DOCSLIB.ORG

Quantum Reference Frame Transformations As Symmetries and the Paradox of the Third Particle

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Quantum Reference Frame Transformations As Symmetries and the Paradox of the Third Particle Quantum reference frame transformations as symmetries and the paradox of the third particle Marius Krumm1,2, Philipp A. Hohn¨ 3,4, and Markus P. Muller¨ 1,2,5 1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria 2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria 3Okinawa Institute of Science and Technology Graduate University, Onna, Okinawa 904 0495, Japan 4Department of Physics and Astronomy, University College London, London, United Kingdom 5Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo ON N2L 2Y5, Canada In a quantum world, reference frames are ulti- dox of the third particle’. We argue that it can mately quantum systems too — but what does it be reduced to the question of how to relation- mean to “jump into the perspective of a quantum ally embed fewer into more particles, and give a particle”? In this work, we show that quantum thorough physical and algebraic analysis of this reference frame (QRF) transformations appear question. This leads us to a generalization of the naturally as symmetries of simple physical sys- partial trace (‘relational trace’) which arguably tems. This allows us to rederive and generalize resolves the paradox, and it uncovers important known QRF transformations within an alterna- structures of constraint quantization within a tive, operationally transparent framework, and simple quantum information setting, such as re- to shed new light on their structure and inter- lational observables which are key in this reso- pretation. We give an explicit description of the lution. While we restrict our attention to finite observables that are measurable by agents con- Abelian groups for transparency and mathemat- strained by such quantum symmetries, and ap- ical rigor, the intuitive physical appeal of our re- ply our results to a puzzle known as the ‘para- sults makes us expect that they remain valid in more general situations. <latexit sha1_base64="1uAEiDp0HbNGJ/CNa5TpdkIjuno=">AAAB9HicbVBNS8NAEJ3Ur1q/qh69BIvgqSRS0GPBiyepYG2hCWWznbRLN5tldyOU2L/hxYOCePXHePPfuG1z0NYHA4/3ZpiZF0nOtPG8b6e0tr6xuVXeruzs7u0fVA+PHnSaKYptmvJUdSOikTOBbcMMx65USJKIYycaX8/8ziMqzVJxbyYSw4QMBYsZJcZKwVMgNQsUEUOO/WrNq3tzuKvEL0gNCrT61a9gkNIsQWEoJ1r3fE+aMCfKMMpxWgkyjZLQMRliz1JBEtRhPr956p5ZZeDGqbIljDtXf0/kJNF6kkS2MyFmpJe9mfif18tMfBXmTMjMoKCLRXHGXZO6swDcAVNIDZ9YQqhi9laXjogi1NiYKjYEf/nlVdK5qPuNuu/fNWrN2yKPMpzAKZyDD5fQhBtoQRsoSHiGV3hzMufFeXc+Fq0lp5g5hj9wPn8ACoOSMA==</latexit> 0 n-1 1 | i 1 Cyclic 2 translations, N=3 <latexit sha1_base64="4PiHjr2w4kH2DzfJT0RJ/k24npg=">AAAB9HicbVBNS8NAFHypX7V+VT16WSyCp5JIQY9FLx4rWFtsQtlst+3SzSbsvggl9G948aAgXv0x3vw3btoctHVgYZh5jzc7YSKFQdf9dkpr6xubW+Xtys7u3v5B9fDowcSpZrzNYhnrbkgNl0LxNgqUvJtoTqNQ8k44ucn9zhPXRsTqHqcJDyI6UmIoGEUr+X5EcRyG2eOsr/rVmlt35yCrxCtIDQq0+tUvfxCzNOIKmaTG9Dw3wSCjGgWTfFbxU8MTyiZ0xHuWKhpxE2TzzDNyZpUBGcbaPoVkrv7eyGhkzDQK7WSe0Sx7ufif10txeBVkQiUpcsUWh4apJBiTvAAyEJozlFNLKNPCZiVsTDVlaGuq2BK85S+vks5F3WvUPe+uUWteF32U4QRO4Rw8uIQm3EIL2sAggWd4hTcndV6cd+djMVpyip1j+APn8wfta5IU</latexit> 