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.

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.

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.

4. Energy, mass, and light

2019 ◽  
pp. 39-51
Author(s):  
Geoff Cottrell
Keyword(s):  
Twentieth Century ◽  
General Theory ◽  
Special Theory ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Space And Time

By the beginning of the twentieth century, our understanding of matter was completely transformed by the great discoveries of electromagnetism and relativity. ‘Energy, mass, and light’ outlines Einstein’s special theory of relativity of 1905, which describes what happens when objects move at speeds close to the speed of light. The theory transformed our understanding of the nature of space and time, and matter through the equivalence of mass and energy. In 1916, Einstein extended the theory to include gravity in the general theory of relativity, which revealed that matter affects space by curving space around it.

The four basic errors of special theory of relativity and the solution offered by extended Galilean relativity

2020 ◽  
Vol 33 (2) ◽  
pp. 211-215 ◽  
Author(s):  
Shukri Klinaku
Keyword(s):  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Addition Formula ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Velocity Addition ◽  
Basic Equations ◽  
Tycho Brahe

Is the special theory of relativity (STR) a “simple” or “tricky” theory? They who think that it is a simple theory say (i) that its postulates are simple, that Nature is such, (ii) that the mathematics of STR is perfect, and (iii) that experiments support it. I consider its two postulates to be very true, whereas the mathematics of the STR has a shortcoming, and, as for the experiments, the question must be posed: which theory do they support best? The problem for STR lies in the transition from its postulates to its basic equations, i.e., Lorentz transformation and the velocity addition formula. The passage from the principle of relativity and the constancy of the speed of light to the basic equations of the STR is affected by four fundamental errors—three physical and one mathematical. Continuous attempts to reconcile these latent mistakes have made STR increasingly tricky. As a result, it is in a similar situation to Ptolemy's geocentric model after “improvements” thereto by Tycho Brahe. However, the “Copernican solution” for relative motion—offered by extended Galilean relativity—is very simple and effective.

Inertia and inertial resistance in the Special Theory of Relativity

2021 ◽  
pp. 1-4
Author(s):  
Peter J. Riggs
Keyword(s):  
Special Relativity ◽  
Minkowski Spacetime ◽  
Special Theory ◽  
Classical Dynamics ◽  
Relativistic Motion ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Particle Inertia ◽  
Spacetime Structure

A broader concept of “resistance to acceleration” than used in classical dynamics, called “inertial resistance”, is quantified for both inertial and non-inertial relativistic motion. Special Relativity shows that inertial resistance is more than particle inertia and originates from Minkowski spacetime structure. Current mainstream explanations of inertia do not take inertial resistance into account and are, therefore, incomplete.

scholarly journals Time in the Special Theory of Relativity

2011 ◽  
Author(s):  
Steven Savitt
Keyword(s):  
Special Relativity ◽  
Reference Frame ◽  
Inertial Frame ◽  
Special Theory ◽  
Inertial Reference Frame ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Crucial Element ◽  
Most Significant Change ◽  
Conventionality Of Simultaneity

Restricted to special relativity, this chapter observes that the most significant change in the concept of time is certainly the relativity of simultaneity. What events are simultaneous with some event for one observer are different from those that are simultaneous with respect to an object traveling in a different inertial frame. Many believe that this relativity can play a role in an argument for eternalism. This chapter critically surveys these arguments before taking on the implications of relativity for the metaphysics of time. It also tackles the conventionality of simultaneity. Many philosophers of science, especially during the early days of relativity, felt that simultaneity is not only relative but also conventional—there is a crucial element of choice in deciding what events are simultaneous for any other in a given inertial reference frame, so that there is no fact of the matter about what is simultaneous.

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