DOCSLIB.ORG

Redalyc.Emerging Gravity from Defects in World Crystal

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Redalyc.Emerging Gravity from Defects in World Crystal Brazilian Journal of Physics ISSN: 0103-9733 [email protected] Sociedade Brasileira de Física Brasil Kleinert, H. Emerging gravity from defects in world crystal Brazilian Journal of Physics, vol. 35, núm. 2A, june, 2005, pp. 359-361 Sociedade Brasileira de Física Sâo Paulo, Brasil Available in: http://www.redalyc.org/articulo.oa?id=46435222 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Brazilian Journal of Physics, vol. 35. no. 2A, June, 2005 359 Emerging Gravity from Defects in World Crystal H. Kleinert Institut f¨ur Theoretische Physik, Freie Universit¨at Berlin, Arnimallee 14, D14195 Berlin Received on 25 January, 2005 I show that Einstein Gravity can be thought of as arising from the defects in a world crystal whose lattice −33 spacing is of the order of the Planck length lP ≈ 10 cm, and whose elastic energy is of the second-gradient type (floppy crystal). No physical experiment so far would be able to detect the lattice structure. I. INTRODUCTION Volterra surfaces via δ-functions on these surfaces [9–11]. The energy density is invariant under the single-valued defect One of the most important features of string theories is that gauge transformations they assume the validity of Lorentz invariance for all energies p → p +(∂ λ + ∂ λ )/ , → + λ . in the trans-Planckian regime [1]. In this lecture we would uµν uµν µ ν ν µ 2 uµ uµ µ (4) like to point out that an entirely different scenario is possi- Physically, they express the fact that defects are not affected ble. It could be that we live in a world crystal with a lattice by elastic distortions of the crystal. Only multivalued gauge constant of the order of the Planck length, without being able p functions λ would change the defect content in u ν. to notice this. None of the present-day relativistic physical µ µ We now rewrite the action (5) in a canonical form introduc- laws would have to be observably violated. The gravitational ing an auxiliary symmetric stress tensor field σ ν as forces could arise from variants of ordinary elastic forces in µ this world crystal, and the observed curvature in gravitational Z 4 1 µν µν p spacetime could be just a signal of the presence of disclina- A = d x σµνσ + iσ (uµν − uµν) . (5) 4µ tions in the world crystal. Matter would be sources of discli- nations. After a partial integration and extremization in u µ, the middle terms yield the equation µν II. PURE GRAVITY ∂νσ = 0. (6) For simplicity, we shall present such a construction only for This may be guaranteed identically, as a Bianchi identity, by a system without torsion [2]. The idea goes back to a 1987 lec- an ansatz ture of mine held in the Einstein house in Caputh [3]. Present κλσ κλτ σ = ε ε ∂ ∂ χ . interest in Emerging Gravity [4–7] instigated me to revitalize µν µ ν λ λ στ (7) it. The field χστ plays the role of an elastic gauge field. It is If the world crystal is distorted by an infinitesimal displace- ( ) ment field the analog of the vector potential A x in magnetism. Inserting (7) into (5), we obtain µ → µ = µ + µ( ), x x x u x (1) Z 2 4 1 µκλσ νκλτ A = d x ε