Interrogating the Legend of Einstein's “Biggest Blunder”
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E
BOOK REVIEW Einstein’s Italian Mathematicians: Ricci, Levi-Civita, and the Birth of General Relativity Reviewed by David E. Rowe Einstein’s Italian modern Italy. Nor does the author shy away from topics Mathematicians: like how Ricci developed his absolute differential calculus Ricci, Levi-Civita, and the as a generalization of E. B. Christoffel’s (1829–1900) work Birth of General Relativity on quadratic differential forms or why it served as a key By Judith R. Goodstein tool for Einstein in his efforts to generalize the special theory of relativity in order to incorporate gravitation. In This delightful little book re- like manner, she describes how Levi-Civita was able to sulted from the author’s long- give a clear geometric interpretation of curvature effects standing enchantment with Tul- in Einstein’s theory by appealing to his concept of parallel lio Levi-Civita (1873–1941), his displacement of vectors (see below). For these and other mentor Gregorio Ricci Curbastro topics, Goodstein draws on and cites a great deal of the (1853–1925), and the special AMS, 2018, 211 pp. 211 AMS, 2018, vast secondary literature produced in recent decades by the world that these and other Ital- “Einstein industry,” in particular the ongoing project that ian mathematicians occupied and helped to shape. The has produced the first 15 volumes of The Collected Papers importance of their work for Einstein’s general theory of of Albert Einstein [CPAE 1–15, 1987–2018]. relativity is one of the more celebrated topics in the history Her account proceeds in three parts spread out over of modern mathematical physics; this is told, for example, twelve chapters, the first seven of which cover episodes in [Pais 1982], the standard biography of Einstein. -
The Son of Lamoraal Ulbo De Sitter, a Judge, and Catharine Theodore Wilhelmine Bertling
558 BIOGRAPHIES v.i WiLLEM DE SITTER viT 1872-1934 De Sitter was bom on 6 May 1872 in Sneek (province of Friesland), the son of Lamoraal Ulbo de Sitter, a judge, and Catharine Theodore Wilhelmine Bertling. His father became presiding judge of the court in Arnhem, and that is where De Sitter attended gymna sium. At the University of Groniiigen he first studied mathematics and physics and then switched to astronomy under Jacobus Kapteyn. De Sitter spent two years observing and studying under David Gill at the Cape Obsen'atory, the obseivatory with which Kapteyn was co operating on the Cape Photographic Durchmusterung. De Sitter participated in the program to make precise measurements of the positions of the Galilean moons of Jupiter, using a heliometer. In 1901 he received his doctorate under Kapteyn on a dissertation on Jupiter's satellites: Discussion of Heliometer Observations of Jupiter's Satel lites. De Sitter remained at Groningen as an assistant to Kapteyn in the astronomical laboratory, until 1909, when he was appointed to the chair of astronomy at the University of Leiden. In 1919 he be came director of the Leiden Observatory. He remained in these posts until his death in 1934. De Sitter's work was highly mathematical. With his work on Jupi ter's satellites, De Sitter pursued the new methods of celestial me chanics of Poincare and Tisserand. His earlier heliometer meas urements were later supplemented by photographic measurements made at the Cape, Johannesburg, Pulkowa, Greenwich, and Leiden. De Sitter's final results on this subject were published as 'New Math ematical Theory of Jupiter's Satellites' in 1925. -
Lecture Notes for Felix Klein Lectures
