardt, Munich, Germany Laurence G. Felker, Reno, Nevada, USA [original German article to be

### Theory of electrons and positrons

P AUL A. M. DIRAC Theory of electrons and positrons Nobel Lecture, December 12, 1933 Matter has been found by experimental physicists to be made up of small particles of various kinds, the particles of

### Chemical shift, fine and hyperfine structure in RFR spectroscopy

Chemical shift, fine and hyperfine structure in RFR spectroscopy 48 Journal of Foundations of Physics and Chemistry, 0, vol (5) 48 49 Chemical shift, fine and hyperfine structure in RFR spectroscopy MW

### DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS

DO PHYSICS ONLINE FROM QUANTA TO QUARKS QUANTUM (WAVE) MECHANICS Quantum Mechanics or wave mechanics is the best mathematical theory used today to describe and predict the behaviour of particles and waves.

### PHYS 1624 University Physics I. PHYS 2644 University Physics II

PHYS 1624 Physics I An introduction to mechanics, heat, and wave motion. This is a calculus- based course for Scientists and Engineers. 4 hours (3 lecture/3 lab) Prerequisites: Credit for MATH 2413 (Calculus

### Second postulate of Quantum mechanics: If a system is in a quantum state represented by a wavefunction ψ, then 2

. POSTULATES OF QUANTUM MECHANICS. Introducing the state function Quantum physicists are interested in all kinds of physical systems (photons, conduction electrons in metals and semiconductors, atoms,

### 1D 3D 1D 3D. is called eigenstate or state function. When an operator act on a state, it can be written as

Chapter 3 (Lecture 4-5) Postulates of Quantum Mechanics Now we turn to an application of the preceding material, and move into the foundations of quantum mechanics. Quantum mechanics is based on a series

### Quantum Mechanics: mysteries and solutions

Quantum Mechanics: mysteries and solutions ANGELO BASSI Department of Theoretical Physics, University of Trieste, Italy and INFN - Trieste Angelo Bassi 1 Quantization of light: Planck s hypothesis (1900)

### THE MEANING OF THE FINE STRUCTURE CONSTANT

THE MEANING OF THE FINE STRUCTURE CONSTANT Robert L. Oldershaw Amherst College Amherst, MA 01002 USA rloldershaw@amherst.edu Abstract: A possible explanation is offered for the longstanding mystery surrounding

### Three Pictures of Quantum Mechanics. Thomas R. Shafer April 17, 2009

Three Pictures of Quantum Mechanics Thomas R. Shafer April 17, 2009 Outline of the Talk Brief review of (or introduction to) quantum mechanics. 3 different viewpoints on calculation. Schrödinger, Heisenberg,

### Introduction to quantum mechanics

Introduction to quantum mechanics Lecture 3 MTX9100 Nanomaterjalid OUTLINE -What is electron particle or wave? - How large is a potential well? -What happens at nanoscale? What is inside? Matter Molecule

### SIMPLE CLASSICAL EXPLANATION OF PLANETARY PRECESSION WITH THREE DIMENSIONAL ORBIT THEORY: THOMAS PRECESSION THEORY. M. W. Evans and H.

-I ~ SIMPLE CLASSICAL EXPLANATION OF PLANETARY PRECESSION WITH THREE DIMENSIONAL ORBIT THEORY: THOMAS PRECESSION THEORY by M. W. Evans and H. Eckardt, Civil List, AlAS and UPITEC (www.webarchive.org.uk,

### 1 Lecture 3: Operators in Quantum Mechanics

1 Lecture 3: Operators in Quantum Mechanics 1.1 Basic notions of operator algebra. In the previous lectures we have met operators: ˆx and ˆp = i h they are called fundamental operators. Many operators

### 1 Classical mechanics vs. quantum mechanics

1 Classical mechanics vs. quantum mechanics What is quantum mechanics and what does it do? In very general terms, the basic problem that both classical Newtonian mechanics and quantum mechanics seek to

### - develop a theory that describes the wave properties of particles correctly

Quantum Mechanics Bohr's model: BUT: In 1925-26: by 1930s: - one of the first ones to use idea of matter waves to solve a problem - gives good explanation of spectrum of single electron atoms, like hydrogen

### Does Quantum Mechanics Make Sense? Size

Does Quantum Mechanics Make Sense? Some relatively simple concepts show why the answer is yes. Size Classical Mechanics Quantum Mechanics Relative Absolute What does relative vs. absolute size mean? Why

