DOCSLIB.ORG

The Lattice World, Quantum Foam and the Universe-Wide Metamaterial

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Lattice World, Quantum Foam and the Universe-Wide Metamaterial The Lattice World, Quantum Foam and the Universe-Wide Metamaterial David Thomas Crouse1 1The City University of New York, USA [email protected] [email protected] Abstract| The concept of a universe-wide gravity crystal that combines Heisenberg´sLattice World and Wheeler´sQuantum Foam is described. It is assumed that space is a crystal with a lattice constant equal to the Planck length and a basis of a Planck mass. Inertial anomalies are calculated that include a parameter that connects the external gravitational field and gravita- tional flux. Similar to the electric permittivity and magnetic permeability of metamaterials, this parameter can take on positive, zero and negative values. In order to provide a solution to the self-energy of the electron, Werner Heisenberg in 1930 3 introduced the concept of space being discretized in cells of volume ro, with ro = ~=cMproton [1]. In correspondence with Niels Bohr, Heisenberg also states that he believes that the discreteness of space underlies the quantum mechanical uncertainty relations [2]. However, he rather quickly sets aside this concept because of its obvious and inherent problems - one being the breaking of continuous rotational and translational symmetries of space. Another problem pointed out by Bohr was that an absolute \minimum" possible length in one frame of reference is length-contracted to a smaller value in a different frame of reference, leading to a contradiction. However the concept did not disappear - being further discussed by Hiesenberg, Wolfgang Pauli, Gleb Wataghin, and recently by a whole host of physicist in the field of quantum gravity [3]. From Heisenberg in the 1930's, one jumps ahead in time to 1957, when John Wheeler introduced the concept of quantum foam as part of a theory emerging at this time called quantum geometro- dynamics (QG), or quantum gravity as it is more widely known by today [4]. His objective for the paper was to introduce the theory of QG and show that all of classical physics is purely geometrical and based throughout on the most firmly established principles of electromagnetism and general relativity [4]. Using concepts within the field of quantum electrodynamics, Wheeler argued that for a possible history to contribute to the transition probability, the phase of the exponent, which is dependent on the metric g, should be small (∼ 1 rad) to avoid destructive interference [4]. This limits fluctuations in g (i.e., ∆g) that can occur over a volume of space L3 to be on the order of −35 ∆g ∼ Lp=L, where Lp is the Planck length (Lp = 1:61x10 m). The fluctuations in the metric ∆g remains small relative to g until L approaches Lp, at which point, ∆g ∼ g and \the character of the space undergoes an essential change... and multiple connectedness develops" [4] that re- sults in an array of \wormholes" in the topology of space with a lattice constant of approximately Lp; he calls this wormhole array a "quantum foam". These wormholes have an electric charge of qfluct = 12e that produces an intense electromagnetic field energy E that has associated with it a −2 q hc −5 mass of mp = c E = G = 2:17 × 10 g. In this paper, the spatial order of Heisenberg's lattice world is imposed upon the quantum foam such that it forms a gravity crystal (GC) throughout all of space. It is assumed that the \local compensation" of electromagnetic energy and gravitational energy discussed by Wheeler either does not occur or is incomplete. It is also assumed that the particles either are stable, and do not come into and out of existence as Wheeler describes, or that they are present over most of a time period −44 given by the Planck time tp = 5:39x10 s and only fleeting into and out of existence every tp step in time so as to satisfy Heisenberg's Uncertainty Principle. With these assumptions, the emperical pseudopotential method (EPM) [5] and tight binding method (TBM)[6] are used to calculate the dispersion curves of non-relativistic and relativistic particles within the GC, as well as the particles' effective mass as a function of momentum and gravitational mass. It is shown that particles in this crystal can appear to violate Einstein's Equivalence Principle equating inertial and gravitational masses, but only because the the system includes not only the particle, but the crystal as well. The inertial mass (mi) can diverge from the gravitational mass (mg) as the particle's momentum 4 b3 ) 9 R 2 3 0 X 1 Γ x b2 Real Space V 2 b M e 1 ( y g r e n 1 E 0 R Γ X M Γ 1 0.5 0 0.5 1 1.5 8 Lp ) 8 - 0 4 1 L p x g k L ( p 0 s s a M -4 -8 R Γ X M Γ 1 0.5 0 0.5 1 1.5 π Crystal Momentum (in units of /LP) Figure 1: Left: The gravity crystal as the fine structure of space. The basis is