[32] **viXra:1803.0396 [pdf]**
*submitted on 2018-03-22 02:13:09*

**Authors:** Eran sinbar, Yoav Weinstein, Gabriel Sinbar

**Comments:** 7 Pages.

Based on Einstein’s field equations , mass curves space time and curvature of space-time dictates the gravitational field around the mass. This article tries to show a paradox that leads to the conclusion that if the gravitational field increases in a local region of the universe ,anti –gravity must increase throughout the universe to prevent a catastrophe that might lead to the end of space-time and information.

**Category:** Relativity and Cosmology

[31] **viXra:1803.0384 [pdf]**
*submitted on 2018-03-21 15:28:01*

**Authors:** Roger J Anderton

**Comments:** 8 Pages.

Einstein’s Relativity is not well-defined; especially special relativity is not well-defined. I will deal with some examples of where it is not well-defined, but there are many other places it is not well-defined. Unfortunately, people seem predisposed that when they encounter a place in Einstein’s writings that is vague they then make different guesses as to what they think must have been meant; and so, come up with different interpretations of what they think Einstein’s relativity “is” instead of recognizing that it is not well-defined. Thus, when dealing with Einstein’s relativity what people engage in is mathematical modelling i.e. Einstein’s relativity is more a mathematical model than it is a theory.

**Category:** Relativity and Cosmology

[30] **viXra:1803.0313 [pdf]**
*submitted on 2018-03-20 07:50:31*

**Authors:** George Rajna

**Comments:** 43 Pages.

The theory of the Breit-Wheeler process says it should be possible to turn light into matter by smashing two particles of light (photons) together to create an electron and a positron. However, past attempts to do this have required the addition of other high-energy particles. [26] Dr. Pascal Del'Haye and his team at NPL have created an optical version of a diode that transmits light in one direction only, and can be integrated in microphotonic circuits. [25] Operation at the single-photon level raises the possibility of developing entirely new communication and computing devices, ranging from hardware random number generators to quantum computers. [24] Considerable interest in new single-photon detector technologies has been scaling in this past decade. [23] Engineers develop key mathematical formula for driving quantum experiments. [22] Physicists are developing quantum simulators, to help solve problems that are beyond the reach of conventional computers. [21] Engineers at Australia's University of New South Wales have invented a radical new architecture for quantum computing, based on novel 'flip-flop qubits', that promises to make the large-scale manufacture of quantum chips dramatically cheaper-and easier-than thought possible. [20] A team of researchers from the U.S. and Italy has built a quantum memory device that is approximately 1000 times smaller than similar devices— small enough to install on a chip. [19] The cutting edge of data storage research is working at the level of individual atoms and molecules, representing the ultimate limit of technological miniaturisation. [18] This is an important clue for our theoretical understanding of optically controlled magnetic data storage media. [17] A crystalline material that changes shape in response to light could form the heart of novel light-activated devices. [16]

**Category:** Relativity and Cosmology

[29] **viXra:1803.0287 [pdf]**
*submitted on 2018-03-21 03:42:58*

**Authors:** Mitali

**Comments:** 4 Pages.

The difference between observed and expected values of velocity discrepancy in mid 1930s gave
rise to the problem of missing mass in galaxies. Further extra mass calculated from the
gravitational lensing effect also supported strongly in favor of missing mass, called dark matter.
However, this non-baryonic matter has not been detected directly. Meanwhile, effect of
gravitational waves energy from galaxy and result of its angular momentum on rotational curve
of spiral arms in outskirts of galaxy is not taken into consideration. Here, it is discussed how
gravity waves energy can eliminate the necessity of dark matter and can explain the
observational facts which are thought to be purely effect of dark matter.

**Category:** Relativity and Cosmology

[28] **viXra:1803.0273 [pdf]**
*submitted on 2018-03-18 15:25:25*

**Authors:** Jerzy Hanckowiak

**Comments:** 10 Pages.

The possible conclusions resulting from the huge speed of massless
objects and certain remarks related to continuity in physics accompanying
revolutionary changes are presented. We also show the relationship of the
constant velocity of waves propagating in a vacuum with the principle of
relativity. We also mention abduction reasoning (retroduction) in science.

