A SIMPLER SOLUTION OF THE NON-UNIQUENESS PROBLEM OF THE COVARIANT DIRAC THEORY

Although the standard generally covariant Dirac equation is unique in a topologically simple spacetime, it has been shown that it leads to non-uniqueness problems for the Hamiltonian and energy operators, including the non-uniqueness of the energy spectrum. These problems should be solved by restricting the choice of the Dirac gamma field in a consistent way. Recently, we proposed to impose the value of the rotation rate of the tetrad field. This is not necessarily easy to implement and works only in a given reference frame. Here, we propose that the gamma field should change only by constant gauge transformations. To get that situation, we are naturally led to assume that the metric can be put in a space-isotropic diagonal form. When this is the case, it distinguishes a preferred reference frame. We show that by defining the gamma field from the "diagonal tetrad" in a chart in which the metric has that form, the uniqueness problems are solved at once for all reference frames. We discuss the physical relevance of the metric considered and our restriction to first-quantized theory.

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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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No Preferred Reference Frame at the Foundation of Quantum Mechanics

Entropy ◽

10.3390/e24010012 ◽

2021 ◽

Vol 24 (1) ◽

pp. 12

Author(s):

William Stuckey ◽

Timothy McDevitt ◽

Michael Silberstein

Keyword(s):

Quantum Mechanics ◽

Quantum Information ◽

Reference Frame ◽

Reference Frames ◽

Quantum Probability ◽

Relativity Principle ◽

Foundation Of Quantum Mechanics ◽

Invariant Measurement ◽

Preferred Reference Frame ◽

Spin Measurements

Quantum information theorists have created axiomatic reconstructions of quantum mechanics (QM) that are very successful at identifying precisely what distinguishes quantum probability theory from classical and more general probability theories in terms of information-theoretic principles. Herein, we show how one such principle, Information Invariance and Continuity, at the foundation of those axiomatic reconstructions, maps to “no preferred reference frame” (NPRF, aka “the relativity principle”) as it pertains to the invariant measurement of Planck’s constant h for Stern-Gerlach (SG) spin measurements. This is in exact analogy to the relativity principle as it pertains to the invariant measurement of the speed of light c at the foundation of special relativity (SR). Essentially, quantum information theorists have extended Einstein’s use of NPRF from the boost invariance of measurements of c to include the SO(3) invariance of measurements of h between different reference frames of mutually complementary spin measurements via the principle of Information Invariance and Continuity. Consequently, the “mystery” of the Bell states is understood to result from conservation per Information Invariance and Continuity between different reference frames of mutually complementary qubit measurements, and this maps to conservation per NPRF in spacetime. If one falsely conflates the relativity principle with the classical theory of SR, then it may seem impossible that the relativity principle resides at the foundation of non-relativisitic QM. In fact, there is nothing inherently classical or quantum about NPRF. Thus, the axiomatic reconstructions of QM have succeeded in producing a principle account of QM that reveals as much about Nature as the postulates of SR.

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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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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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Practical Reference-Frame-Independent Measurement-Device-Independent Quantum Key Distribution Systems Against the Worst Relative Rotation of Reference Frames

Communications in Theoretical Physics ◽

10.1088/0253-6102/70/4/379 ◽

2018 ◽

Vol 70 (4) ◽

pp. 379 ◽

Cited By ~ 1

Author(s):

Chun-Mei Zhang ◽

Jian-Rong Zhu ◽

Qin Wang

Keyword(s):

Reference Frame ◽

Quantum Key Distribution ◽

Distribution Systems ◽

Reference Frames ◽

Key Distribution ◽

Relative Rotation ◽

Independent Measurement ◽

Measurement Device ◽

Measurement Device Independent

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Moving Unstable Particles and Special Relativity

Advances in High Energy Physics ◽

10.1155/2018/4657079 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Eugene V. Stefanovich

Keyword(s):

Special Relativity ◽

Reference Frame ◽

Unstable Particle ◽

Internal Variables ◽

Dirac Theory ◽

Decay Probability ◽

Unstable Particles ◽

Interacting Systems

In Poincaré-Wigner-Dirac theory of relativistic interactions, boosts are dynamical. This means that, just like time translations, boost transformations have a nontrivial effect on internal variables of interacting systems. In this respect, boosts are different from space translations and rotations, whose actions are always universal, trivial, and interaction-independent. Applying this theory to unstable particles viewed from a moving reference frame, we prove that the decay probability cannot be invariant with respect to boosts. Different moving observers may see different internal compositions of the same unstable particle. Unfortunately, this effect is too small to be noticeable in modern experiments.