3 2 group CnZn 4 ... arXiv:2011.01951v2 [quant-ph] 21 Aug 2021 Figure 1: The simplest example of this article’s setup: a discretization of wave functions in one spatial dimension under translation symmetry. The configuration space is the cyclic group Zn, and the one-particle Hilbert space is 2 n ⊗N H = ` (Zn) ' C . We have N distinguishable particles in a joint quantum state |ψi ∈ H , and we study QRF transformations that switch between the “perspectives of the particles”. Marius Krumm: [email protected] Philipp A. H¨ohn: [email protected] Markus P. Muller:¨ [email protected] Accepted in Quantum 2021-06-18, click title to verify. Published under CC-BY 4.0. 1 Contents 1 Introduction 2 2 Quantum information vs. structural approach to reference frames4 2.1 Describing physics with or without external relatum . 4 2.2 Communication scenarios illustrating the two approaches . 6 3 From symmetries to QRF transformations and invariant observables9 3.1 G-systems and their symmetries . 10 3.2 Invariant observables and Hilbert space decomposition . 12 3.3 Group averaging states . 14 3.4 Alignable states as states with a canonical representation . 16 3.5 QRF transformations as symmetry group elements . 16 3.6 Characterization of alignable states . 17 3.7 Alignable and relational observables . 18 3.8 Communication scenario of the structural approach revisited . 20 4 The paradox of the third particle and the relational trace 20 4.1 The non-uniqueness of invariant embeddings . 21 4.2 A class of invariant traces . 24 4.3 Definition of the relational trace . 25 4.4 Relational resolution of the paradox . 28 4.5 Comparison to the resolution by Angelo et al. 28 5 Conclusions 29 Acknowledgments 32 References 32 1 Introduction ticle see the interferometer” [50]? A central topic in this approach is the QRF de- All physical quantities are described relative to pendence of observable properties like superposi- some frame of reference. But since all physical sys- tion, entanglement [38–40], classicality [39, 51, 52], tems are fundamentally quantum, reference frames or of quantum resources [53]. The corresponding must ultimately be quantum systems, too. This sim- QRF transformations admit an unambiguous defi- ple insight is of fundamental importance in a vari- nition of spin in relativistic settings by transform- ety of physical fields, including the foundations of ing to a particle’s rest frame [46, 47], they describe quantum physics [1–11], quantum information the- the comparison of quantum clock readings [42, 45], ory [12–19], quantum thermodynamics [20–28], and and they yield an alternative approach to indefinite quantum gravity [29–37]. causal structure [48,54]. Among other conceived ap- Recently, there has been a wave of interest in plications, they are furthermore conjectured to play a