**Category:** Relativity and Cosmology

[27] **viXra:1803.0272 [pdf]**
*submitted on 2018-03-18 16:03:04*

**Authors:** Mohammed Abdelwhab

**Comments:** 8 Pages.

It is known that space expands at an increasing rate. In this paper we find that phenomenon of space expansion with accelerated rate can be well explained and understood if we postulate that "empty space have a velocity and its velocity is decreased or slowdown with time, this deceleration makes the meter in past is contracted with respect to the meter in present and second in past is dilated with respect to the second in present. The slowdown of space itself means that length contraction and time dilation are decreased with time, the decreasing in length contraction is observed as space expansion because the light travels from the more contracted space to the less contracted space, while decreasing in time dilation of the universe is observed as time speedup because the light travels from a space with more dilated time to another space with less dilated time. Motion of space itself with different velocities opens the door in front of a new branch of relativity called "empty space relativity" that is refer to change of scales of length and time of the empty space along the timeline of the universe.

**Category:** Relativity and Cosmology

[26] **viXra:1803.0261 [pdf]**
*submitted on 2018-03-18 01:45:55*

**Authors:** Ranganath G. Kulkarni

**Comments:** 1 Page.

It is found that mass and time are absolute quantities. If the psuedo force is acting, then the mass of the body is constant at all instants of time. We can distinguish the type of force acting on the body. Therefore equivalence principle is not correct.

**Category:** Relativity and Cosmology

[25] **viXra:1803.0228 [pdf]**
*submitted on 2018-03-16 10:32:34*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

No abstract needed for this elementary proof.

**Category:** Relativity and Cosmology

[24] **viXra:1803.0227 [pdf]**
*submitted on 2018-03-15 13:42:56*

**Authors:** Sergio Garcia Chimeno

**Comments:** 20 Pages. Two previous "letters" in vixra joined in an article

Demonstration of how to do that the light velocity c be the same independently of the velocity of the observer and obtain the mass-energy equivalence E = mc^2 using the Galilean transformations and the 4 dimensions zoom-universe model characteristics.
Demonstration of how to interpret it the time dilation/length contraction typical of the special relativity using the Galilean transformations and the 4 dimensions zoom-universe model characteristics.
Demonstration of how to obtain the typical waves equation with transmission velocity c and how to obtain it through the medium for transmission of light given by the zoom-universe model.
Demonstration of how to obtain the Einstein Field Equations without using the Stress-Energy Tensor, without using the Bianchi Identities and without using the Energy Conservation to obtain it.
Demonstration of how to obtain the Einstein Field Equations only using the Gauss Curvature and the zoom universe model characteristics.
Gravity in zoom universe model.
Special relativity zoom.
General relativity zoom.
Sphere and Hypersphere example to understand it better.

**Category:** Relativity and Cosmology

[23] **viXra:1803.0224 [pdf]**
*replaced on 2018-03-21 15:03:20*

**Authors:** Robert Bennett

**Comments:** 4 Pages.

Static gravity alone accounts for the observation of the double tides on opposite sides of the earth and the different range of the lunar and solar tides. When the centrifugal acceleration of the Earth’s orbital speed is added to the gravitational accelerations, the HelioC theory is exposed as fictitious. There is no evidence of a centrifugal acceleration ...or force... in the tidal behavior. This agrees with other GC tests, like Newton’s Bucket, Sagnac’s rotor and R. Wang’s linear Sagnac version. Conversely, there are no proofs by scientific method testing or realistic interpretation that the Earth orbits the Sun. The rise and fall of the tides around the world is a semi-diurnal repetitive demonstration of the Earth’s central position in the universe.

**Category:** Relativity and Cosmology

[22] **viXra:1803.0215 [pdf]**
*submitted on 2018-03-15 09:47:56*

**Authors:** Bruce Nappi

**Comments:** 244 pages, 30 figures

Space Lattice Theory is a study of the fundamental structure of the universe. The study asks what that structure might be like if, instead of being mostly an empty void, space is a densely packed, crystal-like Lattice, and the existence and interaction of what we call matter is due to movable defects or dislocations in the Lattice. This theoretical study found that a dislocation model could produce a comprehensive set of simple, visualizable explanations for most of the concepts of physics, including many that are currently unanswered. It explains matter, time, cause and effect, energy, and how energy converts to matter. It explains gravity and electric and magnetic fields; how they can be physical realities, and how they could work.