ε ∂λ∂λ χστ it has a strain energy 4µ Z νκλσ µκλτ p µ 4 2 +iε ε ∂λ∂λ χστuµν . (8) A = d x(∂µuν + ∂νuµ) , (2) 4 where µ is some elastic constant. If part of the distortions are A further partial integration brings this to the form of the plastic type, the world crystal contains defects defined Z 2 4 1 µκλσ νκλτ by Volterra surfaces, where crystalline sections have been cut A = d x ε ε ∂λ∂λ χστ out. The displacement field is multivalued, and the action (2) 4µ is the analog of the magnetic action in the presence of a cur- σκλν τκλ p + χ ε ε µ∂ ∂ . rent loop [8]. In order to do field theory with this action, we i στ λ λ uµν (9) have to make the displacement field single-valued with the help of δ-functions describing the jumps across the Volterra This is a double-gauge theory invariant under the defect gauge surfaces, by complete analogy with the gradient representa- transformation (4) and under stress gauge transformations tion of the magnetic energy [8]: χστ → χστ + ∂σΛτ + ∂τΛσ. (10) Z 4 p 2 = µ d x(u ν − u ν) , (3) A µ µ This can be rewritten as Z where uµν ≡ (∂µuν + ∂νuµ)/2 is the elastic strain tensor, and 4 1 µν µν p A = d x σµνσ + iχµνη , (11) uµν the gauge field of plastic deformations describing the 4µ 360 H. Kleinert where ηµν is the four-dimensional defect density and the interaction (18) of an arbitrary distribution of defects would become κλσ κλτ p ηµν = εµ εν ∂λ∂λ uστ. (12) Z 4 p µν A = µ d xu µν(x)η (x). (21) It is invariant under defect gauge transformations (4), and sat- isfies the conservation law This coincides with the linearized Einstein action Z µν 1 √ ∂νη = 0. (13) A = − d4x −gR¯ (22) 2κ p We may now replace uστ by half the metric field gµν, and where κ is the gravitational constant. Indeed, in the linear the tensor ηµν becomes the Einstein tensor associated with the ν ν ν ν approximation gµ = δµ + hµ with |hµ |1, where the metric tensor gµν. Christoffel symbols can be approximated as Let us eliminate the stress gauge field from the action (11). For this we rewrite the stress field (7) as λ 1 Γ¯ µν ≈ ∂µhνλ + ∂νhµλ − ∂λhµν , (23) κλσ κλτ 2 σ ν = ε εν ∂λ∂λ χστ µ µ the Riemann curvature tensor becomes 2 λ λ λ = −(∂ χ ν + ∂ ∂νχλ − ∂ ∂λχ − ∂ν∂λχ ) µ µ µ µ µ 1 +η (∂2χ λ − ∂ ∂ χλκ). R¯ νλκ ≈ ∂ ∂λhνκ − ∂ν∂κh λ − (µ ↔ ν) . (24) µν λ λ κ (14) µ 2 µ µ φ ν ≡ χ ν − 1 δ νχ λ This gives the Ricci tensor Introducing the field µ µ 2 µ λ , and going to the µ ν Hilbert gauge ∂ φµ = 0, the stress tensor reduces to 1 2 R¯µκ ≈ (∂µ∂λhλκ + ∂κ∂λhλµ − ∂µ∂κh − ∂ hµκ), (25) 2 2 σµν = −∂ φµν, (15) λ where h is defined to be the trace of the tensor h µν, i.e. h ≡ hλ . and the action of an arbitrary distribution of defects would The ensuing scalar curvature reads become ¯ ≈−(∂2 − ∂ ∂ µν) Z R h µ νh (26) 1 ν ν λ = 4 ∂2φµ ∂2φ + φ (ηµ − 1 δµ η ) . A d x µν i µ ν 2 ν λ (16) 4µ so that the Einstein tensor becomes φµν 1 Eliminating the field yields the interaction of an arbitrary G¯ µκ = R¯µκ − gµκR¯ (27) distribution of defects 2 1 λ λ Z 2 ≈−(∂ hµκ + ∂µ∂κh − ∂µ∂λh κ − ∂κ∂λh µ) 4 µ µ λ 1 ν ν λ = µ d x(η ν − 1 δ νη λ) (η − 1 δ η λ). (17) 2 A 2 (∂2)2 µ 2 µ 1 2 νλ + η κ(∂ h − ∂ν∂λh ). 