Physics Essays an INTERNATIONALJOURNAL DEDIC�TED to FUNDAMENTAL QUESTIONS in PHYSICS
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S Theorem by Quantifying the Asymmetry of Quantum States
ARTICLE Received 9 Dec 2013 | Accepted 7 Apr 2014 | Published 13 May 2014 DOI: 10.1038/ncomms4821 Extending Noether’s theorem by quantifying the asymmetry of quantum states Iman Marvian1,2,3 & Robert W. Spekkens1 Noether’s theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. Here we address these deficiencies by introducing measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for non- isolated systems they cannot increase, whereas for isolated systems they are conserved. We demonstrate that the problem of finding non-trivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology. 1 Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada N2L 2Y5. 2 Institute for Quantum Computing, University of Waterloo, 200 University Ave. W, Waterloo, Ontario, Canada N2L 3G1. 3 Center for Quantum Information Science and Technology, Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA. Correspondence and requests for materials should be addressed to I.M. (email: [email protected]). -
On the Emergence of Time in Quantum Gravity
Imperial/TP/98–99/23 On the Emergence of Time in Quantum Gravity1 J. Butterfield2 All Souls College Oxford OX1 4AL and C.J. Isham3 The Blackett Laboratory Imperial College of Science, Technology & Medicine South Kensington London SW7 2BZ 13 December 1998 Abstract We discuss from a philosophical perspective the way in which the normal concept of time might be said to ‘emerge’ in a quantum the- ory of gravity. After an introduction, we briefly discuss the notion of arXiv:gr-qc/9901024v1 8 Jan 1999 emergence, without regard to time (Section 2). We then introduce the search for a quantum theory of gravity (Section 3); and review some general interpretative issues about space, time and matter (Section 4). We then discuss the emergence of time in simple quantum ge- ometrodynamics, and in the Euclidean approach (Section 5). Section 6 concludes. 1To appear in The Arguments of Time, ed. J. Butterfield, Oxford University Press, 1999. 2email: [email protected]; jeremy.butterfi[email protected] 3email: [email protected] 1 Introduction The discovery of a satisfactory quantum theory of gravity has been widely regarded as the Holy Grail of theoretical physics for some forty years. In this essay, we will discuss a philosophical aspect of the search for such a theory that bears on our understanding of time: namely, the senses in which our standard ideas of time, and more generally spacetime, might be not fundamental to reality, but instead ‘emergent’ as an approximately valid concept on sufficiently large scales. In taking up this topic, our aim in part is to advertise to philosophers of time an unexplored area that promises to be fruitful. -
A More Direct Representation for Complex Relativity
A more direct representation for complex relativity D.H. Delphenich ∗∗∗ Physics Department, Bethany College, Lindsborg, KS 67456, USA Received 22 Nov 2006, revised 5 July 2007, accepted 5 July 2007 by F. W. Hehl Key words Complex relativity, pre-metric electromagnetism, almost-complex structures, 3- spinors. PACS 02.10.Xm, 02.40.Dr, 03.50.De, 04.50.+h An alternative to the representation of complex relativity by self-dual complex 2-forms on the spacetime manifold is presented by assuming that the bundle of real 2-forms is given an almost- complex structure. From this, one can define a complex orthogonal structure on the bundle of 2- forms, which results in a more direct representation of the complex orthogonal group in three complex dimensions. The geometrical foundations of general relativity are then presented in terms of the bundle of oriented complex orthogonal 3-frames on the bundle of 2-forms in a manner that essentially parallels their construction in terms of self-dual complex 2-forms. It is shown that one can still discuss the Debever-Penrose classification of the Riemannian curvature tensor in terms of the representation presented here. Contents 1 Introduction …………………………………………………………………………. 1 2 The complex orthogonal group …………………………………………………….. 3 3 The geometry of bivectors ………………………………………………………….. 4 3.1 Real vector space structure on A 2……………………………………………….. 5 3.2 Complex vector space structure on A 2…………………………………………... 8 3.3 Relationship to the formalism of self-dual bivectors……………………………. 12 4 Associated principal bundles for the vector bundle of 2-forms ………………….. 16 5 Levi-Civita connection on the bundle SO (3, 1)( M)………………………………… 19 6 Levi-Civita connection on the bundle SO (3; C)( M)………………………………. -
On the Rational Relationship Between Heisenberg Principle and General
CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server On the Rational Relationship between Heisenberg Principle and General Relativity Xiao Jianhua Henan Polytechnic University, Jiaozuo City, Henan, P.R.C. 454000 Abstract: The research shows that the Heisenberg principle is the logic results of general relativity principle. If inertia coordinator system is used, the general relativity will logically be derived from the Heisenberg principle. The intrinsic relation between the quantum mechanics and general relativity is broken by introducing pure-imaginary time to explain the Lorentz transformation. Therefore, this research shows a way to establish an unified field theory of physics. PACS: 01.55.+b, 03.65.-w, 04.20.-q, 04.20.Ky Keywords: Heisenberg principle, general relativity, commoving coordinator, Riemannian geometry, gauge field 1. Introduction There are many documents to treat the relationship between the Newton mechanics and general relativity. There are also many documents to treat the relationship between the quantum mechanics and general relativity. For some researchers, the related research shows that an unified field theory be possible. For others, the actual efforts to establish an unified field theory for physics have shown that such an unified field theory is totally non-possible. The physics world is divided into three kingdoms. Hence, the title of this paper may make the reader think: See! Another nut! However, the unification of matter motion is the basic relieves for science researchers. The real problem is to find the way. This is the topic of this paper. The paper will firstly derive the Heisenberg principle from general relativity principle. -
The Philosophy and Physics of Time Travel: the Possibility of Time Travel
University of Minnesota Morris Digital Well University of Minnesota Morris Digital Well Honors Capstone Projects Student Scholarship 2017 The Philosophy and Physics of Time Travel: The Possibility of Time Travel Ramitha Rupasinghe University of Minnesota, Morris, [email protected] Follow this and additional works at: https://digitalcommons.morris.umn.edu/honors Part of the Philosophy Commons, and the Physics Commons Recommended Citation Rupasinghe, Ramitha, "The Philosophy and Physics of Time Travel: The Possibility of Time Travel" (2017). Honors Capstone Projects. 1. https://digitalcommons.morris.umn.edu/honors/1 This Paper is brought to you for free and open access by the Student Scholarship at University of Minnesota Morris Digital Well. It has been accepted for inclusion in Honors Capstone Projects by an authorized administrator of University of Minnesota Morris Digital Well. For more information, please contact [email protected]. The Philosophy and Physics of Time Travel: The possibility of time travel Ramitha Rupasinghe IS 4994H - Honors Capstone Project Defense Panel – Pieranna Garavaso, Michael Korth, James Togeas University of Minnesota, Morris Spring 2017 1. Introduction Time is mysterious. Philosophers and scientists have pondered the question of what time might be for centuries and yet till this day, we don’t know what it is. Everyone talks about time, in fact, it’s the most common noun per the Oxford Dictionary. It’s in everything from history to music to culture. Despite time’s mysterious nature there are a lot of things that we can discuss in a logical manner. Time travel on the other hand is even more mysterious. -
Two-Boson Quantum Interference in Time
Two-boson quantum interference in time Nicolas J. Cerfa,1 and Michael G. Jabbourb aCentre for Quantum Information and Communication, Ecole polytechnique de Bruxelles, Universite´ libre de Bruxelles, 1050 Bruxelles, Belgium; and bDepartment of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Cambridge CB3 0WA, United Kingdom Edited by Marlan O. Scully, Texas A&M University, College Station, TX, and approved October 19, 2020 (received for review May 27, 2020) The celebrated Hong–Ou–Mandel effect is the paradigm of two- time could serve as a test bed for a wide range of bosonic trans- particle quantum interference. It has its roots in the symmetry of formations. Furthermore, from a deeper viewpoint, it would be identical quantum particles, as dictated by the Pauli principle. Two fascinating to demonstrate the consequence of time-like indistin- identical bosons impinging on a beam splitter (of transmittance guishability in a photonic or atomic platform as it would help in 1/2) cannot be detected in coincidence at both output ports, as elucidating some heretofore overlooked fundamental property confirmed in numerous experiments with light or even matter. of identical quantum particles. Here, we establish that partial time reversal transforms the beam splitter linear coupling into amplification. We infer from this dual- Hong–Ou–Mandel Effect ity the existence of an unsuspected two-boson interferometric The HOM effect is a landmark in quantum optics as it is effect in a quantum amplifier (of gain 2) and identify the underly- the most spectacular manifestation of boson bunching. It is a ing mechanism as time-like indistinguishability. -
