The Quantum Vacuum and the Cosmological Constant Problem
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Astronomy 241: Foundations of Astrophysics I. the Solar System
Astronomy 241: Foundations of Astrophysics I. The Solar System Astronomy 241 is the first part of a year-long Prerequisites: Physics 170, Physics 272 introduction to astrophysics. It uses basic (or concurrent), and Math 242 or 252A. classical mechanics and thermodynamics to Contact: Professor Joshua Barnes analyze the structure and evolution of the ([email protected]; 956-8138) Solar System. www.ifa.hawaii.edu/~barnes/ast241 Tuesday, August 21, 2012 Astrophysics BS Degree Proposal in ASTR PHYS MATH CHEM preparation FALL 241 251A 161, 171 or 181 year 1 161L, 171L, or 181L SPRING 170 242 252A 162 year 1 170L 162L Foundations of Astrophysics I: FALL 241 272 243 253A The Solar System year 2 272L Foundations of Astrophysics II: SPRING 242 274 244 Galaxies & Stars year 2 274L Observational Astronomy & FALL 300 310 311 (or 307?) Laboratory year 3 300L 350 SPRING 301 311 Observational Project year 3 450 FALL 423 480 Stellar Astrophysics year 4 495 SPRING 496 481 Senior Project I, II year4 485 1 of: ASTR 320, 426, or 430 Tuesday, August 21, 2012 Units Text uses MKS units (meter, kilo-gram, second); e.g. G ≃ 6.674 × 10-11 m3 kg-1 s-2 (gravitational constant). Astronomers also use non-standard units: AU ≃ 1.496 × 1011 m (“average” Earth-Sun distance) 30 M⊙ ≃ 1.989 × 10 kg (Sun’s mass) yr ≃ 3.156 × 107 s (Earth’s orbital period) Tuesday, August 21, 2012 Order of Magnitude & Dimensional Analysis: An Example Given that Jupiter’s average density is slightly greater than water, estimate the orbital period of a satellite circling just above the planet. -
The Five Common Particles
The Five Common Particles The world around you consists of only three particles: protons, neutrons, and electrons. Protons and neutrons form the nuclei of atoms, and electrons glue everything together and create chemicals and materials. Along with the photon and the neutrino, these particles are essentially the only ones that exist in our solar system, because all the other subatomic particles have half-lives of typically 10-9 second or less, and vanish almost the instant they are created by nuclear reactions in the Sun, etc. Particles interact via the four fundamental forces of nature. Some basic properties of these forces are summarized below. (Other aspects of the fundamental forces are also discussed in the Summary of Particle Physics document on this web site.) Force Range Common Particles It Affects Conserved Quantity gravity infinite neutron, proton, electron, neutrino, photon mass-energy electromagnetic infinite proton, electron, photon charge -14 strong nuclear force ≈ 10 m neutron, proton baryon number -15 weak nuclear force ≈ 10 m neutron, proton, electron, neutrino lepton number Every particle in nature has specific values of all four of the conserved quantities associated with each force. The values for the five common particles are: Particle Rest Mass1 Charge2 Baryon # Lepton # proton 938.3 MeV/c2 +1 e +1 0 neutron 939.6 MeV/c2 0 +1 0 electron 0.511 MeV/c2 -1 e 0 +1 neutrino ≈ 1 eV/c2 0 0 +1 photon 0 eV/c2 0 0 0 1) MeV = mega-electron-volt = 106 eV. It is customary in particle physics to measure the mass of a particle in terms of how much energy it would represent if it were converted via E = mc2. -
Fundamentals of Particle Physics
Fundamentals of Par0cle Physics Particle Physics Masterclass Emmanuel Olaiya 1 The Universe u The universe is 15 billion years old u Around 150 billion galaxies (150,000,000,000) u Each galaxy has around 300 billion stars (300,000,000,000) u 150 billion x 300 billion stars (that is a lot of stars!) u That is a huge amount of material u That is an unimaginable amount of particles u How do we even begin to understand all of matter? 2 How many elementary particles does it take to describe the matter around us? 3 We can describe the material around us using just 3 particles . 