2 µ This is not the Einstein action for a Riemann spacetime. It would be so if the derivatives ∂2 in (16) would be replaced by This can be written as a four-dimensional version of a double ∂. Then the Green function of (∂2)2 would be replaced by the curl Green function of −∂2. An index rearrangement would lead 1 νλ δστ to the interaction G¯ κ = ε δ εκ ∂ν∂σhλτ. (28) µ 2 µ Z λ 1 ν = 4 (ηµ − 1 δµ η ) η . Thus the Einstein-Hilbert action has the linear approxima- A µ d x ν 2 ν λ µ (18) −∂2 tion η Z The defect tensor µν is composed of the plastic gauge fields 1 4 µν p d xhµνG . (29) uµν in the same way as the stress tensor is in terms of the stress 4κ gauge field in Eq. (14): Recalling the previously established identifications of plastic κλσ κλτ p field and defect density with metric and Einstein tensor, re- ηµν = εµ εν ∂λ∂λ uστ. spectively, the interaction between defects (21) is indeed the = −(∂2 p + ∂ ∂ pλ − ∂ ∂ pλ − ∂ ∂ pλ) uµν µ νuλ µ λuµ ν λuµ linearized version of the Einstein-Hilbert action (22), if we 2 pλ pλκ identify the constant µ with 1/4κ. +ηµν(∂ uλ − ∂λ∂κu ). (19) The world crystal with the elastic energy (5) does not lead pν ≡ pν − 1 δ ν pλ to this action. It must be modified to do so. A first modifi- If we introduce the auxiliary field wµ uµ 2 µ uλ and µ p cation is to introduce two more derivatives and assign to the chose the Hilbert gauge ∂ w ν = 0, the defect density reduces µ crystal the higher-gradient elastic energy to Z ν ν λ 4 p 2 η = −∂2 p , η − 1 δ η = −∂2 p . A = µ d x[∂(uµν − uµν)] . (30) µν wµν µ 2 µ λ uµν (20) Brazilian Journal of Physics, vol. 35. no. 2A, June, 2005 361 This removes one power of −∂2 from the denominator in the by all particles in the world crystal which are tightly bound to interaction (17).
Load more

Recommended publications
  • Uncertainty Relation on a World Crystal and Its Applications to Micro Black Holes
    PHYSICAL REVIEW D 81, 084030 (2010) Uncertainty relation on a world crystal and its applications to micro black holes Petr Jizba,1,2,* Hagen Kleinert,1,† and Fabio Scardigli3,‡ 1ITP, Freie Universita¨t Berlin, Arnimallee 14 D-14195 Berlin, Germany 2FNSPE, Czech Technical University in Prague, Brˇehova´ 7, 115 19 Praha 1, Czech Republic 3Leung Center for Cosmology and Particle Astrophysics (LeCosPA), Department of Physics, National Taiwan University, Taipei 106, Taiwan (Received 17 December 2009; published 16 April 2010) We formulate generalized uncertainty relations in a crystal-like universe—a ‘‘world crystal’’—whose lattice spacing is of the order of Planck length. In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking’s temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. We also briefly mention some connections of the world-crystal paradigm with ’t Hooft’s quantization and double special relativity. DOI: 10.1103/PhysRevD.81.084030 PACS numbers: 04.70.Dy, 03.65. w À I. INTRODUCTION from numerical computations. One may, however, inves- tigate the consequences of taking the lattice no longer as a Recent advances in gravitational and quantum physics mere computational device, but as a bona fide discrete indicate that in order to reconcile the two fields with each network, whose links define the only possible propagation other, a dramatic conceptual shift is required in our under- directions for signals carrying the interactions between standing of spacetime.
