DOCSLIB.ORG

Quantum Mechanical Explanation for Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Mechanical Explanation for Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe Open Astron. 2019; 28: 220–227 Research Article Biswaranjan Dikshit* Quantum Mechanical Explanation for Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe https://doi.org/10.1515/astro-2019-0021 Received Sep 27, 2019; accepted Dec 16, 2019 Abstract: One of the most important problems in astronomy is the cosmological constant problem in which conventional calculation of vacuum energy density using quantum mechanics leads to a value which is ~10123 times more than the vacuum energy estimated from astronomical observations of expanding universe. The cosmic coincidence problem questions why matter energy density is of the same order of magnitude as the vacuum energy density at present time. Finally, the mechanism responsible for spatial flatness is not clearly understood. In this paper, by taking the vacuum as a finite and closed quantum oscillator, we solve all of the above-mentioned problems. At first, by using thepurely quantum mechanical approach, we predict that the dark energy density is c4/(GR2) = 5.27×10−10 J/m3 (where R is radius of 3-sphere of the universe) and matter energy density is c4/(2GR2) = 2.6×10−10 J/m3 which match well with astronomical observations. We also prove that dark energy has always been ~66.7% and matter energy has been ~33.3% of the total energy and thus solve the cosmic coincidence problem. Next, we show how flatness of space could be maintained since the early stage of the universe. Finally, using our model, we derive the expression for age and radius of the universe which match well with the astronomical data. Keywords: dark energy, cosmological constant problem, cosmic coincidence problem, flatness problem, Hubble’s law, age of the universe, radius of the universe 1 Introduction nomical parameters such as dark energy (or vacuum en- ergy) responsible for accelerated expansion of the universe. This is known as cosmological constant problem. Of course, General theory of relativity and quantum mechanics (or there exists some modified gravity theories (Yousaf et al. quantum field theory) developed in last century are thetwo 2016a,b; Yousaf 2017, 2018, 2019a; Yousaf et al. 2019b)) pillars on which the whole of modern physics now rests. such as f (R,T) theory (where R is Ricci scalar and T is trace Independently each of them has proved itself to be correct of energy-momentum tensor) which can explain the gravi- with surprising accuracy. For instance, bending of light tational collapse, structure formation and the expansion of coming from distant stars by the Sun and precession of the universe without bringing in dark energy. But, in this perihelion of Mercury predicted by general relativity have paper, we will not follow that approach as the nature of been exactly reproduced in astronomical observations. Sim- function f (R,T) is arbitrarily assumed and we are in search ilarly, prediction of value of fine structure constant by quan- of a quantum mechanical basis for astronomical observa- tum electrodynamics has been tested with a precision of tions. In other questions related to ratio of matter energy to about one part in billion. So, it is natural to expect both dark energy, flatness of space, present age and size ofuni- these jewels of physics to converge when calculating some verse, presently quantum theory is unable to provide any common parameters of the universe. But, surprisingly, pre- satisfactory explanation and in this article we will attempt dictions of both these theories fall apart by unexpected to solve all these problems. Let us first discuss these prob- amounts while calculating some of the important astro- lems in detail and then progress to the proposed solutions of these in next sections. First comes the cosmological constant problem. The Corresponding Author: Biswaranjan Dikshit: Laser and Plasma original form of Einstein’s field equation which determines Technology Division, Bhabha Atomic Research Centre, Mumbai- 400085, INDIA and Homi Bhabha National Institute, Mumbai, India; Email: [email protected] Open Access. © 2019 B. Dikshit, published by De Gruyter. This work is licensed under the Creative Commons Attribution 4.0 License B. Dikshit, Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe Ë 221 the space-time structure is given by, ground state energy. In fact, the existence of zero-point en- 8πG ergy has been experimentally demonstrated through Lamb G = T (1) µν c4 µν shift of atomic spectra, modification of magnetic moment of electron and Casimir effect (Casimir 1948; Mohideen 1998; Where Gµν is Einstein tensor, Tµν is energy-momentum ten- Lamoreaux 1997; Wilson et al. 2011) which causes an at- sor, G is Newton’s gravitational constant and c is speed of tractive force between two