scholarly journals Special relativity: Interpretation and implications for space-time geometry

2005 ◽  
Vol 219 (2) ◽  
pp. 133-146 ◽  
Author(s):  
H Rahnejat
Keyword(s):  
Special Relativity ◽  
Light Cone ◽  
Small Variation ◽  
Special Theory ◽  
Space Time ◽  
Matter Field ◽  
Theory Of Relativity ◽  
Speed Of Light ◽  
Calculus Of Variation ◽  
Definition Of

The paper commemorates the centenary of the special theory of relativity, which effectively sets the limit for the structure of space-time to that of the stationary system. The long lasting debate for definition of concepts of instantaneity and simultaneity was thus resolved by the declaration of constancy of speed of light in vacuo as a law of physics. All motions were thus bounded by the light cone and described by the properties of differential geometry, firmly anchored in the calculus of variations. The key contribution underpinning the theory was the resolution of the contradiction imposed by the Galilean transformation through physical explanation and the adoption of the Lorentzian transformation. This highlighted the relative nature of both space and time and the linkage of these to preserve the sanctity of the light cone. The resulting space-time geometry was then founded on the traditional calculus of variation with the addition of this transformation. This retains the time as an independent coordinate and its linkage to space in an explicit form. One implication of this approach has been the retention of the concept of infinitum for some physical quantities as a drawback for use of the Lorentzian transformation. The paper shows that this singular behaviour need not arise if the explicit linkage in space-time is abandoned in favour of the implicit inclusion of time as a link between the curved structure of space and the speed of light, thus restating the calculus of variation in line with special relativity. This points to a closed loop space-matter field, which may belie the fabric of the continuum. One implication of this interpretation is that a small variation in speed of light within the field would be required to dispense with the aforementioned singular nature of the Lorentzian boost, while still remaining within the spirit of special relativity.

scholarly journals Special Relativity sans Lorentz Transformation (OR) Perceptional Relativity

2021 ◽  
Author(s):  
Sebastin Patrick Asokan
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Inertial Frames ◽  
Impossible Task

Abstract This paper shows that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a simple and straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in paradoxical Lorentz Transformation. This paper also proves that Lorentz Transformation has failed in its attempt to do the impossible task of establishing t' ≠ t to explain the constancy of the speed of light in all inertial frames without contradicting the interchangeability of frames demanded by the First Postulate of the Special Theory of Relativity. This paper also points out the misconceptions regarding the claimed experimental verifications of Lorentz Transformation's predictions in the Hafele–Keating experiment and μ meson experiment. This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.

scholarly journals Special Relativity sans Lorentz Transformation (OR) Perceptional Relativity

2021 ◽  
Author(s):  
SEBASTIN PATRICK ASOKAN
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Fast Moving ◽  
Inertial Frame ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Slowing Down ◽  
Inertial Frames

Abstract This paper shows that from the fact that the same Reality is perceived differently by the observers in different inertial frames, we can draw a simple and straightforward explanation for the constancy of light's speed in all inertial frames without any need for bringing in paradoxical Lorentz Transformation. This paper shows that the premise that each inertial frame has its unique time, which Lorentz Transformation introduced to explain the constancy of the speed of light in all inertial frames is incompatible with the interchangeability of the frames, an essential requisite of the First Postulate of the Special Theory of Relativity. This paper also points out the misconceptions regarding the claimed experimental verifications of Lorentz Transformation's predictions in the Hafele–Keating experiment and μ meson experiment. This paper hints at the possibility of attributing the observed slowing down of fast-moving clocks to the Relativistic Variation of Mass with Velocity instead of Time Dilation. This paper concludes that Einstein's Special Theory Relativity can stand on its own merits without Lorentz Transformation.

scholarly journals Was Einstein in need to impose the stability of the speed of light in the Theory of Special Relativity

2020 ◽  
Author(s):  
mohamed abouzeid
Keyword(s):  
Special Relativity ◽  
Reference Frames ◽  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
The Stability