### Unamended Quantum Mechanics Rigorously Implies Awareness Is Not Based in the Physical Brain

Unamended Quantum Mechanics Rigorously Implies Awareness Is Not Based in the Physical Brain Casey Blood, PhD Professor Emeritus of Physics, Rutgers University www.quantummechanicsandreality.com CaseyBlood@gmail.com

### The Electronic Structures of Atoms Electromagnetic Radiation

The Electronic Structures of Atoms Electromagnetic Radiation The wavelength of electromagnetic radiation has the symbol λ. Wavelength is the distance from the top (crest) of one wave to the top of the

### Physics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives

Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring

### Losing energy in classical, relativistic and quantum mechanics

Losing energy in classical, relativistic and quantum mechanics David Atkinson ABSTRACT A Zenonian supertask involving an infinite number of colliding balls is considered, under the restriction that the

### An Introduction to Quantum Cryptography

An Introduction to Quantum Cryptography J Robert Buchanan Millersville University of Pennsylvania email: Bob.Buchanan@millersville.edu An Introduction to Quantum Cryptography p.1 Acknowledgments Quantum

### Introduction: what is quantum field theory?

Introduction: what is quantum field theory? Asaf Pe er 1 January 13, 2015 This part of the course is based on Ref. [1] 1. Relativistic quantum mechanics By the mid 1920 s, the basics of quantum mechanics

### Review of the Variational Principles in Different Fields of Physics

International Conference on Mechanics and Ballistics VIII Okunev s Readings 25-28 June 2013. St. Petersburg, Russia Review of the Variational Principles in Different Fields of Physics Terekhovich Vladislav

### Lecture 2. Observables

Lecture 2 Observables 13 14 LECTURE 2. OBSERVABLES 2.1 Observing observables We have seen at the end of the previous lecture that each dynamical variable is associated to a linear operator Ô, and its expectation

### Special Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN

Special Relativity and Electromagnetism Yannis PAPAPHILIPPOU CERN United States Particle Accelerator School, University of California - Santa Cruz, Santa Rosa, CA 14 th 18 th January 2008 1 Outline Notions

### - the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε

Average Particle Energy in an Ideal Gas - the total energy of the system is found by summing up (integrating) over all particles n(ε) at different energies ε - with the integral - we find - note: - the

### Quantum Mechanics I Physics 325. Importance of Hydrogen Atom

Quantum Mechanics I Physics 35 Atomic spectra and Atom Models Importance of Hydrogen Atom Hydrogen is the simplest atom The quantum numbers used to characterize the allowed states of hydrogen can also

### 2. Spin Chemistry and the Vector Model

2. Spin Chemistry and the Vector Model The story of magnetic resonance spectroscopy and intersystem crossing is essentially a choreography of the twisting motion which causes reorientation or rephasing

### PX408: Relativistic Quantum Mechanics

January 2016 PX408: Relativistic Quantum Mechanics Tim Gershon (T.J.Gershon@warwick.ac.uk) Handout 1: Revision & Notation Relativistic quantum mechanics, as its name implies, can be thought of as the bringing

### λν = c λ ν Electromagnetic spectrum classification of light based on the values of λ and ν

Quantum Theory and Atomic Structure Nuclear atom small, heavy, positive nucleus surrounded by a negative electron cloud Electronic structure arrangement of the electrons around the nucleus Classical mechanics

### On the Linkage between Planck s Quantum and Maxwell s Equations

The Finnish Society for Natural Philosophy 25 Years K.V. Laurikainen Honorary Symposium 2013 On the Linkage between Planck s Quantum and Maxwell s Equations Tuomo Suntola Physics Foundations Society E-mail:

### Particle Physics. Michaelmas Term 2009 Prof Mark Thomson. Handout 9 : The Weak Interaction and V-A Prof. M.A. Thomson Michaelmas

Particle Physics Michaelmas Term 2009 Prof Mark Thomson Handout 9 : The Weak Interaction and V-A Prof. M.A. Thomson Michaelmas 2009 284 Parity The parity operator performs spatial inversion through the

### DO WE REALLY UNDERSTAND QUANTUM MECHANICS?

DO WE REALLY UNDERSTAND QUANTUM MECHANICS? COMPRENONS-NOUS VRAIMENT LA MECANIQUE QUANTIQUE? VARIOUS INTERPRETATIONS OF QUANTUM MECHANICS IHES, 29 janvier 2015 Franck Laloë, LKB, ENS Paris 1 INTRODUCTION

### Chapter 18: The Structure of the Atom

Chapter 18: The Structure of the Atom 1. For most elements, an atom has A. no neutrons in the nucleus. B. more protons than electrons. C. less neutrons than electrons. D. just as many electrons as protons.