3 Matter Particles +2/3 U Point like elementary particles that protons and neutrons are made from. Quarks Hence we can construct all nuclei using these two particles -1/3 d -1 Electrons orbit the nuclei and are help to e form molecules. These are also point like elementary particles Leptons We can build the world around us with these 3 particles. But how do they interact. To understand their interactions we have to introduce forces! Force carriers g1 g2 g3 g4 g5 g6 g7 g8 The gluon, of which there are 8 is the force carrier for nuclear forces Consider 2 forces: nuclear forces, and electromagnetism The photon, ie light is the force carrier when experiencing forces such and electricity and magnetism γ SOME FAMILAR THE ATOM PARTICLES ≈10-10m electron (-) 0.511 MeV A Fundamental (“pointlike”) Particle THE NUCLEUS proton (+) 938.3 MeV neutron (0) 939.6 MeV E=mc2. Einstein’s equation tells us mass and energy are equivalent Wave/Particle Duality (Quantum Mechanics) Einstein E -
Supersymmetric Dark Matter
Supersymmetric dark matter G. Bélanger LAPTH- Annecy Plan | Dark matter : motivation | Introduction to supersymmetry | MSSM | Properties of neutralino | Status of LSP in various SUSY models | Other DM candidates z SUSY z Non-SUSY | DM : signals, direct detection, LHC Dark matter: a WIMP? | Strong evidence that DM dominates over visible matter. Data from rotation curves, clusters, supernovae, CMB all point to large DM component | DM a new particle? | SM is incomplete : arbitrary parameters, hierarchy problem z DM likely to be related to physics at weak scale, new physics at the weak scale can also solve EWSB z Stable particle protect by symmetry z Many solutions – supersymmetry is one best motivated alternative to SM | NP at electroweak scale could also explain baryonic asymetry in the universe Relic density of wimps | In early universe WIMPs are present in large number and they are in thermal equilibrium | As the universe expanded and cooled their density is reduced Freeze-out through pair annihilation | Eventually density is too low for annihilation process to keep up with expansion rate z Freeze-out temperature | LSP decouples from standard model particles, density depends only on expansion rate of the universe | Relic density | A relic density in agreement with present measurements (Ωh2 ~0.1) requires typical weak interactions cross-section Coannihilation | If M(NLSP)~M(LSP) then maintains thermal equilibrium between NLSP-LSP even after SUSY particles decouple from standard ones | Relic density then depends on rate for all processes -
Configuration Interaction Study of the Ground State of the Carbon Atom
Configuration Interaction Study of the Ground State of the Carbon Atom María Belén Ruiz* and Robert Tröger Department of Theoretical Chemistry Friedrich-Alexander-University Erlangen-Nürnberg Egerlandstraße 3, 91054 Erlangen, Germany In print in Advances Quantum Chemistry Vol. 76: Novel Electronic Structure Theory: General Innovations and Strongly Correlated Systems 30th July 2017 Abstract Configuration Interaction (CI) calculations on the ground state of the C atom are carried out using a small basis set of Slater orbitals [7s6p5d4f3g]. The configurations are selected according to their contribution to the total energy. One set of exponents is optimized for the whole expansion. Using some computational techniques to increase efficiency, our computer program is able to perform partially-parallelized runs of 1000 configuration term functions within a few minutes. With the optimized computer programme we were able to test a large number of configuration types and chose the most important ones. The energy of the 3P ground state of carbon atom with a wave function of angular momentum L=1 and ML=0 and spin eigenfunction with S=1 and MS=0 leads to -37.83526523 h, which is millihartree accurate. We discuss the state of the art in the determination of the ground state of the carbon atom and give an outlook about the complex spectra of this atom and its low-lying states. Keywords: Carbon atom; Configuration Interaction; Slater orbitals; Ground state *Corresponding author: e-mail address: [email protected] 1 1. Introduction The spectrum of the isolated carbon atom is the most complex one among the light atoms. The ground state of carbon atom is a triplet 3P state and its low-lying excited states are singlet 1D, 1S and 1P states, more stable than the corresponding triplet excited ones 3D and 3S, against the Hund’s rule of maximal multiplicity. -