16 Quantum Computing and Communications
16 Quantum Computing and Communications We've seen many ways in which physical laws set profound limits: messages can't travel faster than the speed of light; transistors can't be shrunk below the size of an atom. Conventional scaling of device performance, which has been based on increasing clock speeds and decreasing feature sizes, is already bumping into such fundamental constraints. But these same laws also contain opportunities. The universe offers many more ways to communicate and manipulate information than we presently use, most notably through quantum coherence. Specifying the state of N quantum bits, called qubits, requires 2N coefficients. That's a lot. Quantum mechanics is essential to explain semiconductor band structure, but the devices this enables perform classical functions. Perfectly good logic families can be based on the flow of a liquid or a gas; this is called fluidic logic [Spuhler, 1983] and is used routinely in automobile transmissions. In fact, quantum effects can cause serious problems as VLSI devices are scaled down to finer linewidths, because small gates no longer work the same as their larger counterparts do. But what happens if the bits themselves are governed by quantum rather than classical laws? Since quantum mechanics is so important, and so strange, a number of early pioneers wondered how a quantum mechanical computer might differ from a classical one [Benioff, 1980; Feynman, 1982; Deutsch, 1985]. Feynman, for example, objected to the exponential cost of simulating a quantum system on a classical computer, and conjectured that a quantum computer could simulate another quantum system efficiently (i.e., with less than exponential resources). -
Quantum Noise Properties of Non-Ideal Optical Amplifiers and Attenuators
Home Search Collections Journals About Contact us My IOPscience Quantum noise properties of non-ideal optical amplifiers and attenuators This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2011 J. Opt. 13 125201 (http://iopscience.iop.org/2040-8986/13/12/125201) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 128.151.240.150 The article was downloaded on 27/08/2012 at 22:19 Please note that terms and conditions apply. IOP PUBLISHING JOURNAL OF OPTICS J. Opt. 13 (2011) 125201 (7pp) doi:10.1088/2040-8978/13/12/125201 Quantum noise properties of non-ideal optical amplifiers and attenuators Zhimin Shi1, Ksenia Dolgaleva1,2 and Robert W Boyd1,3 1 The Institute of Optics, University of Rochester, Rochester, NY 14627, USA 2 Department of Electrical Engineering, University of Toronto, Toronto, Canada 3 Department of Physics and School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, K1N 6N5, Canada E-mail: [email protected] Received 17 August 2011, accepted for publication 10 October 2011 Published 24 November 2011 Online at stacks.iop.org/JOpt/13/125201 Abstract We generalize the standard quantum model (Caves 1982 Phys. Rev. D 26 1817) of the noise properties of ideal linear amplifiers to include the possibility of non-ideal behavior. We find that under many conditions the non-ideal behavior can be described simply by assuming that the internal noise source that describes the quantum noise of the amplifier is not in its ground state. -
Efficient Framework for Quantum Walks and Beyond
University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2015-12-22 Efficient Framework for Quantum Walks and Beyond Dohotaru, Catalin Dohotaru, C. (2015). Efficient Framework for Quantum Walks and Beyond (Unpublished doctoral thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/25844 http://hdl.handle.net/11023/2700 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Efficient Framework for Quantum Walks and Beyond by Cat˘ alin˘ Dohotaru A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN COMPUTER SCIENCE CALGARY, ALBERTA December, 2015 c Cat˘ alin˘ Dohotaru 2015 Abstract In the first part of the thesis we construct a new, simple framework which amplifies to a constant the success probability of any abstract search algorithm. The total query complexity is given by the quantum hitting time of the resulting operator, which we show that it is of the same order as the quantum hitting time of the original algorithm. As a major application of our framework, we show that for any reversible walk P and a single marked state, the quantum walk corresponding to P can find the solution using a number of queries that is quadratically smaller than the classical hitting time of P. -
The No-Boundary Proposal Via the Five-Dimensional Friedmann
