DOCSLIB.ORG

On the Necessity of Quantized Gravity a Critical Comparison of Baym & Ozawa (2009) and Belenchia Et Al

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
On the Necessity of Quantized Gravity a Critical Comparison of Baym & Ozawa (2009) and Belenchia Et Al DEGREE PROJECT IN ENGINEERING PHYSICS, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2021 On the Necessity of Quantized Gravity A critical comparison of Baym & Ozawa (2009) and Belenchia et al. (2018) ERIK RYDVING KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Author Erik Rydving – [email protected] Engineering Physics KTH Royal Institute of Technology Place for Project Stockholm, Sweden Examiner Gunnar Bjork¨ antum- and Biophotonics KTH Royal Institute of Technology Supervisor Erik Aurell Department of Computational Science and Technology KTH Royal Institute of Technology Co-supervisor Igor Pikovski Department of Physics Stockholm University KTH ROYAL INSTITUTE OF TECHNOLOGY M.Sc. esis On the Necessity of antized Gravity A critical comparison of Baym & Ozawa (2009) and Belenchia et al. (2018) Erik O. T. Rydving Supervisor: Erik Aurell, Co-supervisor: Igor Pikovski May 2021 i Abstract One of the main unsolved problems in theoretical physics is combining the theory of quantum mechanics with general relativity. A central question is how to describe gravity as a quantum eld, but also whether a quantum eld description of gravity is necessary in the rst place. ere is now an ongoing search for a Gedankenexperiment that would answer this question of quantization, similar to what Bohr and Rosenfeld’s classic argument did for the electromagnetic case [1]. Two recent papers use Gedankenexperiment arguments to decide whether it is necessary to quantize the gravitational eld, and come to dierent conclusions on the maer [2, 3]. In this work, their arguments are analyzed, compared, and combined. Assuming the Planck length as a fundamental lower bound on distance measurability, we nd that a quantum eld theory of gravity is not a logical necessity, in contrary to the conclusion drawn in [3]. ii Sammanfaning Eav de storsta¨ olosta¨ problemen i teoretisk fysik ar¨ akombinera kvantmekaniken med den allmanna¨ relativitetsteorin. En central fraga˚ ar¨ hur gravitation ska beskrivas som e kvantfalt,¨ men ocksa˚ om en kvantfaltsbeskrivning¨ av gravitation ens ar¨ nodv¨ andig.¨ Det pag˚ ar˚ forskning som fors¨ oker¨ asvara pa˚ fragan˚ om kvantisering med hjalp¨ av tankeexperiment, likt hur Bohr och Rosenfelds klassiska argument svarade pa˚ fragan˚ om det elektromagnetiska faltets¨ kvantisering [1]. Tva˚ moderna artiklar anvander¨ argument med tankeexperiment for¨ abesvara om gravitationsfaltet¨ behover¨ kvantiseras, och kommer till olika slutsatser [2, 3]. I dea examensarbete analyseras, jamf¨ ors¨ och kombineras deras argument. Det visas a, sal˚ ange¨ Planck-langden¨ kan antas som en nedre grans¨ for¨ matbarhet¨ av avstand,˚ ar¨ inte en kvantfaltsteori¨ for¨ gravitation en logisk nodv¨ andighet,¨ i motsa¨ning till konklusionen i [3]. iii Acknowledgements First I want to thank my supervisors for their constant support and many fruitful discussions. My weekly meetings with Erik Aurell always forced me to make my arguments clear and presentable, and his critical questions oen hit exactly where they where necessary. Igor Pikovski let me be part of his team and suggested to join an Essay contest which also helped solidify my thoughts further. I also want to thank my study friends and fellow physicists, especially Ludvig and Marcus with whom I spent countless early mornings and late aernoons in the library. ank you Yuri for a daily dose of love and happiness. Lastly I want to thank my family. My parents for always being supportive of even my smallest achievement, while keeping rm but healthy high expectations, and my brother Martin for many thought- provoking discussions about the fundamentals of the universe. iv Contents 1 Introduction 1 1.1 Planck Units ..................................... 2 1.2 Problem Formulation ................................ 4 1.3 Outline ........................................ 5 2 Theoretical Background 7 2.1 antum Mechanics ................................ 7 2.1.1 antum Interference ........................... 9 2.1.2 Decoherence of a antum State ..................... 12 2.2 General Relativity .................................. 14 2.3 Field antization .................................. 16 2.3.1 Classical Fields and Newtonian Gravity ................. 16 2.3.2 antization of the Electromagnetic Field ................ 17 2.4 Aempts at antum Gravity ........................... 18 3 Method 20 3.1 Comparing Arguments ............................... 20 3.2 Thought Experiments ................................ 21 3.3 Scope of the Thesis ................................. 22 4 Bohr & Rosenfeld 23 4.1 My Take on Bohr & Rosenfeld ........................... 23 4.2 Bronstein and Gravity ................................ 