Spacetime Quantum Reference Frames and superpositions of proper times

In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in nature. A relativistic description of the laws of physics hence needs to take into account such quantum reference frames (QRFs), through which spacetime can be given an operational meaning. Here, we introduce the notion of a spacetime quantum reference frame, associated to a quantum particle in spacetime. Such formulation has the advantage of treating space and time on equal footing, and of allowing us to describe the dynamical evolution of a set of quantum systems from the perspective of another quantum system, where the parameter in which the rest of the physical systems evolves coincides with the proper time of the particle taken as the QRF. Crucially, the proper times in two different QRFs are not related by a standard transformation, but they might be in a quantum superposition one with respect to the other.Concretely, we consider a system of N relativistic quantum particles in a weak gravitational field, and introduce a timeless formulation in which the global state of the N particles appears "frozen", but the dynamical evolution is recovered in terms of relational quantities. The position and momentum Hilbert space of the particles is used to fix the QRF via a transformation to the local frame of the particle such that the metric is locally inertial at the origin of the QRF. The internal Hilbert space corresponds to the clock space, which keeps the proper time in the local frame of the particle. Thanks to this fully relational construction we show how the remaining particles evolve dynamically in the relational variables from the perspective of the QRF. The construction proposed here includes the Page-Wootters mechanism for non interacting clocks when the external degrees of freedom are neglected. Finally, we find that a quantum superposition of gravitational redshifts and a quantum superposition of special-relativistic time dilations can be observed in the QRF.

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Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser Ranging

Acta Physica Slovaca Reviews and Tutorials ◽

10.2478/v10155-010-0004-0 ◽

2010 ◽

Vol 60 (4) ◽

Cited By ~ 2

Author(s):

Yi Xie ◽

Sergei Kopeikin

Keyword(s):

Solar System ◽

Reference Frame ◽

Reference Frames ◽

Laser Ranging ◽

Lunar Laser Ranging ◽

Local Frame ◽

The Earth ◽

Lunar Laser ◽

Lunar Motion ◽

New Generation

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser RangingWe overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, β and γ, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames - geocentric (GRF) and selenocentric (SRF) - have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable quantities such as the proper time and the round-trip laser-light distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the post-Newtonian multipole moments of the gravitational field of Earth and Moon. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom.

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Answering Mermin’s challenge with conservation per no preferred reference frame

Scientific Reports ◽

10.1038/s41598-020-72817-7 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

W. M. Stuckey ◽

Michael Silberstein ◽

Timothy McDevitt ◽

T. D. Le

Keyword(s):

Special Relativity ◽

Reference Frame ◽

Reference Frames ◽

Relativistic Quantum ◽

Symmetry Plane ◽

Real Space ◽

Relativistic Quantum Mechanics ◽

General Reader ◽

Famous Paper ◽

Preferred Reference Frame

Abstract In 1981, Mermin published a now famous paper titled, “Bringing home the atomic world: Quantum mysteries for anybody” that Feynman called, “One of the most beautiful papers in physics that I know.” Therein, he presented the “Mermin device” that illustrates the conundrum of quantum entanglement per the Bell spin states for the “general reader.” He then challenged the “physicist reader” to explain the way the device works “in terms meaningful to a general reader struggling with the dilemma raised by the device.” Herein, we show how “conservation per no preferred reference frame (NPRF)” answers that challenge. In short, the explicit conservation that obtains for Alice and Bob’s Stern-Gerlach spin measurement outcomes in the same reference frame holds only on average in different reference frames, not on a trial-by-trial basis. This conservation is SO(3) invariant in the relevant symmetry plane in real space per the SU(2) invariance of its corresponding Bell spin state in Hilbert space. Since NPRF is also responsible for the postulates of special relativity, and therefore its counterintuitive aspects of time dilation and length contraction, we see that the symmetry group relating non-relativistic quantum mechanics and special relativity via their “mysteries” is the restricted Lorentz group.

