An Alternative Theory on the Spacetime of Non-inertial Reference Frame

In present paper, we have proposed an alternative theory on the spacetime of non-inertial reference frame (NRF) which bases on the requirement of general completeness (RGC) and the principle of equality of all reference frames (PERF). The RGC is that the physical equations used to describe the dynamics of matter and/or fields should include the descriptions that not only the matter and/or fields are at rest, but also they move relative to this reference frame, and the structure of the spacetime of reference frame has been considered. The PERF is that any reference frame can be used to describe the motion of matter and/or fields. The spacetime of NRF is inhomogeneous and deformed caused by the accelerating motion of the reference frame. The inertial force is the manifestation of deformed spacetime. The Riemann curvature tensor of the spacetime of NRF equals zero, but the Riemann-Christoffel symbol never vanishs no matter what coordinate system is selected in the NRF. The physical equations satisfied the RGC remain covariance under the coordinate transformation between the reference frames. Mach’s principle is incorrect. The problem of spacetime of NRF can be solved without considering gravitation.

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Accelerated frames and galactic rotation curves

Modern Physics Letters A ◽

10.1142/s0217732319502183 ◽

2019 ◽

Vol 34 (27) ◽

pp. 1950218

Author(s):

S. C. Ulhoa ◽

F. L. Carneiro

Keyword(s):

Experimental Data ◽

General Relativity ◽

Dark Matter ◽

Reference Frame ◽

Rotation Curve ◽

Reference Frames ◽

Galactic Rotation ◽

Inertial Reference Frame ◽

Galactic Rotation Curve ◽

Accelerated Frames

In this paper, the galactic rotation curve is analyzed as an effect of an accelerated reference frame. Such a rotation curve was the first evidence for the so-called dark matter. We show another possibility for this experimental data: non-inertial reference frame can fit the experimental curve. We also show that general relativity is not enough to completely explain that which encouraged alternatives paths such as the MOND approach. The accelerated reference frames hypothesis is well-suited to deal with the rotation curve of galaxies and perhaps has some role to play concerning other evidences for dark matter.

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Nutation and reference frame

Highlights of Astronomy ◽

10.1017/s1539299600011072 ◽

1995 ◽

Vol 10 ◽

pp. 228-231

Author(s):

N. Capitaine

Keyword(s):

Perturbation Theory ◽

Reference Frame ◽

Euler Equations ◽

Coordinate Transformation ◽

Earth Rotation ◽

Reference System ◽

Reference Frames ◽

Fundamental Importance ◽

Terrestrial Reference System ◽

Celestial Reference System

The reference frames are of fundamental importance in all kinds of the precession and nutation studies involving the theory, the coordinate transformation and the observations. The aim of this paper is to review all the frames used in such studies and to lead to a better consistency between them in order that theory and reductions of observations be referred, as close as possible, to the frames to which observables are actually sensitive.The equations of Earth rotation can be expressed either as Euler equations in the Terrestrial Reference System (TRS), or as perturbation theory in the Celestial Reference System (CRS) (Kinoshita 1977). Euler equations are transformed to the CRS in the astronomical approach (Woolard 1953) and solved by the method of variation of the parameters, whereas, in the geophysical approach (Melchior 1971), the solutions, first obtained in the TRS, are transformed to the CRS and then solved by an integration with respect to time.

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Using the Hubble Space Telescope to Relate the HIPPARCOS and Extragalactic Reference Frames

Symposium - International Astronomical Union ◽

10.1017/s0074180900134916 ◽

1988 ◽

Vol 129 ◽

pp. 335-336

Author(s):

P. D. Hemenway ◽

R. L. Duncombe

Keyword(s):

Reference Frame ◽

Solid Body ◽

Reference System ◽

Reference Frames ◽

Hubble Space Telescope ◽

Inertial Reference Frame ◽

Body Rotation ◽

Space Telescope ◽

Solid Body Rotation ◽

Instrumental System

The HIPPARCOS satellite will produce positions, motions and parallaxes of celestial objects with previously unattained accuracy. This HIPPARCOS Instrumental System, however, will have an unknown solid body rotation with respect to an inertial reference frame. One aspect of our program of astrometric observations with the Hubble Space Telescope is to determine the rotation of the HIPPARCOS reference frame with respect to an extragalactic reference system.

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PERFORMANCE OF BURSA-WOLF MODEL FOR DEFORMING REGION: CASE STUDY IN MALAYSIA

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-archives-xlvi-4-w3-2021-39-2022 ◽

2022 ◽

Vol XLVI-4/W3-2021 ◽

pp. 39-43

Author(s):

N. Azahar ◽

W. A. Wan Aris ◽

T. A. Musa ◽

A. H. Omar ◽

I. A. Musliman

Keyword(s):