### Chapter 16. The Hubble Expansion

Chapter 16 The Hubble Expansion The observational characteristics of the Universe coupled with theoretical interpretation to be discussed further in subsequent chapters, allow us to formulate a standard

### arxiv:quant-ph/0404128v1 22 Apr 2004

How to teach Quantum Mechanics arxiv:quant-ph/0404128v1 22 Apr 2004 Oliver Passon Fachbereich Physik, University of Wuppertal Postfach 100 127, 42097 Wuppertal, Germany E-mail: Oliver.Passon@cern.ch In

### Hermitian Operators An important property of operators is suggested by considering the Hamiltonian for the particle in a box: d 2 dx 2 (1)

CHAPTER 4 PRINCIPLES OF QUANTUM MECHANICS In this Chapter we will continue to develop the mathematical formalism of quantum mechanics, using heuristic arguments as necessary. This will lead to a system

### White Dwarf Properties and the Degenerate Electron Gas

White Dwarf Properties and the Degenerate Electron Gas Nicholas Rowell April 10, 2008 Contents 1 Introduction 2 1.1 Discovery....................................... 2 1.2 Survey Techniques..................................

### The Quantum Harmonic Oscillator Stephen Webb

The Quantum Harmonic Oscillator Stephen Webb The Importance of the Harmonic Oscillator The quantum harmonic oscillator holds a unique importance in quantum mechanics, as it is both one of the few problems

### Till now, almost all attention has been focussed on discussing the state of a quantum system.

Chapter 13 Observables and Measurements in Quantum Mechanics Till now, almost all attention has been focussed on discussing the state of a quantum system. As we have seen, this is most succinctly done

### Assessment Plan for Learning Outcomes for BA/BS in Physics

Department of Physics and Astronomy Goals and Learning Outcomes 1. Students know basic physics principles [BS, BA, MS] 1.1 Students can demonstrate an understanding of Newton s laws 1.2 Students can demonstrate

### Special Theory of Relativity

June 1, 2010 1 1 J.D.Jackson, Classical Electrodynamics, 3rd Edition, Chapter 11 Introduction Einstein s theory of special relativity is based on the assumption (which might be a deep-rooted superstition

### Concepts in Theoretical Physics

Concepts in Theoretical Physics Lecture 6: Particle Physics David Tong e 2 The Structure of Things 4πc 1 137 e d ν u Four fundamental particles Repeated twice! va, 9608085, 9902033 Four fundamental forces

### STRING THEORY: Past, Present, and Future

STRING THEORY: Past, Present, and Future John H. Schwarz Simons Center March 25, 2014 1 OUTLINE I) Early History and Basic Concepts II) String Theory for Unification III) Superstring Revolutions IV) Remaining

### Basic Principles of Experimental Design. Basic Principles. Control. Theory and Scientific Judgment. Positivism. Not Identifying the Real Cause

1 Basic Principles of Experimental Design Basic Principles Cause and Effect: the cause must precede the effect in time. X Y (Sufficient) Z X Y We must control Z or include it. X Y (Necessary) Treatment

### Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014

Where is Fundamental Physics Heading? Nathan Seiberg IAS Apr. 30, 2014 Disclaimer We do not know what will be discovered. This is the reason we perform experiments. This is the reason scientific research

### Physics - programme subject in programmes for specialization in general studies

Physics - programme subject in programmes for specialization in Dette er en oversettelse av den fastsatte læreplanteksten. Læreplanen er fastsatt på Bokmål Laid down as a regulation by the Norwegian Directorate

### Physics 53. Wave Motion 1

Physics 53 Wave Motion 1 It's just a job. Grass grows, waves pound the sand, I beat people up. Muhammad Ali Overview To transport energy, momentum or angular momentum from one place to another, one can

### Chapter 22 The Hamiltonian and Lagrangian densities. from my book: Understanding Relativistic Quantum Field Theory. Hans de Vries

Chapter 22 The Hamiltonian and Lagrangian densities from my book: Understanding Relativistic Quantum Field Theory Hans de Vries January 2, 2009 2 Chapter Contents 22 The Hamiltonian and Lagrangian densities

