The Trouble with Quantum Mechanics | by Steven Weinberg
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Unrestricted Immigration and the Foreign Dominance Of
Unrestricted Immigration and the Foreign Dominance of United States Nobel Prize Winners in Science: Irrefutable Data and Exemplary Family Narratives—Backup Data and Information Andrew A. Beveridge, Queens and Graduate Center CUNY and Social Explorer, Inc. Lynn Caporale, Strategic Scientific Advisor and Author The following slides were presented at the recent meeting of the American Association for the Advancement of Science. This project and paper is an outgrowth of that session, and will combine qualitative data on Nobel Prize Winners family histories along with analyses of the pattern of Nobel Winners. The first set of slides show some of the patterns so far found, and will be augmented for the formal paper. The second set of slides shows some examples of the Nobel families. The authors a developing a systematic data base of Nobel Winners (mainly US), their careers and their family histories. This turned out to be much more challenging than expected, since many winners do not emphasize their family origins in their own biographies or autobiographies or other commentary. Dr. Caporale has reached out to some laureates or their families to elicit that information. We plan to systematically compare the laureates to the population in the US at large, including immigrants and non‐immigrants at various periods. Outline of Presentation • A preliminary examination of the 609 Nobel Prize Winners, 291 of whom were at an American Institution when they received the Nobel in physics, chemistry or physiology and medicine • Will look at patterns of -
Path Integrals in Quantum Mechanics
Path Integrals in Quantum Mechanics Dennis V. Perepelitsa MIT Department of Physics 70 Amherst Ave. Cambridge, MA 02142 Abstract We present the path integral formulation of quantum mechanics and demon- strate its equivalence to the Schr¨odinger picture. We apply the method to the free particle and quantum harmonic oscillator, investigate the Euclidean path integral, and discuss other applications. 1 Introduction A fundamental question in quantum mechanics is how does the state of a particle evolve with time? That is, the determination the time-evolution ψ(t) of some initial | i state ψ(t ) . Quantum mechanics is fully predictive [3] in the sense that initial | 0 i conditions and knowledge of the potential occupied by the particle is enough to fully specify the state of the particle for all future times.1 In the early twentieth century, Erwin Schr¨odinger derived an equation specifies how the instantaneous change in the wavefunction d ψ(t) depends on the system dt | i inhabited by the state in the form of the Hamiltonian. In this formulation, the eigenstates of the Hamiltonian play an important role, since their time-evolution is easy to calculate (i.e. they are stationary). A well-established method of solution, after the entire eigenspectrum of Hˆ is known, is to decompose the initial state into this eigenbasis, apply time evolution to each and then reassemble the eigenstates. That is, 1In the analysis below, we consider only the position of a particle, and not any other quantum property such as spin. 2 D.V. Perepelitsa n=∞ ψ(t) = exp [ iE t/~] n ψ(t ) n (1) | i − n h | 0 i| i n=0 X This (Hamiltonian) formulation works in many cases. -
Steven Weinberg Cv Born
STEVEN WEINBERG CV BORN: May 3, 1933, in New York, N.Y. EDUCATION: Cornell University, 1950–1954 (A.B., 1954) Copenhagen Institute for Theoretical Physics, 1954–1955 Princeton University, 1955–1957 (Ph.D.,1957). HONORARY DEGREES: Harvard University, A.M., 1973 Knox College, D.Sc., 1978 University of Chicago, Sc.D., 1978 University of Rochester, Sc.D., l979 Yale University, Sc.D., 1979 City University of New York,Sc.D., 1980 Clark University, Sc.D., 1982 Dartmouth College, Sc.D., 1984 Weizmann Institute, Ph.D. Hon.Caus., 1985 Washington College, D.Litt., 1985 Columbia University, Sc.D., 1990 University of Salamanca, Sc.D., 1992 University of Padua, Ph.D. Hon.Caus., 1992 University of Barcelona, Sc.D., 1996 Bates College, Sc. D., 2002 McGill University, Sc. D., 2003 University of Waterloo, Sc. D., 2004 Renssalear Polytechnic Institue, Sc. D., 2016 Rockefeller University, Sc. D., 2017 PRESENT POSITION: Josey Regental Professor of Science, University of Texas, 1982– PAST POSITIONS: Columbia University, 1957–1959 Lawrence Radiation Laboratory, 1959–1960 University of California, Berkeley, 1960–1969 On leave, Imperial College, London, 1961–1962 Steven Weinberg 2 Became full professor, 1964 On leave, Harvard University, 1966–1967 On leave, Massachusetts Institute of Technology, 1967–1969 Massachusetts Institute of Technology, 1969–1973, Professor of Physics Harvard University, 1973–1983, Higgins Professor of Physics On leave 1976–1977, as Visiting Professor of Physics, Stanford University Smithsonian Astrophysical Observatory, 1973-1983, Senior -