Space Lattice Theory supports a “big bang”-like beginning for a 3-D “visible” universe, explaining how it could easily emerge from what appears to be the nothingness of space, but without having to change any laws of physics. Puzzles like the particle-wave nature of photons are explained. Problems with current theories for subatomic particles, cosmology and Special Relativity are discussed. New models are suggested.

Most significantly, Space Lattice Theory presents a comprehensive model for the Grand Unification of all forces and matter in the universe.

**Category:** Relativity and Cosmology

[21] **viXra:1803.0211 [pdf]**
*submitted on 2018-03-15 12:26:45*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved. info@cec-services dot com

Using four variables, we replicate the logic in and confirm the refutation of Stephen J. Crothers for the special theory of relativity.

**Category:** Relativity and Cosmology

[20] **viXra:1803.0210 [pdf]**
*submitted on 2018-03-15 12:47:07*

**Authors:** George R. Briggs

**Comments:** 5 Pages.

Abstract: A more complete and improved forward-time, reverse-time energy cycle of the 9th cycle of an HCE8S universe for a full loop of the cycle shown.

**Category:** Relativity and Cosmology

[19] **viXra:1803.0208 [pdf]**
*submitted on 2018-03-14 13:08:33*

**Authors:** Stephen J Crothers

**Comments:** 4 Pages.

The Pythagorean Theorem, combined with the analytic geometry of a right circular cone, has been used by H. Minkowski and subsequent investigators to establish the 4-dimensional spacetime continuum associated with A. Einstein's Special Theory of Relativity. Although the mathematics appears sound, the incorporation of a hyper-cone into the analytic geometry of a right triangle in Euclidean 3-space is in conflict with
the rules of pure mathematics. A metric space of n dimensions is necessarily defined in terms of n independent coordinates, one for each dimension. Any coordinate that is a combination of the others for a given space is not independent so cannot be an independent dimension. Minkowski-Einstein spacetime contains a dimensional coordinate, via the speed of light, that is not independent. Consequently, Minkowski-Einstein spacetime does not exist.

**Category:** Relativity and Cosmology

[18] **viXra:1803.0205 [pdf]**
*submitted on 2018-03-14 20:57:49*

**Authors:** douG Snell

**Comments:** 19 Pages. Keywords: Cosmological Redshift, Hubble Expansion, Relativity, Gravity, covariance.

Abstract- This paper is an analysis of three data sets modeled to represent the physical processes of single mass points in a well defined geometric space. The First data set represents gravitational contraction modeled as derivative of Einstein Field Equation(s), a well confirmed accepted equation with theory. The Second data set modeled is a reverse of the First data set. This is a model of the physical processes of expansion of single mass points in well defined space using the reverse of First data set’s modeled physical processes. The Third data set represents the Hubble Space Telescope Key Project cosmological redshift data set modeled as single mass points, representing the Hubble expansion. All three data sets are modeled with respective physical processes, represented by 3 dimensional cubes with vector arrows plotted, then analyzed by comparison of three individual single dimension slices of each of the three data set models. The three dimensional slices are analyzed, comparing one slice from each of the x, y z axis with each of the three data sets. The Second data set when compared to the Third data set provides significant findings. The Third data set indicates physical processes limited to a single dimension, the z axis, giving a appearance of a self-centered expansion. The First and Second data set Point of View analysis indicate no contradiction, the Third data set Point of View analysis indicates a contradiction.

**Category:** Relativity and Cosmology

[17] **viXra:1803.0195 [pdf]**
*submitted on 2018-03-14 10:31:10*

**Authors:** Sangwha Yi

**Comments:** 4 Pages. Thank you for reading

In the general relativity theory, we discover new vacuum solution by Einstein’s gravity field equation in general relativity theory. We investigate the new coordinate in general
relativity theory.