The no-boundary proposal via the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model Peter K.F. Kuhfittig* and Vance D. Gladney* ∗Department of Mathematics, Milwaukee School of Engineering, Milwaukee, Wisconsin 53202-3109, USA Abstract Hawking’s proposal that the Universe has no temporal boundary and hence no be- ginning depends on the notion of imaginary time and is usually referred to as the no-boundary proposal. This paper discusses a simple alternative approach by means of the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model. PAC numbers: 04.20.-q, 04.50.+h Keywords: no-boundary proposal, FLRW model 1 Introduction It is well known that Stephen Hawking introduced the no-boundary proposal using the concept of imaginary time, making up what is called Euclidean spacetime [1]. While ordi- nary time would still have a big-bang singularity, imaginary time avoids this singularity, implying that the Universe has no temporal boundary and hence no beginning. By elim- inating the singularity, the Universe becomes self-contained in the sense that one would arXiv:1510.07311v2 [gr-qc] 7 Jan 2016 not have to appeal to something outside the Universe to determine how the Universe began. Given that imaginary time is orthogonal to ordinary time, one could view imaginary time as an extra dimension. The existence of an extra dimension suggests a different start- ing point, the five-dimensional Friedmann-Lemaˆıtre-Robertson-Walker model (FLRW) [2]. This model produces a simple alternative version of the no-boundary proposal. 2 The FLRW model Let us recall the FLRW model in the usual four dimensions [3]: dr2 ds2 = dt2 + a2(t) + r2(dθ2 + sin2θdφ2) , (1) − 1 Kr2 − ∗kuhfi[email protected] 1 where a2(t) is a scale factor. -
THE PHYSICS of TIMLESSNESS Dr
Cosmos and History: The Journal of Natural and Social Philosophy, vol. 14, no. 2, 2018 THE PHYSICS OF TIMLESSNESS Dr. Varanasi Ramabrahmam ABSTRACT: The nature of time is yet to be fully grasped and finally agreed upon among physicists, philosophers, psychologists and scholars from various disciplines. Present paper takes clue from the known assumptions of time as - movement, change, becoming - and the nature of time will be thoroughly discussed. The real and unreal existences of time will be pointed out and presented. The complex number notation of nature of time will be put forward. Natural scientific systems and various cosmic processes will be identified as constructing physical form of time and the physical existence of time will be designed. The finite and infinite forms of physical time and classical, quantum and cosmic times will be delineated and their mathematical constructions and loci will be narrated. Thus the physics behind time-construction, time creation and time-measurement will be given. Based on these developments the physics of Timelessness will be developed and presented. KEYWORDS: physical time, psychological time, finite and infinite times, scalar and vector times, Classical, quantum and cosmic times, timelessness, movement, change, becoming INTRODUCTION: “Our present picture of physical reality, particularly in relation to the nature of time, is due for a grand shake-up—even greater, perhaps, than that which has already been provided by present-day relativity and quantum mechanics” [1]. Time is considered as www.cosmosandhistory.org 1 COSMOS AND HISTORY 2 one of the fundamental quantities in physics. Second, which is the duration of 9,192,631,770 cesium-133 atomic oscillations, is the unit. -
Swinging in Imaginary Time More on the Not-So-Simple Pendulum
GENERAL ARTICLE Swinging in Imaginary Time More on the Not-So-Simple Pendulum Cihan Saclioglu When the small angle approximation is not made, the exact solution of the simple pendulum is a Jacobian elliptic function with one real and one imaginary period. Far from being a physically meaningless mathematical curiosity, the second period represents the imaginary time the pendu- lum takes to swing upwards and tunnel through Cihan Saclioglu teaches the potential barrier in the semi-classical WKB physics at Sabanci approximation1 in quantum mechanics. The tun- University, Istanbul, neling here provides a simple illustration of simi- Turkey. His research lar phenomena in Yang{Mills theories describing interests include solutions of Yang–Mills, Einstein weak and strong interactions. and Seiberg–Witten equations and group 1. Introduction theoretical aspects of string theory. Consider a point mass m at the end of a rigid massless stick of length l. The acceleration due to gravity is g and the oscillatory motion is con¯ned to a vertical plane. Denoting the angular displacement of the stick from the 1When the exact quantum me- vertical by Á and taking the gravitational potential to chanical calculation of the tun- be zero at the bottom, the constant total energy E is neling probability for an arbitrary given by potential U(x) is impracticable, the Wentzel–Kramers–Brillouin 1 dÁ 2 approach, invented indepen- E = ml2 + mgl(1 cos Á) dently by all three authors in the 2 dt ¡ µ ¶ same year as the Schrödinger = mgl(1 cos Á0); (1) equation, provides an approxi- ¡ mate answer. 2 where Á0 is the maximum angle.