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Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz
FUNDAMENTALS OF PHYSICS – Vol. I - Quantum Mechanical Laws - Bogdan Mielnik and Oscar Rosas-Ruiz QUANTUM MECHANICAL LAWS Bogdan Mielnik and Oscar Rosas-Ortiz Departamento de Física, Centro de Investigación y de Estudios Avanzados, México Keywords: Indeterminism, Quantum Observables, Probabilistic Interpretation, Schrödinger’s cat, Quantum Control, Entangled States, Einstein-Podolski-Rosen Paradox, Canonical Quantization, Bell Inequalities, Path integral, Quantum Cryptography, Quantum Teleportation, Quantum Computing. Contents: 1. Introduction 2. Black body radiation: the lateral problem becomes fundamental. 3. The discovery of photons 4. Compton’s effect: collisions confirm the existence of photons 5. Atoms: the contradictions of the planetary model 6. The mystery of the allowed energy levels 7. Luis de Broglie: particles or waves? 8. Schrödinger’s wave mechanics: wave vibrations explain the energy levels 9. The statistical interpretation 10. The Schrödinger’s picture of quantum theory 11. The uncertainty principle: instrumental and mathematical aspects. 12. Typical states and spectra 13. Unitary evolution 14. Canonical quantization: scientific or magic algorithm? 15. The mixed states 16. Quantum control: how to manipulate the particle? 17. Measurement theory and its conceptual consequences 18. Interpretational polemics and paradoxes 19. Entangled states 20. Dirac’s theory of the electron as the square root of the Klein-Gordon law 21. Feynman: the interference of virtual histories 22. Locality problems 23. The idea UNESCOof quantum computing and future – perspectives EOLSS 24. Open questions Glossary Bibliography Biographical SketchesSAMPLE CHAPTERS Summary The present day quantum laws unify simple empirical facts and fundamental principles describing the behavior of micro-systems. A parallel but different component is the symbolic language adequate to express the ‘logic’ of quantum phenomena. -
Albert Einstein - Wikipedia, the Free Encyclopedia Page 1 of 27
Albert Einstein - Wikipedia, the free encyclopedia Page 1 of 27 Albert Einstein From Wikipedia, the free encyclopedia Albert Einstein ( /ælbərt a nsta n/; Albert Einstein German: [albt a nʃta n] ( listen); 14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics.[2] He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect". [3] The latter was pivotal in establishing quantum theory within physics. Near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led to the development of his special theory of relativity. He Albert Einstein in 1921 realized, however, that the principle of relativity could also be extended to gravitational fields, and with his Born 14 March 1879 subsequent theory of gravitation in 1916, he published Ulm, Kingdom of Württemberg, a paper on the general theory of relativity. He German Empire continued to deal with problems of statistical Died mechanics and quantum theory, which led to his 18 April 1955 (aged 76) explanations of particle theory and the motion of Princeton, New Jersey, United States molecules. He also investigated the thermal properties Residence Germany, Italy, Switzerland, United of light which laid the foundation of the photon theory States of light. In 1917, Einstein applied the general theory of relativity to model the structure of the universe as a Ethnicity Jewish [4] whole. -
1 Introduction
Phosphine-catalysed reductive coupling of Dihalophosphanes Jan-Erik Siewert,[a] André Schumann[a] and Christian Hering-Junghans*[a] [a] M.Sc. Jan-Erik Siewert, Dr. André Schumann, Dr. Chirstian Hering-Junghans Leibniz Institute of Catalysis e.V. Rostock (LIKAT) Albert-Einstein-Straße 29a, 18059 Rostock, Germany E-Mail: [email protected] Abstract Classically, tetraorgano diphosphanes have been synthesized through Wurtz-type reductive coupling of halophosphanes R2PX or more recently, through the dehydrocoupling of phosphines R2PH. Catalytic variants of the dehydrocoupling reaction have been reported but are limited to R2PH compounds. Using PEt3 as a catalyst, we now show that TipPBr2 (Tip = 2,4,6-iPr3C6H2) is selectively coupled to give the dibromodiphosphane (TipPBr)2 (1), a compound not accessible using classic Mg reduction. Surprisingly, when using DipPBr2 (Dip = 2,6-iPr3C6H3) in the PEt3-catalysed reductive coupling the diphosphene (PDip) 2 (2) with a P=P double was formed selectively. In benzene solutions (PDip)2 has a half life-time of ca. 28 days and can be utilized with NHCs to access NHC-phosphinidene adducts. Control experiments show that [BrPEt3]Br is a potential oxidation product in the catalytic cycle, which can be then debrominated by using Zn dust as sacrificial reductant. 1 Introduction The formation of element-element bonds in main group chemistry is still dominated by classic stoichiometric salt metathesis and reductive coupling reactions. Only in S1 recent years, catalytic protocols for the dehydrocoupling of main group (p-block) substrates to species with homonuclear (E−E) or heteronuclear (E−E’) bonds have emerged.1-3 Catalysis with earth-abundant metals, in particular Zr, Fe and Ni,4 has been shown to be a viable alternative to using rather expensive systems based on Rh,5-7 Ir7- 10 and Ru.11 Using main-group species to facilitate the homo- or heterocoupling of p- block elements has also been in the focus of current research. -