Preprint typeset in JHEP style - HYPER VERSION Lecture Notes for Felix Klein Lectures Gregory W. Moore Abstract: These are lecture notes for a series of talks at the Hausdorff Mathematical Institute, Bonn, Oct. 1-11, 2012 December 5, 2012 Contents 1. Prologue 7 2. Lecture 1, Monday Oct. 1: Introduction: (2,0) Theory and Physical Mathematics 7 2.1 Quantum Field Theory 8 2.1.1 Extended QFT, defects, and bordism categories 9 2.1.2 Traditional Wilsonian Viewpoint 12 2.2 Compactification, Low Energy Limit, and Reduction 13 2.3 Relations between theories 15 3. Background material on superconformal and super-Poincar´ealgebras 18 3.1 Why study these? 18 3.2 Poincar´eand conformal symmetry 18 3.3 Super-Poincar´ealgebras 19 3.4 Superconformal algebras 20 3.5 Six-dimensional superconformal algebras 21 3.5.1 Some group theory 21 3.5.2 The (2, 0) superconformal algebra SC(M1,5|32) 23 3.6 d = 6 (2, 0) super-Poincar´e SP(M1,5|16) and the central charge extensions 24 3.7 Compactification and preserved supersymmetries 25 3.7.1 Emergent symmetries 26 3.7.2 Partial Topological Twisting 26 3.7.3 Embedded Four-dimensional = 2 algebras and defects 28 N 3.8 Unitary Representations of the (2, 0) algebra 29 3.9 List of topological twists of the (2, 0) algebra 29 4. Four-dimensional BPS States and (primitive) Wall-Crossing 30 4.1 The d = 4, = 2 super-Poincar´ealgebra SP(M1,3|8). 30 N 4.2 BPS particle representations of four-dimensional = 2 superpoincar´eal- N gebras 31 4.2.1 Particle representations 31 4.2.2 The half-hypermultiplet 33 4.2.3 Long representations 34 -
The State of the Multiverse: the String Landscape, the Cosmological Constant, and the Arrow of Time
The State of the Multiverse: The String Landscape, the Cosmological Constant, and the Arrow of Time Raphael Bousso Center for Theoretical Physics University of California, Berkeley Stephen Hawking: 70th Birthday Conference Cambridge, 6 January 2011 RB & Polchinski, hep-th/0004134; RB, arXiv:1112.3341 The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Magnitude of contributions to the vacuum energy graviton (a) (b) I Vacuum fluctuations: SUSY cutoff: ! 10−64; Planck scale cutoff: ! 1 I Effective potentials for scalars: Electroweak symmetry breaking lowers Λ by approximately (200 GeV)4 ≈ 10−67. The cosmological constant problem −121 I Each known contribution is much larger than 10 (the observational upper bound on jΛj known for decades) I Different contributions can cancel against each other or against ΛEinstein. I But why would they do so to a precision better than 10−121? Why is the vacuum energy so small? 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 Recent observations Supernovae/CMB/ Large Scale Structure: Λ ≈ 0:4 × 10−121 6= 0 Why is the energy of the vacuum so small, and why is it comparable to the matter density in the present era? The Cosmological Constant Problem The Landscape of String Theory Cosmology: Eternal inflation and the Multiverse The Observed Arrow of Time The Arrow of Time in Monovacuous Theories A Landscape with Two Vacua A Landscape with Four Vacua The String Landscape Many ways to make empty space Topology and combinatorics RB & Polchinski (2000) I A six-dimensional manifold contains hundreds of topological cycles. -
Felix Klein and His Erlanger Programm D
WDS'07 Proceedings of Contributed Papers, Part I, 251–256, 2007. ISBN 978-80-7378-023-4 © MATFYZPRESS Felix Klein and his Erlanger Programm D. Trkovsk´a Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. The present paper is dedicated to Felix Klein (1849–1925), one of the leading German mathematicians in the second half of the 19th century. It gives a brief account of his professional life. Some of his activities connected with the reform of mathematics teaching at German schools are mentioned as well. In the following text, we describe fundamental ideas of his Erlanger Programm in more detail. References containing selected papers relevant to this theme are attached. Introduction The Erlanger Programm plays an important role in the development of mathematics in the 19th century. It is the title of Klein’s famous lecture Vergleichende Betrachtungen ¨uber neuere geometrische Forschungen [A Comparative Review of Recent Researches in Geometry] which was presented on the occasion of his admission as a professor at the Philosophical Faculty of the University of Erlangen in October 1872. In this lecture, Felix Klein elucidated the importance of the term group for the classification of various geometries and presented his unified way of looking at various geometries. Klein’s basic idea is that each geometry can be characterized by a group of transformations which preserve elementary properties of the given geometry. Professional Life of Felix Klein Felix Klein was born on April 25, 1849 in D¨usseldorf,Prussia. Having finished his study at the grammar school in D¨usseldorf,he entered the University of Bonn in 1865 to study natural sciences. -
