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.

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 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.

scholarly journals Spacetime Quantum Reference Frames and superpositions of proper times

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 508
Author(s):  
Flaminia Giacomini
Keyword(s):  
Hilbert Space ◽  
Reference Frame ◽  
Degrees Of Freedom ◽  
Reference Frames ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Dynamical Evolution ◽  
Quantum Superposition ◽  
Local Frame ◽  
Physical Systems

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.

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.

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.

Constructing physical systems with dynamical symmetry

2014 ◽  
Vol 92 (4) ◽  
pp. 335-340
Author(s):  
Yan Li ◽  
Fu-Lin Zhang ◽  
Rui-Juan Gu ◽  
Jing-Ling Chen ◽  
L.C. Kwek
Keyword(s):  
Hydrogen Atom ◽  
Harmonic Oscillator ◽  
Dynamical Symmetry ◽  
Algebraic Method ◽  
Quantum Systems ◽  
Physical Systems ◽  
Generalized Systems ◽  
Dependent Mass ◽  
Position Dependent Mass

An approach to constructing quantum systems with dynamical symmetry is proposed. As examples, we construct generalized systems of the hydrogen atom and harmonic oscillator, which can be regarded as the systems with position-dependent mass. They have symmetries that are similar to the corresponding ones, and can be solved by using the algebraic method. We also exhibit an example of the method applied to the noncentral field.

scholarly journals Entanglement perturbation theory for infinite quasi-1D quantum systems

2015 ◽  
Vol 29 (07) ◽  
pp. 1550042 ◽  
Author(s):  
Lihua Wang ◽  
Sung Gong Chung
Keyword(s):  
Phase Diagram ◽  
Perturbation Theory ◽  
Nearest Neighbor ◽  
Quantum Systems ◽  
Easy Plane ◽  
Heisenberg Chain ◽  
The Third ◽  
Plane Anisotropy ◽  
Improved Accuracy

We develop entanglement perturbation theory (EPT) for infinite Quasi-1D quantum systems. The spin-1/2 Heisenberg chain with ferromagnetic nearest neighbor (NN) and antiferromagnetic next nearest neighbor (NNN) interactions with an easy-plane anisotropy is studied as a prototypical system. The obtained phase diagram is compared with a recent prediction [Phys. Rev. B 81, 094430 (2010)] that dimer and Néel orders appear alternately as the XXZ anisotropy Δ approaches the isotropic limit Δ = 1. The first and second transitions (across dimer, Néel and dimer phases) are detected with improved accuracy at Δ ≈ 0.722 and 0.930. The third transition (from dimer to Néel phases), previously predicted to be at Δ ≈ 0.98, is not detected at this Δ in our method, strongly indicating that the second Néel phase is absent.

Sign in / Sign up

Export Citation Format

Share Document