Young Alumni Build on Early Success
OFARIZONASTATEUNIVERSITY Ahead of their time THEMAGAZINE Young alumni build on early success “It’s Time” for a new look for Sun Devil Athletics Coping with technological change Playwrights explore drama in the desert MAY 2011 | VOL. 14 NO. 4 ASU ALUMNI ASSOCIATION BOARD AND NATIONAL COUNCIL 2010–2011 OFFICERS CHAIR Chris Spinella ’83 B.S. CHAIR-ELECT George Diaz Jr. ’96 B.A., ’99 M.P.A. TREASURER President’s Letter Robert Boschee ’83 B.S., ’85 M.B.A. This month, we celebrated the achievements PAST CHAIR of the Class of 2011 at Spring Commencement. Bill Kavan ’92 B.A. This year’s graduating class is filled with PRESIDENT thousands of talented, accomplished students, many of whom have not only studied the top Christine Wilkinson ’66 B.A.E., ’76 Ph.D. challenges in their professions, but taken the first steps toward being part of the solution to BOARD OF DIRECTORS* those challenges. We also have welcomed back Barbara Clark ’84 M.Ed. the Class of 1961 whose members participated in Commencement and other Andy Hanshaw ’87 B.S. activities provided by the Alumni Association as part of Golden Reunion, the 50th anniversary of their graduation from ASU. This is such a special time as Barbara Hoffnagle ’83 M.S.E. we bring back alumni to the university to see what ASU looks like today, Ivan Johnson ’73 B.A., ’86 M.B.A. tour some of the new facilities, learn about new programs and share their Tara McCollum Plese ’78 B.A., ’84 M.P.A. fondest college memories. -
"Goodness Without Godness", with Professor Phil Zuckerman
The HSSB Secular Circular – March 2020 1 Newsletter of the Humanist Society of Santa Barbara www.SBHumanists.org MARCH 2020 Please join us for our March Speaker… How Foreign Policy Really Works: Diplomats’ Tricks of the Trade Hugh Neighbour spent four fascinating decades working around the globe as a U.S. diplomat and as a naval officer. Examine how diplomacy actually works in the real world. The talk will be followed by open discussion and a lively Q & A. Our Speaker: During his long career, Hugh Neighbour specialized in political and economic affairs, working on U.S. Foreign Service Officer (Retired) and Lecturer, Hugh Neighbour multilateral issues, including both arms control and human rights. Hugh's final diplomatic post was as Chief Arms Control Delegate for the U.S. at the OSCE in Vienna, responsible for conventional arms control across Europe, Central Asia, and North America. He was assigned to Germany when the Berlin Wall fell and Germany unified, to Bolivia when an uprising cut off food supplies for weeks, to Panama as General Noriega stole an election, and to Australia when the ANZUS treaty was fundamentally altered. He was stationed in London during the height of the Cold War, in Stockholm when non-aligned Sweden helped NATO intervene in Bosnia, and in the Fiji Islands where he ran U.S. relations with 8 island countries and territories. He was awarded the Secretary of State's Career Achievement Award. Prior to this, Hugh was a bridge watch officer in the U.S. Navy. After service at sea on a missile cruiser, he served ashore in the Middle East. -
Analysis of Nonlinear Dynamics in a Classical Transmon Circuit
Analysis of Nonlinear Dynamics in a Classical Transmon Circuit Sasu Tuohino B. Sc. Thesis Department of Physical Sciences Theoretical Physics University of Oulu 2017 Contents 1 Introduction2 2 Classical network theory4 2.1 From electromagnetic fields to circuit elements.........4 2.2 Generalized flux and charge....................6 2.3 Node variables as degrees of freedom...............7 3 Hamiltonians for electric circuits8 3.1 LC Circuit and DC voltage source................8 3.2 Cooper-Pair Box.......................... 10 3.2.1 Josephson junction.................... 10 3.2.2 Dynamics of the Cooper-pair box............. 11 3.3 Transmon qubit.......................... 12 3.3.1 Cavity resonator...................... 12 3.3.2 Shunt capacitance CB .................. 12 3.3.3 Transmon Lagrangian................... 13 3.3.4 Matrix notation in the Legendre transformation..... 14 3.3.5 Hamiltonian of transmon................. 15 4 Classical dynamics of transmon qubit 16 4.1 Equations of motion for transmon................ 16 4.1.1 Relations with voltages.................. 17 4.1.2 Shunt resistances..................... 17 4.1.3 Linearized Josephson inductance............. 18 4.1.4 Relation with currents................... 18 4.2 Control and read-out signals................... 18 4.2.1 Transmission line model.................. 18 4.2.2 Equations of motion for coupled transmission line.... 20 4.3 Quantum notation......................... 22 5 Numerical solutions for equations of motion 23 5.1 Design parameters of the transmon................ 23 5.2 Resonance shift at nonlinear regime............... 24 6 Conclusions 27 1 Abstract The focus of this thesis is on classical dynamics of a transmon qubit. First we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit. -
SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA
TOWARDS A UNIFIED THEORY - THREADS IN A TAPESTRY Nobel Lecture, 8 December, 1979 by SHELDON LEE GLASHOW Lyman Laboratory of Physics Harvard University Cambridge, Mass., USA INTRODUCTION In 1956, when I began doing theoretical physics, the study of elementary particles was like a patchwork quilt. Electrodynamics, weak interactions, and strong interactions were clearly separate disciplines, separately taught and separately studied. There was no coherent theory that described them all. Developments such as the observation of parity violation, the successes of quantum electrodynamics, the discovery of hadron resonances and the appearance of strangeness were well-defined parts of the picture, but they could not be easily fitted together. Things have changed. Today we have what has been called a “standard theory” of elementary particle physics in which strong, weak, and electro- magnetic interactions all arise from a local symmetry principle. It is, in a sense, a complete and apparently correct theory, offering a qualitative description of all particle phenomena and precise quantitative predictions in many instances. There is no experimental data that contradicts the theory. In principle, if not yet in practice, all experimental data can be expressed in terms of a small number of “fundamental” masses and cou- pling constants. The theory we now have is an integral work of art: the patchwork quilt has become a tapestry. Tapestries are made by many artisans working together. The contribu- tions of separate workers cannot be discerned in the completed work, and the loose and false threads have been covered over. So it is in our picture of particle physics. Part of the picture is the unification of weak and electromagnetic interactions and the prediction of neutral currents, now being celebrated by the award of the Nobel Prize. -
Path Integrals in Quantum Mechanics
Path Integrals in Quantum Mechanics Emma Wikberg Project work, 4p Department of Physics Stockholm University 23rd March 2006 Abstract The method of Path Integrals (PI’s) was developed by Richard Feynman in the 1940’s. It offers an alternate way to look at quantum mechanics (QM), which is equivalent to the Schrödinger formulation. As will be seen in this project work, many "elementary" problems are much more difficult to solve using path integrals than ordinary quantum mechanics. The benefits of path integrals tend to appear more clearly while using quantum field theory (QFT) and perturbation theory. However, one big advantage of Feynman’s formulation is a more intuitive way to interpret the basic equations than in ordinary quantum mechanics. Here we give a basic introduction to the path integral formulation, start- ing from the well known quantum mechanics as formulated by Schrödinger. We show that the two formulations are equivalent and discuss the quantum mechanical interpretations of the theory, as well as the classical limit. We also perform some explicit calculations by solving the free particle and the harmonic oscillator problems using path integrals. The energy eigenvalues of the harmonic oscillator is found by exploiting the connection between path integrals, statistical mechanics and imaginary time. Contents 1 Introduction and Outline 2 1.1 Introduction . 2 1.2 Outline . 2 2 Path Integrals from ordinary Quantum Mechanics 4 2.1 The Schrödinger equation and time evolution . 4 2.2 The propagator . 6 3 Equivalence to the Schrödinger Equation 8 3.1 From the Schrödinger equation to PI’s . 8 3.2 From PI’s to the Schrödinger equation . -
Quantum Mechanics