    [Show full text]
  • Emergent Gravity As the Nematic Dual of Lorentz-Invariant Elasticity
    SMR 1646 - 12 ___________________________________________________________ Conference on Higher Dimensional Quantum Hall Effect, Chern-Simons Theory and Non-Commutative Geometry in Condensed Matter Physics and Field Theory 1 - 4 March 2005 ___________________________________________________________ Emergent gravity as the nematic dual of Lorentz-invariant Elasticity Johannes ZAANEN Stanford Univ., Stanford, U.S.A. ___________________________________________________________________ These are preliminary lecture notes, intended only for distribution to participants. EmergentEmergent gravitygravity asas thethe nematicnematic dualdual ofof LorentzLorentz--invariantinvariant ElasticityElasticityTalk Jan Zaanen Hagen Kleinert Sergei Mukhin Zohar Nussinov Vladimir Cvetkovic 1 Emergent Einstein Gravity c 3 S =− dV −g R + S 16πG ∫ matter Einstein’s space time = the Lorentz invariant topological nematic superfluid (at least in 2+1D) A medium characterized by: - emergent general covariance - absence of torsion- and compressional rigidity - presence of curvature rigidity (topological order) 2 Plan of talk 1. Plasticity (defected elasticity) and differential geometry 2. Fluctuating order and high Tc superconductivity 3. Dualizing non-relativistic quantum elasticity 3.a Quantum nematic orders 3.b Superconductivity: dual Higgs is Higgs 4. The quantum nematic world crystal and Einstein’s space time 3 Quantum-elasticity: basics Quantum elastic action, isotropic medium ν ⎡ 2 2 2 2 2 2⎤ S = µ u + 2u + u + ()u + u + ()∂τ u + ()∂τ u ⎣⎢ xx xy yy 1−ν xx yy x y ⎦⎥ Shear modulus µ, Poisson ratio ν, compression modulus κ = µ()1 + ν /1()− ν 2 = µ ρ = = = ()∂ + ∂ c ph 2 / 1, h 1, uab a ub b ua /2 Describes transversal- (T) and longitudinal (L) phonon, 2 2 ⎡⎛ q ⎞ ⎛ q ⎞ ⎤ S = µ ⎢⎜ + ω 2 ⎟ | uT |2 +⎜ + ω 2 ⎟ | uL |2⎥ ⎣⎝ 2 ⎠ ⎝ 1−ν ⎠ ⎦ 4 Elasticity and topology: the dislocation J.M.
    [Show full text]
  • Arxiv:0912.2253V2 [Hep-Th] 19 Dec 2009 ‡ † ∗ Rcsi Ellratmt 1,1,1,1,15]
    Uncertainty relation on world crystal and its applications to micro black holes Petr Jizba,1,2, ∗ Hagen Kleinert,1, † and Fabio Scardigli3, ‡ 1ITP, Freie Universit¨at Berlin, Arnimallee 14 D-14195 Berlin, Germany 2FNSPE, Czech Technical University in Prague, B˘rehov´a7, 115 19 Praha 1, Czech Republic 3Leung Center for Cosmology and Particle Astrophysics (LeCosPA), Department of Physics, National Taiwan University, Taipei 106, Taiwan We formulate generalized uncertainty relations in a crystal-like universe whose lattice spacing is of the order of Planck length — “world crystal”. In the particular case when energies lie near the border of the Brillouin zone, i.e., for Planckian energies, the uncertainty relation for position and momenta does not pose any lower bound on involved uncertainties. We apply our results to micro black holes physics, where we derive a new mass-temperature relation for Schwarzschild micro black holes. In contrast to standard results based on Heisenberg and stringy uncertainty relations, our mass-temperature formula predicts both a finite Hawking’s temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. We also briefly mention some connections of the world crystal paradigm with ’t Hooft’s quantization and double special relativity. PACS numbers: 04.70.Dy, 03.65.-w I. INTRODUCTION tions. One may, however, investigate the consequences of taking the lattice no longer as a mere computational Recent advances in gravitational and quantum physics device, but as a bona-fide discrete network, whose links indicate that in order to reconcile the two fields with define the only possible propagation directions for sig- each other, a dramatic conceptual shift is required in nals carrying the interactions between fields sitting on our understanding of spacetime.