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Hilbert Space Structure Induced by Quantum Probes

Proceedings ◽

10.3390/proceedings2019012004 ◽

2019 ◽

Vol 12 (1) ◽

pp. 4

Author(s):

Kato ◽

Owari ◽

Maruyama

Keyword(s):

Hilbert Space ◽

Quantum System ◽

Degrees Of Freedom ◽

Quantum Control ◽

Space Structure ◽

Direct Access ◽

High Dimensional ◽

Direct Control ◽

Physical Systems ◽

Controllability And Observability

It is unrealistic to control all of the degrees of freedom of a high-dimensional quantum system. Here, we consider a scenario where our direct access is restricted to a small subsystem S that is constantly interacting with the rest of the system E. What we investigate is the fundamental structures of the Hilbert space and the algebra of hamiltonians that are caused solely by the restrictedness of the direct control. One key finding is that hamiltonians form a Jordan algebra, and this leads to a significant observation that there is a sharp distinction between the cases of dimHS ≥ 3 and dimHS = 2 in terms of the nature of possible operations in E. Since our analysis is totally free from specific properties of any physical systems, it would form a solid basis for obtaining deeper insights into quantum control related issues, such as controllability and observability.

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The Definition and Stability of Local Inertial Reference Frames

Symposium - International Astronomical Union ◽

10.1017/s0074180900086903 ◽

1990 ◽

Vol 141 ◽

pp. 253-260

Author(s):

R. N. Treuhaft ◽

S. T. Lowe

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Broad Class ◽

Radio Sources ◽

Local Frame ◽

Long Baseline ◽

Angular Deflection ◽

Limiting Error ◽

Local Reference ◽

Single Epoch

Inertial reference frames spanning approximately 10°-30° square on the sky and capable of locating objects to few-hundred microarcsecond accuracies are useful for a broad class of astrometric measurements. Deep space tracking and general relativistic angular deflection experiments are examples of astrometric measurements which can profitably reference the positions and/or motions of objects to a field of radio sources in a local frame. A method for defining local inertial reference frames has been developed based on Very Long Baseline Interferometry (VLBI) measurements of extragalactic radio sources. By observing the radio emission from the object to be located in the frame, as well as that from about five radio sources which define the frame, dominant systematic astrometric errors can be minimized through parameter estimation. The entire reference frame measurement is of the order of 30 minutes including all the sources in a frame. The limiting error for single-epoch position determination in a local frame is the unknown structure of both target and reference objects. Structure can cause systematic milliarcsecond-level errors. The limiting error for epoch-to-epoch differential position measurements is tropospheric fluctuations, assuming that the radio source structures do not change from one epoch to the next. Preliminary results of an epoch-to-epoch measurement of relativistic gravitational deflection by Jupiter, in which the total deflection was about 600 microarcseconds, suggest that the local reference frame is stable at the 240-microarcsecond level over twelve days. Data have been taken at longer time intervals to determine the annual stability of the frames. At the time of preparation of these proceedings, those data have not yet been analyzed.

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Quantum reference frame transformations as symmetries and the paradox of the third particle

Quantum ◽

10.22331/q-2021-08-27-530 ◽

2021 ◽

Vol 5 ◽

pp. 530

Author(s):

Marius Krumm ◽

Philipp A. Höhn ◽

Markus P. Müller

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Quantum Particle ◽

Quantum Systems ◽

Finite Abelian Groups ◽

Partial Trace ◽

Physical Systems ◽

The Third ◽

Simple Quantum ◽

Quantum Symmetries

In a quantum world, reference frames are ultimately quantum systems too – but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to a puzzle known as the `paradox of the third particle'. We argue that it can be reduced to the question of how to relationally embed fewer into more particles, and give a thorough physical and algebraic analysis of this question. This leads us to a generalization of the partial trace (`relational trace') which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution. While we restrict our attention to finite Abelian groups for transparency and mathematical rigor, the intuitive physical appeal of our results makes us expect that they remain valid in more general situations.