**Category:** Relativity and Cosmology

[16] **viXra:1803.0194 [pdf]**
*submitted on 2018-03-14 12:54:14*

**Authors:** William JE Brown

**Comments:** 117 Pages.

Although mathematically basic, the geometrical principles enshrined within Edwin Abbott Abbott’s 1884 work, Flatland: A Romance of Many Dimensions are unyieldingly consistent, and although Albert Einstein did not directly credit EA Abbott in Part III of his 1916 popular work Relativity, he deployed the little Flatlanders to great effect assuring us that ‘the three-dimensional spherical space is quite analogous to the two-dimensional spherical surface’. In this series of 15 concise scientific essays we will follow through on the simplicity and consistency of Abbott’s approach. Deriving from Flatland a set of named principles [Appendix 1] which are held to be true of the geometrical relationships between (n-1)D, nD, and (n+1)D, these are brought to bear on the contemporary scientific paradigm with the aim of exploring the potential for a consistent dimensional structure for the whole of nature. Flatland extrapolation through 1/2/3/4D reveals the action of the temporal dimension to be a product of the dimensional viewpoint of the observer; time is therefore not intrinsic to the 4th Dimension. The dimensional structure thus derived exists as a fundamental framework for all of nature, of which combinations of length, width, height, and time merely exhibit properties. Within this structure the universe emerges at the level of the 3rd Dimension (observable) and 4th Dimension (global), adhering strictly to Flatland principles applied spherically throughout. The model described is the finite 3-sphere of Einstein, with the crucial difference that observer and origin are located at antipodean centres (poles) of the 3-hemispheres, rendering the whole ‘observer-centric’. Without altering constants, GR, or QM, the model solves the horizon problem of CMB uniformity, explains the 1998 distant SNe Ia light anomaly, shows the universe to have net zero gravity (explaining so-called dark energy), reveals the correct mechanism behind expansion, shows in terms of information transfer why both gravity and light exist at c, describes the mechanism by which the universe diminishes to a Big Bang singularity, and provides a theoretical basis for the Equivalence principle. In the process it dispenses with infinity, superluminality, Cosmic Inflation, the G/DE knife-edge, recent acceleration, and the cosmological constant.

**Category:** Relativity and Cosmology

[15] **viXra:1803.0165 [pdf]**
*replaced on 2018-03-15 19:50:42*

**Authors:** Peter V. Raktoe

**Comments:** 5 Pages.

The universe is enormous and it looks endless to us, but a clue tells us that it must also have a shell. That clue is the speed properties of light, they are similar to the properties of a transfer speed of a medium. A transfer speed of a medium is an internal speed that can only be found in a medium with a shell, and that tells us that the universe is a medium with some kind of a shell.

**Category:** Relativity and Cosmology

[14] **viXra:1803.0145 [pdf]**
*submitted on 2018-03-11 04:53:55*

**Authors:** Mamaev A.V.

**Comments:** 2 Pages.

Transformation of the new relativistic space-time theory based only on the single Galileo’s
relativity principle is derived using the method of academician Logunov A.A.
Keywords: New relativistic space-time theory.

**Category:** Relativity and Cosmology

[13] **viXra:1803.0131 [pdf]**
*submitted on 2018-03-10 03:12:47*

**Authors:** Franz Unterleitner

**Comments:** 8 Pages.

The focus of this work is on an integration constant which appears when the geodesic equations for the Schwarzschild solution are solved directly.
The constant has a dimension of speed-squared and is interpreted as vacuum energy.
When it is set to zero, the solution is Newtonian in the far limit, otherwise it causes orbital velocities to be constant in the long range, explaining flat rotation curves.
The literature is rich of examples where the four geodesic equations are solved, but the constant was not produced.
This is because the direct solution one of the geodesic equations was avoided and an `equivalent` equation was solved instead.
In this work the direct solution is achieved by using an integrating factor which results in the hitherto unknown integration constant.
The existence of fossile disks in the velocity profiles of galaxies is interpreted as a consequence of the vacuum energy decreasing in time.
Again, in short: The geodesic equations in their geometric form are second order differential equations.
They deliver additional integration constants when they are integrated to first order.
Not all of the constants survive, but one of them does and when it is not deliberately set to zero it saturates velocities at far distances.

**Category:** Relativity and Cosmology

[12] **viXra:1803.0114 [pdf]**
*replaced on 2018-03-13 13:13:20*

**Authors:** Theophile Caby

**Comments:** 12 Pages.

We discuss the notion of perception, and describe a simple mechanism by which distortion of observed distances occurs in a static universe, that is compatible with many cosmological observations.