closely separated conducting light. bodies. However, when we go for a quantitative comparison, When Einstein (1917) applied above equation to a static, a huge surprise appears before us. Considering all possi- isotropic and homogenous universe in the form of 3-sphere ble modes of zero-point oscillation, as shown by Weinberg containing only matter (pressure less dust), he found that (1989), quantum mechanical vacuum zero-point energy Eq. (1) is not satisfied. So, to solve the problem, he added a 2 π ~c density is given by ~ 4 , where lp is the minimum possi- cosmological constant Λ at the left-hand side of Eq. (1) as lp given below. ble wavelength taken to be Planck length. By putting the Λ 8πG values of constants, this quantum vacuum zero-point en- G + g = T (2) µν c2 µν c4 µν ergy density comes out to be ~ 10114 J/m3 which is about 123 where gµν is metric tensor with local space-time signature 10 times more than the value estimated from astronomi- (−,+,+,+). We have to note that the constant Λ had been ar- cal observations. This is the worst theoretical predication tificially added by Einstein just to make the universe static. in the history of modern physics which is commonly known Later on, Friedmann (1922) developed a model for an ex- as cosmological constant problem (Weinberg 1989; Banks panding universe using Einstein’s field equation given by 2004; Peebles 2003). Eq. (2) that includes the cosmological constant Λ. The Fried- In an effort to explain the astronomically observed mann’s equations are (Carroll 2001), small value of vacuum energy, few theories have been pro- 2 posed in literature which certainly are not convincing. De- (︂ R˙ )︂ 8πG Λ k = ρ + c2 − c2 (3) tails of these theories and their loop holes are described R 3 nonvac 3 R2 by Weinberg (1989). For example, supersymmetry assumes that corresponding to each fermion, there exists a boson R¨ 4πG (︁ p )︁ Λ = − ρ + 3 + c2 (4) resulting in cancellation of energy. But how can this can- R 3 nonvac c2 3 cellation be so precise that vacuum energy density comes Where ‘R’ is the scale factor in Friedmann-Robertson- down from ~10114 J/m3 to ~5.4×10−10 J/m3? In addition, Walker (FRW) metric and physically it is the radius of till date no supersymmetric particle has been detected ex- the universe in the form of 3-sphere expanding in 4- perimentally. Another important proposal is the anthropic dimensional space. k is curvature constant which can be principle. In this principle, it is stated that even if cosmolog- +1 (for closed universe), 0 (for flat universe) or −1 (for open ical constant can take any random values, we will observe universe), ρnonvac is density of non-vacuum component it to be as it is today since it is the only value that allows (ordinary matter, dark matter and radiation). formation of galaxies and stars by gravitational conden- 8πG If we write Λ = c2 ρvac, Eq. (3) becomes, sation and creation of intelligent life who can measure it. (︂ )︂2 But in my view, our existence can be an effect of present R˙ 8πG k 2 = (ρnonvac + ρvac) − c (5) state of the universe, it cannot be the cause. In another ap- R 3 R2 proach to explain the present low value of vacuum energy Using the redshift-brightness data of type Ia supernovae density, Chen and Wu (1990) have postulated cosmologi- in distant galaxies which act as standard candles, we can cal constant to be varying as R−2 where R is scale factor of measure the ratio of velocity of recession of galaxies to their universe. But, they have not given any scientific justifica- (︁ R˙ )︁ distance from us which is known as R = H (Hubble’s tion for such a variation. Similarly, many other researchers constant). Taking observed data from (Planck Collabora- (Berman 1991; Carvalho et al. 1992; Fujii and Nishioka 1990; −1 −1 tion 2016), H ≈ 67.9 km s Mpc and ρnonvac ≈ 0.31ρcrit Rubakov 2000) have also assumed relaxation of cosmo- 3H2 where critical density ρcrit = 8πG . Putting k=0 (since uni- logical constant with time, that too again without suffi- verse is found to be flat), we can calculate the vacuum en- cient reason. They have just analyzed the consequences of 2 ergy density ρvac c from Eq. (5) and its value is found to be such a variation. Understanding the origin of dark energy ~ 5.4×10−10 J/m3. This is also called dark energy density. becomes more important considering the recent work of Qualitatively, the idea of vacuum energy in general (Yousaf 2019a; Yousaf et al. 2019b) on gravastar (gravita- relativity is very well compatible with quantum field the- tional vacuum star) using modified gravity. Gravastar is a ory which considers the free space to have zero-point or 222 Ë B. Dikshit, Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe (hypothesized) celestial body that has a central vacuum is not a coincidence at all.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • An Introduction to Quantum Field Theory
