Physics Meets Philosophy at the Planck Scale: Contemporary
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Raiders of the Lost Spacetime
Raiders of the lost spacetime Christian W¨uthrich∗ For Dennis Lehmkuhl (ed.), Towards a Theory of Spacetime Theories. Birkh¨auser. Abstract Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure of the world back to the classical spacetime of GR. The present essay investigates how spacetime is lost and how it may be regained in one major approach to quantum gravity, loop quantum gravity. Keywords: quantum gravity, problem of time, quantum GR, loop quantum gravity, emergence of spacetime. Many approaches to quantum gravity (QG) suggest or imply that space and time do not exist at the most fundamental ontological level, at least not in anything like their usual form. Thus deprived of their former status as part of the fundamental furniture of the world, together, perhaps, with quarks and leptons, they merely `emerge' from the deeper physics that does not rely on, or even permit, their (fundamental) existence, rather like tables and chairs. The extent to which the fundamental structures described by competing approaches to QG diverge from relativistic spacetimes varies, along different dimensions (Huggett and W¨uthrich 2012). That modern physics puts time under pressure is widely accepted. One can read the history of modern physics from the advent of relativity theory to the present day as a continuing peeling away of the structure that time was initially believed to exemplify (Huggett et al. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Conformal Symmetry in Field Theory and in Quantum Gravity
universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals). -
Quantum Topology and Categorification Seminar, Spring 2017
QUANTUM TOPOLOGY AND CATEGORIFICATION SEMINAR, SPRING 2017 ARUN DEBRAY APRIL 25, 2017 These notes were taken in a learning seminar in Spring 2017. I live-TEXed them using vim, and as such there may be typos; please send questions, comments, complaints, and corrections to [email protected]. Thanks to Michael Ball for finding and fixing a typo. CONTENTS Part 1. Quantum topology: Chern-Simons theory and the Jones polynomial 1 1. The Jones Polynomial: 1/24/171 2. Introduction to quantum field theory: 1/31/174 3. Canonical quantization and Chern-Simons theory: 2/7/177 4. Chern-Simons theory and the Wess-Zumino-Witten model: 2/14/179 5. The Jones polynomial from Chern-Simons theory: 2/21/17 13 6. TQFTs and the Kauffman bracket: 2/28/17 15 7. TQFTs and the Kauffman bracket, II: 3/7/17 17 Part 2. Categorification: Khovanov homology 18 8. Khovanov homology and computations: 3/21/17 18 9. Khovanov homology and low-dimensional topology: 3/28/17 21 10. Khovanov homology for tangles and Frobenius algebras: 4/4/17 23 11. TQFT for tangles: 4/11/17 24 12. The long exact sequence, functoriality, and torsion: 4/18/17 26 13. A transverse link invariant from Khovanov homology: 4/25/17 28 References 30 Part 1. Quantum topology: Chern-Simons theory and the Jones polynomial 1. THE JONES POLYNOMIAL: 1/24/17 Today, Hannah talked about the Jones polynomial, including how she sees it and why she cares about it as a topologist. 1.1. Introduction to knot theory. -
The Theory of (Exclusively) Local Beables
The Theory of (Exclusively) Local Beables Travis Norsen Marlboro College Marlboro, VT 05344 (Dated: June 17, 2010) Abstract It is shown how, starting with the de Broglie - Bohm pilot-wave theory, one can construct a new theory of the sort envisioned by several of QM’s founders: a Theory of Exclusively Local Beables (TELB). In particular, the usual quantum mechanical wave function (a function on a high-dimensional configuration space) is not among the beables posited by the new theory. Instead, each particle has an associated “pilot- wave” field (living in physical space). A number of additional fields (also fields on physical space) maintain what is described, in ordinary quantum theory, as “entanglement.” The theory allows some interesting new perspective on the kind of causation involved in pilot-wave theories in general. And it provides also a concrete example of an empirically viable quantum theory in whose formulation the wave function (on configuration space) does not appear – i.e., it is a theory according to which nothing corresponding to the configuration space wave function need actually exist. That is the theory’s raison d’etre and perhaps its only virtue. Its vices include the fact that it only reproduces the empirical predictions of the ordinary pilot-wave theory (equivalent, of course, to the predictions of ordinary quantum theory) for spinless non-relativistic particles, and only then for wave functions that are everywhere analytic. The goal is thus not to recommend the TELB proposed here as a replacement for ordinary pilot-wave theory (or ordinary quantum theory), but is rather to illustrate (with a crude first stab) that it might be possible to construct a plausible, empirically arXiv:0909.4553v3 [quant-ph] 17 Jun 2010 viable TELB, and to recommend this as an interesting and perhaps-fruitful program for future research. -
Detailing Coherent, Minimum Uncertainty States of Gravitons, As