    [Show full text]
  • Three Duality Symmetries Between Photons and Cosmic String Loops, and Macro and Micro Black Holes
    Symmetry 2015, 7, 2134-2149; doi:10.3390/sym7042134 OPEN ACCESS symmetry ISSN 2073-8994 www.mdpi.com/journal/symmetry Article Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes David Jou 1;2;*, Michele Sciacca 1;3;4;* and Maria Stella Mongiovì 4;5 1 Departament de Física, Universitat Autònoma de Barcelona, Bellaterra 08193, Spain 2 Institut d’Estudis Catalans, Carme 47, Barcelona 08001, Spain 3 Dipartimento di Scienze Agrarie e Forestali, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy 4 Istituto Nazionale di Alta Matematica, Roma 00185 , Italy 5 Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica (DICGIM), Università di Palermo, Viale delle Scienze, Palermo 90128, Italy; E-Mail: [email protected] * Authors to whom correspondence should be addressed; E-Mails: [email protected] (D.J.); [email protected] (M.S.); Tel.: +34-93-581-1658 (D.J.); +39-091-23897084 (M.S.). Academic Editor: Sergei Odintsov Received: 22 September 2015 / Accepted: 9 November 2015 / Published: 17 November 2015 Abstract: We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed. Keywords: photons; cosmic string loops; black holes thermodynamics; duality symmetry 1. Introduction Thermal duality relates high-energy and low-energy states of corresponding dual systems in such a way that the thermal properties of a state of one of them at some temperature T are related to the properties of a state of the other system at temperature 1=T [1–6].
    [Show full text]
  • Verlinde's Emergent Gravity and Whitehead's Actual Entities
    The Founding of an Event-Ontology: Verlinde's Emergent Gravity and Whitehead's Actual Entities by Jesse Sterling Bettinger A Dissertation submitted to the Faculty of Claremont Graduate University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate Faculty of Religion and Economics Claremont, California 2015 Approved by: ____________________________ ____________________________ © Copyright by Jesse S. Bettinger 2015 All Rights Reserved Abstract of the Dissertation The Founding of an Event-Ontology: Verlinde's Emergent Gravity and Whitehead's Actual Entities by Jesse Sterling Bettinger Claremont Graduate University: 2015 Whitehead’s 1929 categoreal framework of actual entities (AE’s) are hypothesized to provide an accurate foundation for a revised theory of gravity to arise compatible with Verlinde’s 2010 emergent gravity (EG) model, not as a fundamental force, but as the result of an entropic force. By the end of this study we should be in position to claim that the EG effect can in fact be seen as an integral sub-sequence of the AE process. To substantiate this claim, this study elaborates the conceptual architecture driving Verlinde’s emergent gravity hypothesis in concert with the corresponding structural dynamics of Whitehead’s philosophical/scientific logic comprising actual entities. This proceeds to the extent that both are shown to mutually integrate under the event-based covering logic of a generative process underwriting experience and physical ontology. In comparing the components of both frameworks across the epistemic modalities of pure philosophy, string theory, and cosmology/relativity physics, this study utilizes a geomodal convention as a pre-linguistic, neutral observation language—like an augur between the two theories—wherein a visual event-logic is progressively enunciated in concert with the specific details of both models, leading to a cross-pollinized language of concepts shown to mutually inform each other.