    AN INTRODUCTION TO QUANTUM FIELD THEORY By Dr M Dasgupta University of Manchester Lecture presented at the School for Experimental High Energy Physics Students Somerville College, Oxford, September 2009 - 1 - - 2 - Contents 0 Prologue....................................................................................................... 5 1 Introduction ................................................................................................ 6 1.1 Lagrangian formalism in classical mechanics......................................... 6 1.2 Quantum mechanics................................................................................... 8 1.3 The Schrödinger picture........................................................................... 10 1.4 The Heisenberg picture............................................................................ 11 1.5 The quantum mechanical harmonic oscillator ..................................... 12 Problems .............................................................................................................. 13 2 Classical Field Theory............................................................................. 14 2.1 From N-point mechanics to field theory ............................................... 14 2.2 Relativistic field theory ............................................................................ 15 2.3 Action for a scalar field ............................................................................ 15 2.4 Plane wave solution to the Klein-Gordon equation ...........................
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies
    2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies The National Academies—comprising the National Academy of Sciences, the National Academy of Engineering, the Institute of Medicine, and the National Research Council—work together to enlist the nation’s top scientists, engineers, health professionals, and other experts to study specific issues in science, technology, and medicine that underlie many questions of national importance. The results of their deliberations have inspired some of the nation’s most significant and lasting efforts to improve the health, education, and welfare of the United States and have provided independent advice on issues that affect people’s lives worldwide. To learn more about the Academies’ activities, check the website at www.nationalacademies.org. Copyright 2011 by the National Academy of Sciences. All rights reserved. Printed in the United States of America This study was supported by Contract NNX08AN97G between the National Academy of Sciences and the National Aeronautics and Space Administration, Contract AST-0743899 between the National Academy of Sciences and the National Science Foundation, and Contract DE-FG02-08ER41542 between the National Academy of Sciences and the U.S. Department of Energy. Support for this study was also provided by the Vesto Slipher Fund. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the agencies that provided support for the project. 2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics Committee for a Decadal Survey of Astronomy and Astrophysics ROGER D.
    [Show full text]
  • The Union of Quantum Field Theory and Non-Equilibrium Thermodynamics
    The Union of Quantum Field Theory and Non-equilibrium Thermodynamics Thesis by Anthony Bartolotta In Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2018 Defended May 24, 2018 ii c 2018 Anthony Bartolotta ORCID: 0000-0003-4971-9545 All rights reserved iii Acknowledgments My time as a graduate student at Caltech has been a journey for me, both professionally and personally. This journey would not have been possible without the support of many individuals. First, I would like to thank my advisors, Sean Carroll and Mark Wise. Without their support, this thesis would not have been written. Despite entering Caltech with weaker technical skills than many of my fellow graduate students, Mark took me on as a student and gave me my first project. Mark also granted me the freedom to pursue my own interests, which proved instrumental in my decision to work on non-equilibrium thermodynamics. I am deeply grateful for being provided this priviledge and for his con- tinued input on my research direction. Sean has been an incredibly effective research advisor, despite being a newcomer to the field of non-equilibrium thermodynamics. Sean was the organizing force behind our first paper on this topic and connected me with other scientists in the broader community; at every step Sean has tried to smoothly transition me from the world of particle physics to that of non-equilibrium thermody- namics. My research would not have been nearly as fruitful without his support. I would also like to thank the other two members of my thesis and candidacy com- mittees, John Preskill and Keith Schwab.