According to Einstein's first hypothesis only, it can be reached to transfer formats Between reference frames in the special theory of relativity

Special relativity and the Lorentz sphere

2020 ◽  
Vol 33 (1) ◽  
pp. 15-22 ◽  
Author(s):  
Stephen J. Crothers
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Spherical Wave ◽  
Special Theory ◽  
Inertial System ◽  
Rectilinear Motion ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Principle Of Relativity

The special theory of relativity demands, by Einstein's two postulates (i) the principle of relativity and (ii) the constancy of the speed of light in vacuum, that a spherical wave of light in one inertial system transforms, via the Lorentz transformation, into a spherical wave of light (the Lorentz sphere) in another inertial system when the systems are in constant relative rectilinear motion. However, the Lorentz transformation in fact transforms a spherical wave of light into a translated ellipsoidal wave of light even though the speed of light in vacuum is invariant. The special theory of relativity is logically inconsistent and therefore invalid.

scholarly journals Einstein's special relativity beyond the speed of light

2012 ◽  
Vol 468 (2148) ◽  
pp. 4174-4192 ◽  
Author(s):  
James M. Hill ◽  
Barry J. Cox
Keyword(s):  
Special Relativity ◽  
Lorentz Transformation ◽  
Relative Velocity ◽  
Special Theory ◽  
Mathematical Framework ◽  
Theory Of Relativity ◽  
Speed Of Light ◽  
Inertial Frames ◽  
Controversial Topic ◽  
Energy Equations

We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light, and that are complementary to the Lorentz transformation, giving rise to the Einstein special theory of relativity that applies to relative velocities less than the speed of light. The new transformations arise from the same mathematical framework as the Lorentz transformation, displaying singular behaviour when the relative velocity approaches the speed of light and generating the same addition law for velocities, but, most importantly, do not involve the need to introduce imaginary masses or complicated physics to provide well-defined expressions. Making use of the dependence on relative velocity of the Lorentz transformation, the paper provides an elementary derivation of the new transformations between inertial frames for relative velocities v in excess of the speed of light c , and further we suggest two possible criteria from which one might infer one set of transformations as physically more likely than the other. If the energy–momentum equations are to be invariant under the new transformations, then the mass and energy are given, respectively, by the formulae and where denotes the limiting momentum for infinite relative velocity. If, however, the requirement of invariance is removed, then we may propose new mass and energy equations, and an example having finite non-zero mass in the limit of infinite relative velocity is given. In this highly controversial topic, our particular purpose is not to enter into the merits of existing theories, but rather to present a succinct and carefully reasoned account of a new aspect of Einstein's theory of special relativity, which properly allows for faster than light motion.

scholarly journals Complex Numbers for Relativistic Operations

2021 ◽  
Author(s):  
Dmitry S Kulyabov ◽  
Anna V Korolkova ◽  
Leonid A Sevastianov
Keyword(s):  
Special Relativity ◽  
Additive Group ◽  
Special Theory ◽  
Complex Numbers ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Relativistic Extension ◽  
Algebraic Operations ◽  
Klein Model

When presenting special relativity, it is customary to single out the so-called paradoxes. One of these paradoxes is the formal occurrence of speeds exceeding the speed of light. An essential part of such paradoxes arises from the incompleteness of the relativistic calculus of velocities. In special relativity, the additive group is used for velocities. However, the use of only group operations imposes artificial restrictions on possible computations. Naive expansion to vector space is usually done by using non-relativistic operations. We propose to consider arithmetic operations in the special theory of relativity in the framework of the Cayley–Klein model for projective spaces. We show that such paradoxes do not arise in the framework of the proposed relativistic extension of algebraic operations.