assumed to be particle of mass mp that produces the spherically symmetric periodic Coulombic potential. The crystal is cubic with a lattice constant of Lp. The dispersion curve (Top Right) and effective mass (Bottom Right) of a non-relativistic point particle of mass mp within the crystal calculated using EPM. The TBM yields similar results but is most accurate for heavier particles. It is seen that the effective inertial mass is not constant and is dependent on the crystal momentum of the particle. At low velocities, it is equal to the gravitational mass (blue dashed line), but at high velocities it can be large and positive, near zero or negative. increases and can assume effective values either much larger or smaller than the gravitational mass, be near zero, or even be negative. Inertial anomalies of black holes and galaxies are then discussed. Once the effective inertial mass is calculated, the concept of the GC is connected to the field of metamaterials. This is done by introducing a constitutive relation between the gravitational field and gravitational flux (similar to electric and magnetic fluxes in materials) with a constant of proportionality (a gravitational permeability µg) that can unexpectedly take on values other than those normally encountered (unity in the case of gravity and for optical metamaterials anything other than double negative materials (i.e., < 0 and µ < 0)). Thus, the inclusion of the crystal´s effects is done via µg while keeping the inertial mass and gravitational masses equal to each other. Values for µg can vary from large and positive, to near-zero, to negative values. However if this concept proves to be true, then this new metamaterial is not meta at all - it is not beyond nature, but the fabric of nature itself. In conclusion, this paper revisits two historical concepts introduced by Werner Heisenberg and John Wheeler concerning the discretization of space in the form of a universe-wide gravity crystal. The calculation of the dispersion curves is performed, as well as the effective masses of particles within this crystal. The inertial anomalies that the crystal produces and its connection to the field of metamaterials are discussed. REFERENCES 1. W. Heisenberg. The Self-Energy of the Electron. In A. Miller, editor, Early Quantum Electro- dynamics, pages 121-128. Cambridge Univeristy Press, 1994/1930. 2. B. Carazza and H. Kragh. Heisenberg's Lattice World: The 1930 Theory Sketch. American Journal of Physics, 63:597-598, 1995. 3. Hagar, Amit. Discrete or continuous?: the quest for fundamental length in modern physics., pages 69-78 Cambridge University Press, 2014. 4. Wheeler, John A. "On the nature of quantum geometrodynamics." Annals of Physics 2.6 (1957): 604-614. 5. Vasileska, Dragica, Stephen M. Goodnick, and Gerhard Klimeck. Computational Electronics: Semiclassical and Quantum Device Modeling and Simulation. CRC press, 2010. 6. Ashcroft, N. W. (1976). ND Mermin Solid state physics. pages 176-185, Saunders College, Philadelphia...
Load more

Recommended publications
  • Engineering the Quantum Foam
    Engineering the Quantum Foam Reginald T. Cahill School of Chemistry, Physics and Earth Sciences, Flinders University, GPO Box 2100, Adelaide 5001, Australia [email protected] _____________________________________________________ ABSTRACT In 1990 Alcubierre, within the General Relativity model for space-time, proposed a scenario for ‘warp drive’ faster than light travel, in which objects would achieve such speeds by actually being stationary within a bubble of space which itself was moving through space, the idea being that the speed of the bubble was not itself limited by the speed of light. However that scenario required exotic matter to stabilise the boundary of the bubble. Here that proposal is re-examined within the context of the new modelling of space in which space is a quantum system, viz a quantum foam, with on-going classicalisation. This model has lead to the resolution of a number of longstanding problems, including a dynamical explanation for the so-called `dark matter’ effect. It has also given the first evidence of quantum gravity effects, as experimental data has shown that a new dimensionless constant characterising the self-interaction of space is the fine structure constant. The studies here begin the task of examining to what extent the new spatial self-interaction dynamics can play a role in stabilising the boundary without exotic matter, and whether the boundary stabilisation dynamics can be engineered; this would amount to quantum gravity engineering. 1 Introduction The modelling of space within physics has been an enormously challenging task dating back in the modern era to Galileo, mainly because it has proven very difficult, both conceptually and experimentally, to get a ‘handle’ on the phenomenon of space.
    [Show full text]
  • Does LIGO Prove General Relativity?