specific approach to quantum reference frames a crucial rule in the implementation of a “quan- (QRFs) that we can broadly classify as structural in tum equivalence principle” [55] as well as in space- nature, including e.g. Refs. [38–49]. This approach time singularity resolution [56] and the description extends the usual concept of reference frames by as- of early universe power spectra [57, 58] in quantum sociating them with quantum systems, and by de- gravity and cosmology. scribing the physical situation of interest from the Despite the broad appeal, several fundamental “internal perspective” of that quantum system. For and conceptual questions remain open. For exam- example, if an interferometer has a particle travel- ple, how should we make concrete sense of the ling in a superposition of paths, how “does the par- idea of “jumping into the reference frame of a parti- Accepted in Quantum 2021-06-18, click title to verify. Published under CC-BY 4.0. 2 cle”? How are QRF transformations different from broader conceptual framework. any other unitary change of basis in Hilbert space? What kind of physical symmetry claim is associ- <latexit sha1_base64="6S6WBk7iUa+MqlZtKhcadui8Yck=">AAACA3icbVBPS8MwHE3nvzn/VT2Jl+AQPI1WBnocevE4wbrBWkqapVtYkpYkFUYpXvwqXjwoiFe/hDe/jenWg24+CDze+/3I+70oZVRpx/m2aiura+sb9c3G1vbO7p69f3Cvkkxi4uGEJbIfIUUYFcTTVDPSTyVBPGKkF02uS7/3QKSiibjT05QEHI0EjSlG2kihfeT5VPgc6TFGLPeKMPclh2rKi9BuOi1nBrhM3Io0QYVuaH/5wwRnnAiNGVJq4DqpDnIkNcWMFA0/UyRFeIJGZGCoQJyoIJ+dUMBTowxhnEjzhIYz9fdGjrgyqSIzWYZVi14p/ucNMh1fBjkVaaaJwPOP4oxBncCyDzikkmDNpoYgLKnJCvEYSYS1aa1hSnAXT14mvfOW22657m272bmq+qiDY3ACzoALLkAH3IAu8AAGj+AZvII368l6sd6tj/lozap2DsEfWJ8/gmeX9A==</latexit> U ated with the intuition that QRF changes “leave Alignable states 2 Usym the physics invariant”? Furthermore, there are re- symmetry group ported difficulties to extend basic quantum infor- <latexit sha1_base64="oNGgkMRW12WpYpkUDVUeT6b3kt8=">AAAB9XicdVBNS8NAEJ34WetX1aOXxSJ4CkkNrd4KXjxWsLbQhLLZbtqlm03c3RRK6O/w4kFBvPpfvPlv3LYRVPTBwOO9GWbmhSlnSjvOh7Wyura+sVnaKm/v7O7tVw4O71SSSULbJOGJ7IZYUc4EbWumOe2mkuI45LQTjq/mfmdCpWKJuNXTlAYxHgoWMYK1kQK/xfq5L2PExGTWr1Qd26vV6ucOWpLLRkGcOnJtZ4EqFGj1K+/+ICFZTIUmHCvVc51UBzmWmhFOZ2U/UzTFZIyHtGeowDFVQb44eoZOjTJAUSJNCY0W6veJHMdKTePQdMZYj9Rvby7+5fUyHV0EORNppqkgy0VRxpFO0DwBNGCSEs2nhmAimbkVkRGWmGiTU9mE8PUp+p90arbr2a5741WbXpFHCY7hBM7AhQY04Rpa0AYC9/AAT/BsTaxH68V6XbauWMXMEfyA9fYJs2uSfg==</latexit> <latexit sha1_base64="oNGgkMRW12WpYpkUDVUeT6b3kt8=">AAAB9XicdVBNS8NAEJ34WetX1aOXxSJ4CkkNrd4KXjxWsLbQhLLZbtqlm03c3RRK6O/w4kFBvPpfvPlv3LYRVPTBwOO9GWbmhSlnSjvOh7Wyura+sVnaKm/v7O7tVw4O71SSSULbJOGJ7IZYUc4EbWumOe2mkuI45LQTjq/mfmdCpWKJuNXTlAYxHgoWMYK1kQK/xfq5L2PExGTWr1Qd26vV6ucOWpLLRkGcOnJtZ4EqFGj1K+/+ICFZTIUmHCvVc51UBzmWmhFOZ2U/UzTFZIyHtGeowDFVQb44eoZOjTJAUSJNCY0W6veJHMdKTePQdMZYj9Rvby7+5fUyHV0EORNppqkgy0VRxpFO0DwBNGCSEs2nhmAimbkVkRGWmGiTU9mE8PUp+p90arbr2a5741WbXpFHCY7hBM7AhQY04Rpa0AYC9/AAT/BsTaxH68V6XbauWMXMEfyA9fYJs2uSfg==</latexit> mation concepts into this context. For example, <latexit