The Ultimate Sophistication of Special Theory of Relativity

2021 ◽  
Vol 11 (3) ◽  
pp. 43-49
Author(s):  
Hamdoon A. Khan ◽  
Keyword(s):  
Special Relativity ◽  
Special Theory ◽  
Mathematical Approach ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
The Real ◽  
The Past ◽  
The One ◽  
The Universe ◽  
Faster Than Light

With the consideration of the light which carries the photon particles, the Lorentz transformation was constructed with an impressive mathematical approach. But the generalization of that equation for all the velocities of the universe is direct enforcement on other things not to travel faster than light. It has created serious issues in every scientific research that was done in the last century based on the special theory of relativity. This paper replaces the velocity of light with some other velocities and shows us the possible consequences and highlights the issues of special relativity. If I travel through my past or future and was able to see another me there, who would be the real Hamdoon I or the one I see there in the past or future! If the real one is only me, the one I saw, is not me, so, I could not travel through my or someone else's past or future. Therefore, no one can travel through time. If both of us are the same, can the key of personal identity be duplicated or be separated into two or more parts? These are some of the fundamental philosophical arguments that annihilate the concept of time travel which is one of the sequels of special relativity.

scholarly journals On the Dependence of the Relativistic Angular Momentum of a Uniform Ball on the Radius and Angular Velocity of Rotation

2020 ◽  
Vol 15 ◽  
pp. 9-14
Author(s):  
Sergey G. Fedosin
Keyword(s):  
Angular Momentum ◽  
Neutron Star ◽  
Angular Velocity ◽  
Mass Density ◽  
Nonlinear Function ◽  
Kerr Black Hole ◽  
Special Theory ◽  
Spherical Body ◽  
Theory Of Relativity ◽  
Speed Of Light

In the framework of the special theory of relativity, elementary formulas are used to derive the formula for determining the relativistic angular momentum of a rotating ideal uniform ball. The moment of inertia of such a ball turns out to be a nonlinear function of the angular velocity of rotation. Application of this formula to the neutron star PSR J1614-2230 shows that due to relativistic corrections the angular momentum of the star increases tenfold as compared to the nonrelativistic formula. For the proton and neutron star PSR J1748-2446ad the velocities of their surface’s motion are calculated, which reach the values of the order of 30% and 19% of the speed of light, respectively. Using the formula for the relativistic angular momentum of a uniform ball, it is easy to obtain the formula for the angular momentum of a thin spherical shell depending on its thickness, radius, mass density, and angular velocity of rotation. As a result, considering a spherical body consisting of a set of such shells it becomes possible to accurately determine its angular momentum as the sum of the angular momenta of all the body’s shells. Two expressions are provided for the maximum possible angular momentum of the ball based on the rotation of the ball’s surface at the speed of light and based on the condition of integrity of the gravitationally bound body at the balance of the gravitational and centripetal forces. Comparison with the results of the general theory of relativity shows the difference in angular momentum of the order of 25% for an extremal Kerr black hole.

Related to Relativity

2019 ◽  
pp. 265-284
Author(s):  
Steven J. Osterlind
Keyword(s):  
Twentieth Century ◽  
General Relativity ◽  
Special Relativity ◽  
Golden Age ◽  
Albert Einstein ◽  
Space Time ◽  
Theory Of Relativity ◽  
Scientific Exploration ◽  
Richard Burton ◽  
Time Continuum

This chapter provides the context for the early twentieth-century events contributing to quantification. It was the golden age of scientific exploration, with explorers like David Livingstone, Sir Richard Burton, and Sir Ernest Shackleton, and intellectual pursuits, such as Hilbert’s set of unsolved problems in mathematics. However, most of the chapter is devoted to discussing the last major influencer of quantification: Albert Einstein. His life and accomplishments, including his theory of relativity, make up the final milestone on our road to quantification. The chapter describes his time in Bern, especially in 1905, when he published several famous papers, most particularly his law of special relativity, and later, in 1915, when he expanded it to his theory of general relativity. The chapter also provides a layperson’s description of the space–time continuum. Women of major scientific accomplishments are mentioned, including Madame Currie and the mathematician Maryam Mirzakhani.

Sign in / Sign up

Export Citation Format

Share Document