Cosmic Background Explorer (COBE) and Beyond
From the Big Bang to the Nobel Prize: Cosmic Background Explorer (COBE) and Beyond Goddard Space Flight Center Lecture John Mather Nov. 21, 2006 Astronomical Search For Origins First Galaxies Big Bang Life Galaxies Evolve Planets Stars Looking Back in Time Measuring Distance This technique enables measurement of enormous distances Astronomer's Toolbox #2: Doppler Shift - Light Atoms emit light at discrete wavelengths that can be seen with a spectroscope This “line spectrum” identifies the atom and its velocity Galaxies attract each other, so the expansion should be slowing down -- Right?? To tell, we need to compare the velocity we measure on nearby galaxies to ones at very high redshift. In other words, we need to extend Hubble’s velocity vs distance plot to much greater distances. Nobel Prize Press Release The Royal Swedish Academy of Sciences has decided to award the Nobel Prize in Physics for 2006 jointly to John C. Mather, NASA Goddard Space Flight Center, Greenbelt, MD, USA, and George F. Smoot, University of California, Berkeley, CA, USA "for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation". The Power of Thought Georges Lemaitre & Albert Einstein George Gamow Robert Herman & Ralph Alpher Rashid Sunyaev Jim Peebles Power of Hardware - CMB Spectrum Paul Richards Mike Werner David Woody Frank Low Herb Gush Rai Weiss Brief COBE History • 1965, CMB announced - Penzias & Wilson; Dicke, Peebles, Roll, & Wilkinson • 1974, NASA AO for Explorers: ~ 150 proposals, including: – JPL anisotropy proposal (Gulkis, Janssen…) – Berkeley anisotropy proposal (Alvarez, Smoot…) – Goddard/MIT/Princeton COBE proposal (Hauser, Mather, Muehlner, Silverberg, Thaddeus, Weiss, Wilkinson) COBE History (2) • 1976, Mission Definition Science Team selected by HQ (Nancy Boggess, Program Scientist); PI’s chosen • ~ 1979, decision to build COBE in-house at GSFC • 1982, approval to construct for flight • 1986, Challenger explosion, start COBE redesign for Delta launch • 1989, Nov. -
David Kirkby University of California, Irvine, USA 4 August 2020 Expanding Universe
COSMOLOGY IN THE 2020S David Kirkby University of California, Irvine, USA 4 August 2020 Expanding Universe... 2 expansion history a(t |Ωm, ΩDE, …) 3 4 redshift 5 6 0.38Myr opaque universe last scatter 7 inflation opaque universe last scatter gravity waves? 8 CHIME SPT-3G DES 9 TCMB=2.7K, λ~2mm 10 CMB TCMB=2.7K, λ~2mm Galaxies 11 microwave projects: cosmic microwave background (primordial gravity waves, neutrinos, ...) CMB Galaxies optical & NIR projects: galaxy surveys (dark energy, neutrinos, ...) 12 CMB Galaxies telescope location: ground / above atmosphere 13 CMB Atacama desert, Chile CMB ground telescope location: Atacama desert / South Pole 14 Galaxies Galaxy survey instrument: spectrograph / imager 15 Dark Energy Spectroscopic Instrument (DESI) Vera Rubin Observatory 16 Dark Energy Spectroscopic Instrument (DESI) Vera Rubin Observatory 17 EXPANSION HISTORY VS STRUCTURE GROWTH Measurements of our cosmic expansion history constrain the parameters of an expanding homogenous universe: SN LSS , …) expansion historyDE m, Ω a(t |Ω CMB Small inhomogeneities are growing against this backdrop. Measurements of this structure growth provide complementary constraints. 18 Structure Growth 19 Redshift is not a perfect proxy for distance because of galaxy peculiar motions. Large-scale redshift-space distortions (RSD) trace large-scale matter fluctuations: signal! 20 Angles measured on the sky are also distorted by weak lensing (WL) as light is deflected by the same large-scale matter fluctuations: signal! Large-scale redshift-space distortions (RSD) trace large-scale matter fluctuations: signal! 21 CMB measures initial conditions of structure growth at z~1090: Temperature CMB photons also experience weak lensing! https://wiki.cosmos.esa.int/planck-legacy-archive/index.php/CMB_maps Polarization 22 CMB: INFLATION ERA SIGNATURES https://www.annualreviews.org/doi/abs/10.1146/annurev-astro-081915-023433 lensing E-modes lensing B-modes GW B-modes https://arxiv.org/abs/1907.04473 Lensing B modes already observed. -