    Does LIGO Prove General Relativity? by Clark M. Thomas © May 12, 2016; modified Sept. 11, 2016 ABSTRACT LIGO-detected "gravitational waves" are very real. This successful experiment in early 2016 did open up a new form of astronomy. Despite the hype, the initial explanation for what was discovered neither confirms nor denies Einstein's full theory of General Relativity, including the concept of gravity membranes (branes). The LIGO discovery can be explained by a model somewhat similar to de Broglie-Bohm quantum pilot waves. LIGO-detected "gravitational waves" are real. The successful experiment in early 2016 did open up a new form of astronomy. However, despite the hype, the initial explanation for what was discovered neither confirms nor denies Einstein's full theory of Page !1 of !11 General Relativity, including the concept of gravity membranes (branes). It merely confirms his 2016 guess that gravity waves should be generated, and that they potentially could be detected and measured. That’s a long way from the core of his GR thesis.1 “Spacetime” is a cool idea, but it merely records the timely effects of motion within a 3D Universe, making up frame-specific 4D spacetimes – with seemingly infinite discrete inertial frames of reference.2 Einstein's idea of "c" being the somewhat mystical absolute limit of measured speed in any direction simply acknowledges the initial acceleration of electromagnetic particle strings from their graviton base within a frame of reference. Speed of light within a vacuum is only the initial burst of acceleration for each yin/yang photon string as it leaves its graviton “mother ship.”3 A better explanation for the waves detected by LIGO is a 21st century paradigm of push/shadow gravity – within a 3D set sea of “quantum foam” (primarily Yin/Yang particles, Y/Y strings, Y/Y graviton rings, and some larger particles).
    [Show full text]
  • Quantum Geometrodynamics with Intrinsic Time Development
    2nd LeCosPA International Symposium, Nat.Taiwan U. (December 17th 2015) Quantum geometrodynamics with intrinsic time development 許 Chopin Soo 祖 斌 Department of Physics, Nat. Cheng Kung U, Taiwan Everything? What about (let’s not forget) the `problem of time’ ? A very wise man once said “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know”, pondering the mystery of what time really is, Saint Augustine (of Hippo) (354-430 A.D.) wrote in his Confessions《懺悔錄》, “Si nemo ex me quaerat scio; Si quaerente explicare velim, nescio ’’ Time: We all have some intuitive understanding of time. But what is time? Where does it comes from? Physical theory of space and time Einstein’s GR: Classical space-time <-> (pseudo-Riemannian)Geometry Quantum Gravity: “`Spacetime’ - a concept of limited applicability” ---J. A. Wheeler What, if anything at all, plays the role of “time” in Quantum Gravity? Importance of time: 1)Quantum probabilities are normalized at fixed instances of time 2)Time <-> Hamiltonian as generator of time translation/evolution Hamiltonian <-> Energy Time: Is it 1) fundamental (present even in Quantum Gravity)? 2) emergent (present in the (semi)-classical context only)? 3) an illusion (!)? … Nemeti, Istvan et al. arXiv:0811.2910 [gr-qc] Getting to know Einstein’s theory Spacetime tells matter how to move; matter tells spacetime how to curve John Wheeler, in Geons, Black Holes, and Quantum Foam p.235 This saying has seeped into popular culture and public discourse; but with all due respect to Wheeler, it is the Hamiltonian which tells everything (including the metric) how to move! from The Early Universe (E.
    [Show full text]
  • Quantum Information Hidden in Quantum Fields
    Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 21 July 2020 Peer-reviewed version available at Quantum Reports 2020, 2, 33; doi:10.3390/quantum2030033 Article Quantum Information Hidden in Quantum Fields Paola Zizzi Department of Brain and Behavioural Sciences, University of Pavia, Piazza Botta, 11, 27100 Pavia, Italy; [email protected]; Phone: +39 3475300467 Abstract: We investigate a possible reduction mechanism from (bosonic) Quantum Field Theory (QFT) to Quantum Mechanics (QM), in a way that could explain the apparent loss of degrees of freedom of the original theory in terms of quantum information in the reduced one. This reduction mechanism consists mainly in performing an ansatz on the boson field operator, which takes into account quantum foam and non-commutative geometry. Through the reduction mechanism, QFT reveals its hidden internal structure, which is a quantum network of maximally entangled multipartite states. In the end, a new approach to the quantum simulation of QFT is proposed through the use of QFT's internal quantum network Keywords: Quantum field theory; Quantum information; Quantum foam; Non-commutative geometry; Quantum simulation 1. Introduction Until the 1950s, the common opinion was that quantum field theory (QFT) was just quantum mechanics (QM) plus special relativity. But that is not the whole story, as well described in [1] [2]. There, the authors mainly say that the fact that QFT was "discovered" in an attempt to extend QM to the relativistic regime is only historically accidental. Indeed, QFT is necessary and applied also in the study of condensed matter, e.g. in the case of superconductivity, superfluidity, ferromagnetism, etc.