ABSTRACT Investigation Into Compactified Dimensions: Casimir
ABSTRACT Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects Richard K. Obousy, Ph.D. Chairperson: Gerald B. Cleaver, Ph.D. The primary focus of this dissertation is the study of the Casimir effect and the possibility that this phenomenon may serve as a mechanism to mediate higher dimensional stability, and also as a possible mechanism for creating a small but non- zero vacuum energy density. In chapter one we review the nature of the quantum vacuum and discuss the different contributions to the vacuum energy density arising from different sectors of the standard model. Next, in chapter two, we discuss cosmology and the introduction of the cosmological constant into Einstein's field equations. In chapter three we explore the Casimir effect and study a number of mathematical techniques used to obtain a finite physical result for the Casimir energy. We also review the experiments that have verified the Casimir force. In chapter four we discuss the introduction of extra dimensions into physics. We begin by reviewing Kaluza Klein theory, and then discuss three popular higher dimensional models: bosonic string theory, large extra dimensions and warped extra dimensions. Chapter five is devoted to an original derivation of the Casimir energy we derived for the scenario of a higher dimensional vector field coupled to a scalar field in the fifth dimension. In chapter six we explore a range of vacuum scenarios and discuss research we have performed regarding moduli stability. Chapter seven explores a novel approach to spacecraft propulsion we have proposed based on the idea of manipulating the extra dimensions of string/M theory. -
Quantum Field Theory*
Quantum Field Theory y Frank Wilczek Institute for Advanced Study, School of Natural Science, Olden Lane, Princeton, NJ 08540 I discuss the general principles underlying quantum eld theory, and attempt to identify its most profound consequences. The deep est of these consequences result from the in nite number of degrees of freedom invoked to implement lo cality.Imention a few of its most striking successes, b oth achieved and prosp ective. Possible limitation s of quantum eld theory are viewed in the light of its history. I. SURVEY Quantum eld theory is the framework in which the regnant theories of the electroweak and strong interactions, which together form the Standard Mo del, are formulated. Quantum electro dynamics (QED), b esides providing a com- plete foundation for atomic physics and chemistry, has supp orted calculations of physical quantities with unparalleled precision. The exp erimentally measured value of the magnetic dip ole moment of the muon, 11 (g 2) = 233 184 600 (1680) 10 ; (1) exp: for example, should b e compared with the theoretical prediction 11 (g 2) = 233 183 478 (308) 10 : (2) theor: In quantum chromo dynamics (QCD) we cannot, for the forseeable future, aspire to to comparable accuracy.Yet QCD provides di erent, and at least equally impressive, evidence for the validity of the basic principles of quantum eld theory. Indeed, b ecause in QCD the interactions are stronger, QCD manifests a wider variety of phenomena characteristic of quantum eld theory. These include esp ecially running of the e ective coupling with distance or energy scale and the phenomenon of con nement. -
European Astroparticle Physics Strategy 2017-2026 Astroparticle Physics European Consortium