The Multiverse: Conjecture, Proof, and Science
The multiverse: conjecture, proof, and science George Ellis Talk at Nicolai Fest Golm 2012 Does the Multiverse Really Exist ? Scientific American: July 2011 1 The idea The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology - separate places [Vilenkin, Linde, Guth] - separate times [Smolin, cyclic universes] - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch] - the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind] - totally disjoint [Sciama, Tegmark] 2 Our Cosmic Habitat Martin Rees Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. 3 Scientific American May 2003 issue COSMOLOGY “Parallel Universes: Not just a staple of science fiction, other universes are a direct implication of cosmological observations” By Max Tegmark 4 Brian Greene: The Hidden Reality Parallel Universes and The Deep Laws of the Cosmos 5 Varieties of Multiverse Brian Greene (The Hidden Reality) advocates nine different types of multiverse: 1. Invisible parts of our universe 2. Chaotic inflation 3. Brane worlds 4. Cyclic universes 5. Landscape of string theory 6. Branches of the Quantum mechanics wave function 7. Holographic projections 8. Computer simulations 9. All that can exist must exist – “grandest of all multiverses” They can’t all be true! – they conflict with each other. -
Modified Standard Einstein's Field Equations and the Cosmological
Issue 1 (January) PROGRESS IN PHYSICS Volume 14 (2018) Modified Standard Einstein’s Field Equations and the Cosmological Constant Faisal A. Y. Abdelmohssin IMAM, University of Gezira, P.O. BOX: 526, Wad-Medani, Gezira State, Sudan Sudan Institute for Natural Sciences, P.O. BOX: 3045, Khartoum, Sudan E-mail: [email protected] The standard Einstein’s field equations have been modified by introducing a general function that depends on Ricci’s scalar without a prior assumption of the mathemat- ical form of the function. By demanding that the covariant derivative of the energy- momentum tensor should vanish and with application of Bianchi’s identity a first order ordinary differential equation in the Ricci scalar has emerged. A constant resulting from integrating the differential equation is interpreted as the cosmological constant introduced by Einstein. The form of the function on Ricci’s scalar and the cosmologi- cal constant corresponds to the form of Einstein-Hilbert’s Lagrangian appearing in the gravitational action. On the other hand, when energy-momentum is not conserved, a new modified field equations emerged, one type of these field equations are Rastall’s gravity equations. 1 Introduction term in his standard field equations to represent a kind of “anti ff In the early development of the general theory of relativity, gravity” to balance the e ect of gravitational attractions of Einstein proposed a tensor equation to mathematically de- matter in it. scribe the mutual interaction between matter-energy and Einstein modified his standard equations by introducing spacetime as [13] a term to his standard field equations including a constant which is called the cosmological constant Λ, [7] to become Rab = κTab (1.1) where κ is the Einstein constant, Tab is the energy-momen- 1 Rab − gabR + gabΛ = κTab (1.6) tum, and Rab is the Ricci curvature tensor which represents 2 geometry of the spacetime in presence of energy-momentum. -
Appendix E Nobel Prizes in Nuclear Science