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Group Field Theory and Its Cosmology in a Matter Reference Frame

Universe ◽

10.3390/universe4100103 ◽

2018 ◽

Vol 4 (10) ◽

pp. 103 ◽

Cited By ~ 10

Author(s):

Steffen Gielen

Keyword(s):

Field Theory ◽

Quantum Gravity ◽

Coordinate System ◽

Reference Frame ◽

Degrees Of Freedom ◽

Reference Frames ◽

Scalar Fields ◽

General Idea ◽

Theory Approach ◽

Group Field Theory

While the equations of general relativity take the same form in any coordinate system, choosing a suitable set of coordinates is essential in any practical application. This poses a challenge in background-independent quantum gravity, where coordinates are not a priori available and need to be reconstructed from physical degrees of freedom. We review the general idea of coupling free scalar fields to gravity and using these scalars as a “matter reference frame”. The resulting coordinate system is harmonic, i.e., it satisfies the harmonic (de Donder) gauge. We then show how to introduce such matter reference frames in the group field theory approach to quantum gravity, where spacetime is emergent from a “condensate” of fundamental quantum degrees of freedom of geometry, and how to use matter coordinates to extract physics. We review recent results in homogeneous and inhomogeneous cosmology, and give a new application to the case of spherical symmetry. We find tentative evidence that spherically-symmetric group field theory condensates defined in this setting can reproduce the near-horizon geometry of a Schwarzschild black hole.

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Macroscopic superpositions require tremendous measurement devices

Quantum ◽

10.22331/q-2017-11-21-34 ◽

2017 ◽

Vol 1 ◽

pp. 34 ◽

Cited By ~ 6

Author(s):

Michalis Skotiniotis ◽

Wolfgang Dür ◽

Pavel Sekatski

Keyword(s):

Reference Frame ◽

Degrees Of Freedom ◽

Superposition State ◽

Quantum Superposition ◽

Measurement Device ◽

Fundamental Limits ◽

Quantum Mechanical Treatment ◽

Measurement Devices ◽

Superposition States ◽

Macroscopic Superpositions

We consider fundamental limits on the detectable size of macroscopic quantum superpositions. We argue that a full quantum mechanical treatment of system plus measurement device is required, and that a (classical) reference frame for phase or direction needs to be established to certify the quantum state. When taking the size of such a classical reference frame into account, we show that to reliably distinguish a quantum superposition state from an incoherent mixture requires a measurement device that is quadratically bigger than the superposition state. Whereas for moderate system sizes such as generated in previous experiments this is not a stringent restriction, for macroscopic superpositions of the size of a cat the required effort quickly becomes intractable, requiring measurement devices of the size of the Earth. We illustrate our results using macroscopic superposition states of photons, spins, and position. Finally, we also show how this limitation can be circumvented by dealing with superpositions in relative degrees of freedom.

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Allocentric to Egocentric Spatial Switching: Impairment in aMCI and Alzheimer's Disease Patients?

Current Alzheimer Research ◽

10.2174/1567205014666171030114821 ◽

2018 ◽

Vol 15 (3) ◽

pp. 229-236 ◽

Cited By ~ 8

Author(s):

Gennaro Ruggiero ◽

Alessandro Iavarone ◽

Tina Iachini

Keyword(s):