sha1_base64="cFO3MjBWKSc70gnQMOo+VEYxG0c=">AAAB/HicbVBNS8NAEJ3Ur1q/Yj16WSyCp5JIQY8FLx4rWFtoQthsN+3S3STsbsQQ8le8eFAQr/4Qb/4bt20O2vpg4PHeDDPzwpQzpR3n26ptbG5t79R3G3v7B4dH9nHzQSWZJLRPEp7IYYgV5Symfc00p8NUUixCTgfh7GbuDx6pVCyJ73WeUl/gScwiRrA2UmA3vSnWXo8FhScFSqe5KgO75bSdBdA6cSvSggq9wP7yxgnJBI014Vipkeuk2i+w1IxwWja8TNEUkxme0JGhMRZU+cXi9hKdG2WMokSaijVaqL8nCiyUykVoOgXWU7XqzcX/vFGmo2u/YHGaaRqT5aIo40gnaB4EGjNJiea5IZhIZm5FZIolJtrE1TAhuKsvr5PBZdvttF33rtPqdqo86nAKZ3ABLlxBF26hB30g8ATP8ApvVmm9WO/Wx7K1ZlUzJ/AH1ucPw9yUrg==</latexit> <latexit sha1_base64="cFO3MjBWKSc70gnQMOo+VEYxG0c=">AAAB/HicbVBNS8NAEJ3Ur1q/Yj16WSyCp5JIQY8FLx4rWFtoQthsN+3S3STsbsQQ8le8eFAQr/4Qb/4bt20O2vpg4PHeDDPzwpQzpR3n26ptbG5t79R3G3v7B4dH9nHzQSWZJLRPEp7IYYgV5Symfc00p8NUUixCTgfh7GbuDx6pVCyJ73WeUl/gScwiRrA2UmA3vSnWXo8FhScFSqe5KgO75bSdBdA6cSvSggq9wP7yxgnJBI014Vipkeuk2i+w1IxwWja8TNEUkxme0JGhMRZU+cXi9hKdG2WMokSaijVaqL8nCiyUykVoOgXWU7XqzcX/vFGmo2u/YHGaaRqT5aIo40gnaB4EGjNJiea5IZhIZm5FZIolJtrE1TAhuKsvr5PBZdvttF33rtPqdqo86nAKZ3ABLlxBF26hB30g8ATP8ApvVmm9WO/Wx7K1ZlUzJ/AH1ucPw9yUrg==</latexit>
Load more

Recommended publications
  • Mixing Indistinguishable Systems Leads to a Quantum Gibbs Paradox ✉ ✉ ✉ Benjamin Yadin 1,2 , Benjamin Morris 1 & Gerardo Adesso 1
    ARTICLE https://doi.org/10.1038/s41467-021-21620-7 OPEN Mixing indistinguishable systems leads to a quantum Gibbs paradox ✉ ✉ ✉ Benjamin Yadin 1,2 , Benjamin Morris 1 & Gerardo Adesso 1 The classical Gibbs paradox concerns the entropy change upon mixing two gases. Whether an observer assigns an entropy increase to the process depends on their ability to distinguish the gases. A resolution is that an “ignorant” observer, who cannot distinguish the gases, has 1234567890():,; no way of extracting work by mixing them. Moving the thought experiment into the quantum realm, we reveal new and surprising behaviour: the ignorant observer can extract work from mixing different gases, even if the gases cannot be directly distinguished. Moreover, in the macroscopic limit, the quantum case diverges from the classical ideal gas: as much work can be extracted as if the gases were fully distinguishable. We show that the ignorant observer assigns more microstates to the system than found by naive counting in semiclassical sta- tistical mechanics. This demonstrates the importance of accounting for the level of knowl- edge of an observer, and its implications for genuinely quantum modifications to thermodynamics. 1 School of Mathematical Sciences and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University Park, University ✉ of Nottingham, Nottingham, UK. 2 Wolfson College, University of Oxford, Oxford, UK. email: [email protected]; benjamin. [email protected]; [email protected] NATURE COMMUNICATIONS | (2021) 12:1471 | https://doi.org/10.1038/s41467-021-21620-7 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-21620-7 espite its phenomenological beginnings, thermodynamics work from apparently indistinguishable gases as the informed Dhas been inextricably linked throughout the past century observer.
