Review of Relativistic Quantum Mechanics Contents
Total Page:16
File Type:pdf, Size:1020Kb

Load more
Recommended publications
-
Motion and Time Study the Goals of Motion Study
Motion and Time Study The Goals of Motion Study • Improvement • Planning / Scheduling (Cost) •Safety Know How Long to Complete Task for • Scheduling (Sequencing) • Efficiency (Best Way) • Safety (Easiest Way) How Does a Job Incumbent Spend a Day • Value Added vs. Non-Value Added The General Strategy of IE to Reduce and Control Cost • Are people productive ALL of the time ? • Which parts of job are really necessary ? • Can the job be done EASIER, SAFER and FASTER ? • Is there a sense of employee involvement? Some Techniques of Industrial Engineering •Measure – Time and Motion Study – Work Sampling • Control – Work Standards (Best Practices) – Accounting – Labor Reporting • Improve – Small group activities Time Study • Observation –Stop Watch – Computer / Interactive • Engineering Labor Standards (Bad Idea) • Job Order / Labor reporting data History • Frederick Taylor (1900’s) Studied motions of iron workers – attempted to “mechanize” motions to maximize efficiency – including proper rest, ergonomics, etc. • Frank and Lillian Gilbreth used motion picture to study worker motions – developed 17 motions called “therbligs” that describe all possible work. •GET G •PUT P • GET WEIGHT GW • PUT WEIGHT PW •REGRASP R • APPLY PRESSURE A • EYE ACTION E • FOOT ACTION F • STEP S • BEND & ARISE B • CRANK C Time Study (Stopwatch Measurement) 1. List work elements 2. Discuss with worker 3. Measure with stopwatch (running VS reset) 4. Repeat for n Observations 5. Compute mean and std dev of work station time 6. Be aware of allowances/foreign element, etc Work Sampling • Determined what is done over typical day • Random Reporting • Periodic Reporting Learning Curve • For repetitive work, worker gains skill, knowledge of product/process, etc over time • Thus we expect output to increase over time as more units are produced over time to complete task decreases as more units are produced Traditional Learning Curve Actual Curve Change, Design, Process, etc Learning Curve • Usually define learning as a percentage reduction in the time it takes to make a unit. -
On the Reality of Quantum Collapse and the Emergence of Space-Time
Article On the Reality of Quantum Collapse and the Emergence of Space-Time Andreas Schlatter Burghaldeweg 2F, 5024 Küttigen, Switzerland; [email protected]; Tel.: +41-(0)-79-870-77-75 Received: 22 February 2019; Accepted: 22 March 2019; Published: 25 March 2019 Abstract: We present a model, in which quantum-collapse is supposed to be real as a result of breaking unitary symmetry, and in which we can define a notion of “becoming”. We show how empirical space-time can emerge in this model, if duration is measured by light-clocks. The model opens a possible bridge between Quantum Physics and Relativity Theory and offers a new perspective on some long-standing open questions, both within and between the two theories. Keywords: quantum measurement; quantum collapse; thermal time; Minkowski space; Einstein equations 1. Introduction For a hundred years or more, the two main theories in physics, Relativity Theory and Quantum Mechanics, have had tremendous success. Yet there are tensions within the respective theories and in their relationship to each other, which have escaped a satisfactory explanation until today. These tensions have also prevented a unified view of the two theories by a more fundamental theory. There are, of course, candidate-theories, but none has found universal acceptance so far [1]. There is a much older debate, which concerns the question of the true nature of time. Is reality a place, where time, as we experience it, is a mere fiction and where past, present and future all coexist? Is this the reason why so many laws of nature are symmetric in time? Or is there really some kind of “becoming”, where the present is real, the past irrevocably gone and the future not yet here? Admittedly, the latter view only finds a minority of adherents among today’s physicists, whereas philosophers are more balanced. -
1 the Principle of Wave–Particle Duality: an Overview
3 1 The Principle of Wave–Particle Duality: An Overview 1.1 Introduction In the year 1900, physics entered a period of deep crisis as a number of peculiar phenomena, for which no classical explanation was possible, began to appear one after the other, starting with the famous problem of blackbody radiation. By 1923, when the “dust had settled,” it became apparent that these peculiarities had a common explanation. They revealed a novel fundamental principle of nature that wascompletelyatoddswiththeframeworkofclassicalphysics:thecelebrated principle of wave–particle duality, which can be phrased as follows. The principle of wave–particle duality: All physical entities have a dual character; they are waves and particles at the same time. Everything we used to regard as being exclusively a wave has, at the same time, a corpuscular character, while everything we thought of as strictly a particle behaves also as a wave. The relations between these two classically irreconcilable points of view—particle versus wave—are , h, E = hf p = (1.1) or, equivalently, E h f = ,= . (1.2) h p In expressions (1.1) we start off with what we traditionally considered to be solely a wave—an electromagnetic (EM) wave, for example—and we associate its wave characteristics f and (frequency and wavelength) with the corpuscular charac- teristics E and p (energy and momentum) of the corresponding particle. Conversely, in expressions (1.2), we begin with what we once regarded as purely a particle—say, an electron—and we associate its corpuscular characteristics E and p with the wave characteristics f and of the corresponding wave. -