### The Early History of Quantum Mechanics

Chapter 2 The Early History of Quantum Mechanics In the early years of the twentieth century, Max Planck, Albert Einstein, Louis de Broglie, Neils Bohr, Werner Heisenberg, Erwin Schrödinger, Max Born,

### Wave Function, ψ. Chapter 28 Atomic Physics. The Heisenberg Uncertainty Principle. Line Spectrum

Wave Function, ψ Chapter 28 Atomic Physics The Hydrogen Atom The Bohr Model Electron Waves in the Atom The value of Ψ 2 for a particular object at a certain place and time is proportional to the probability

### Chapter 1: Introduction to Quantum Physics

Chapter 1: Introduction to Quantum Physics Luis M. Molina Departamento de Física Teórica, Atómica y Óptica Quantum Physics Luis M. Molina (FTAO) Chapter 1: Introduction to Quantum Physics Quantum Physics

### A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant

A Theory for the Cosmological Constant and its Explanation of the Gravitational Constant H.M.Mok Radiation Health Unit, 3/F., Saiwanho Health Centre, Hong Kong SAR Govt, 8 Tai Hong St., Saiwanho, Hong

### From Einstein to Klein-Gordon Quantum Mechanics and Relativity

From Einstein to Klein-Gordon Quantum Mechanics and Relativity Aline Ribeiro Department of Mathematics University of Toronto March 24, 2002 Abstract We study the development from Einstein s relativistic

### It Must Be Beautiful: Great Equations of Modern Science CONTENTS The Planck-Einstein Equation for the Energy of a Quantum by Graham Farmelo E = mc 2

It Must Be Beautiful: Great Equations of Modern Science CONTENTS The Planck-Einstein Equation for the Energy of a Quantum by Graham Farmelo E = mc 2 by Peter Galison The Einstein Equation of General Relativity

### 1 Scalars, Vectors and Tensors

DEPARTMENT OF PHYSICS INDIAN INSTITUTE OF TECHNOLOGY, MADRAS PH350 Classical Physics Handout 1 8.8.2009 1 Scalars, Vectors and Tensors In physics, we are interested in obtaining laws (in the form of mathematical

### How Fundamental is the Curvature of Spacetime? A Solar System Test. Abstract

Submitted to the Gravity Research Foundation s 2006 Essay Contest How Fundamental is the Curvature of Spacetime? A Solar System Test Robert J. Nemiroff Abstract Are some paths and interactions immune to

### Topic 1. Atomic Structure and Periodic Properties

Topic 1 1-1 Atomic Structure and Periodic Properties Atomic Structure 1-2 History Rutherford s experiments Bohr model > Interpretation of hydrogen atom spectra Wave - particle duality Wave mechanics Heisenberg

### AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity

AP Chemistry A. Allan Chapter 7 Notes - Atomic Structure and Periodicity 7.1 Electromagnetic Radiation A. Types of EM Radiation (wavelengths in meters) 10-1 10-10 10-8 4 to 7x10-7 10-4 10-1 10 10 4 gamma

### PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA

PHYSICS FOUNDATIONS SOCIETY THE DYNAMIC UNIVERSE TOWARD A UNIFIED PICTURE OF PHYSICAL REALITY TUOMO SUNTOLA Published by PHYSICS FOUNDATIONS SOCIETY Espoo, Finland www.physicsfoundations.org Printed by

### Time dependence in quantum mechanics Notes on Quantum Mechanics

Time dependence in quantum mechanics Notes on Quantum Mechanics http://quantum.bu.edu/notes/quantummechanics/timedependence.pdf Last updated Thursday, November 20, 2003 13:22:37-05:00 Copyright 2003 Dan

### Derivation of the relativistic momentum and relativistic equation of motion from Newton s second law and Minkowskian space-time geometry

Apeiron, Vol. 15, No. 3, July 2008 206 Derivation of the relativistic momentum and relativistic equation of motion from Newton s second law and Minkowskian space-time geometry Krzysztof Rȩbilas Zak lad

### Commentary on Sub-Quantum Physics

David L. Bergman 1 Sub-Quantum Physics Commentary on Sub-Quantum Physics David L. Bergman Common Sense Science P.O. Box 1013 Kennesaw, GA 30144 USA INTRODUCTION According to Alan McCone, Jr., the objectives

### 3-9 EPR and Bell s theorem. EPR Bohm s version. S x S y S z V H 45

1 3-9 EPR and Bell s theorem EPR Bohm s version S x S y S z n P(n) n n P(0) 0 0 V H 45 P(45) D S D P(0) H V 2 ( ) Neumann EPR n P(n) EPR PP(n) n EPR ( ) 2 5 2 3 But even at this stage there is essentially