    [Show full text]
  • Arxiv:1607.00955V1 [Gr-Qc] 4 Jul 2016 ML Second Law of Planetary Motion (Figure 1)
    Thermal Time and Kepler's Second Law∗ Deepak Vaidy National Institute of Technology, Karnataka (Dated: September 26, 2018) It is shown that a recent result regarding the average rate of evolution of a dynamical system at equilibrium in combination with the quantization of geometric areas coming from LQG, implies the validity of Kepler's Second Law of planetary motion. INTRODUCTION Ehrenfest effect and the rate of dynamical evolution of a system - i.e. the number of distinguishable (orthog- One of the leading contenders for a theory of quan- onal) states a given system transitions through in each tum gravity is the field known as Loop Quantum Grav- unit of time. The last of these is also the subject of ity (LQG) [1]. A fundamental result of this approach to- the Margolus-Levitin theorem [17] according to which the wards reconciling geometry and quantum mechanics, is rate of dynamical evolution of a macroscopic system with the quantization of geometric degrees of freedom such as fixed average energy (E), has an upper bound (ν?) given areas and volumes [2,3]. LQG predicts that the area of by: any surface is quantized in units of the Planck length 2E squared l2. ν ≤ (1) p ? h Despite its many impressive successes, in for instance, solving the riddle of black hole entropy [4,5] or in under- Note that ν? is the maximum possible rate of dy- standing the evolution of geometry near classical singu- namical evolution, not the average or mean rate, and larities such as at the Big Bang or at the center of black also that in [17] the bound is determined by the aver- P holes [6,7,8], LQG is yet to satisfy the primary criteria age energy: E = cnEnj ni of a system in a state P n for any successful theory of quantum gravity - agreement jΨi = n cnj ni, where fj nig is a basis of energy eigen- between predictions of the quantum gravity theory and states of the given system.
    [Show full text]
  • The Emergence of Gauge Invariance: the Stay-At-Home Gauge Versus Local–Global Duality
    The emergence of gauge invariance: the stay-at-home gauge versus local{global duality. J. Zaanen∗ and A.J. Beekman Instituut-Lorentz for Theoretical Physics, Universiteit Leiden, P. O. Box 9506, 2300 RA Leiden, The Netherlands (Dated: August 13, 2011) In condensed matter physics gauge symmetries other than the U(1) of electromagnetism are of an emergent nature. Two emergence mechanisms for gauge symmetry are well established: the way these arise in Kramers{Wannier type local{global dualities, and as a way to encode local constraints encountered in (doped) Mott insulators. We demonstrate that these gauge structures are closely related, and appear as counterparts in either the canonical or field-theoretical language. The restoration of symmetry in a disorder phase transition is due to having the original local variables subjected to a coherent superposition of all possible topological defect configurations, with the effect that correlation functions are no longer well-defined. This is completely equivalent to assigning gauge freedom to those variables. Two cases are considered explicitly: the well-known vortex duality in bosonic Mott insulators serves to illustrate the principle. The acquired wisdoms are then applied to the less familiar context of dualities in quantum elasticity, where we elucidate the relation between the quantum nematic and linearized gravity. We reflect on some deeper implications for the emergence of gauge symmetry in general. PACS numbers: 11.25.Tq, 05.30.Rt, 04.20.Cv, 71.27. I. INTRODUCTION. ality) language. The case is very simple and we will illustrate it in section II with the most primitive of all many-particle systems governed by continuous symme- Breaking symmetry is easy but making symmetry is try: the Bose-Hubbard model at zero chemical poten- hard: this wisdom applies to global symmetry but not tial, or alternatively the Abelian-Higgs duality associ- to local symmetry.
    [Show full text]
  • Arxiv:2012.09158V2 [Gr-Qc] 5 Apr 2021 Quantum Cosmology With
    Quantum Cosmology with Dynamical Vacuum in a Minimal-Length Scenario M. F. Gusson, A. Oakes O. Gon¸calves,∗ R. G. Furtado, †‡ J. C. Fabris and J. A. Nogueira§ Universidade Federal do Esp´ırito Santo – Ufes Vit´oria, Esp´ırito Santo, 29.075-910, Brasil Abstract In this work, we consider effects of the dynamical vacuum in quan- tum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation ~ relation [X,ˆ Pˆ] := i . We determine the wave function of the Uni- 1 βPˆ2 − verse ψqp(ξ,t), which is solution of the modified Wheeler-DeWitt equa- tion in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although ψqp(ξ,t) is a physi- cally acceptable state it is not a realizable state of the Universe because ψqp(ξ,t) has infinite norm, as in the ordinary case with no minimal length. PACS numbers: 98.80.Qc, 04.60.-m, 04.50.Kd, Keywords: Minimal length; generalized uncertainty principle; quantum gravity; quantum cos- mology; dynamical vacuum. arXiv:2012.09158v2 [gr-qc] 5 Apr 2021 1 Introduction The Standard Cosmological Model (SCM) is based on an expanding universe which has a very hot and dense origin. The extrapolation of the SCM for very early times leads to energy scales deep in the Planck regime and, strictly speaking, the expanding universe would have a singular initial state. On the other hand, in order to explain many features of the observed Universe today, a period of short but rapid, almost exponential, expansion, which is called inflationary phase, is necessary in the very early Universe.