Relativistic Quantum Mechanics 1
Relativistic Quantum Mechanics 1 The aim of this chapter is to introduce a relativistic formalism which can be used to describe particles and their interactions. The emphasis 1.1 SpecialRelativity 1 is given to those elements of the formalism which can be carried on 1.2 One-particle states 7 to Relativistic Quantum Fields (RQF), which underpins the theoretical 1.3 The Klein–Gordon equation 9 framework of high energy particle physics. We begin with a brief summary of special relativity, concentrating on 1.4 The Diracequation 14 4-vectors and spinors. One-particle states and their Lorentz transforma- 1.5 Gaugesymmetry 30 tions follow, leading to the Klein–Gordon and the Dirac equations for Chaptersummary 36 probability amplitudes; i.e. Relativistic Quantum Mechanics (RQM). Readers who want to get to RQM quickly, without studying its foun- dation in special relativity can skip the first sections and start reading from the section 1.3. Intrinsic problems of RQM are discussed and a region of applicability of RQM is defined. Free particle wave functions are constructed and particle interactions are described using their probability currents. A gauge symmetry is introduced to derive a particle interaction with a classical gauge field. 1.1 Special Relativity Einstein’s special relativity is a necessary and fundamental part of any Albert Einstein 1879 - 1955 formalism of particle physics. We begin with its brief summary. For a full account, refer to specialized books, for example (1) or (2). The- ory oriented students with good mathematical background might want to consult books on groups and their representations, for example (3), followed by introductory books on RQM/RQF, for example (4). -
Newtonian Mechanics Is Most Straightforward in Its Formulation and Is Based on Newton’S Second Law
CLASSICAL MECHANICS D. A. Garanin September 30, 2015 1 Introduction Mechanics is part of physics studying motion of material bodies or conditions of their equilibrium. The latter is the subject of statics that is important in engineering. General properties of motion of bodies regardless of the source of motion (in particular, the role of constraints) belong to kinematics. Finally, motion caused by forces or interactions is the subject of dynamics, the biggest and most important part of mechanics. Concerning systems studied, mechanics can be divided into mechanics of material points, mechanics of rigid bodies, mechanics of elastic bodies, and mechanics of fluids: hydro- and aerodynamics. At the core of each of these areas of mechanics is the equation of motion, Newton's second law. Mechanics of material points is described by ordinary differential equations (ODE). One can distinguish between mechanics of one or few bodies and mechanics of many-body systems. Mechanics of rigid bodies is also described by ordinary differential equations, including positions and velocities of their centers and the angles defining their orientation. Mechanics of elastic bodies and fluids (that is, mechanics of continuum) is more compli- cated and described by partial differential equation. In many cases mechanics of continuum is coupled to thermodynamics, especially in aerodynamics. The subject of this course are systems described by ODE, including particles and rigid bodies. There are two limitations on classical mechanics. First, speeds of the objects should be much smaller than the speed of light, v c, otherwise it becomes relativistic mechanics. Second, the bodies should have a sufficiently large mass and/or kinetic energy. -
Motion and Forces Notes Key Speed • to Describe How Fast Something Is Traveling, You Have to Know Two Things About Its Motion
Motion and Forces Notes Key Speed • To describe how fast something is traveling, you have to know two things about its motion. • One is the distance it has traveled, or how far it has gone. • The other is how much time it took to travel that distance. Average Speed • To calculate average speed, divide the distance traveled by the time it takes to travel that distance. • Speed Equation Average speed (in m/s) = distance traveled (in m) divided by time (in s) it took to travel the distance s = d t • Because average speed is calculated by dividing distance by time, its units will always be a distance unit divided by a time unit. • For example, the average speed of a bicycle is usually given in meters per second. • Average speed is useful if you don't care about the details of the motion. • When your motion is speeding up and slowing down, it might be useful to know how fast you are going at a certain time. Instantaneous Speed • The instantaneous speed is the speed of an object at any instant of time. Constant Speed • Sometimes an object is moving such that its instantaneous speed doesn’t change. • When the instantaneous speed doesn't change, an object is moving with constant speed. • The average speed and the instantaneous speed are the same. Calculating Distance • If an object is moving with constant speed, then the distance it travels over any period of time can be calculated using the equation for average speed. • When both sides of this equation are multiplied by the time, you have the equation for distance. -