24 5 Baym & Ozawa 28 5.1 Introduction ..................................... 28 5.2 Electromagnetic Case ................................ 29 5.3 Gravitational Case .................................. 30 6 Belenchia et al. 34 6.1 Introduction ..................................... 34 6.1.1 The Paradox ................................. 35 v CONTENTS 6.2 Electromagnetic Case ................................ 35 6.2.1 antum Fluctuations ........................... 36 6.2.2 antum Radiation ............................. 39 6.2.3 Solving the Paradox ............................. 41 6.3 Gravitational Case .................................. 42 6.3.1 antum Fluctuations ........................... 42 6.3.2 antum Radiation ............................. 45 6.3.3 Solving the Paradox ............................. 46 7 Critical Comparative Analysis and New Results 47 7.1 Details of the Interference Experiments ...................... 47 7.2 Calculation of Eective adrupole Moment ................... 49 7.3 Distinguishability of Bob and Interference .................... 50 7.4 Radiation of Alice’s Particle and Interference ................... 52 8 Discussion and Conclusion 54 8.1 Planck Length as a Lower Bound .......................... 54 8.2 Bohr & Rosenfeld in Perspective .......................... 55 8.3 Conclusion ...................................... 56 8.4 Future Work ..................................... 58 Bibliography 59 Appendices 66 AEective adrupole Moment of Two Masses in a Spatial Superposition 66 B Translation of Bronstein (1934) 69 C Essay for Gravity Research Foundation 73 vi Chapter 1 Introduction Physics has come a long way. Some theoretical predictions, like black holes [4, 5] and the Higgs boson [6–8], were presented already several decades ago. Only recently, however, thanks to the advancement in measurement technology, have they been experimentally veried [9–11]. Both these discoveries are strong indications that the theories that explain the phenomena are correct descriptions of nature. General relativity, predicting black holes, describes how massive objects interact with space and time, while the standard model, predicting the Higgs boson, is based on quantum mechanics and describes subatomic particles and their interactions. Both theories give extremely accurate descriptions of nature and far outperform their predecessors [12, 13]. e problem is: our two best theories are in many cases not compatible with each other [14, 15]. is fact is the basis for the almost century-long search for antum Gravity, a theory which combines quantum mechanics with gravity. Many questions remain, partly because it is dicult to nd feasible measurements where quantum gravitational eects are present [16– 18]. ese eects have to dier from what can be predicted by our current theories, which are already so accurate. e diculty in seeing these quantum gravitational phenomena is a question of scales. e scales in which quantum mechanics and general relativity become relevant are quite dierent. On the scale of a human, things of interest are mostly in the orders of magnitude around a meter. Anything smaller than a millimeter becomes dicult to see clearly and control accurately. Similarly, anything larger than about a hundred meters becomes too large to be seen as a single entity. Within these scales our lives take place, and most physical phenomena we encounter can be explained using the laws of physics discovered before the 1 CHAPTER 1. INTRODUCTION 20th century. If we try looking at smaller scales, our intuitions start breaking down. Friction and surface tension work dierently from our everyday experience, and mass becomes less relevant. Smaller still, and we enter the realm of antum Mechanics. Here, even the concept of “here” breaks down. ings are cloudy, uncertain, and unlike anything we are used to. Going in the other direction and looking at larger scales, we see that things change more slowly. Now surface tension becomes less relevant and mass plays a larger role. On the scale of the size of the Earth the weakness of gravity becomes apparent. Even having the mass of a whole planet pulling at a glass of water, one can easily win the tug-of-war and liit up. Going above the scale of the Earth, gravity stands as the major force, keeping the planets in orbit around the sun. It is now perhaps easier to see why the eects of quantum gravity are hard to come by; they involve combining the two opposite ends of the scale! In this project, we will nevertheless try to probe these eects, using clever thought experiments [2, 3]. We will see that it is not as easy as some might think. 1.1 Planck Units A scale which will be of great importance in this work is the Planck scale, rst introduced by Planck in 1899 [19]. He realized that using three fundamental constants of nature — the speed of light 2, Newton’s gravitational constant ⌧, and the
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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).