    [Show full text]
  • Gravitons Explained
    Gravitons Explained By Clark M. Thomas © August 16, 2021 Abstract There are two totally different gravity paradigms within physics and astrophysics. Separate models of gravitons support each paradigm. These gravity paradigms could be called Tractor-Beam Gravity, and Push/Shadow Gravity. This introductory essay examines each paradigm, with a surprising winner. Tractor-Beam Gravity (TBG) embraces the currently popular model of gravitons. They are at the foundation of geometric General Relativity and string theories. This model has been embraced because its supporting ideas can appear elegant with carefully manipulated math. Once the correlative math has been reverse engineered from sketchy data to fit the general model – ideas of graviton tractor beams can emerge that are impossible to exclusively verify within all dimensions, even though popular publications have claimed as much for a century. Push/Shadow Gravity (PSG) has an older pedigree, going back to Nicolas Fatio, a friend of Newton, in the 17th century. As PSG was originally developed, using the idea of swarms of very tiny impactors, some mass-blocked, it was flawed and easy to refute. Toward the late 19th century the antique PSG model was ignored. It was soon to be superseded by emerging ideas involving Maxwellian electromagnetic fields, culminating with geometric !1 of 11! General Relativity and the truly weird realm of string theory maths. Even quantum field theory has joined the gravity game. Experimental particle physics (within lower-case relativity) examines phenomena inside some intermediate logarithmic dimensions. Explored energy realms are limited by the limited power of particle accelerators. At reality’s particulate limits the ultimate building blocks are much smaller – and combine to create matter worlds much larger than we could dimensionally verify with our instruments.
    [Show full text]
  • Gr-Qc/9211012V1 9 Nov 1992 AS Ubr:9.0D,04.90.+E 98.80.DR, R Numbers: PACS
    INFLATING LORENTZIAN WORMHOLES Thomas A. Roman Physics and Earth Sciences Department Central Connecticut State University, New Britain, Connecticut 06050 Abstract It has been speculated that Lorentzian wormholes of the Morris-Thorne type might be allowed by the laws of physics at submicroscopic, e.g. Planck, scales and that a sufficiently advanced civilization might be able to enlarge them to classical size. The purpose of this paper is to explore the possibility that inflation might provide a natural mechanism for the enlargement of such wormholes to macroscopic size. A new classical metric is presented for a Lorentzian wormhole which is imbedded in a flat deSitter space. It is shown that the throat and the proper length of the wormhole inflate. The resulting properties and stress-energy tensor associated with this metric are discussed. PACS. numbers: 98.80.DR, 04.90.+E arXiv:gr-qc/9211012v1 9 Nov 1992 1 I. INTRODUCTION There has been much interest recently in the Lorentzian signature, traversable worm- holes conjectured by Morris and Thorne (MT) [1,2]. These wormholes have no horizons and thus allow two-way passage through them. As a result, violations of all known en- ergy conditions, including the weak (WEC) [3] and averaged weak (AWEC) [4] energy conditions, must unavoidably occur at the throat of the wormhole. Another disturbing (or intriguing, depending on one’s point of view) property of these wormholes is the possibility of transforming them into time machines for backward time travel [5,6] and thereby, per- haps, for causality violation. Whether such wormholes are actually allowed by the laws of physics is currently unknown.
    [Show full text]
  • Planck Length
    Friday, November 18, 2011 Reading: Chapter 12, Chapter 13, Chapter 14 Astronomy in the news? Fabric of the Cosmos, Quantum Leap, weird world of quantum uncertainty, quantum entanglement (instantaneous action at a distance), quantum computing. The Fabric of the Cosmos, fourth installment, Universe or Multiverse, Wednesday, November 23, PBS (KLRU) 8 PM (re-runs http://www.klru.org/schedule/viewProgram.php?id=246736). Pic of the day: false color topographical map from Lunar Reconnaissance Orbiter Goal: To understand what the Dark Energy implies for the shape and fate of the Universe. Nature of Dark Energy Energy of vacuum - quantum fluctuations, particle/anti-particle (recall role in Hawking radiation) predict an acceleration that is too large by a factor x 10120. It works on Earth, but not, somehow, in deep space. “Worst prediction ever in physics,” Steven Weinberg (UT Nobel Laureate) Related phase early in Big Bang, when the Universe was a fraction of a second old, A huge “inflation” by anti-gravitating vacuum force blows the Universe so big that it is essentially flat (like the surface of the Earth appears to us, only moreso!) Anti-gravitating energy went away - has come back gently in the last 5 billion years. What is it??? “Space-time diagrams” illustrate how the Big Bang led to inflation, then deceleration, and now acceleration The Fate of the Universe? If the acceleration stays constant, the fate is rather dismal: galaxies will be pulled infinitely far apart, then even small mass, long-lived stars age and die, protons, neutrons and electrons will decay to photons, black holes will evaporate by Hawking radiation.