    [Show full text]
  • Arxiv:1812.08053V1 [Quant-Ph] 19 Dec 2018 This Motivates the Study of Quantum Communication Without a Shared Reference Frame [4]
    Communicating without shared reference frames Alexander R. H. Smith1, ∗ 1Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire 03755, USA (Dated: December 20, 2018) We generalize a quantum communication protocol introduced by Bartlett et al. [New. J. Phys. 11, 063013 (2009)] in which two parties communicating do not share a classical reference frame, to the case where changes of their reference frames form a one-dimensional noncompact Lie group. Alice sends to Bob the state ρR ⊗ρS , where ρS is the state of the system Alice wishes to communicate and ρR is the state of an ancillary system serving as a token of her reference frame. Because Bob is ignorant of the relationship between his reference frame and Alice's, he will describe the state ρR ⊗ ρS as an average over all possible reference frames. Bob measures the reference token and applies a correction to the system Alice wished to communicate conditioned on the outcome of the 0 measurement. The recovered state ρS is decohered with respect to ρS , the amount of decoherence depending on the properties of the reference token ρR. We present an example of this protocol when Alice and Bob do not share a reference frame associated with the one-dimensional translation group 0 and use the fidelity between ρS and ρS to quantify the success of the recovery operation. I. INTRODUCTION quire highly entangled states of many qubits. Another possibility for Alice and Bob to communicate Most quantum communication protocols assume that without a shared reference frame is for Alice to send Bob the parties communicating share a classical background a quantum system ρR to serve as a token of her reference reference frame.
    [Show full text]
  • Reference Frame Induced Symmetry Breaking on Holographic Screens
    S S symmetry Article Reference Frame Induced Symmetry Breaking on Holographic Screens Chris Fields 1,* , James F. Glazebrook 2,† and Antonino Marcianò 3,‡ 1 23 Rue des Lavandières, 11160 Caunes Minervois, France 2 Department of Mathematics and Computer Science, Eastern Illinois University, Charleston, IL 61920, USA; [email protected] 3 Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai 200433, China; [email protected] * Correspondence: fi[email protected]; Tel.: +33-6-44-20-68-69 † Adjunct Faculty: Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL 61820, USA. ‡ Also: Laboratori Nazionali di Frascati INFN, Frascati, Rome 00044, Italy. Abstract: Any interaction between finite quantum systems in a separable joint state can be viewed as encoding classical information on an induced holographic screen. Here we show that when such an interaction is represented as a measurement, the quantum reference frames (QRFs) deployed to identify systems and pick out their pointer states induce decoherence, breaking the symmetry of the holographic encoding in an observer-relative way. Observable entanglement, contextuality, and classical memory are, in this representation, logical and temporal relations between QRFs. Sharing entanglement as a resource requires a priori shared QRFs. Keywords: black hole; contextuality; decoherence; quantum error-correcting code; quantum refer- ence frame; system identification; channel theory Citation: Fields, C.; Glazebrook, J.F.; Marcianò, A. Reference Frame Induced Symmetry Breaking on Holographic Screens. Symmetry 2021, 1. Introduction 13, 408. https://doi.org/10.3390/ The holographic principle (HP) states, in its covariant formulation, that for any finite sym13030408 spacelike boundary B, open or closed, the classical, thermodynamic entropy S(L(B)) of Academic Editor: Kazuharu Bamba any light-sheet L(B) of B satisfies: S(L(B)) ≤ A(B) Received: 9 February 2021 /4 , (1) Accepted: 27 February 2021 where A(B) is the area of B in Planck units [1].
    [Show full text]
  • Equivalence of the Symbol Grounding and Quantum System Identification Problems
    Information 2014, 5, 172-189; doi:10.3390/info5010172 OPEN ACCESS information ISSN 2078-2489 www.mdpi.com/journal/information Article Equivalence of the Symbol Grounding and Quantum System Identification Problems Chris Fields 528 Zinnia Court, Sonoma, CA 95476, USA; E-Mail: fi[email protected]; Tel.: +1-707-980-5091 Received: 13 November 2013; in revised form: 4 December 2013 / Accepted: 26 February 2014 / Published: 27 February 2014 Abstract: The symbol grounding problem is the problem of specifying a semantics for the representations employed by a physical symbol system in a way that is neither circular nor regressive. The quantum system identification problem is the problem of relating observational outcomes to specific collections of physical degrees of freedom, i.e., to specific Hilbert spaces. It is shown that with reasonable physical assumptions these problems are equivalent. As the quantum system identification problem is demonstrably unsolvable by finite means, the symbol grounding problem is similarly unsolvable. Keywords: decoherence; decompositional equivalence; physical symbol system; observable-dependent exchange symmetry; semantics; tensor-product structure 1. Introduction The symbol grounding problem (SGP) was introduced by Harnad [1] as a generalization and clarification of the semantic under-determination issues raised by Searle [2] in his famous “Chinese room” argument. With reference to a “physical symbol system” model of cognition that posits purely syntactic operations (e.g., [3–6]), Harnad stated the SGP as follows: How can the semantic interpretation of a formal symbol system be made intrinsic to the system, rather than just parasitic on the meanings in our heads? How can the meanings of the meaningless symbol tokens, manipulated solely on the basis of their (arbitrary) shapes, be grounded in anything but other meaningless symbols? [1] (p.