**Category:** Relativity and Cosmology

[11] **viXra:1803.0090 [pdf]**
*submitted on 2018-03-07 00:31:21*

**Authors:** Eric Su

**Comments:** 3 Pages.

A stellar system of two identical stars in orbital motion
is chosen to manifest a physics law, conservation of momentum, in Special Relativity.
Both stars move around each other in a non-circular orbit.
The single gravitational force between two stars demands that total momentum of
this stellar system remains constant in any inertial reference frame in which
the center of mass moves at a constant velocity.
The calculation of total momentum in two different inertial reference frames shows that
the momentum expression from Special
Relativity violates conservation of momentum.

**Category:** Relativity and Cosmology

[10] **viXra:1803.0086 [pdf]**
*replaced on 2018-03-10 11:51:12*

**Authors:** Jaykov Foukzon, S.A.Podosenov, A.A.Potapov, E.Menkova

**Comments:** 135 Pages.

In present article the original proposition is a generalization of the Einstein's world tensor g ij by the introduction of pure inertial field tensor g ac ij such that R α μνλ (g ac ij )≠0 .Bimetric theory of gravitational-inertial field is considered for the case when the gravitational-Inertial field is governed by either a perfect magnetic fluid.In a series of papers published during the past decade with respect to Mössbauer experiments in a rotating system [71]-[75],it has been experimentally shown that the relative energy shift ΔE/E between the source of resonant radiation (situated at the center of the rotating system) and the resonant absorber (located on the rotor rim) is described by the relationship ΔE/E=−ku 2 /c 2 , where u is the tangential velocity of the absorber, c the velocity of light in vacuum, and k some coefficient, which -- contrary to what had been classically predicted equal 1/2 (see for example [35]) -- turns out to be substantially larger than 1/2. It cannot be stressed enough that the equality k=1/2 had been predicted by general theory of relativity (GTR) on account of the special relativistic time dilation effect delineated by the tangential displacement of the rotating absorber, where the "clock hypothesis" by Einstein (i.e., the non-reliance of the time rate of any clock on its acceleration [35]) was straightly adopted. Hence, the revealed inequality k>1/2 indicates the presence of some additional energy shift (next to the usual time dilation effect arising from tangential displacement alone) between the emitted and absorbed resonant radiation. By using Bimetric Theory of Gravitational-Inertial Field [76] we obtain k=0.625 in a good agreement with experimental result k=0.69 [75].

**Category:** Relativity and Cosmology

[9] **viXra:1803.0082 [pdf]**
*submitted on 2018-03-06 11:51:29*

**Authors:** Walter Orlov

**Comments:** 7 Pages. In German

A proposal of an experiment to check the validity of the Lorentz transformations. Lorentz's interpretation of the experiment by Michelson and Morley is logical in the sense of geometric optics. But the light consists of the electromagnetic waves. This leads to conflict, if we recall that the electromagnetic fields can interact with charged particles. A vivid experiment can leave the validity of the Lorentz transformations regardless of the existence of the ether wind. Fourth figure shows the experimental setup.

**Category:** Relativity and Cosmology

[8] **viXra:1803.0078 [pdf]**
*submitted on 2018-03-05 21:17:37*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 2 Pages.

An aspect of the continuum paradox.

**Category:** Relativity and Cosmology

[7] **viXra:1803.0067 [pdf]**
*submitted on 2018-03-05 08:02:12*

**Authors:** Adham Ahmed Mohamed Ahmed

**Comments:** 2 Pages.

its about the dual properties of matter

**Category:** Relativity and Cosmology

[6] **viXra:1803.0059 [pdf]**
*submitted on 2018-03-05 00:51:20*

**Authors:** Eric Su

**Comments:** 3 Pages.

A physical system of a mechanical spring
is chosen to manifest a physics law, conservation of momentum, in Special Relativity.
Two identical objects are attached to the ends of this mechanical spring.
The single force between two identical objects demands that total momentum of
this physical system remains constant in any inertial reference frame in which
the center of mass moves at a constant velocity.
The calculation of total momentum in two different inertial reference frames shows that
the momentum expression from Special
Relativity violates conservation of momentum.