    [Show full text]
  • Quantum Vacuum Energy Density and Unifying Perspectives Between Gravity and Quantum Behaviour of Matter
    Annales de la Fondation Louis de Broglie, Volume 42, numéro 2, 2017 251 Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter Davide Fiscalettia, Amrit Sorlib aSpaceLife Institute, S. Lorenzo in Campo (PU), Italy corresponding author, email: [email protected] bSpaceLife Institute, S. Lorenzo in Campo (PU), Italy Foundations of Physics Institute, Idrija, Slovenia email: [email protected] ABSTRACT. A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. This model introduces the possibility to interpret gravity and the quantum behaviour of matter as two different aspects of the same origin. The change of the quantum vacuum energy density can be considered as the fundamental medium which determines a bridge between gravity and the quantum behaviour, leading to new interest- ing perspectives about the problem of unifying gravity with quantum theory. PACS numbers: 04. ; 04.20-q ; 04.50.Kd ; 04.60.-m. Key words: general relativity, three-dimensional space, quantum vac- uum energy density, quantum mechanics, generalized Klein-Gordon equation for the quantum vacuum energy density, generalized Dirac equation for the quantum vacuum energy density. 1 Introduction The standard interpretation of phenomena in gravitational fields is in terms of a fundamentally curved space-time. However, this approach leads to well known problems if one aims to find a unifying picture which takes into account some basic aspects of the quantum theory. For this reason, several authors advocated different ways in order to treat gravitational interaction, in which the space-time manifold can be considered as an emergence of the deepest processes situated at the fundamental level of quantum gravity.
    [Show full text]
  • String Theory, QCD and Black Holes
    Black Hole Microstate Structure Fuzzballs and Firewalls Iosif Bena IPhT, CEAEA Saclay with Nick Warner, Jan deBoer, Micha Berkooz, Simon Ross, Gianguido Dall’Agata, Stefano Giusto, Masaki Shigemori, Dieter van den Bleeken, Monica Guica, Sheer El-Showk, Stanislav Kuperstein, Hagen Triendl, Bert Vercnocke, Andrea Puhm, Ref. Ares(2012)790792 - 29/06/2012 ! Department C "Grant Management" ! Mittwoch, 12. März 2014 ! Subject: Aggressive marketing from publishing houses Dear Madam, Dear Sir, The European Research Council Executive Agency (ERCEA) would like to alert you of publishing houses and online publications which try to make profit out of publishing articles, or interviewing researchers funded from the EU budget, either by the European Research Council (ERC) or by the European Commission (EC). From time to time participants in projects funded under the EU framework programmes are contacted – often by telephone - by organisations seeking payment in return for publishing information on the work being undertaken within their projects. As with "cold calling" in general, the claims and assertions made should be treated with an appropriate level of caution before a decision is made on the best course of action. These publications and their services have not been endorsed by the EC, or the ERCEA. Common tactics to secure business may include vague references to high-level contributions from decision makers, or making the project participant believe that his or her activities have been identified on the basis of special merit which may not be the case. Commercial entities use many ways of promoting their services, but grant-holders are not obliged to use them. Whatever the impression given by such service providers, their products have not received any formal approval or endorsement from the EC or the ERCEA.