    [Show full text]
  • Are Right Angles Special? the Optimal Primitive Reference Frame
    Optimal primitive reference frames. David Jennings1, 2 1Institute for Mathematical Sciences, Imperial College London, London SW7 2BW, United Kingdom 2QOLS, The Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2BW, United Kingdom (Dated: November 2, 2018) We consider the smallest possible directional reference frames allowed and determine the best one can ever do in preserving quantum information in various scenarios. We find that for the preservation of a single spin state, two orthogonal spins are optimal primitive reference frames, and in a product state do approximately 22% as well as an infinite-sized classical frame. By adding a small amount of entanglement to the reference frame this can be raised to 2(2/3)5 = 26%. Under the different criterion of entanglement-preservation a very similar optimal reference frame is found, however this time for spins aligned at an optimal angle of 87 degrees. In this case 24% of the negativity is preserved. The classical limit is considered numerically, and indicates under the criterion of entanglement preservation, that 90 degrees is selected out non-monotonically, with a peak optimal angle of 96.5 degrees for L = 3 spins. PACS numbers: 03.67.-a, 03.65.Ud, 03.65.Ta I. INTRODUCTION not. In the absence of a shared classical frame, the di- rectionality must be encoded in quantum systems QRFA In information processing it is generally assumed that and QRFB that accompany the two halves of the singlet a large, classical background reference frame is defined state. The quantum information, here entanglement, is and readily available. For example, to measure the spin only partially preserved in the relational properties of of a particle along a certain axis, a Cartesian frame is the composite state.
    [Show full text]
  • Time Contraction Within Lightweight Reference Frames
    Braz J Phys (2017) 47:333–338 DOI 10.1007/s13538-017-0501-4 GENERAL AND APPLIED PHYSICS Time Contraction Within Lightweight Reference Frames Matheus F. Savi1 · Renato M. Angelo1 Received: 3 April 2017 / Published online: 20 April 2017 © Sociedade Brasileira de F´ısica 2017 Abstract The special theory of relativity teaches us that, its position, velocity, energy, mass, spin, charge, tempera- although distinct inertial frames perceive the same dynam- ture, and wave function? Some people would answer this ical laws, space and time intervals differ in value. We question in the affirmative by arguing that one can always revisit the problem of time contraction using the paradig- consider an immaterial reference system for which such matic model of a fast-moving laboratory within which a assertions would make sense. In contrast, we defend that photon is emitted and posteriorly absorbed. In our model, this position is not useful in physics because, within any sci- however, the laboratory is composed of two independent entific theory, we always look for a description that can be parallel plates, each of which allowed to be sufficiently light empirically verified by some observer. Now, the notion of so as to get kickbacks upon emission and absorption of “observer” does not need to be linked with a brain-endowed light. We show that the lightness of the laboratory accentu- organism. It suffices to think of a laboratory equipped with ates the time contraction. We also discuss how the photon apparatuses whose measurement outcomes make reference frequency shifts upon reflection in a light moving mirror. to a space-time structure, which is defined by rods and Although often imperceptible, these effects will inevitably clocks rigidly attached to this laboratory.