Introducing Quantum and Statistical Physics in the Footsteps of Einstein: a Proposal †
universe Article Introducing Quantum and Statistical Physics in the Footsteps of Einstein: A Proposal † Marco Di Mauro 1,*,‡ , Salvatore Esposito 2,‡ and Adele Naddeo 2,‡ 1 Dipartimento di Matematica, Universitá di Salerno, Via Giovanni Paolo II, 84084 Fisciano, Italy 2 INFN Sezione di Napoli, Via Cinthia, 80126 Naples, Italy; [email protected] (S.E.); [email protected] (A.N.) * Correspondence: [email protected] † This paper is an extended version from the proceeding paper: Di Mauro, M.; Esposito, S.; Naddeo, A. Introducing Quantum and Statistical Physics in the Footsteps of Einstein: A Proposal. In Proceedings of the 1st Electronic Conference on Universe, online, 22–28 February 2021. ‡ These authors contributed equally to this work. Abstract: Introducing some fundamental concepts of quantum physics to high school students, and to their teachers, is a timely challenge. In this paper we describe ongoing research, in which a teaching–learning sequence for teaching quantum physics, whose inspiration comes from some of the fundamental papers about the quantum theory of radiation by Albert Einstein, is being developed. The reason for this choice goes back essentially to the fact that the roots of many subtle physical concepts, namely quanta, wave–particle duality and probability, were introduced for the first time in one of these papers, hence their study may represent a useful intermediate step towards tackling the final incarnation of these concepts in the full theory of quantum mechanics. An extended discussion of some elementary tools of statistical physics, mainly Boltzmann’s formula for entropy and statistical distributions, which are necessary but may be unfamiliar to the students, is included. -
Simplifying Einstein's Thought Experiments
Simplifying Einstein’s Thought Experiments Edward G. Lake Independent Researcher June 11, 2018 [email protected] Abstract: Einstein’s “Gedanken” experiments (thought experiments) - particularly his train-embankment thought experiments - were apparently intended to explain Special Relativity logically and in layman’s terms, but they were written in an incredibly convoluted way, which seems to have resulted in them being misinterpreted by many physicists. This is the simplified logic of Einstein’s key thought experiments. Key words: Light; train; embankment; speed of light; relativity. I. What is a “Thought Experiment”? A thought experiment (or in German: “Gedankenexperiment”) is a scientific experiment which is conducted entirely in one’s mind. It is different from a “fantasy” in that the experiment must obey all the rules of physics, and its key components and procedures have to be entirely logical. However, instead of using equipment that has not yet been constructed, you are imagining doing a scientific experiment using existing objects and events, such as moving trains, railroad embankments, boxcars, laboratories, dropped stones, the flashes of light from lightning bolts, and lighting flash simulators. Einstein’s train-embankment experiments, for example, involve a train (presumably a steam-powered train since Einstein devised the thought experiments around 1916 and earlier) that travels at about thirty or forty percent of the speed of light. That is certainly not possible, but the fact that a train is being imagined to travel at that speed is doesn’t affect the experiment. The experiment is not really about trains (or embankments), it is about what a human observer would see as happening from any type of vehicle traveling at those speeds, and what another observer would see from a stationary location as the vehicle passes close by. -
Einstein, Mileva Maric
ffirs.qrk 5/13/04 7:34 AM Page i Einstein A to Z Karen C. Fox Aries Keck John Wiley & Sons, Inc. ffirs.qrk 5/13/04 7:34 AM Page ii For Mykl and Noah Copyright © 2004 by Karen C. Fox and Aries Keck. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008. Limit of Liability/Disclaimer of Warranty: While the publisher and the author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. -
"ENTWURF" FIELD EQUATIONS to the EINSTEIN TENSOR II: November 1915 Until March 1916