    [Show full text]
  • Gravity, Inertia, and Quantum Vacuum Zero Point Fields
    Foundations of Physics, Vol.31,No. 5, 2001 Gravity, Inertia, and Quantum Vacuum Zero Point Fields James F. Woodward1 Received July 27, 2000 Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electri- cally charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reac- tion forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. 1. INTRODUCTION Several years ago Haisch, Rueda, and Puthoff (1) (hereafter, HRP) pub- lished a lengthy paper in which they claimed that a substantial part, indeed perhaps all of normal inertial reaction forces could be understood as the action of the electromagnetic zero-point field (EZPF), expected on the basis of quantum field theory, on electric charges of normal matter. In several subsequent papers Haisch and Rueda particularly have pressed this claim, making various modifications to the fundamental argument to try to deflect several criticisms.
    [Show full text]
  • Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
    universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical.
    [Show full text]
  • Gravitational Interaction to One Loop in Effective Quantum Gravity A
    IT9700281 LABORATORI NAZIONALI Dl FRASCATI SIS - Pubblicazioni LNF-96/0S8 (P) ITHf 00 Z%i 31 ottobre 1996 gr-qc/9611018 Gravitational Interaction to one Loop in Effective Quantum Gravity A. Akhundov" S. Bellucci6 A. Shiekhcl "Universitat-Gesamthochschule Siegen, D-57076 Siegen, Germany, and Institute of Physics, Azerbaijan Academy of Sciences, pr. Azizbekova 33, AZ-370143 Baku, Azerbaijan 6INFN-Laboratori Nazionali di Frascati, P.O. Box 13, 00044 Frascati, Italy ^International Centre for Theoretical Physics, Strada Costiera 11, P.O. Box 586, 34014 Trieste, Italy Abstract We carry out the first step of a program conceived, in order to build a realistic model, having the particle spectrum of the standard model and renormalized masses, interaction terms and couplings, etc. which include the class of quantum gravity corrections, obtained by handling gravity as an effective theory. This provides an adequate picture at low energies, i.e. much less than the scale of strong gravity (the Planck mass). Hence our results are valid, irrespectively of any proposal for the full quantum gravity as a fundamental theory. We consider only non-analytic contributions to the one-loop scattering matrix elements, which provide the dominant quantum effect at long distance. These contributions are finite and independent from the finite value of the renormalization counter terms of the effective lagrangian. We calculate the interaction of two heavy scalar particles, i.e. close to rest, due to the effective quantum gravity to the one loop order and compare with similar results in the literature. PACS.: 04.60.+n Submitted to Physics Letters B 1 E-mail addresses: [email protected], bellucciQlnf.infn.it, [email protected] — 2 1 Introduction A longstanding puzzle in quantum physics is how to marry the description of gravity with the field theory of elementary particles.