    [Show full text]
  • Kinematics and Dynamics in Noninertial Quantum Frames of Reference
    Home Search Collections Journals About Contact us My IOPscience Kinematics and dynamics in noninertial quantum frames of reference This article has been downloaded from IOPscience. Please scroll down to see the full text article. 2012 J. Phys. A: Math. Theor. 45 465306 (http://iopscience.iop.org/1751-8121/45/46/465306) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 200.17.209.129 The article was downloaded on 01/11/2012 at 10:30 Please note that terms and conditions apply. IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 45 (2012) 465306 (19pp) doi:10.1088/1751-8113/45/46/465306 Kinematics and dynamics in noninertial quantum frames of reference R M Angelo and A D Ribeiro Departamento de F´ısica, Universidade Federal do Parana,´ PO Box 19044, 81531-980, Curitiba, PR, Brazil E-mail: renato@fisica.ufpr.br Received 4 May 2012, in final form 21 September 2012 Published 31 October 2012 Online at stacks.iop.org/JPhysA/45/465306 Abstract From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this frame of reference is shown to be rather unconventional. In particular, we discuss several subtleties emerging in the relative formulation of central notions, such as vector states, the classical limit, entanglement, uncertainty relations and the complementary principle. A Hamiltonian formulation is also derived which correctly encapsulates effects of fictitious forces associated with the accelerated motion of the frame.
    [Show full text]
  • Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics
    This is a repository copy of Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics. White Rose Research Online URL for this paper: https://eprints.whiterose.ac.uk/127575/ Version: Accepted Version Article: Loveridge, Leon orcid.org/0000-0002-2650-9214, Miyadera, Takayuki and Busch, Paul orcid.org/0000-0002-2559-9721 (2018) Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics. Foundations of Physics. ISSN 0015-9018 https://doi.org/10.1007/s10701-018-0138-3 Reuse Items deposited in White Rose Research Online are protected by copyright, with all rights reserved unless indicated otherwise. They may be downloaded and/or printed for private study, or other acts as permitted by national copyright laws. The publisher or other rights holders may allow further reproduction and re-use of the full text version. This is indicated by the licence information on the White Rose Research Online record for the item. Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ To appear in Foundations of Physics 48 (2018) Symmetry, Reference Frames, and Relational Quantities in Quantum Mechanics Leon Loveridge · Takayuki Miyadera · Paul Busch Abstract We propose that observables in quantum theory are properly under- stood as representatives of symmetry-invariant quantities relating one system to another, the latter to be called a reference system. We provide a rigorous mathematical language to introduce and study quantum reference systems, showing that the orthodox “absolute” quantities are good representatives of observable relative quantities if the reference state is suitably localised.
    [Show full text]
  • A Relational Approach to Quantum Reference Frames for Spins
    A relational approach to quantum reference frames for spins Jacques Pienaar In the literature on quantum reference frames, the internal (relative) properties of a system are defined as those which are preserved under an arbitrary change of reference frame. For a system of quantum spins, these are all properties preserved by proper spatial rotations of the laboratory. However, this approach does not account for the hypothetical possibility of the laboratory becoming entangled to the system, as described by a second laboratory (the ‘Wigner’s friend’ scenario), in which case the relationship between the two laboratories is not a rotation, but is fundamentally quantum. To overcome this limitation, we re-define the reference frame transformations to be those that preserve the fidelities between subsystems. This enables us to derive U(2) as the correct symmetry group for transformations of a system of N spin-half particles. Next, we propose that systems having the same internal properties should be regarded as physically equivalent in the absence of an external frame. Remarkably, this implies that a single spin in a superposition relative to a spin magnet is equivalent to a macroscopic superposition of the magnet relative to the spin. We discuss the implications of this result for the Wigner’s friend paradox. I. INTRODUCTION spired by Rovelli’s relational interpretation, according to which different observers may give different accounts of the same physical situation. It follows that any disagree- What is the meaning of a quantum state Ψ ? It can ments between them must be about external quantities. ultimately only have meaning in the context| i of a lab- However, since the observers themselves must obey quan- oratory in which it is possible to prepare and measure tum mechanics, their accounts must also be consistent quantum systems under controlled conditions.