1 FROM THE BERLIN "ENTWURF" FIELD EQUATIONS TO THE EINSTEIN TENSOR II: November 1915 until March 1916 Galina Weinstein Visitor Scholar, Center for Einstein Studies, Philosophy Department, Boston University January 25, 2012 I discuss Einstein's path-breaking November 1915 General Relativity papers. I show that Einstein's field equations of November 25, 1915 with an additional term on the right hand side involving the trace of the energy-momentum tensor appear to have sprung from his first November 1915 paper: the November 4, 1915 equations. Second paper among three papers. 1 Introduction: David Hilbert Enters the Game, the priority dispute in a nutshell According to Stachel Einstein's Odyssey to general covariance during November 1915 went through two stages:1 1) Sometime in October 1915 Einstein dropped the Einstein-Grossman "Entwurf" theory. During October 1915 Einstein realized that the key to the solution lays in equations (14) and (17) of page 1041 of his 1914 review article "The Formal Foundation of the General Theory of Relativity", and adopted the determinant in equation (14), 1 as a postulate.2 This led him to general covariance. Starting on November 4 Einstein gradually expanded the range of the covariance of his field equations. 2) Between November 4 and November 11 Einstein realized that he did not need this postulate and he adopted it as a coordinate condition to simplify the field equations. Einstein was able to write the field equations of gravitation in a general covariant form. In the November 11 field equations the trace of the energy-momentum tensor vanishes. Between November 18 and November 25 Einstein found that he could write the field equations with an additional term on the right hand side of the field equations involving the trace of the energy-momentum tensor, which now need not vanish. -
General Relativity: Gravitation As Geometry and the Machian Programme
Physics Before and After Einstein 93 M. Mamone Capria (Ed.) IOS Press, 2005 © 2005 The authors Chapter 5 General Relativity: Gravitation as Geometry and the Machian Programme Marco Mamone Capria To put it in another way, if only a relative meaning can be attached to the concept of velocity, ought we nevertheless to persevere in treating acceleration as an absolute concept? Albert Einstein, 1934 The path that led to the birth of general relativity is one of the most fascinating sequences of events in the whole history of theoretical physics. It was a tortuous path, to be sure, not without a fair amount of wandering and misunderstanding. The outcome was a theory with a curious destiny. On one hand it elicited the admiration of generations of theoretical physicists and provided the ground for several observational programs in astronomy and astrophysics up to the present day. On the other hand, the theory was judged inadequate by its very creator, who worked to the end of his life to devise a radical improvement of it, which eventually he did not achieve to his own satisfaction. The very name of the theory contains a degree of ambiguity: ‘general relativity’ can be read as a shortening of either ‘general theory of relativity – meaning a generalization of the previous theory of relativity – or ‘theory of general relativity – meaning something more specific, i.e. a generalization of the principle of relativity. The latter is what Einstein had in mind. In fact his primary aim was to generalize the principle of relativity which he had introduced in his 1905 theory, the validity of which was restricted to inertial reference frames. -
Physical Principles in Revealing the Working Mechanisms of Brain
BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI Publicat de Universitatea Tehnică „Gheorghe Asachi” din Iaşi Volumul 66 (70), Numărul 3, 2020 Secţia MATEMATICĂ. MECANICĂ TEORETICĂ. FIZICĂ PHYSICAL PRINCIPLES IN REVEALING THE WORKING MECHANISMS OF BRAIN. PART III BY NICOLAE MAZILU1,2, 13707 Dauphin Dr, NE, Canton, OH 44721, USA 2Timotei Cipariu, #1, Focșani, Vrancea, 600004, Romania Received: July 1, 2020 Accepted for publication: September 17, 2020 Abstract. The living brain is physically modeled as a universe, analgous to the existing physical model of the universe. While in the physical model the gravitation prevails, in the brain universe the electricity prevails, but the mathematical description we provide is essentially the same in both cases. What is imperiously necessary in this approach is, first, a metric description of matter, then, of course, the physical interpretation of this description. These issues were treated, in their essentials, in the previous two instalments of the work. The object of the present episode of the work is a classical space image of the matter, as described from a „central‟ point of view. This image is connected with the concept of memory, for which we uphold the idea that in classical physics it has a well-known counterpart: the inertia. It is accomplished based on a general approach of the motion, suggested by generalizing Kepler‟s classical model of motion. Keywords: inertia; memory; matter density; Euclidean reference frame; torsion of space; Kepler‟s laws; celestial matter; neurons. Corresponding author; e-mail: [email protected] 10 Nicolae Mazilu 1. By Way of Introduction: a Synopsis of Bygone Ideas The series of works already publishedin this Bulletin [(Mazilu, 2019, 2020); these articles will be cited here as I and II respectively], or in the course of publication from now on, intends to fill an important gap in the physical science: a missing physical theory of brain. -