    [Show full text]
  • Quantum Gravity : Motivations and Alternatives 1
    Quantum Gravity : Motivations and Alternatives 1 Reiner Hedrich 2 Institut für Philosophie und Politikwissenschaft Fakultät Humanwissenschaften und Theologie Technische Universität Dortmund Emil-Figge-Strasse 50 44227 Dortmund Germany Zentrum für Philosophie und Grundlagen der Wissenschaft Justus-Liebig-Universität Giessen Otto-Behaghel-Strasse 10 C II 35394 Giessen Germany Abstract The mutual conceptual incompatibility between General Relativity and Quantum Mechanics / Quan- tum Field Theory is generally seen as the most essential motivation for the development of a theory of Quantum Gravity. It leads to the insight that, if gravity is a fundamental interaction and Quantum Mechanics is universally valid, the gravitational field will have to be quantized, not at least because of the inconsistency of semi-classical theories of gravity. The objective of a theory of Quantum Gravity would then be to identify the quantum properties and the quantum dynamics of the gravitational field. If this means to quantize General Relativity, the general-relativistic identification of the gravitational field with the spacetime metric has to be taken into account. The quantization has to be conceptually adequate, which means in particular that the resulting quantum theory has to be background-independ- ent. This can not be achieved by means of quantum field theoretical procedures. More sophisticated strategies, like those of Loop Quantum Gravity , have to be applied. One of the basic requirements for 1 Research for this paper was generously supported by the Fritz-Thyssen-Stiftung für Wissenschaftsförderung under the project Raumzeitkonzeptionen in der Quantengravitation . Thanks also to Brigitte Falkenburg! 2 Email: [email protected] & [email protected] 2 such a quantization strategy is that the resulting quantum theory has a classical limit that is (at least approximately, and up to the known phenomenology) identical to General Relativity.
    [Show full text]
  • The Gravity, Measurability and Quantum Foam 1 Introduction
    Advanced Studies in Theoretical Physics Vol. 14, 2020, no. 2, 81 - 97 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/astp.2020.91250 The Gravity, Measurability and Quantum Foam Alexander Shalyt-Margolin Institute for Nuclear Problems, Belarusian State University 11 Bobruiskaya str., Minsk 220040, Belarus This article is distributed under the Creative Commons by-nc-nd Attribution License. Copyright c 2020 Hikari Ltd. Abstract Using the previously introduced measurability notion, in this work the author continues his studies of space-time (or otherwise quantum) fluctuations, i.e. quantum foam. At the beginning, the author presents his earlier results which are needed for better understanding of his con- cept and also the structure of gravity in the measurable form at all energy scales. In the second part of the paper these results are applied to study the quantum foam in the case of a measurable consideration. It is demonstrated that measurability allows for a new approach to investigation of quantum fluctuations of the metric, especially at high (Planck) energies, i.e. in the quantum-gravitational region, leading to new approaches to studies of the quantum foam. Then the possibility for applying the obtained results to the well-known problems of Gen- eral Relativity, in particular to the problem of the existence of Closed Time-like Curves (CTC) is discussed. Subject Classification: 03.65, 05.20 Keywords: gravity, measurability, quantum foam 1 Introduction This paper is a continuation of previous works written by the author [1]{ [7] with the use of the measurability concept. Section 2 presents a short description of the prior information with the relevant references.
    [Show full text]
  • Is N=8 Supergravity Finite?
