THE SPECIAL THEORY OF RELATIVITY AND THE SPACE-TIME DOMAIN D_{0} The first paper in this category is primarily to demonstrate the use of a new representation of Pseudo-Euclidean Space-Time. This is based upon Hermann Minkowski's four dimensional "world", and is a linear complex-variable continuum in which the temporal dimension is the imaginary part, and the three spatial dimensions are the real part. The subsequent papers extend the use of this concept into the analysis of various related scenarios as well as further extending the Special Theory itself. The links below are to the introductory pages to the papers themselves. |
The Special Theory, (R1 Ver. 2.4.0) - The paper on the Special Theory develops, from first principles, the kinematic and kinetic theory of relativistic rectilinear, curvi-linear and central orbital motion of an individual mass when subjected to appropriate accelerating forces. The development is effected within a linear four dimensional Relativistic Space-Time Domain, (space-time continuum), as briefy described above, and designated D_{0}. This Domain is subsequently shown to be equivalent to Pseudo-Euclidean Space-Time. The paper also acts as a precursor to the main paper on the new theory of gravitation in that section of the site. |
Spinning Spherical Masses, (R2 Ver. 1.0.1) - This paper analyses the relativistic characteristics of typical parameters associated with spherical masses, when such masses are spinning at high angular rates. The results are largely of mathematical interest only, apart from one result which could have significant implications in the fields of cosmology and the theory of atomic structure. |
Temporal Rate Variability, (R3 Ver. 1.0.0) - This short paper investigates the purported variability of temporal rate in Pseudo-Euclidean Space-Time by analysing the effects of a variety of moving reference frames on the characteristics of the first order relativistic variations of spectral Doppler shift and the velocity of light. |
The Twin Paradox. (R4 Ver. 1.0.0) - The "Twin Paradox" is a thought experiment in Special Relativity, that has attracted a considerable amount of discussion and analysis since Einstein first demonstrated the existence of time dilatation in the Special Theory. It is essentially a "paradox" concerning the comparison of the ages of twins, after one of them has made a high speed journey over a long period of time, while the other has remained stationary. Because each sees the other as in motion throughout the journey, the paradox maintains that each should see the other as having aged more slowly than himself. Opinions are divided as to whether this is a paradox at all, and efforts to date have not satisfactorily resolved the issue. It is believed that this is because such efforts have not fully considered the temporal aspects of the problem, only the spatial. This short paper now analyses the problem using the Relativistic Domain mathematical formulation of the Special Theory, thereby giving equal prominence to its temporal and spatial aspects. This provides a simple resolution, which demonstrates that the problem is not paradoxical at all, as each twin is able to correctly identify the age difference resulting from the time dilatation effects of the journey. |
Time Travel, (R5 Ver. 1.0.0) - Although largely the subject of science fiction writers in the past, this subject is now being actively investigated by some researchers. This paper therefore analyses the possibility of time travel using the techniques of Relativistic Domain Theory. The nature of time, as depicted in the third paper in the Gravitation section of this site, indicates that travelling through time is not possible. The analysis presented here confirms that, but does lead to other potential possibilities. |
The Laws of Relativistic Motion (R6 Ver. 1.0.0) - This paper reviews the relativistic applicability of both Sir Isaac Newton's three general laws, and Johanne Kepler's three planetary laws of motion. Of Newton's set, only the first is found to be fully applicable, the second and third requiring a re-statement and mathematical modification. On the other hand, Kepler's three laws are found to be largely applicable as is , needing only, in some cases, a minor degree of modification to their mathematical representation. |
The Spatial -Temporal Distribution of Energy in the Relativistic Motion of Ponderable Matter. (R7 Ver 1.0.0) - This paper investigates the spatial - temporal distribution of both matter and kinetic energy of ponderable matter when subjected to an external accelerative force. The results of the most pertinent relationships are converted to ones containing Psuedo - Euclidean time to exhibit limiting values in that parameter. |
Relativistic Solutions for (i) The Value of the Velocity of Light, (ii) The Fitzgerald Length Contraction and, (iii) The Ehrenfest Paradox. (R8 Ver. 1.0.0) - This paper, via the application of the Special Theory of Relativity, provides a physical and mathematical solution to (i) the value of the velocity of light, (ii) the contraction of the length of a rod in motion in the direction of its length with a relativistic velocity, and (iii) the Ehrenfest Paradox concerning the contraction of the circumference of the perimeter of a spinning disc. |
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