The Evolution of the Concepts of Energy, Momentum, and Mass From
The evolution of the concepts of energy, momentum, and mass from Newton and Lomonosov to Einstein and Feynman L.B.Okun [email protected] ITEP, Moscow, Russia No2PPT - Prosper – p. 1/75 Abstract These are slides of the talk at the 13th Lomonosov conference, 23 August,2007. The talk stresses the importance of the concept of rest energy E0 and explains how to use it in various situations. No2PPT - Prosper – p. 2/75 1. Introduction This conference is the first in a series of conferences celebrating 300 years since the birth of Mikhail Lomonosov (1711–1765). Therefore it is appropriate to consider the evolution of the laws of conservation of mass, energy, and momentum during this period. The main message of the talk is the equivalence of the 2 rest energy of a body and its mass: E0 = mc . This equivalence is a corollary of relativity principle. The total energy of a body and its mass are not equivalent: E =6 mc2 No2PPT - Prosper – p. 3/75 2. Contents 1. Introduction 2. Contents 3. XVII – XIX centuries 3.1. Galileo, Newton: relativity 3.2. Lomonosov, Lavoisier: conservation of mass 3.4. Conservation of energy 4. The first part of the XXth century 4.1. Rest energy E0 4.2. Energy and inertia 4.3. Energy and gravity 4.4. “Relativistic mass” vs mass 4.5. Famous vs true 2 4.6. Einstein supports E0 = mc No2PPT - Prosper – p. 4/75 5. The second part of the XXth century 5.1. Landau and Lifshitz 5.2. Feynman diagrams 5.3. Feynman Lectures 6. -
Mach's Principle and the Origin of Inertia Apeiron Ams, Ph.D
Proceedings of the International Workshop on Mach’s Principle and the M. Sachs/A.R. eds. Roy Origin of Inertia, Indian Institute of Technology, Kharagpur, India, Feb. 6-8, 2002. Ernst Mach’s non-atomistic model of matter and the associated interpretation of inertial mass (the “Mach principle”) influenced the holistic approach embodied in the continuous field concept of the theory of general relativity as a general theory of matter. The articles in these Proceedings demonstrate Mach’s MACH’S PRINCIPLE influence on contemporary thinking. We see here the views of an international group of scholars on the impact of the Mach principle in physics and astro- AND THE ORIGIN OF INERTIA physics. The ideas presented here will inspire research in physics for many generations to come. Mach's Principleand the OriginofInertia About the editors: Mendel Sachs is presently Professor of Physics Emeritus at the State University of New York at Buffalo, where he was a professor of physics from 1966 to 1997. Earlier positions were at Boston University, McGill University and the University of California Radiation Laboratory. Prof. Sachs earned his Ph.D. in theoretical physics at University of California, Los Angeles, in 1954. His main interests and publications during his professional career have been on foundational problems in theoretical physics (mainly general relativity and particle physics) and the philosophy of physics. A strong early influence came from the writings of Ernst Mach. The main theme of Mendel Sachs’s research has been a generalization of the works of Albert Einstein as a future course of physics, from the domain of micromatter to cosmology. -
Status of Inorganic Chemistry Research in India
Proc Indian Natn Sci Acad 86 No. 2 June 2020 pp. 983-999 Printed in India. DOI: 10.16943/ptinsa/2019/49735 Review Article Status of Inorganic Chemistry Research in India V CHANDRASEKHAR1,2,* and A CHAKRABORTY2 1Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur 208 016, India 2Tata Institute of Fundamental Research Hyderabad, Gopanpally, Hyderabad 500 107, India (Received on 03 March 2019; Revised on 25 May 2019; Accepted on 05 June 2019) The current status of research in the area of Inorganic chemistry in India is discussed. The article focuses on various aspects of inorganic chemistry being pursued in the country such as main-group chemistry, coordination chemistry, supramolecular chemistry, molecular materials and bio-inorganic chemistry. The strengths of the subject in the country and the possible future directions are discussed. Keywords: Inorganic Chemistry; Modern Chemistry; Chemical Research; Mercurous Nitrite Introduction for a long time and the amount of funding was substantially lower. It is only in the last two decades Modern chemistry research in India began with that reasonable funding became available for Acharya Prafulla Chandra Ray in Kolkata. The fact researchers across the country and this is reflected that he was an inorganic chemist by training is in the number of publications resulting from the incidental. His influence on chemical research in India country. The increased funding has resulted in higher is profound (Chakravorty, 2014). His most important number of publications. By a search of web-of-science contribution is the preparation of mercurous nitrite, using the key words “India” and “Address” (in topics Hg (NO ) , whose molecular structure was 2 2 2 search) the publications in the decades 1980-2019 is established several years later (Samanta et al., 2011).