Relativistic Solutions 11.1 Free Particle Motion
Physics 411 Lecture 11 Relativistic Solutions Lecture 11 Physics 411 Classical Mechanics II September 21st, 2007 With our relativistic equations of motion, we can study the solutions for x(t) under a variety of different forces. The hallmark of a relativistic solution, as compared with a classical one, is the bound on velocity for massive particles. We shall see this in the context of a constant force, a spring force, and a one-dimensional Coulomb force. This tour of potential interactions leads us to the question of what types of force are even allowed { we will see changes in the dynamics of a particle, but what about the relativistic viability of the mechanism causing the forces? A real spring, for example, would break long before a mass on the end of it was accelerated to speeds nearing c. So we are thinking of the spring force, for example, as an approximation to a well in a more realistic potential. To the extent that effective potentials are uninteresting (or even allowed in general), we really only have one classical, relativistic force { the Lorentz force of electrodynamics. 11.1 Free Particle Motion For the equations of motion in proper time parametrization, we have x¨µ = 0 −! xµ = Aµ τ + Bµ: (11.1) Suppose we rewrite this solution in terms of t { inverting the x0 = c t equation with the initial conditions that t(τ = 0) = 0, we have c t τ = (11.2) A0 and then the rest of the equations read: c t c t c t x = A1 + B1 y = A2 + B2 z = A3 + B3; (11.3) A0 A0 A0 1 of 8 11.2. -
Gravity, Orbital Motion, and Relativity
Gravity, Orbital Motion,& Relativity Early Astronomy Early Times • As far as we know, humans have always been interested in the motions of objects in the sky. • Not only did early humans navigate by means of the sky, but the motions of objects in the sky predicted the changing of the seasons, etc. • There were many early attempts both to describe and explain the motions of stars and planets in the sky. • All were unsatisfactory, for one reason or another. The Earth-Centered Universe • A geocentric (Earth-centered) solar system is often credited to Ptolemy, an Alexandrian Greek, although the idea is very old. • Ptolemy’s solar system could be made to fit the observational data pretty well, but only by becoming very complicated. Copernicus’ Solar System • The Polish cleric Copernicus proposed a heliocentric (Sun centered) solar system in the 1500’s. Objections to Copernicus How could Earth be moving at enormous speeds when we don’t feel it? . (Copernicus didn’t know about inertia.) Why can’t we detect Earth’s motion against the background stars (stellar parallax)? Copernicus’ model did not fit the observational data very well. Galileo • Galileo Galilei - February15,1564 – January 8, 1642 • Galileo became convinced that Copernicus was correct by observations of the Sun, Venus, and the moons of Jupiter using the newly-invented telescope. • Perhaps Galileo was motivated to understand inertia by his desire to understand and defend Copernicus’ ideas. Orbital Motion Tycho and Kepler • In the late 1500’s, a Danish nobleman named Tycho Brahe set out to make the most accurate measurements of planetary motions to date, in order to validate his own ideas of planetary motion. -
The Von Neumann/Stapp Approach
4. The von Neumann/Stapp Approach Von Neumann quantum theory is a formulation in which the entire physical universe, including the bodies and brains of the conscious human participant/observers, is represented in the basic quantum state, which is called the state of the universe. The state of a subsystem, such as a brain, is formed by averaging (tracing) this basic state over all variables other than those that describe the state of that subsystem. The dynamics involves three processes. Process 1 is the choice on the part of the experimenter about how he will act. This choice is sometimes called “The Heisenberg Choice,” because Heisenberg emphasized strongly its crucial role in quantum dynamics. At the pragmatic level it is a “free choice,” because it is controlled, at least in practice, by the conscious intentions of the experimenter/participant, and neither the Copenhagen nor von Neumann formulations provide any description of the causal origins of this choice, apart from the mental intentions of the human agent. Each intentional action involves an effort that is intended to result in a conceived experiential feedback, which can be an immediate confirmation of the success of the action, or a delayed monitoring the experiential consequences of the action. Process 2 is the quantum analog of the equations of motion of classical physics. As in classical physics, these equations of motion are local (i.e., all interactions are between immediate neighbors) and deterministic. They are obtained from the classical equations by a certain quantization procedure, and are reduced to the classical equations by taking the classical approximation of setting to zero the value of Planck’s constant everywhere it appears. -
