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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. -
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. -
London Gaudiya Calendar 2010-11
All glories to Sri Guru and Sri Gauranga Gaudiya Vaishnava Festival Calendar (2010 – 2011) Founder Acharyya—Srila Bhakti Rakshak Sridhar Dev-Goswami Maharaj President Acharyya—Srila Bhakti Sundar Govinda Dev-Goswami Maharaj Sri Chaitanya Saraswat Math London, United Kingdom All glories to Sri Guru and Sri Gauranga Gaudiya Vaishnava Festival Calendar 2010 to 2011 - Sri Gaurabda 525 This calendar is based on the translation of the Bengali Vaisnava Calendar, "Sri Gaudiya Parvva Talika," compiled by Sriyukta Dibyendu Bhattacharyya, M.Sc., B.T., Jyotibhushan, Headmaster. Translated to English by Sripad Bhakti Nirmal Acharyya Maharaj. All dates and times listed here are calculated for Kolkata, India, as referred to at Sri Chaitanya Saraswat Math, Sri Nabadwip Dham. Ekadasi dates and paran times are calculated for London, United Kingdom by Sri Devashis Das with corrections by Sri Natabara Das. During his 21st World Tour, Srila Bhakti Sundar Govinda Dev-Goswami Maharaj instructed that throughout the world the devotees will follow this calendar for all dates except for Ekadasis and their associated paran (break fast) times which may be calculated locally according to the lunar calendar. In this way the days of Appearance, Disappearance, and other Pastimes of the Lord and His great devotees will be observed on the actual day they took place in India, rather than according to the technical local calculation of the 'tithi' (lunar day) which often had devotees observing, for example, the Appearance of Mahaprabhu a day before He actually appeared in Nabadwip. Start of 525 Gaurabda year. MARCH 2010 VISHNU 1. (Mon) Krishna-pratipad. Paran between 06:52 and 10:26 a.m. -
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. -
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]. -
Spiritual Successors of the Six Goswamis
All glory to Sri Guru and Gauranga Spiritual Successors Of The Six Goswamis By the Grace of the Founder-President-Acharya Of Nabadwip Sri Chaitanya Saraswat Math Ananta sri vibhusita Nitya-lila-pravistha Om Vishnupada Paramahamsa Parivrajakarchary kula chudamani Srila Bhakti Rakshak Sridhar Dev Goswami Maharaj Under the Divine Guidance and Inspiration Graciously Granted by His Most Beloved Attendent and Authorized Successor Om Vishnupada Paramahamsa Parivrajakacharya Astottara-sata Sri Srimad Bhakti Sundar Govinda Dev Goswami Maharaj This book was published from Sri Chaitanya Saraswat Sridhar Mission, Sydney Australia, by Muralidhar das. Contents Vande Rupa Sanatana......................................................................3 Sri Srinivas Acharya .......................................................................6 Srila Narottam das Thakur ............................................................11 Srila Shyamananda Prabhu ...........................................................16 Sri Vishnupriya Devi..................................................................... 20 The Gaudiya Vaishnava Sampradaya............................................24 The Gaura Purnima festival at Kheturi..........................................29 After the Kheturi festival...............................................................36 Srila Visvanatha Chakravarti Thakur ........................................... 41 The clash of Spirituality and Sectarianism.................................... 47 Srila Baladeva Vidyabhusan .........................................................52 -
Sri Vyasa Puja 2003