Reference Frame ◽

Global Positioning System ◽

Coordinate Transformation ◽

Reference Frames ◽

Seismic Events ◽

External Assessment ◽

Global Positioning ◽

Non Linear ◽

Transformation Approach

Abstract. Bursa-Wolf model is a common mathematical approach for coordinate transformation practice between two reference frames. For the case of deforming region, the existing reference frame has been experiencing a non-linear shifting over the time due to co-seismic and post seismic occurrences. Imprecise coordinate in the reference frame definition could degrading critical positioning, surveying, and navigation activities. This require a new realization of reference frame and the coordinate transformation linkage is suggested to be developed in relating the new and existing reference frame. This study provides performance of Bursa-Wolf model as coordinate transformation approach for a deforming region that is experiencing non-linear shifting due to the co-seismic and post-seismic events. The Bursa-Wolf were generated from 32 dependent Global Positioning System (GPS) Continuously Operating Reference Stations (CORS) in Malaysia meanwhile another 20 independent neighbouring stations were utilized for assessment purposes. Seven parameters (7p) of Bursa-Wolf were estimated with RMS at ±4.5mm, ±9.2mm and ±2.1mm respectively. The independent stations were classified as internal and external assessment station and the root mean square (RMS) were found at less than 10mm. The internal station has depicted a better RMS in each component which are ±5.1mm, ±6.5mm and ±1.5mm respectively. Meanwhile for external stations RMS in each component are ±6.1mm, ±8.7mm and ±3.5mm respectively. The result shows that Bursa-Wolf model is sufficient to be used as coordinate transformation approach for deforming region.

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Radio Astrometry

Symposium - International Astronomical Union ◽

10.1017/s007418090007844x ◽

1984 ◽

Vol 110 ◽

pp. 339-346 ◽

Cited By ~ 2

Author(s):

K. J. Johnston

Keyword(s):

Reference Frame ◽

Reference Frames ◽

Radio Sources ◽

Inertial Reference Frame ◽

Extragalactic Radio Sources ◽

Optical Reference

Radio astrometry is now the premier astrometric technique for measuring the positions of celestial objects. The precision with which absolute positions can be determined is approaching a few milliarc-seconds. The progress towards establishing an almost inertial reference frame based upon the positions of extragalactic radio sources is reviewed as of June 1983. The outlook for relating this reference frame to optical reference frames is also reviewed.

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An All-in-One Application for Temporal Coordinate Transformation in Geodesy and Geoinformatics

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi9050323 ◽

2020 ◽

Vol 9 (5) ◽

pp. 323

Author(s):

Antonio Banko ◽

Tedi Banković ◽

Marko Pavasović ◽

Almin Đapo

Keyword(s):

Reference Frame ◽

Coordinate Transformation ◽

Reference System ◽

Plate Tectonics ◽

Reference Frames ◽

Spatial Scales ◽

Global Navigation Satellite Systems ◽

Tectonic Plate ◽

Kinematic Models ◽

Terrestrial Reference System

Over the years, Global Navigation Satellite Systems (GNSS) have been established in the geosciences as a tool that determines the positions of discrete points (stations) on the Earth’s surface, on global to local spatial scales in a very simple and economical manner. Coordinates obtained by space geodetic measurements ought to be processed, adjusted, and propagated in a given reference frame. As points on the Earth’s surface do not have a fixed position, but rather, are moving with associated velocities, it is inevitable to include those velocities in the coordinate transformation procedure. Station velocities can be obtained from kinematic models of tectonic plate motions. The development and realization of an all-in-one standalone desktop application is presented in this paper. The application unifies coordinate transformation between different realizations (reference frames) of the International Terrestrial Reference System (ITRS) and European Terrestrial Reference System 1989 (ETRS89) following European Reference Frame Technical Note (EUREF TN) recommendations with temporal shifts of discrete points on the Earth’s surface caused by plate tectonics by integrating no-net rotation (NNR) kinematic models of the Eurasian tectonic plate.

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Accelerated Frames and Galactic Rotation Curves

10.20944/preprints201808.0544.v1 ◽

2018 ◽

Author(s):

Sergio C. Ulhoa ◽

Fernando L. Carneiro

Keyword(s):

Experimental Data ◽

General Relativity ◽

Dark Matter ◽

Reference Frame ◽

Rotation Curve ◽

Reference Frames ◽

Galactic Rotation ◽

Inertial Reference Frame ◽

Galactic Rotation Curve ◽

Accelerated Frames

In this article the galactic rotation curve is analyzed as an effect of an accelerated reference frame. This phenomenon is the strongest evidence for the so called dark matter. We show that a non-inertial reference frame could explain the experimental data. We also show that general relativity is not enough to complete explain that which encouraged alternatives paths such as the MOND approach. Considering the effect of dark matter as a realization of accelerated reference frames is a simple but powerful hypothesis.

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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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Curvature of quaternionic Kähler manifolds with $$S^1$$-symmetry

manuscripta mathematica ◽

10.1007/s00229-021-01294-7 ◽

2021 ◽

Author(s):

V. Cortés ◽

A. Saha ◽

D. Thung

Keyword(s):

Curvature Tensor ◽

Decomposition Theorem ◽

Kähler Manifolds ◽

Kahler Manifolds ◽

Riemann Curvature ◽

Riemann Curvature Tensor ◽

Cohomogeneity One ◽

Civita Connection ◽

Levi Civita Connection ◽

Quaternionic Kähler

AbstractWe study the behavior of connections and curvature under the HK/QK correspondence, proving simple formulae expressing the Levi-Civita connection and Riemann curvature tensor on the quaternionic Kähler side in terms of the initial hyper-Kähler data. Our curvature formula refines a well-known decomposition theorem due to Alekseevsky. As an application, we compute the norm of the curvature tensor for a series of complete quaternionic Kähler manifolds arising from flat hyper-Kähler manifolds. We use this to deduce that these manifolds are of cohomogeneity one.

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