### CHAPTER 16: Quantum Mechanics and the Hydrogen Atom

CHAPTER 16: Quantum Mechanics and the Hydrogen Atom Waves and Light Paradoxes in Classical Physics Planck, Einstein, and Bohr Waves, Particles, and the Schrödinger equation The Hydrogen Atom Questions

### Investigation of the Equilibrium Speed Distribution of Relativistic Particles

I. Introduction Investigation of the Equilibrium Speed Distribution of Relativistic Pavlos Apostolidis Supervisor: Prof. Ian Ford Condensed Matter & Material Physics Dept. of Physics & Astronomy, UCL June-July

### BIG IDEAS. 1D Momentum. Electric Circuits Kinematics allows us to predict, describe, and analyze an object s motion.

Area of Learning: SCIENCE Physics Grade 11 Ministry of Education BIG IDEAS 1D Kinematics 1D Dynamics 1D Momentum Energy Electric Circuits Kinematics allows us to predict, describe, and analyze an object

### The integrating factor method (Sect. 2.1).

The integrating factor method (Sect. 2.1). Overview of differential equations. Linear Ordinary Differential Equations. The integrating factor method. Constant coefficients. The Initial Value Problem. Variable

### On principles of repulsive gravity: the Elementary Process Theory. M. Cabbolet (VUB) WAG2015

On principles of repulsive gravity: the Elementary Process Theory M. Cabbolet (VUB) WAG2015 overview acronyms: EPT: Elementary Process Theory GR: General Relativity WEP: Weak Equivalence Principle QM:

### People s Physics book

The Big Idea Quantum Mechanics, discovered early in the 20th century, completely shook the way physicists think. Quantum Mechanics is the description of how the universe works on the very small scale.

### Journal of Engineering Science and Technology Review 2 (1) (2009) 76-81. Lecture Note

Journal of Engineering Science and Technology Review 2 (1) (2009) 76-81 Lecture Note JOURNAL OF Engineering Science and Technology Review www.jestr.org Time of flight and range of the motion of a projectile

### Chemistry 417! 1! Fall Chapter 2 Notes

Chemistry 417! 1! Fall 2012 Chapter 2 Notes September 3, 2012! Chapter 2, up to shielding 1. Atomic Structure in broad terms a. nucleus and electron cloud b. nomenclature, so we may communicate c. Carbon-12

### Time-Space Models in Science and Art. Paolo Manzelli pmanzelli@gmail.com ; www.egocreanet.it ; www.wbabin.net; www.edscuola.it/lre.

Time-Space Models in Science and Art. Paolo Manzelli pmanzelli@gmail.com ; www.egocreanet.it ; www.wbabin.net; www.edscuola.it/lre.html In the Classical Mechanics model of space- time, the role of time

### Gauge theories and the standard model of elementary particle physics

Gauge theories and the standard model of elementary particle physics Mark Hamilton 21st July 2014 1 / 35 Table of contents 1 The standard model 2 3 2 / 35 The standard model The standard model is the most

### Relativistic Electromagnetism

Chapter 8 Relativistic Electromagnetism In which it is shown that electricity and magnetism can no more be separated than space and time. 8.1 Magnetism from Electricity Our starting point is the electric

### Roman Pasechnik LU, THEP Group We must be able to understand even those things which are impossible to imagine of Lev Landau

The Physical Vacuum: Where Particle Physics Meets Cosmology Roman Pasechnik LU, THEP Group We must be able to understand even those things which are impossible to imagine of Lev Landau The greatest challenge

Nuclear Fusion and Radiation Lecture 2 (Meetings 3 & 4) Eugenio Schuster schuster@lehigh.edu Mechanical Engineering and Mechanics Lehigh University Nuclear Fusion and Radiation p. 1/40 Modern Physics Concepts

### DOCTOR OF PHILOSOPHY IN PHYSICS

DOCTOR OF PHILOSOPHY IN PHYSICS The Doctor of Philosophy in Physics program is designed to provide students with advanced graduate training in physics, which will prepare them for scientific careers in

### Units, Physical Quantities and Vectors

Chapter 1 Units, Physical Quantities and Vectors 1.1 Nature of physics Mathematics. Math is the language we use to discuss science (physics, chemistry, biology, geology, engineering, etc.) Not all of the

### The Evolution of the Atom

The Evolution of the Atom 1808: Dalton s model of the atom was the billiard ball model. He thought the atom was a solid, indivisible sphere. Atoms of each element were identical in mass and their properties.