    [Show full text]
  • Vacuum Energy
    Vacuum Energy Mark D. Roberts, 117 Queen’s Road, Wimbledon, London SW19 8NS, Email:[email protected] http://cosmology.mth.uct.ac.za/ roberts ∼ February 1, 2008 Eprint: hep-th/0012062 Comments: A comprehensive review of Vacuum Energy, which is an extended version of a poster presented at L¨uderitz (2000). This is not a review of the cosmolog- ical constant per se, but rather vacuum energy in general, my approach to the cosmological constant is not standard. Lots of very small changes and several additions for the second and third versions: constructive feedback still welcome, but the next version will be sometime in coming due to my sporadiac internet access. First Version 153 pages, 368 references. Second Version 161 pages, 399 references. arXiv:hep-th/0012062v3 22 Jul 2001 Third Version 167 pages, 412 references. The 1999 PACS Physics and Astronomy Classification Scheme: http://publish.aps.org/eprint/gateway/pacslist 11.10.+x, 04.62.+v, 98.80.-k, 03.70.+k; The 2000 Mathematical Classification Scheme: http://www.ams.org/msc 81T20, 83E99, 81Q99, 83F05. 3 KEYPHRASES: Vacuum Energy, Inertial Mass, Principle of Equivalence. 1 Abstract There appears to be three, perhaps related, ways of approaching the nature of vacuum energy. The first is to say that it is just the lowest energy state of a given, usually quantum, system. The second is to equate vacuum energy with the Casimir energy. The third is to note that an energy difference from a complete vacuum might have some long range effect, typically this energy difference is interpreted as the cosmological constant.
    [Show full text]
  • An Introduction to Loop Quantum Gravity with Application to Cosmology
    DEPARTMENT OF PHYSICS IMPERIAL COLLEGE LONDON MSC DISSERTATION An Introduction to Loop Quantum Gravity with Application to Cosmology Author: Supervisor: Wan Mohamad Husni Wan Mokhtar Prof. Jo~ao Magueijo September 2014 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London Abstract The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce. i Acknowledgement In the name of Allah, the Most Gracious, the Most Merciful. All praise be to Allah for giving me the opportunity to pursue my study of the fundamentals of nature. In particular, I am very grateful for the opportunity to explore loop quantum gravity and its application to cosmology for my MSc dissertation.
    [Show full text]
  • Quantum Gravity: a Primer for Philosophers∗
    Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts.
    [Show full text]
  • The Confrontation Between General Relativity and Experiment
    The Confrontation between General Relativity and Experiment Clifford M. Will Department of Physics University of Florida Gainesville FL 32611, U.S.A. email: [email protected]fl.edu http://www.phys.ufl.edu/~cmw/ Abstract The status of experimental tests of general relativity and of theoretical frameworks for analyzing them are reviewed and updated. Einstein’s equivalence principle (EEP) is well supported by experiments such as the E¨otv¨os experiment, tests of local Lorentz invariance and clock experiments. Ongoing tests of EEP and of the inverse square law are searching for new interactions arising from unification or quantum gravity. Tests of general relativity at the post-Newtonian level have reached high precision, including the light deflection, the Shapiro time delay, the perihelion advance of Mercury, the Nordtvedt effect in lunar motion, and frame-dragging. Gravitational wave damping has been detected in an amount that agrees with general relativity to better than half a percent using the Hulse–Taylor binary pulsar, and a growing family of other binary pulsar systems is yielding new tests, especially of strong-field effects. Current and future tests of relativity will center on strong gravity and gravitational waves. arXiv:1403.7377v1 [gr-qc] 28 Mar 2014 1 Contents 1 Introduction 3 2 Tests of the Foundations of Gravitation Theory 6 2.1 The Einstein equivalence principle . .. 6 2.1.1 Tests of the weak equivalence principle . .. 7 2.1.2 Tests of local Lorentz invariance . .. 9 2.1.3 Tests of local position invariance . 12 2.2 TheoreticalframeworksforanalyzingEEP. ....... 16 2.2.1 Schiff’sconjecture ................................ 16 2.2.2 The THǫµ formalism .............................