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Gravity as entanglement, entanglement as gravity

10.31226/osf.io/4z56f ◽

2020 ◽

Author(s):

Vasil Dinev Penchev

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Reference Frame ◽

Common Sense ◽

Reference Frames ◽

General Covariance ◽

The Universe

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, the latter is that of quantum mechanics and information.Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant.That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics.e

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Dual Sequence Controller with Delayed Signal Cancellation in the Rotating Reference Frame

10.36227/techrxiv.17142341.v1 ◽

2021 ◽

Author(s):

Daniel Mota ◽

Erick Alves ◽

Elisabetta Tedeschi

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Formal Proof ◽

Voltage Source ◽

Phase Measurements ◽

Current Controller ◽

Signal Cancellation ◽

Rotating Reference Frames ◽

Dsc Method ◽

Dual Sequence

Manuscript submitted to the Twenty-second IEEE Workshop on Control and Modeling for Power Electronics (COMPEL 2021).<div>Abstract: Dual-sequence current controllers of voltage source converters (VSCs) feature two separate rotating reference frames (RRFs), commonly named dq frames, and rely on techniques that isolate the positive and negative sequences of three-phase measurements. One of these techniques is the delayed signal cancellation (DSC). It is performed in the stationary reference frame (SRF), also known as αβ frame. The DSC combines old values of one axis with new values of the other axis of the SRF. The results are, then, transformed into the RRFs for use in the current controller. This filtering process introduces an extra layer of complexity for dual-sequence current controllers, which could otherwise operate solely in the RRFs. This paper introduces a frequency adaptive DSC method that operates directly in the RRF. Moreover, an averaging of two of the proposed DSC filters with contiguous integer delays is employed for reducing discretization errors caused by grid frequency excursions. A formal proof of the equivalence between the αβ and dq DSC methods is presented. Furthermore, computer simulations of a case study support the interpretation of the results.</div>

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Dual Sequence Controller with Delayed Signal Cancellation in the Rotating Reference Frame

10.36227/techrxiv.17142341 ◽

2021 ◽

Author(s):

Daniel Mota ◽

Erick Alves ◽

Elisabetta Tedeschi

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Formal Proof ◽

Voltage Source ◽

Phase Measurements ◽

Current Controller ◽

Signal Cancellation ◽

Rotating Reference Frames ◽

Dsc Method ◽

Dual Sequence

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Imagine Your Crossed Hands as Uncrossed: Visual Imagery Impacts the Crossed-Hands Deficit

Multisensory Research ◽

10.1163/22134808-bja10065 ◽

2021 ◽

pp. 1-29

Author(s):

Lisa Lorentz ◽

Kaian Unwalla ◽

David I. Shore

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Internal Reference ◽

Integration Model ◽

Tactile Localization ◽

Tactile Stimuli ◽

External Reference ◽

Spatial Coordinates ◽

Localization Performance ◽

Males And Females

Abstract Successful interaction with our environment requires accurate tactile localization. Although we seem to localize tactile stimuli effortlessly, the processes underlying this ability are complex. This is evidenced by the crossed-hands deficit, in which tactile localization performance suffers when the hands are crossed. The deficit results from the conflict between an internal reference frame, based in somatotopic coordinates, and an external reference frame, based in external spatial coordinates. Previous evidence in favour of the integration model employed manipulations to the external reference frame (e.g., blindfolding participants), which reduced the deficit by reducing conflict between the two reference frames. The present study extends this finding by asking blindfolded participants to visually imagine their crossed arms as uncrossed. This imagery manipulation further decreased the magnitude of the crossed-hands deficit by bringing information in the two reference frames into alignment. This imagery manipulation differentially affected males and females, which was consistent with the previously observed sex difference in this effect: females tend to show a larger crossed-hands deficit than males and females were more impacted by the imagery manipulation. Results are discussed in terms of the integration model of the crossed-hands deficit.

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