New Varying Speed of Light Theories
New varying speed of light theories Jo˜ao Magueijo The Blackett Laboratory,Imperial College of Science, Technology and Medicine South Kensington, London SW7 2BZ, UK ABSTRACT We review recent work on the possibility of a varying speed of light (VSL). We start by discussing the physical meaning of a varying c, dispelling the myth that the constancy of c is a matter of logical consistency. We then summarize the main VSL mechanisms proposed so far: hard breaking of Lorentz invariance; bimetric theories (where the speeds of gravity and light are not the same); locally Lorentz invariant VSL theories; theories exhibiting a color dependent speed of light; varying c induced by extra dimensions (e.g. in the brane-world scenario); and field theories where VSL results from vacuum polarization or CPT violation. We show how VSL scenarios may solve the cosmological problems usually tackled by inflation, and also how they may produce a scale-invariant spectrum of Gaussian fluctuations, capable of explaining the WMAP data. We then review the connection between VSL and theories of quantum gravity, showing how “doubly special” relativity has emerged as a VSL effective model of quantum space-time, with observational implications for ultra high energy cosmic rays and gamma ray bursts. Some recent work on the physics of “black” holes and other compact objects in VSL theories is also described, highlighting phenomena associated with spatial (as opposed to temporal) variations in c. Finally we describe the observational status of the theory. The evidence is slim – redshift dependence in alpha, ultra high energy cosmic rays, and (to a much lesser extent) the acceleration of the universe and the WMAP data. -
MITOCW | L0.8 Introduction to Nuclear and Particle Physics: Relativistic Kinematics
MITOCW | L0.8 Introduction to Nuclear and Particle Physics: Relativistic Kinematics MARKUS Now back to 8.701. So in this section, we'll talk about relativistic kinematics. Let me start by saying that one of KLUTE: my favorite classes here at MIT is a class called 8.20, special relativity, where we teach students about special relativity, of course, but Einstein and paradoxes. And it's one of my favorite classes. And in their class, there's a component on particle physics, which has to do with just using relativistic kinematics in order to understand how to create antimatter, how to collide beams, how we can analyze decays. And in this introductory section, we're going to do a very similar thing. I trust that you all had some sort of class introduction of special relativity, some of you maybe general relativity. What we want to do here is review this content very briefly, but then more use it in a number of examples. So in particle physics, nuclear physics, we often deal particles who will travel close to the speed of light. The photon travels at the speed of light. We typically define the velocity as v/c in natural units. Beta is the velocity, gamma is defined by 1 over square root 1 minus the velocity squared. Beta is always smaller or equal to 1, smaller for massive particle. And gamma is always equal or greater than 1. The total energy of a particle with 0 mass-- sorry, with non-zero mass, is then given by gamma times m c squared. -
On Relativistic Theory of Spinning and Deformable Particles
On relativistic theory of spinning and deformable particles A.N. Tarakanov ∗ Minsk State High Radiotechnical College Independence Avenue 62, 220005, Minsk, Belarus Abstract A model of relativistic extended particle is considered with the help of gener- alization of space-time interval. Ten additional dimensions are connected with six rotational and four deformational degrees of freedom. An obtained 14-dimensional space is assumed to be an embedding one both for usual space-time and for 10- dimensional internal space of rotational and deformational variables. To describe such an internal space relativistic generalizations of inertia and deformation tensors are given. Independence of internal and external motions from each other gives rise to splitting the equation of motion and some conditions for 14-dimensional metric. Using the 14-dimensional ideology makes possible to assign a unique proper time for all points of extended object, if the metric will be degenerate. Properties of an internal space are discussed in details in the case of absence of spatial rotations. arXiv:hep-th/0703159v1 17 Mar 2007 1 Introduction More and more attention is spared to relativistic description of extended objects, which could serve a basis for construction of dynamics of interacting particles. Necessity of introduction extended objects to elementary particle theory is out of doubt. Therefore, since H.A.Lorentz attempts to introduce particles of finite size were undertaken. However a relativization of extended body is found prove to be a difficult problem as at once there was a contradiction to Einstein’s relativity principle. Even for simplest model of absolutely rigid body [1] it is impossible for all points of a body to attribute the same proper time.