### What does Quantum Mechanics tell us about the universe?

Fedora GNU/Linux; L A TEX 2ǫ; xfig What does Quantum Mechanics tell us about the universe? Mark Alford Washington University Saint Louis, USA More properly: What do experiments tell us about the universe?

### 1. INTRODUCTION A. Matter, space and some questions of substance Matter, which occurs in an infinite number of forms, appears on Earth in its three

1. INTRODUCTION A. Matter, space and some questions of substance Matter, which occurs in an infinite number of forms, appears on Earth in its three basic states: solid, liquid and gaseous. It seems to

### Open Letter to Prof. Andrew George, University of Denver, Dept of Physics, Colorado, 80208 USA.

Open Letter to Prof. Andrew George, University of Denver, Dept of Physics, Colorado, 80208 USA. Ref. Einstein s Sep 1905 derivation predicts that, When body emits Light Energy, its Mass must also Increase.

### Evaluation of Quantitative Data (errors/statistical analysis/propagation of error)

Evaluation of Quantitative Data (errors/statistical analysis/propagation of error) 1. INTRODUCTION Laboratory work in chemistry can be divided into the general categories of qualitative studies and quantitative

### What are Scalar Waves?

What are Scalar Waves? Horst. Eckardt A.I.A.S. and UPITEC (www.aias.us, www.atomicprecision.com, www.upitec.org) January 2, 2012 Abstract There is a wide confusion on what are scalar waves in serious and

### THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS

Bulg. J. Phys. 29 (2002 97 108 THE DOUBLE SLIT INTERFERENCE OF THE PHOTON-SOLITONS P. KAMENOV, B. SLAVOV Faculty of Physics, University of Sofia, 1126 Sofia, Bulgaria Abstract. It is shown that a solitary

### Matter Waves Understanding Matter. Particle-Wave Duality

Matter Waves Exactly what is an electron? Albert Einstein was puzzled about matter: You know, it would be sufficient to understand the electron. The consensus on the dual nature of electrons is much like

### Mathematics Course 111: Algebra I Part IV: Vector Spaces

Mathematics Course 111: Algebra I Part IV: Vector Spaces D. R. Wilkins Academic Year 1996-7 9 Vector Spaces A vector space over some field K is an algebraic structure consisting of a set V on which are

### The Essence of Gravitational Waves and Energy

The Essence of Gravitational Waves and Energy F. I. Cooperstock Department of Physics and Astronomy University of Victoria P.O. Box 3055, Victoria, B.C. V8W 3P6 (Canada) March 26, 2015 Abstract We discuss

### Discovery of the Higgs boson at the Large Hadron Collider

Discovery of the Higgs boson at the Large Hadron Collider HEP101-9 March 25, 2013 Al Goshaw 1 The Higgs What? 2 Outline 1. Some history: From electromagnetism to the weak interaction and the Higgs boson

### Nmv 2 V P 1 3 P 2 3 V. PV 2 3 Ne kin. 1. Kinetic Energy - Energy of Motion. 1.1 Kinetic theory of gases

Molecular Energies *********************************************************** Molecular Energies ********************************************************** Newtonian mechanics accurately describes the

### waves. A.2.3 Discuss the modes of vibration of strings and air in open and in closed

IB Physics Parts A and D A1 The eye and sight A.1.1 Describe the basic structure of the human eye. A.1.2 State and explain the process of depth of vision and accommodation. A.1.3 State that the retina

### Chapter 13. Rotating Black Holes

Chapter 13 Rotating Black Holes The Schwarzschild solution, which is appropriate outside a spherical, non-spinning mass distribution, was discovered in 1916. It was not until 1963 that a solution corresponding

### Atomic Structure: Chapter Problems

Atomic Structure: Chapter Problems Bohr Model Class Work 1. Describe the nuclear model of the atom. 2. Explain the problems with the nuclear model of the atom. 3. According to Niels Bohr, what does n stand

### The Paradigm of Projectile Motion and its Consequences for Special Relativity. Making Sense of Physics

The Paradigm of Projectile Motion and its Consequences for Special Relativity. Making Sense of Physics Paul A. Klevgard, Ph.D. Sandia National Laboratory, Ret. pklevgard@gmail.com Abstract The classical