    [Show full text]
  • Explaining Phenomenologically Observed Space-Time Flatness
    Explaining Phenomenologically Observed Spacetime Flatness Requires New Fundamental Scale Physics D. L. Bennett Brookes Institute for Advanced Studies, Bøgevej 6, 2900 Hellerup, Denmark [email protected] H. B. Nielsen The Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen Ø [email protected] February 27, 2018 Abstract The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional ar- guments it is demonstrated that any immaginable action will lead to Christoffel symbols that are chaotic. We put forward new physics in the form of fundamental fields that spontaneously break translational invariance. Using these new fields as coordinates we define the met- ric in such a way that the Riemann tensor vanishes identically as a Bianchi identity. Hence the new fundamental fields define a flat space. General relativity with curvature is recovered as an effective theory at larger scales at which crystal defects in the form of disclinations come into play as the sources of curvature. arXiv:1306.2963v1 [gr-qc] 12 Jun 2013 1 1 Introduction We address the fundamental mystery of why the spacetime that we experi- ence in our everyday lives is so nearly flat. More provocatively one could ask why the macroscopic spacetime in which we are immersed doesn’t consist of spacetime foam[1, 2]. This question is approached by putting up a NO-GO for having the spacetime flatness that we observe phenomenologically. This NO-GO builds upon an argumentation that starts with the assumption that spacetime is a continuum down to arbitrarily small scales a with a<<lP l where lP l is the Planck length.
    [Show full text]
  • Quantum Mechanics on a Planck Lattice and Black Hole Physics
    5th International Workshop DICE2010 IOP Publishing Journal of Physics: Conference Series 306 (2011) 012026 doi:10.1088/1742-6596/306/1/012026 Quantum Mechanics on a Planck Lattice and Black Hole Physics Petr Jizba1, Hagen Kleinert2, Fabio Scardigli3 1 FNSPE, Czech Technical University in Prague, B¸rehov¶a7, 115 19 Praha 1, Czech Republic 2 ITP, Freie UniversitÄatBerlin, Arnimallee 14 D-14195 Berlin, Germany 3 Leung Center for Cosmology and Particle Astrophysics (LeCosPA), Department of Physics, National Taiwan University, Taipei 106, Taiwan E-mail: [email protected] E-mail: [email protected] E-mail: [email protected] Abstract. We study uncertainty relations as formulated in a crystal-like universe, whose lat- tice spacing is of order of Planck length. For Planck energies, the uncertainty relation for position and momenta has a lower bound equal to zero. Connections of this result with double special relativity, and with 't Hooft's deterministic quantization proposal, are briefly pointed out. We then apply our formulae to micro black holes, and we derive a new mass-temperature relation for Schwarzschild (micro) black holes. In contrast to standard results based on Heisen- berg and stringy uncertainty relations, we obtain both a ¯nite Hawking's temperature and a zero rest-mass remnant at the end of the micro black hole evaporation. 1. Introduction The idea of a discrete structure of the space-time can be traced back to the mid 50's when John Wheeler presented his space-time foam concept [1]. Recent advances in physics indicate that the notion of space-time as a continuum is indeed likely to be superseded at the Planck scale, where gravitation and strong-electro-weak interactions become comparable in strength.