    [Show full text]
  • Path Integral Implementation of Relational Quantum Mechanics Jianhao M
    www.nature.com/scientificreports OPEN Path integral implementation of relational quantum mechanics Jianhao M. Yang Relational formulation of quantum mechanics is based on the idea that relational properties among quantum systems, instead of the independent properties of a quantum system, are the most fundamental elements to construct quantum mechanics. In a recent paper (Yang in Sci Rep 8:13305, 2018), basic relational quantum mechanics framework is formulated to derive quantum probability, Born’s Rule, Schrödinger Equations, and measurement theory. This paper further extends the reformulation efort in three aspects. First, it gives a clearer explanation of the key concepts behind the framework to calculate measurement probability. Second, we provide a concrete implementation of the relational probability amplitude by extending the path integral formulation. The implementation not only clarifes the physical meaning of the relational probability amplitude, but also allows us to elegantly explain the double slit experiment, to describe the interaction history between the measured system and a series of measuring systems, and to calculate entanglement entropy based on path integral and infuence functional. In return, the implementation brings back new insight to path integral itself by completing the explanation on why measurement probability can be calculated as modulus square of probability amplitude. Lastly, we clarify the connection between our reformulation and the quantum reference frame theory. A complete relational formulation of quantum mechanics needs to combine the present works with the quantum reference frame theory. Quantum mechanics was originally developed as a physical theory to explain the experimental observations of a quantum system in a measurement. In the early days of quantum mechanics, Bohr had emphasized that the description of a quantum system depends on the measuring apparatus1–3.
    [Show full text]
  • S41467-018-08155-0.Pdf
    ARTICLE https://doi.org/10.1038/s41467-018-08155-0 OPEN Quantum mechanics and the covariance of physical laws in quantum reference frames Flaminia Giacomini1,2, Esteban Castro-Ruiz1,2 & Časlav Brukner1,2 In physics, every observation is made with respect to a frame of reference. Although refer- ence frames are usually not considered as degrees of freedom, in all practical situations it is a physical system which constitutes a reference frame. Can a quantum system be considered 1234567890():,; as a reference frame and, if so, which description would it give of the world? Here, we introduce a general method to quantise reference frame transformations, which generalises the usual reference frame transformation to a “superposition of coordinate transformations”. We describe states, measurement, and dynamical evolution in different quantum reference frames, without appealing to an external, absolute reference frame, and find that entangle- ment and superposition are frame-dependent features. The transformation also leads to a generalisation of the notion of covariance of dynamical physical laws, to an extension of the weak equivalence principle, and to the possibility of defining the rest frame of a quantum system. 1 Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, A-1090 Vienna, Austria. 2 Institute of Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria. Correspondence and requests for materials should be addressed to F.G. (email: fl[email protected]) NATURE COMMUNICATIONS | (2019) 10:494 | https://doi.org/10.1038/s41467-018-08155-0 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-018-08155-0 he state of a physical system has no absolute meaning, but via a ‘generalised coordinate transformation’ from an initial QRF Tis only defined relative to the observer’s reference frame in to a final QRF, which does not only involve the observed system, the laboratory.
    [Show full text]
  • The Quantum Mechanical Frame of Reference
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by PhilSci Archive The Quantum Mechanical Frame of Reference Andrew Soltau Abstract: Everett demonstrates the appearance of collapse, within the context of the unitary linear dynamics. However, he does not state clearly how observers are to have determinate measurement records, hence 50 years of debate. This, however, is inherent. He defines the observer as the record of observations, which, naturally, is the record of correlations established with the physical environment. As in Rovelli©s Relational Quantum Mechanics , the correlations record is the sole determinant of the effective physical environment, here the quantum mechanical frame of reference: due to multiple realisation of the functional identity of the observer, the physical environment is a simultaneity of all the physical environments in which it is instantiated, a ©universe superposition©, in which only the environment correlated with the observer by observations is determinate. This effects a discrete and idiosyncratic physical environment for each version of an observer, in which determinate measurement records are recorded. Quantum mechanics is on this view fully relational, demonstrated as not only viable but necessary by Rovelli & Laudisa. The quantum mechanical frame of reference is Everett©s ©Relative State©, and on Tegmark©s ©inside view©, the time evolution follows the standard von Neumann-Dirac formulation. Thus observers get precisely the measurement records predicted by the standard formulation, but since objectively there is only the appearance of collapse, there is neither a measurement problem nor a disparity with relativity. The linear dynamics and the collapse dynamics are directly experienced, as the passage of time and the making of observations, respectively.
    [Show full text]