**Category:** Relativity and Cosmology

[5] **viXra:1803.0049 [pdf]**
*submitted on 2018-03-03 12:03:58*

**Authors:** R. G. Chester

**Comments:** 17 Pages.

Tensegrity structures exhibit several counterintuitive behaviors. Among these is expansion resulting solely from internal tension. Replacing the physical tendons of a six-strut tensegrity icosahedron with classical gravitational attraction suggests that universal accelerated expansion may be due to ordinary gravity acting solely as an inverse second-power attractive force. Speculation is included on the ultimate fate of the universe.

**Category:** Relativity and Cosmology

[4] **viXra:1803.0025 [pdf]**
*submitted on 2018-03-01 08:43:28*

**Authors:** Dmitri Martila

**Comments:** 2 Pages.

Attempt to discredit the GR.

**Category:** Relativity and Cosmology

[3] **viXra:1803.0006 [pdf]**
*submitted on 2018-03-02 01:45:47*

**Authors:** Dmitri Martila

**Comments:** 2 Pages.

Is perfectly known, that the Einstein has disapproved the Black Hole solutions. It was horrible to have an divergence, the infinities (BH, BB) in the equations? The Einstein has assumed Matter conservation during the derivation of GR, but it is violated in the consequences: BH, BB. Thus, the GR is wrong. Recall, the Nikola Tesla (who was blessed by his father, Eastern Orthodox Christian) that Nikola was in disagreement with Einstein.

**Category:** Relativity and Cosmology

[2] **viXra:1803.0005 [pdf]**
*replaced on 2018-03-02 14:53:45*

**Authors:** Eric Su

**Comments:** 3 Pages.

In the history of physics, momentum has been represented by two expressions.
One from Issac Newton, the other from Special Relativity. Both expressions are expected
to describe a physical system that demands conservation of momentum. By examining
the gravitational force between two identical particles in two different inertial reference frames,
the momentum expression from Issac Newton
is found to obey conservation of momentum while the momentum expression from Special
Relativity is found to violate conservation of momentum.

**Category:** Relativity and Cosmology

[1] **viXra:1803.0004 [pdf]**
*submitted on 2018-03-02 04:35:36*

**Authors:** Ratikanta Das

**Comments:** 17 pages

Important features of our new four-dimensional model are - 1. Our universe is four dimensional filled with two kinds of four dimensional (4D) hyper spherical * particles. 2. Every object in universe moves as wave due to local transverse motion of these 4D particles 3. Fundamental particles are created from these 4D particles when our flat ** three-dimensional space deforms locally along fourth dimension. 4. Fundamental particles have special 4D structures with infinite extent which justifies action at a distance for electromagnetic and gravitational influences 5. Equal magnitude of charges (±e) of fundamental particles of different mass is due to their similar shape (shape and size determines the property of charge and mass respectively). 6. Schrödinger equation and de Broglie hypothesis can be obtained from 4D structure of fundamental particle. 6. The 4D wave pulse of a fundamental particle is more appropriate to resolve wave-particle duality of matter than that done by a wave packet of 3D model. 7. The net energy of the 4D structure of a fundamental particle that is formed satisfying some equilibrium conditions determines it’s mass). 8. The model also describes a four-dimensional classical technique (named as spiral transformation) for conversion of radiation into matter and vice versa. Standard model does not give us a classical picture of this phenomenon. 9. 4D Structures of fundamental particles are responsible for unifying Coulomb force and strong force. This explains why electron-positron pair annihilates but electron-proton pair forms a stable combination and why n-n or p-p combination is unstable in spite of strong attractive force but n-p combination (deuteron) is stable. 10. New model resolves the puzzle behind dual nature of radiation by assuming photon as a 4D hyper surface wave of finite length(There is no single classical picture in traditional physics to describe nature of light, we have to accept both photon model and wave model ).11. Existence of spin quantum number is consistent with extra space dimension. 12 New model also hints how neutron is created from electron and proton.-----------------------------------------------------------------------------------------------------------------------------------------------------------.
* A circle of area πr2 is enclosed by a line of length 2πr and sphere of volume 4/3πr3 is enclosed by a spherical surface of area 4πr2. Similarly a 4D hyper sphere of hyper volume ½ π2r4 is enclosed by a 3D hyper spherical surface of volume 2π2 r3.
** Straight line, plane surface and flat space (volume) have analogous meanings in one, two and three dimensions respectively.

**Category:** Relativity and Cosmology