    [Show full text]
  • Vortex Duality in Higher Dimensions
    Vortex duality in higher dimensions PROEFSCHRIFT TER VERKRIJGING VAN DE GRAAD VAN DOCTOR AAN DE UNIVERSITEIT LEIDEN, OP GEZAG VAN RECTOR MAGNIFICUS PROF. MR. P. F. VAN DER HEIJDEN, VOLGENS BESLUIT VAN HET COLLEGE VOOR PROMOTIES TE VERDEDIGEN OP DONDERDAG 1 DECEMBER 2011 KLOKKE 13.45 UUR DOOR Aron Jonathan Beekman GEBOREN TE GOUDA IN 1979 Promotiecommissie Promotor: Prof. dr. J. Zaanen Overige leden: Prof. dr. N. Nagaosa Universiteit van Tokyo Prof. dr. A. Sudbø Norges teknisk-naturvitenskaplige universitet Trondheim Prof. dr. P.H. Kes Prof. dr. J.M. van Ruitenbeek Dr. K.E. Schalm Prof. dr. E.R. Eliel Dit werk maakt deel uit van het onderzoekprogramma van de Stichting voor Fundamenteel Onderzoek der Materie (FOM), die deel uit maakt van de Ne- derlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). Dit werk is tevens ondersteund vanuit een NWO Spinozapremie. This work is part of the research programme of the Foundation for Funda- mental Research on Matter (FOM), which is part of the Netherlands Organi- sation for Scientific Research (NWO). This work has also been supported via a NWO Spinoza grant. Typeset in LATEX cover design: Rolf de Jonker / Studio Loupe cover photo: Sander Foederer Casimir PhD series, Delft–Leiden 2011-24 ISBN 978-90-8593-113-3 On April 8, 1911, in the physics laboratory located at ‘het Steenschuur’ in Leiden, Heike Kamerlingh Onnes and his coworkers Cornelis Dorsman, Ger- rit Jan Flim and Gilles Holst, measured the instantaneous drop in resistivity of mercury when they cooled it below 4.2 degrees above absolute zero. They were the first people in the world to have beheld the phenomenon of super- conductivity, and thereby the first macroscopic quantum fluid.
    [Show full text]
  • Quantum Gravitational Decoherence from Fluctuating Minimal Length And
    ARTICLE https://doi.org/10.1038/s41467-021-24711-7 OPEN Quantum gravitational decoherence from fluctuating minimal length and deformation parameter at the Planck scale ✉ ✉ Luciano Petruzziello 1,2 & Fabrizio Illuminati 1,2 Schemes of gravitationally induced decoherence are being actively investigated as possible mechanisms for the quantum-to-classical transition. Here, we introduce a decoherence 1234567890():,; process due to quantum gravity effects. We assume a foamy quantum spacetime with a fluctuating minimal length coinciding on average with the Planck scale. Considering deformed canonical commutation relations with a fluctuating deformation parameter, we derive a Lindblad master equation that yields localization in energy space and decoherence times consistent with the currently available observational evidence. Compared to other schemes of gravitational decoherence, we find that the decoherence rate predicted by our model is extremal, being minimal in the deep quantum regime below the Planck scale and maximal in the mesoscopic regime beyond it. We discuss possible experimental tests of our model based on cavity optomechanics setups with ultracold massive molecular oscillators and we provide preliminary estimates on the values of the physical parameters needed for actual laboratory implementations. 1 Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno, Fisciano, (SA), Italy. 2 INFN, Sezione di Napoli, Gruppo collegato di Salerno, Fisciano, ✉ (SA), Italy. email: [email protected]; fi[email protected] NATURE COMMUNICATIONS | (2021) 12:4449 | https://doi.org/10.1038/s41467-021-24711-7 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-24711-7 ollowing early pioneering studies1–4, the investigation of the gravitational effects are deemed to be comparably important.
    [Show full text]