scholarly journals Quantum reference frames for general symmetry groups

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 367
Author(s):  
Anne-Catherine de la Hamette ◽  
Thomas D. Galley
Keyword(s):  
Symmetry Group ◽  
Reference Frame ◽  
Direct Product ◽  
Reference Frames ◽  
Quantum Systems ◽  
Coordinate Systems ◽  
General Operator ◽  
General Symmetry ◽  
Regular Representations ◽  
Wigner’S Friend

A fully relational quantum theory necessarily requires an account of changes of quantum reference frames, where quantum reference frames are quantum systems relative to which other systems are described. By introducing a relational formalism which identifies coordinate systems with elements of a symmetry group G, we define a general operator for reversibly changing between quantum reference frames associated to a group G. This generalises the known operator for translations and boosts to arbitrary finite and locally compact groups, including non-Abelian groups. We show under which conditions one can uniquely assign coordinate choices to physical systems (to form reference frames) and how to reversibly transform between them, providing transformations between coordinate systems which are `in a superposition' of other coordinate systems. We obtain the change of quantum reference frame from the principles of relational physics and of coherent change of reference frame. We prove a theorem stating that the change of quantum reference frame consistent with these principles is unitary if and only if the reference systems carry the left and right regular representations of G. We also define irreversible changes of reference frame for classical and quantum systems in the case where the symmetry group G is a semi-direct product G=N⋊P or a direct product G=N×P, providing multiple examples of both reversible and irreversible changes of quantum reference system along the way. Finally, we apply the relational formalism and changes of reference frame developed in this work to the Wigner's friend scenario, finding similar conclusions to those in relational quantum mechanics using an explicit change of reference frame as opposed to indirect reasoning using measurement operators.

scholarly journals Quantum clocks and the temporal localisability of events in the presence of gravitating quantum systems

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Esteban Castro-Ruiz ◽  
Flaminia Giacomini ◽  
Alessio Belenchia ◽  
Časlav Brukner
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Quantum Systems ◽  
Indefinite Metric ◽  
Causal Order ◽  
Quantum Operations ◽  
Unitary Dilation ◽  
Local Quantum ◽  
Fixed Space ◽  
Quantum Clocks

AbstractThe standard formulation of quantum theory relies on a fixed space-time metric determining the localisation and causal order of events. In general relativity, the metric is influenced by matter, and is expected to become indefinite when matter behaves quantum mechanically. Here, we develop a framework to operationally define events and their localisation with respect to a quantum clock reference frame, also in the presence of gravitating quantum systems. We find that, when clocks interact gravitationally, the time localisability of events becomes relative, depending on the reference frame. This relativity is a signature of an indefinite metric, where events can occur in an indefinite causal order. Even if the metric is indefinite, for any event we can find a reference frame where local quantum operations take their standard unitary dilation form. This form is preserved when changing clock reference frames, yielding physics covariant with respect to quantum reference frame transformations.

scholarly journals QUANTUM ESTIMATION OF RELATIVE INFORMATION

2006 ◽  
Vol 04 (01) ◽  
pp. 131-149 ◽  
Author(s):  
NETANEL H. LINDNER ◽  
PETRA F. SCUDO ◽  
DAGMAR BRUß
Keyword(s):  
Symmetry Group ◽  
Prior Knowledge ◽  
Reference Frame ◽  
Spatial Orientation ◽  
Degrees Of Freedom ◽  
Estimation Procedure ◽  
Quantum Systems ◽  
Relative Information ◽  
Rotation Parameters ◽  
Require Information

We derive optimal schemes for preparation and estimation of relational degrees of freedom between two quantum systems. We specifically analyze the case of rotation parameters representing relative angles between elements of the SU(2) symmetry group. Our estimation procedure does not assume prior knowledge of the absolute spatial orientation of the systems and as such does not require information on the underlying classical reference frame in which the states are prepared.

scholarly journals Reference Frame Induced Symmetry Breaking on Holographic Screens

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 408
Author(s):  
Chris Fields ◽  
James F. Glazebrook ◽  
Antonino Marcianò
Keyword(s):  
Symmetry Breaking ◽  
Reference Frame ◽  
Reference Frames ◽  
A Priori ◽  
Quantum Systems ◽  
Classical Information ◽  
Pointer States ◽  
Finite Quantum Systems ◽  
Holographic Screen ◽  
Holographic Screens

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.

Derivation of Generalized Datum Reference Frames for Geometric Tolerance Analysis

1993 ◽  
Author(s):  
Swami D. Nigam ◽  
James D. Guilford ◽  
Joshua U. Turner
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference Frames ◽  
Tolerance Analysis ◽  
Intermediate Representation ◽  
Coordinate Systems ◽  
Geometric Tolerance ◽  
Geometric Tolerances ◽  
Concise Representation ◽  
General Method

Abstract Datum reference frames define coordinate systems for use in determining part compliance with geometric tolerances. A datum reference frame is specified based on the perfect nominal geometry of the part features called out as datums. However, the actual computation of a coordinate system frame of reference from the datum callouts becomes quite challenging when the features depart from nominal location, orientation, size, and form. We present a general method for representing datum reference frames (both partial and complete), and for computing a coordinate system from a simulated varianced part and a datum reference frame specification. The method makes use of built-in construction procedures, and derived or “virtual” geometry, in conjunction with a powerful parts positioning module that simulates the placement of the varianced part in a fixture represented by the datum surfaces. The reliance on virtual geometry as an intermediate representation, permits the concise representation of not only the datum reference frame types defined in the standard, but also allows for any arbitrary datum reference frames constructed by the user.

scholarly journals Coordinate systems in the general relativistic framework

1986 ◽  
Vol 114 ◽  
pp. 145-168 ◽  
Author(s):  
T. Fukushima ◽  
M.-K Fujimoto ◽  
H. Kinoshita ◽  
S. Aoki
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference Frames ◽  
Special Theory ◽  
Newtonian Mechanics ◽  
Theory Of Relativity ◽  
Coordinate Systems ◽  
Relativistic Extension ◽  
General Relativistic ◽  
Relativistic Framework

The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.

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

Quantum ◽  
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.

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

2018 ◽  
Vol 15 (3) ◽  
pp. 229-236 ◽  
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.

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

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.

scholarly journals The Celestial Reference System in Relativistic Framework

1990 ◽  
Vol 141 ◽  
pp. 99-110
Author(s):  
Han Chun-Hao ◽  
Huang Tian-Yi ◽  
Xu Bang-Xin
Keyword(s):  
Coordinate System ◽  
Reference Frame ◽  
Reference System ◽  
Light Deflection ◽  
Coordinate Systems ◽  
Definition Of ◽  
Celestial Sphere ◽  
Celestial Reference System ◽  
Relativistic Framework

The concept of reference system, reference frame, coordinate system and celestial sphere in a relativistic framework are given. The problems on the choice of celestial coordinate systems and the definition of the light deflection are discussed. Our suggestions are listed in Sec. 5.

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