Sri Vyasa Puja 2003 All glories to Sri Sri Guru and Gauranga! Dear Srila Govinda Maharaj, Please accept my most sincere dandavat pranams at your lotus feet. All glories to Srila Guru Maharaj. I wish you a happy Vyasa Puja day, and I hope that the Lord protects you for thousands and thousands of years, so we can continue receiving your association. You are the true representative of the Sweet Lord in this material world. With love and affection from a fallen soul, Shyamagouri devi dasi Caracas, Venezuela All glories to Sri Guru and Gauranga All glories to Srila Bhakti Sundar Govinda Dev-Goswami Maharaj All glories to Srila Bhakti Rakshak Sridhar Dev-Goswami Maharaj Holy Gurudev, I hope you are doing well. I’ve been busy trying to succeed here, but I cannot for- get the Holy Dham. Please give me the strength to surrender myself unto the lotus feet of your servants. I remember you, my dear Gurudev, as the sweet one who always has a place for everyone. I also remember your holy mother; she touched my head, blessing me with her touch. I remember your relatives, and I also remember your associates, the holy places, the holy Guru Maharaj’s place, the holy air, the holy sun. Please give me strength to bear this empty gap between us. I’m sure you’re having a happy celebration for your Vyasa Puja, as you always deserve. I wish I could be there next to you; but what is better, maybe I can do some real service for you. -
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. -
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. -
Srila Bhakti Rakshak Sridhar Dev-Goswami Maharaj 002 81.08.31.A2.B1 Quest for Rasa
Srila Bhakti Rakshak Sridhar Dev-Goswami Maharaj 002_81.08.31.A2.B1 Quest for Rasa 81.08.30.31.A2 Gaura haribol, gaura haribol, gaura haribol. raso vai saḥ rasaṁ hy evāyaṁ labdhvānandī bhavati [Taittirīya Upaniṣad 2.7.1] After all we want pure rasa, ananda. That is our quest. And we are told that is in the service of the rasa himself. Rasa is a person, akhila rasamrita murti. Everyone is in quest for rasa. The status of rasa is the highest. So if we are person, we have got subjective existence. Rasa has got his supersubjective existence. He is a person. He is akhila rasamrta murti. He is Krishna. Rasa is Krishna. There cannot be rasa in any other place but in Krishna, the highest conception, the source. The fountainhead of all rasa of different type is only in Him. So, by nature of our construction, we are to search after Krishna. Krishna-anusandan. That will be the type, the nature of a normal person here. Krishna-anusandan. That will be the type, the nature of a normal person here, krishna-anusandan. Just as Brahma jijnasa in Vedanta. In Vedanta sutra we find: "brahma jijnasa", "inquire after the supreme cause of this world, search what is the supreme cause". Yato vā imāni bhūtāni jāyante yena jātāni jīvanti yat prayanty abhisaṁviśant [Taittirīya Upaniṣad 3.1.1] Wherefrom all has come and where it is being, it is maintaining its existence, how, by whom and ultimately where do they enter after death. That is Brahma, the most fundamental plane. Wherefrom everything is springing up and remains and then enters. -
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. -
The Guardian of Devotion
All Glories to Sri Guru and Gauranga The Guardian of Devotion A Chronicle of a Transcendental Relationship His Divine Grace Srila Bhakti Rakshak Sridhar Maharaj Founder-Acharya of Sri Chaitanya Saraswat Math Srila Bhakti Rakshak Sridhar Maharaj and Srila Bhaktivedanta Swami Prabhupad Forward Sri Chaitanya-caritamrta, the post-graduate study for Gaudiya Vais- navas begins with the invocation vande gurun, “I offer my respectful obeisances unto the spiritual master.” Therein, Srila Krsnadasa Kaviraja Goswami reveals that the fully blossoming spiritual conception comes to embrace a plurality of gurus. The scriptures in general present a very broad and universal conception of Sri Guru, laying stress on the spiritual substance – that divine current of nectar that flows down to this plane from the highest domain through the inspiration that is found in the heart of a real Vaisnava. To deny divine revelation through another agent in the name of being chaste to one’s guru can be offensive and even suicidal. As guru is the functioning principle of Divinity revealing Himself in this world, according to our different stages of realizations, he may appear in different forms. The chastity of a disciple is demonstrated in recognizing the divine presence of Sri Guru wherever it is found, and bowing his head at the lotus feet of the agent through whom Divinity is so kindly revealing Himself. The true chastity of the Vraja gopis was shown in their answering the flute-call of Sri Krsna in the dead of night, although apparently abandoning their husbands to do so (ya nisa sarva-bhutanam tasyam jagarti samyami).