Journal of Modern Physics, 2011, 2, 730-751 doi:10.4236/jmp.2011.27086 Published Online July 2011 (http://www.SciRP.org/journal/jmp) Detailing Coherent, Minimum Uncertainty States of Gravitons, as Semi Classical Components of Gravity Waves, and How Squeezed States Affect Upper Limits to Graviton Mass Andrew Beckwith1 Department of Physics, Chongqing University, Chongqing, China E-mail: [email protected] Received April 12, 2011; revised June 1, 2011; accepted June 13, 2011 Abstract We present what is relevant to squeezed states of initial space time and how that affects both the composition of relic GW, and also gravitons. A side issue to consider is if gravitons can be configured as semi classical “particles”, which is akin to the Pilot model of Quantum Mechanics as embedded in a larger non linear “de- terministic” background. Keywords: Squeezed State, Graviton, GW, Pilot Model 1. Introduction condensed matter application. The string theory metho- dology is merely extending much the same thinking up to Gravitons may be de composed via an instanton-anti higher than four dimensional situations. instanton structure. i.e. that the structure of SO(4) gauge 1) Modeling of entropy, generally, as kink-anti-kinks theory is initially broken due to the introduction of pairs with N the number of the kink-anti-kink pairs. vacuum energy [1], so after a second-order phase tran- This number, N is, initially in tandem with entropy sition, the instanton-anti-instanton structure of relic production, as will be explained later, gravitons is reconstituted. This will be crucial to link 2) The tie in with entropy and gravitons is this: the two graviton production with entropy, provided we have structures are related to each other in terms of kinks and sufficiently HFGW at the origin of the big bang. -
Cvi, 1999: 5-24
Nicholas Huggett OFFICE: HOME: Department of Philosophy, M/C 267, 3730 N. Lake Shore Drive, #3B University of Illinois at Chicago, Chicago, IL 60613 601 South Morgan St, Chicago, IL 60607-7114 Telephone: 312-996-3022 773-818-5495/773-281-5728 Fax: 312-413-2093 Email: [email protected] EMPLOYMENT: 2015- : LAS Distinguished Professor, University of Illinois at Chicago. Spring 2018: Visiting Associate Dean, College of Liberal Arts and Sciences, University of Illinois at Chicago. 2009-15: Full Professor, University of Illinois at Chicago. 2001-9: Associate Professor, University of Illinois at Chicago. 1996-2001: Assistant Professor, University of Illinois at Chicago. 1995-6: Visiting Assistant Professor, Brown University. 1994-5: Visiting Assistant Professor, University of Kentucky. EDUCATION: Rutgers University: PhD, 1995. (Dissertation: The Philosophy of Fields and Particles in Classical and Quantum Mechanics, including The Problem of Renormalization. Supervised by Robert Weingard.) Oxford University: BA Hons in Physics and Philosophy, 1988. AWARDS AND FELLOWSHIPS: Foundational Questions Institute Member, 2017-. Outstanding Graduate Mentor Award, Graduate College, University of Illinois at Chicago, 2015. Professorial Fellow, Institute of Philosophy, School of Advanced Studies, University of London, April-May 2011. American Council of Learned Societies Collaborative Fellowship, 2010-13. Grant for full-time research. University of Illinois at Chicago Humanities Institute Fellow, 2005-6. Grant for full-time research. University of Illinois at Chicago, University Scholar, 2002-5. National Science Foundation Science and Technology Studies Scholars Award, 2001-2002. Grant for full-time research. !1/!13 Nicholas Huggett University of Illinois at Chicago Humanities Institute Fellow, 1999 -2000. Grant for full-time research. -
Classical Topology and Quantum States∗
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server SU-4240-716 February 2000 Classical Topology and Quantum States∗ A.P. Balachandran Department of Physics, Syracuse University, Syracuse, NY 13244-1130, USA Abstract Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘Quantum Mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its CK− and C∞− structures) can be reconstructed using Gel’fand - Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed. ∗Talk presented at the Winter Institute on Foundations of Quantum Theory and Quantum Op- tics,S.N.Bose National Centre for Basic Sciences,Calcutta,January 1-13,2000. -
The Kalam Cosmological Argument Meets the Mentaculus
The Kalam Cosmological Argument Meets The Mentaculus Dan Linford Abstract According to the orthodox interpretation of bounce cosmologies, the universe was born from an entropy reducing phase in a previous universe. To defend the thesis that the whole of physical reality was caused to exist a finite time ago, William Lane Craig and co-author James Sinclair have argued the low entropy interface between universes should instead be understood as the beginning of two universes. Here, I present Craig and Sinclair with a dilemma. On the one hand, if the direction of time is reducible, as friends of the Mentaculus – e.g., David Albert, Barry Loewer, and David Papineau – maintain, then there is reason to think that the direction of time and the entropic arrow of time align. But on that account, efficient causation is likely reducible to non-causal phenomena. In consequence, contrary to Craig and Sinclair’s theological aims, things can begin to exist without causes. On the other hand, if the direction of time is not reducible, Craig and Sinclair’s interpretation of bounce cosmologies is unjustified. Lastly, a reply to a potential objection motivates a discussion of how to interpret bounce cosmologies on the tensed theory of absolute time favored by Craig and Sinclair. I offer two interpretations of bounce cosmologies that, given a tensed theory of absolute time, are preferable to those Craig and Sinclair offer, yet inconsistent with their project in natural theology; on one interpretation, the universe does not require a supernatural cause and, on the other, bounce cosmologies represent the universe as never having begun to exist. -