European Astroparticle Physics Strategy 2017-2026 Astroparticle Physics European Consortium August 2017 European Astroparticle Physics Strategy 2017-2026 www.appec.org Executive Summary Astroparticle physics is the fascinating field of research long-standing mysteries such as the true nature of Dark at the intersection of astronomy, particle physics and Matter and Dark Energy, the intricacies of neutrinos cosmology. It simultaneously addresses challenging and the occurrence (or non-occurrence) of proton questions relating to the micro-cosmos (the world decay. of elementary particles and their fundamental interactions) and the macro-cosmos (the world of The field of astroparticle physics has quickly celestial objects and their evolution) and, as a result, established itself as an extremely successful endeavour. is well-placed to advance our understanding of the Since 2001 four Nobel Prizes (2002, 2006, 2011 and Universe beyond the Standard Model of particle physics 2015) have been awarded to astroparticle physics and and the Big Bang Model of cosmology. the recent – revolutionary – first direct detections of gravitational waves is literally opening an entirely new One of its paths is targeted at a better understanding and exhilarating window onto our Universe. We look of cataclysmic events such as: supernovas – the titanic forward to an equally exciting and productive future. explosions marking the final evolutionary stage of massive stars; mergers of multi-solar-mass black-hole Many of the next generation of astroparticle physics or neutron-star binaries; and, most compelling of all, research infrastructures require substantial capital the violent birth and subsequent evolution of our infant investment and, for Europe to remain competitive Universe. -
Quantum Statistics: Is There an Effective Fermion Repulsion Or Boson Attraction? W
Quantum statistics: Is there an effective fermion repulsion or boson attraction? W. J. Mullin and G. Blaylock Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 ͑Received 13 February 2003; accepted 16 May 2003͒ Physicists often claim that there is an effective repulsion between fermions, implied by the Pauli principle, and a corresponding effective attraction between bosons. We examine the origins and validity of such exchange force ideas and the areas where they are highly misleading. We propose that explanations of quantum statistics should avoid the idea of an effective force completely, and replace it with more appropriate physical insights, some of which are suggested here. © 2003 American Association of Physics Teachers. ͓DOI: 10.1119/1.1590658͔ ͒ϭ ͒ Ϫ␣ Ϫ ϩ ͒2 I. INTRODUCTION ͑x1 ,x2 ,t C͕f ͑x1 ,x2 exp͓ ͑x1 vt a Ϫ͑x ϩvtϪa͒2͔Ϫ f ͑x ,x ͒ The Pauli principle states that no two fermions can have 2 2 1 ϫ Ϫ␣ Ϫ ϩ ͒2Ϫ ϩ Ϫ ͒2 the same quantum numbers. The origin of this law is the exp͓ ͑x2 vt a ͑x1 vt a ͔͖, required antisymmetry of the multi-fermion wavefunction. ͑1͒ Most physicists have heard or read a shorthand way of ex- pressing the Pauli principle, which says something analogous where x1 and x2 are the particle coordinates, f (x1 ,x2) ϭ ͓ Ϫ ប͔ to fermions being ‘‘antisocial’’ and bosons ‘‘gregarious.’’ Of- exp imv(x1 x2)/ , C is a time-dependent factor, and the ten this intuitive approach involves the statement that there is packet width parameters ␣ and  are unequal. -
Zero-Point Energy in Bag Models
Ooa/ea/oHsnif- ^*7 ( 4*0 0 1 5 4 3 - m . Zero-Point Energy in Bag Models by Kimball A. Milton* Department of Physics The Ohio State University Columbus, Ohio 43210 A b s t r a c t The zero-point (Casimir) energy of free vector (gluon) fields confined to a spherical cavity (bag) is computed. With a suitable renormalization the result for eight gluons is This result is substantially larger than that for a spher ical shell (where both interior and exterior modes are pre sent), and so affects Johnson's model of the QCD vacuum. It is also smaller than, and of opposite sign to the value used in bag model phenomenology, so it will have important implications there. * On leave ifrom Department of Physics, University of California, Los Angeles, CA 90024. I. Introduction Quantum chromodynamics (QCD) may we 1.1 be the appropriate theory of hadronic matter. However, the theory is not at all well understood. It may turn out that color confinement is roughly approximated by the phenomenologically suc cessful bag model [1,2]. In this model, the normal vacuum is a perfect color magnetic conductor, that iis, the color magnetic permeability n is infinite, while the vacuum.in the interior of the bag is characterized by n=l. This implies that the color electric and magnetic fields are confined to the interior of the bag, and that they satisfy the following boundary conditions on its surface S: n.&jg= 0, nxBlg= 0, (1) where n is normal to S. Now, even in an "empty" bag (i.e., one containing no quarks) there will be non-zero fields present because of quantum fluctua tions. -