Nuclear Science—A Guide to the Nuclear Science Wall Chart ©2018 Contemporary Physics Education Project (CPEP) Appendix E Nobel Prizes in Nuclear Science Many Nobel Prizes have been awarded for nuclear research and instrumentation. The field has spun off: particle physics, nuclear astrophysics, nuclear power reactors, nuclear medicine, and nuclear weapons. Understanding how the nucleus works and applying that knowledge to technology has been one of the most significant accomplishments of twentieth century scientific research. Each prize was awarded for physics unless otherwise noted. Name(s) Discovery Year Henri Becquerel, Pierre Discovered spontaneous radioactivity 1903 Curie, and Marie Curie Ernest Rutherford Work on the disintegration of the elements and 1908 chemistry of radioactive elements (chem) Marie Curie Discovery of radium and polonium 1911 (chem) Frederick Soddy Work on chemistry of radioactive substances 1921 including the origin and nature of radioactive (chem) isotopes Francis Aston Discovery of isotopes in many non-radioactive 1922 elements, also enunciated the whole-number rule of (chem) atomic masses Charles Wilson Development of the cloud chamber for detecting 1927 charged particles Harold Urey Discovery of heavy hydrogen (deuterium) 1934 (chem) Frederic Joliot and Synthesis of several new radioactive elements 1935 Irene Joliot-Curie (chem) James Chadwick Discovery of the neutron 1935 Carl David Anderson Discovery of the positron 1936 Enrico Fermi New radioactive elements produced by neutron 1938 irradiation Ernest Lawrence -
Cockcroft: a Novel This One, the Comprehensive Compilation Lutely Fundamental Discovery
~7~~-------------------------------------SPRINGBCXJKS------------------------N_A_ru_~__ v_o_L._Jo_s_~_AP __ Rr_L_r9M_ same, when it's compiled as successfully as what was in the sheer physics of it an abso Cockcroft: a novel this one, the comprehensive compilation lutely fundamental discovery. The authors perspective undeniably earns its place in the library. of this book take in their stride Cockcroft I was an admirer of Cockcroft, a fine, and Walton's being made to wait so long William Cooper stocky, sensible, cautious Yorkshireman, theirs not to reason why, they say. But what who indulged in a minimum of speech and about ours? Did it take the Nobel Cockcroft and the Atom. in practically no change of facial committee nineteen years to recognize the By Guy Hartcup and T.E. Allibone. expression. (That expression was neverthe experiment as breaking open an entirely Adam Hilger, Bristol!Heyden, Phila- less amiable, thoughtful, smiling.) If one new line of powerful experiments to be delphia: 1984. Pp.320. £18.95, $34. addressed a remark to him, it was only made with particle-accelerators? Or did it when, after the ensuing silence, he either take those members who opposed the took the famous black notebook out of his award all that time to disappear from the SrNCE the title of Hartcup and Allibone's pocket or actually said something, that one scene? Or what? Someone must know. book may sound a bit vague, perhaps I knew for certain that he'd heard. It gave me There's a fascinating detail I should really should begin by saying what Cockcroft and lasting pleasure to think that at a dinner like to be told. -
The Big-Bang Theory AST-101, Ast-117, AST-602
AST-101, Ast-117, AST-602 The Big-Bang theory Luis Anchordoqui Thursday, November 21, 19 1 17.1 The Expanding Universe! Last class.... Thursday, November 21, 19 2 Hubbles Law v = Ho × d Velocity of Hubbles Recession Distance Constant (Mpc) (Doppler Shift) (km/sec/Mpc) (km/sec) velocity Implies the Expansion of the Universe! distance Thursday, November 21, 19 3 The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light Thursday, November 21, 19 4 The redshift of a Galaxy is: A. The rate at which a Galaxy is expanding in size B. How much reader the galaxy appears when observed at large distances C. the speed at which a galaxy is orbiting around the Milky Way D. the relative speed of the redder stars in the galaxy with respect to the blues stars E. The recessional velocity of a galaxy, expressed as a fraction of the speed of light Thursday, November 21, 19 5 To a first approximation, a rough maximum age of the Universe can be estimated using which of the following? A. the age of the oldest open clusters B. 1/H0 the Hubble time C. the age of the Sun D.