    [Show full text]
  • Path Integral and Asset Pricing
    Path Integral and Asset Pricing Zura Kakushadze§†1 § Quantigicr Solutions LLC 1127 High Ridge Road #135, Stamford, CT 06905 2 † Free University of Tbilisi, Business School & School of Physics 240, David Agmashenebeli Alley, Tbilisi, 0159, Georgia (October 6, 2014; revised: February 20, 2015) Abstract We give a pragmatic/pedagogical discussion of using Euclidean path in- tegral in asset pricing. We then illustrate the path integral approach on short-rate models. By understanding the change of path integral measure in the Vasicek/Hull-White model, we can apply the same techniques to “less- tractable” models such as the Black-Karasinski model. We give explicit for- mulas for computing the bond pricing function in such models in the analog of quantum mechanical “semiclassical” approximation. We also outline how to apply perturbative quantum mechanical techniques beyond the “semiclas- sical” approximation, which are facilitated by Feynman diagrams. arXiv:1410.1611v4 [q-fin.MF] 10 Aug 2016 1 Zura Kakushadze, Ph.D., is the President of Quantigicr Solutions LLC, and a Full Professor at Free University of Tbilisi. Email: [email protected] 2 DISCLAIMER: This address is used by the corresponding author for no purpose other than to indicate his professional affiliation as is customary in publications. In particular, the contents of this paper are not intended as an investment, legal, tax or any other such advice, and in no way represent views of Quantigic Solutions LLC, the website www.quantigic.com or any of their other affiliates. 1 Introduction In his seminal paper on path integral formulation of quantum mechanics, Feynman (1948) humbly states: “The formulation is mathematically equivalent to the more usual formulations.
    [Show full text]
  • Critical Notice: the Quantum Revolution in Philosophy (Richard Healey; Oxford University Press, 2017)
    Critical notice: The Quantum Revolution in Philosophy (Richard Healey; Oxford University Press, 2017) DAVID WALLACE Richard Healey’s The Quantum Revolution in Philosophy is a terrific book, and yet I disagree with nearly all its main substantive conclusions. The purpose of this review is to say why the book is well worth your time if you have any interest in the interpretation of quantum theory or in the general philosophy of science, and yet why in the end I think Healey’s ambitious project fails to achieve its full goals. The quantum measurement problem is the central problem in philosophy of quantum mechanics, and arguably the most important issue in philosophy of physics more generally; not coincidentally, it has seen some of the field’s best work, and some of its most effective engagement with physics. Yet the debate in the field largely now appears deadlocked: the last few years have seen developments in our understanding of many of the proposed solutions, but not much movement in the overall dialectic. This is perhaps clearest with a little distance: metaphysicians who need to refer to quantum mechanics increasingly tend to talk of “the three main interpretations” (they mean: de Broglie and Bohm’s hidden variable theory; Ghirardi, Rimini and Weber’s (‘GRW’) dynamical-collapse theory; Everett’s many- universes theory) and couch their discussions so as to be, as much as possible, equally valid for any of those three. It is not infrequent for philosophers of physics to use the familiar framework of underdetermination of theory by evidence to discuss the measurement problem.
    [Show full text]
  • (Aka Second Quantization) 1 Quantum Field Theory
    221B Lecture Notes Quantum Field Theory (a.k.a. Second Quantization) 1 Quantum Field Theory Why quantum field theory? We know quantum mechanics works perfectly well for many systems we had looked at already. Then why go to a new formalism? The following few sections describe motivation for the quantum field theory, which I introduce as a re-formulation of multi-body quantum mechanics with identical physics content. 1.1 Limitations of Multi-body Schr¨odinger Wave Func- tion We used totally anti-symmetrized Slater determinants for the study of atoms, molecules, nuclei. Already with the number of particles in these systems, say, about 100, the use of multi-body wave function is quite cumbersome. Mention a wave function of an Avogardro number of particles! Not only it is completely impractical to talk about a wave function with 6 × 1023 coordinates for each particle, we even do not know if it is supposed to have 6 × 1023 or 6 × 1023 + 1 coordinates, and the property of the system of our interest shouldn’t be concerned with such a tiny (?) difference. Another limitation of the multi-body wave functions is that it is incapable of describing processes where the number of particles changes. For instance, think about the emission of a photon from the excited state of an atom. The wave function would contain coordinates for the electrons in the atom and the nucleus in the initial state. The final state contains yet another particle, photon in this case. But the Schr¨odinger equation is a differential equation acting on the arguments of the Schr¨odingerwave function, and can never change the number of arguments.
    [Show full text]