Effective Field Theories, Reductionism and Scientific Explanation Stephan
To appear in: Studies in History and Philosophy of Modern Physics Effective Field Theories, Reductionism and Scientific Explanation Stephan Hartmann∗ Abstract Effective field theories have been a very popular tool in quantum physics for almost two decades. And there are good reasons for this. I will argue that effec- tive field theories share many of the advantages of both fundamental theories and phenomenological models, while avoiding their respective shortcomings. They are, for example, flexible enough to cover a wide range of phenomena, and concrete enough to provide a detailed story of the specific mechanisms at work at a given energy scale. So will all of physics eventually converge on effective field theories? This paper argues that good scientific research can be characterised by a fruitful interaction between fundamental theories, phenomenological models and effective field theories. All of them have their appropriate functions in the research process, and all of them are indispens- able. They complement each other and hang together in a coherent way which I shall characterise in some detail. To illustrate all this I will present a case study from nuclear and particle physics. The resulting view about scientific theorising is inherently pluralistic, and has implications for the debates about reductionism and scientific explanation. Keywords: Effective Field Theory; Quantum Field Theory; Renormalisation; Reductionism; Explanation; Pluralism. ∗Center for Philosophy of Science, University of Pittsburgh, 817 Cathedral of Learning, Pitts- burgh, PA 15260, USA (e-mail: [email protected]) (correspondence address); and Sektion Physik, Universit¨at M¨unchen, Theresienstr. 37, 80333 M¨unchen, Germany. 1 1 Introduction There is little doubt that effective field theories are nowadays a very popular tool in quantum physics. -
Casimir Effect on the Lattice: U (1) Gauge Theory in Two Spatial Dimensions
Casimir effect on the lattice: U(1) gauge theory in two spatial dimensions M. N. Chernodub,1, 2, 3 V. A. Goy,4, 2 and A. V. Molochkov2 1Laboratoire de Math´ematiques et Physique Th´eoriqueUMR 7350, Universit´ede Tours, 37200 France 2Soft Matter Physics Laboratory, Far Eastern Federal University, Sukhanova 8, Vladivostok, 690950, Russia 3Department of Physics and Astronomy, University of Gent, Krijgslaan 281, S9, B-9000 Gent, Belgium 4School of Natural Sciences, Far Eastern Federal University, Sukhanova 8, Vladivostok, 690950, Russia (Dated: September 8, 2016) We propose a general numerical method to study the Casimir effect in lattice gauge theories. We illustrate the method by calculating the energy density of zero-point fluctuations around two parallel wires of finite static permittivity in Abelian gauge theory in two spatial dimensions. We discuss various subtle issues related to the lattice formulation of the problem and show how they can successfully be resolved. Finally, we calculate the Casimir potential between the wires of a fixed permittivity, extrapolate our results to the limit of ideally conducting wires and demonstrate excellent agreement with a known theoretical result. I. INTRODUCTION lattice discretization) described by spatially-anisotropic and space-dependent static permittivities "(x) and per- meabilities µ(x) at zero and finite temperature in theories The influence of the physical objects on zero-point with various gauge groups. (vacuum) fluctuations is generally known as the Casimir The structure of the paper is as follows. In Sect. II effect [1{3]. The simplest example of the Casimir effect is we review the implementation of the Casimir boundary a modification of the vacuum energy of electromagnetic conditions for ideal conductors and propose its natural field by closely-spaced and perfectly-conducting parallel counterpart in the lattice gauge theory.