Alzheimer’S Disease ◽

Alzheimer's Disease ◽

Reference Frame ◽

Reference Frames ◽

Memory Task ◽

Spatial Representations ◽

The Novel ◽

Spatial Memory Task ◽

Switching Condition ◽

Normal Controls

Objective: Deficits in egocentric (subject-to-object) and allocentric (object-to-object) spatial representations, with a mainly allocentric impairment, characterize the first stages of the Alzheimer's disease (AD). Methods: To identify early cognitive signs of AD conversion, some studies focused on amnestic-Mild Cognitive Impairment (aMCI) by reporting alterations in both reference frames, especially the allocentric ones. However, spatial environments in which we move need the cooperation of both reference frames. Such cooperating processes imply that we constantly switch from allocentric to egocentric frames and vice versa. This raises the question of whether alterations of switching abilities might also characterize an early cognitive marker of AD, potentially suitable to detect the conversion from aMCI to dementia. Here, we compared AD and aMCI patients with Normal Controls (NC) on the Ego-Allo- Switching spatial memory task. The task assessed the capacity to use switching (Ego-Allo, Allo-Ego) and non-switching (Ego-Ego, Allo-Allo) verbal judgments about relative distances between memorized stimuli. Results: The novel finding of this study is the neat impairment shown by aMCI and AD in switching from allocentric to egocentric reference frames. Interestingly, in aMCI when the first reference frame was egocentric, the allocentric deficit appeared attenuated. Conclusion: This led us to conclude that allocentric deficits are not always clinically detectable in aMCI since the impairments could be masked when the first reference frame was body-centred. Alongside, AD and aMCI also revealed allocentric deficits in the non-switching condition. These findings suggest that switching alterations would emerge from impairments in hippocampal and posteromedial areas and from concurrent dysregulations in the locus coeruleus-noradrenaline system or pre-frontal cortex.

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A path integral formulation for particle detectors: the Unruh-DeWitt model as a line defect

Journal of High Energy Physics ◽

10.1007/jhep03(2021)076 ◽

2021 ◽

Vol 2021 (3) ◽

Author(s):

Ivan M. Burbano ◽

T. Rick Perche ◽

Bruno de S. L. Torres

Keyword(s):

Path Integral ◽

Degrees Of Freedom ◽

Wilson Line ◽

Transition Probability ◽

Relativistic Quantum ◽

Quantum Fields ◽

Line Defect ◽

Particle Detectors ◽

Nonlocal Operators ◽

Detector Model

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.

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Reference frames in spatial communication for navigation and sports: an empirical study in ultimate frisbee players

Cognitive Research Principles and Implications ◽

10.1186/s41235-020-00254-1 ◽

2020 ◽

Vol 5 (1) ◽

Author(s):

Steven M. Weisberg ◽

Anjan Chatterjee

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Spatial Information ◽

Spatial Reference ◽

Spatial Reference Frames ◽

The North ◽

Communication Task ◽

Spatial Communication ◽

Spatial Domains ◽

Ultimate Frisbee

Abstract Background Reference frames ground spatial communication by mapping ambiguous language (for example, navigation: “to the left”) to properties of the speaker (using a Relative reference frame: “to my left”) or the world (Absolute reference frame: “to the north”). People’s preferences for reference frame vary depending on factors like their culture, the specific task in which they are engaged, and differences among individuals. Although most people are proficient with both reference frames, it is unknown whether preference for reference frames is stable within people or varies based on the specific spatial domain. These alternatives are difficult to adjudicate because navigation is one of few spatial domains that can be naturally solved using multiple reference frames. That is, while spatial navigation directions can be specified using Absolute or Relative reference frames (“go north” vs “go left”), other spatial domains predominantly use Relative reference frames. Here, we used two domains to test the stability of reference frame preference: one based on navigating a four-way intersection; and the other based on the sport of ultimate frisbee. We recruited 58 ultimate frisbee players to complete an online experiment. We measured reaction time and accuracy while participants solved spatial problems in each domain using verbal prompts containing either Relative or Absolute reference frames. Details of the task in both domains were kept as similar as possible while remaining ecologically plausible so that reference frame preference could emerge. Results We pre-registered a prediction that participants would be faster using their preferred reference frame type and that this advantage would correlate across domains; we did not find such a correlation. Instead, the data reveal that people use distinct reference frames in each domain. Conclusion This experiment reveals that spatial reference frame types are not stable and may be differentially suited to specific domains. This finding has broad implications for communicating spatial information by offering an important consideration for how spatial reference frames are used in communication: task constraints may affect reference frame choice as much as individual factors or culture.

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