Quantum Mechanics Richard Fitzpatrick Professor of Physics The University of Texas at Austin Contents 1 Introduction 5 1.1 Intendedaudience................................ 5 1.2 MajorSources .................................. 5 1.3 AimofCourse .................................. 6 1.4 OutlineofCourse ................................ 6 2 Probability Theory 7 2.1 Introduction ................................... 7 2.2 WhatisProbability?.............................. 7 2.3 CombiningProbabilities. ... 7 2.4 Mean,Variance,andStandardDeviation . ..... 9 2.5 ContinuousProbabilityDistributions. ........ 11 3 Wave-Particle Duality 13 3.1 Introduction ................................... 13 3.2 Wavefunctions.................................. 13 3.3 PlaneWaves ................................... 14 3.4 RepresentationofWavesviaComplexFunctions . ....... 15 3.5 ClassicalLightWaves ............................. 18 3.6 PhotoelectricEffect ............................. 19 3.7 QuantumTheoryofLight. .. .. .. .. .. .. .. .. .. .. .. .. .. 21 3.8 ClassicalInterferenceofLightWaves . ...... 21 3.9 QuantumInterferenceofLight . 22 3.10 ClassicalParticles . .. .. .. .. .. .. .. .. .. .. .. .. .. .. 25 3.11 QuantumParticles............................... 25 3.12 WavePackets .................................. 26 2 QUANTUM MECHANICS 3.13 EvolutionofWavePackets . 29 3.14 Heisenberg’sUncertaintyPrinciple . ........ 32 3.15 Schr¨odinger’sEquation . 35 3.16 CollapseoftheWaveFunction . 36 4 Fundamentals of Quantum Mechanics 39 4.1 Introduction .................................. -
Nobel Prize for Physics, 1979
Nobel Prize for Physics, 1979 Abdus Sal am Physics' most prestigious accolade forces is a significant milestone in goes this year to Sheldon Glashow, the constant quest to describe as Abdus Salam and Steven Weinberg much as possible of the world for their work in elucidating the inter around us from a minimal set of actions of elementary particles, and initial ideas. in particular for the development of 'At first sight there may be little or the theory which unifies the electro no similarity between electromag magnetic and weak forces. netic effects and the phenomena This synthesis of two of the basic associated with weak interactions', forces of nature must be reckoned as wrote Sheldon Glashow in 1960. one of the crowning achievements 'Yet remarkable parallels emerge...' of a century which has already seen Both kinds of interactions affect the birth of both quantum mechanics leptons and hadrons; both appear to and relativity. be 'vector' interactions brought Electromagnetism and the weak about by the exchange of particles force might appear to have little to carrying unit spin and negative pari do with each other. Electromagne ty; both have their own universal tism is our everyday world — it holds coupling constant which governs the atoms together and produces light, strength of the interactions. while the weak force was for a long These vital clues led Glashow to time known only for the relatively propose an ambitious theory which obscure phenomenon of beta-decay attempted to unify the two forces. radioactivity. However there was one big difficul The successful unification of these ty, which Glashow admitted had to two apparently highly dissimilar be put to one side. -
Zero-Point Energy and Interstellar Travel by Josh Williams
;;;;;;;;;;;;;;;;;;;;;; itself comes from the conversion of electromagnetic Zero-Point Energy and radiation energy into electrical energy, or more speciÞcally, the conversion of an extremely high Interstellar Travel frequency bandwidth of the electromagnetic spectrum (beyond Gamma rays) now known as the zero-point by Josh Williams spectrum. ÒEre many generations pass, our machinery will be driven by power obtainable at any point in the universeÉ it is a mere question of time when men will succeed in attaching their machinery to the very wheel work of nature.Ó ÐNikola Tesla, 1892 Some call it the ultimate free lunch. Others call it absolutely useless. But as our world civilization is quickly coming upon a terrifying energy crisis with As you can see, the wavelengths from this part of little hope at the moment, radical new ideas of usable the spectrum are incredibly small, literally atomic and energy will be coming to the forefront and zero-point sub-atomic in size. And since the wavelength is so energy is one that is currently on its way. small, it follows that the frequency is quite high. The importance of this is that the intensity of the energy So, what the hell is it? derived for zero-point energy has been reported to be Zero-point energy is a type of energy that equal to the cube (the third power) of the frequency. exists in molecules and atoms even at near absolute So obviously, since weÕre already talking about zero temperatures (-273¡C or 0 K) in a vacuum. some pretty high frequencies with this portion of At even fractions of a Kelvin above absolute zero, the electromagnetic spectrum, weÕre talking about helium still remains a liquid, and this is said to be some really high energy intensities. -
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).