    [Show full text]
  • Loop Quantum Gravity
    QUANTUM GRAVITY Loop gravity combines general relativity and quantum theory but it leaves no room for space as we know it – only networks of loops that turn space–time into spinfoam Loop quantum gravity Carlo Rovelli GENERAL relativity and quantum the- ture – as a sort of “stage” on which mat- ory have profoundly changed our view ter moves independently. This way of of the world. Furthermore, both theo- understanding space is not, however, as ries have been verified to extraordinary old as you might think; it was introduced accuracy in the last several decades. by Isaac Newton in the 17th century. Loop quantum gravity takes this novel Indeed, the dominant view of space that view of the world seriously,by incorpo- was held from the time of Aristotle to rating the notions of space and time that of Descartes was that there is no from general relativity directly into space without matter. Space was an quantum field theory. The theory that abstraction of the fact that some parts of results is radically different from con- matter can be in touch with others. ventional quantum field theory. Not Newton introduced the idea of physi- only does it provide a precise mathemat- cal space as an independent entity ical picture of quantum space and time, because he needed it for his dynamical but it also offers a solution to long-stand- theory. In order for his second law of ing problems such as the thermodynam- motion to make any sense, acceleration ics of black holes and the physics of the must make sense.
    [Show full text]
  • Quantum Dynamics of Supergravity
    Quantum Dynamics of Supergravity David Tong Work with Carl Turner Based on arXiv:1408.3418 Crete, September 2014 1 2GM 2GM − distance2 = 1 δt2 + 1 dr2 + r2 δθ2 +sin2 θδφ2 − − rc2 − rc2 x = R sin θ sin φ y = R sin θ cos φ z = R cos θ δx =(R cos θ sin φ)δθ +(R sin θ cos φ)δφ δy =(R cos θ cos φ)δθ (R sin θ sin φ)δφ − δz = (R sin θ)δθ − θ φ Acknowledgement My thanks to Nick Dorey for many useful discussions. I’m supported by the Royal Society. An Old Idea: Euclidean Quantum Gravity References [1] J. Polchinski, “Dirichlet-Branes and Ramond-Ramond Charges,” Phys. Rev. Lett. 75, 4724 (1995) [arXiv:hep-th/9510017]. = g exp d4x √g Z D − R topology 17 1 2GM 2GM − distance2 = 1 δt2 + 1 dr2 + r2 δθ2 +sin2 θδφ2 − − rc2 − rc2 x = R sin θ sin φ y = R sin θ cos φ z = R cos θ δx =(R cos θ sin φ)δθ +(R sin θ cos φ)δφ δy =(R cos θ cos φ)δθ (R sin θ sin φ)δφ − δz = (R sin θ)δθ − θ A Preview of the Main Results φ 1,d 1 1 Kaluza-Klein Theory: = R − S M × 1 ∂ σ = F νρ µ 2 µνρ Λ M grav pl R Acknowledgement My thanks to Nick Dorey for many useful discussions. I’m supported by the Royal Society.There is a long history of quantum instabilities of these backgrounds • Casimir Forces References • Tunneling to “Nothing” Appelquist and Chodos ‘83 [1] J.
    [Show full text]
  • The Philosophy Behind Quantum Gravity
    The Philosophy behind Quantum Gravity Henrik Zinkernagel Department of Philosophy, Campus de Cartuja, 18071, University of Granada, Spain. [email protected] Published in Theoria - An International Journal for Theory, History and Foundations of Science (San Sebastián, Spain), Vol. 21/3, 2006, pp. 295-312. Abstract This paper investigates some of the philosophical and conceptual issues raised by the search for a quantum theory of gravity. It is critically discussed whether such a theory is necessary in the first place, and how much would be accomplished if it is eventually constructed. I argue that the motivations behind, and expectations to, a theory of quantum gravity are entangled with central themes in the philosophy of science, in particular unification, reductionism, and the interpretation of quantum mechanics. I further argue that there are –contrary to claims made on behalf of string theory –no good reasons to think that a quantum theory of gravity, if constructed, will provide a theory of everything, that is, a fundamental theory from which all physics in principle can be derived. 1. Introduction One of the outstanding tasks in fundamental physics, according to many theoretical physicists, is the construction of a quantum theory of gravity. The so far unsuccessful attempt to construct such a theory is an attempt to unify Einstein's general theory of relativity with quantum theory (or quantum field theory). While quantum gravity aims to describe everything in the universe in terms of quantum theory, the purpose of the closely related project of quantum cosmology is to describe even the universe as a whole as a quantum system.
    [Show full text]