    Do We Need String Theory to Quantize Gravity? Lance Dixon (CERN & SLAC) in collaboration with Z. Bern, J.J. Carrasco, H. Johansson, R. Roiban Theory Colloquium University of Padova and INFN Padova 3 February 2011 Gravity Governs the Very Big Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 2 But Per Particle It Is Very Weak Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 3 Quantum Mechanics Rules the Very Small Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 4 How Can Gravity And Quantum Mechanics Coexist? • Since Einstein, physicists have sought to unify all the fundamental forces and particles in the universe. • 3 of 4 forces – strong, weak and electromagnetic – have been put on a common footing, fully quantum mechanical and relativistic, and subject to a multitude of experimental tests. • Gravity is very different. • Conventional wisdom for 25 years: The only way to make gravity consistent with quantum mechanics is if all elementary particles are really oscillation modes of strings. • Here I want to describe another possible way that quantum gravity might work, without strings, with only point-like particles. Do we need string theory to quantize gravity? L. Dixon Padova 3 Feb. 2011 5 Hawking Radiation • Involves both quantum mechanics and gravity • Particles produced in curved spacetime near a black hole • Very well accepted theoretically, although also poses paradoxes • However, main effect is not quantum gravity – spacetime geometry is treated classically, not as fluctuating Do we need string theory to quantize gravity? L.
    [Show full text]
  • Quantum Pre-Geometry Models for Quantum Gravity
    Quantum pre-geometry models for Quantum Gravity by Francesco Caravelli A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2012 © Francesco Caravelli 2012 AUTHOR’S DECLARATION I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii ABSTRACT In this thesis we review the status of an approach to Quantum Gravity through lattice toy models, Quantum Graphity. In particular, we describe the two toy models introduced in the literature and describe with a certain level of details the results obtained so far. We emphasize the connection between Quantum Graphity and emergent gravity, and the relation with Variable Speed of Light theories. iii ACKNOWLEDGEMENTS A long list of sincere thanks has to be given here. First of all, to my supervisors, Fotini Markopoulou and Lee Smolin, for the continuous and discrete support during the PhD. Then, a sincere thanks goes to the people I have closely collaborated with (and friends), Leonardo Modesto, Alioscia Hamma and Simone Severini, Arnau Riera, Dario Benedetti, Daniele Oriti, Lorenzo Sindoni, Razvan Gurau, Olaf Dreyer, Emanuele Alesci, Isabeau Premont-Schwarz,´ Sylvain Carrozza and Cosimo Bambi. A particular thanks goes also to my family (Mamma, Papa´ e le sorelline), for continuous support, moral and economi- cal. Then a long list of friends goes here. Having shared a double life between Waterloo (Canada) and Berlin (Germany), a list of people from all over the world follows! In Wa- terloo, I have to thank my buddy Cozmin(/Cozster Cosniverse Cosferatu) Ududec and my dear friend Mitzy Herrera, Owen Cherry (on top), Cohl Fur(e)y, Coco Escobedo, John Daly and Jessica Phillips, Jonathan Hackett and Sonia Markes .
    [Show full text]
  • Spin Foam Model and Emergent Gravity
    Spin Foam Model and Emergent Gravity Muxin Han (韩慕⾟) （in collaboration with Zichang Huang (⻩⼦⾿) and Antonia Zipfel） General Relativity: Gravity = Curved Spacetime Geometry Quantum Gravity = Quantum Spacetime Geometry What is a Quantum Spacetime? ( In this talk, the spacetime dimension is 4 = 3+1 ) !2 Wheeler & Hawking’s Quantum Foam J.A. Wheeler, Geometrodynamics and the issue of the final state, in Relativity, groups and topology, C. DeWitt and B.S. DeWitt eds., Gordon and Breach, New York U.S.A. (1964). S.W. Hawking, Space-time foam, Nucl. Phys. B 144 (1978) 349. !3 Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. General Relativity: If energy and momentum grow too much, it collapses and forms a black hole. Singularities, infinities, difficulies Quantum Mechanics: If we localize too much a particle in spacetime, its energy and momentum grow. General Relativity: If energy and momentum grow too much, it collapses and forms a black hole. Singularities, infinities, difficulies Resolution: There is a minimal scale (Planck scale p) in spacetime against localization. Quantum Spacetime is Foam-like A minimal cell of quantum spacetime A Complementary Point of View: Emergent Gravity Quantum Gravity as an Ocean of Entangled Qubits Xiao-Gang Wen, Zhenghan Wang 2018 Zheng-Cheng Gu, Xiao-Gang Wen 2009 !8 A Complementary Point of View: Emergent Gravity Quantum Spacetime is a Tensor Network Swingle 2009,
    [Show full text]