Hamilton Equations, Commutator, and Energy Conservation †
quantum reports Article Hamilton Equations, Commutator, and Energy Conservation † Weng Cho Chew 1,* , Aiyin Y. Liu 2 , Carlos Salazar-Lazaro 3 , Dong-Yeop Na 1 and Wei E. I. Sha 4 1 College of Engineering, Purdue University, West Lafayette, IN 47907, USA; [email protected] 2 College of Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA; [email protected] 3 Physics Department, University of Illinois at Urbana-Champaign, Urbana, IL 61820, USA; [email protected] 4 College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310058, China; [email protected] * Correspondence: [email protected] † Based on the talk presented at the 40th Progress In Electromagnetics Research Symposium (PIERS, Toyama, Japan, 1–4 August 2018). Received: 12 September 2019; Accepted: 3 December 2019; Published: 9 December 2019 Abstract: We show that the classical Hamilton equations of motion can be derived from the energy conservation condition. A similar argument is shown to carry to the quantum formulation of Hamiltonian dynamics. Hence, showing a striking similarity between the quantum formulation and the classical formulation. Furthermore, it is shown that the fundamental commutator can be derived from the Heisenberg equations of motion and the quantum Hamilton equations of motion. Also, that the Heisenberg equations of motion can be derived from the Schrödinger equation for the quantum state, which is the fundamental postulate. These results are shown to have important bearing for deriving the quantum Maxwell’s equations. Keywords: quantum mechanics; commutator relations; Heisenberg picture 1. Introduction In quantum theory, a classical observable, which is modeled by a real scalar variable, is replaced by a quantum operator, which is analogous to an infinite-dimensional matrix operator. -
The Conjugate Variable Method in Hamilton-Lie Perturbation Theory −Applications to Plasma Physics−
Plasma and Fusion Research: Regular Articles Volume 3, 057 (2008) The Conjugate Variable Method in Hamilton-Lie Perturbation Theory −Applications to Plasma Physics− Shinji TOKUDA Japan Atomic Energy Agency, Naka, Ibaraki, 311-0193 Japan (Received 21 February 2008 / Accepted 29 July 2008) The conjugate variable method, an essential ingredient in the path-integral formalism of classical statistical dynamics, is used to apply the Hamilton-Lie perturbation theory to a system of ordinary differential equations that does not have the Hamiltonian dynamic structure. The method endows the system with this structure by doubling the unknown variables; hence, the canonical Hamilton-Lie perturbation theory becomes applicable to the system. The method is applied to two classical problems of plasma physics to demonstrate its effectiveness and study its properties: a non-linear oscillator that can explode and the guiding center motion of a charged particle in a magnetic field. c 2008 The Japan Society of Plasma Science and Nuclear Fusion Research Keywords: one-form, Hamilton-Lie perturbation method, conjugate variable, non-linear oscillator, guiding cen- ter motion, plasma physics DOI: 10.1585/pfr.3.057 1. Introduction Since the Hamilton-Lie perturbation method is a pow- We begin by considering the following two non-linear erful analytical tool that enables us to investigate the prob- oscillators lem deeply, it would be a significant contribution to the de- velopment of approximation methods in physics if it were dx dy = y, = −x − x3, (1) made applicable for equations such as Eq. (2), which do dt dt not have the Hamiltonian structure. This seems impossi- and ble since the Hamilton-Lie perturbation method assumes the Hamiltonian structure of the equations. -
A Direction of Time in Time-Symmetric Electrodynamics
COLUMBIA UNIVERSITY MASTER’S THESIS A Direction of Time in Time-Symmetric Electrodynamics Author: Supervisor: Kathleen TATEM Dr. Erick WEINBERG A thesis submitted in fulfillment of the requirements for the degree of Master of Arts in the Philosophical Foundations of Physics Graduate School of Arts and Sciences May 17, 2017 ii In grateful memory of my mentor, Dr. John M. J. Madey. iii Columbia University Abstract Departments of Physics and Philosophy Graduate School of Arts and Sciences Master of Arts A Direction of Time in Time-Symmetric Electrodynamics by Kathleen TATEM This thesis introduces a recent analytical verification which is of significance to the philosophical debate on the direction of time in the case of electromagnetic radiation. I give an overview of a the problem of the direction of time in thermodynamics, as well as how it is solved with the Past Hypothesis, a hypothesis that the macrostate of the universe at the moment of the Big Bang was an extremely low-entropy state. I also describe the standard accepted textbook solution to the radiation problem, as well as an alternative time-symmetric theory presented by Feynman and Wheeler that had historically been considered less favorable to physicists. Analytical ver- ification supports that time-symmetric accounts of radiation such as Feynman and Wheeler’s theory are needed for radiation fields to comply with energy conservation and the fundamental equations of electromagnetism. I describe two other philo- sophical accounts of the direction of time in radiation theory, and then argue that proposed experiments based on this recent analytical result can help us rule out some of the alternative philosophical proposals on the origin of the direction of time in radiation theory.