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Abstract
A Euclidean interpretation of special relativity is given wherein proper time [itex]\tau[/itex] acts as the fourth Euclidean coordinate, and time [itex]t[/itex] becomes a fifth Euclidean dimension. Velocity components in both space and time are formalized while their vector sum in four dimensions has invariant magnitude [itex]c[/itex]. Classical equations are derived from this Euclidean concept. The velocity addition formula shows a deviation from the standard one; an analysis and justification is given for that.
Introduction
Euclidean relativity, both special and general, is steadily gaining attention as a viable alternative to the Minkowski framework, after the works of a number of authors. Amongst others Montanus [1,2], Gersten [3] and Almeida [4] (for references see second attachment), have paved the way. Its history goes further back, as early as 1963 when Robert d'E Atkinson [5] first proposed Euclidean general relativity.
The version in the present paper emphasizes extending the notion of velocity to the time dimension. Next, the consistency of this concept in 4D Euclidean space is shown with the classical Lorentz transformations, after which the major inconsistency with classical special relativity, the velocity addition formula, is addressed. Following paragraphs treat energy and momentum in 4D Euclidean space, partly using methods of relativistic Lagrangian formalism already explored by others after which some Euclidean 4vectors are established.
With permission of the moderator, I refer to the attached document parts for the remaining sections. Each attachment contains 5 pages of the article.
The article has been accepted for publication in Galilean Electrodynamics and is copied here with permission.
A Euclidean interpretation of special relativity is given wherein proper time [itex]\tau[/itex] acts as the fourth Euclidean coordinate, and time [itex]t[/itex] becomes a fifth Euclidean dimension. Velocity components in both space and time are formalized while their vector sum in four dimensions has invariant magnitude [itex]c[/itex]. Classical equations are derived from this Euclidean concept. The velocity addition formula shows a deviation from the standard one; an analysis and justification is given for that.
Introduction
Euclidean relativity, both special and general, is steadily gaining attention as a viable alternative to the Minkowski framework, after the works of a number of authors. Amongst others Montanus [1,2], Gersten [3] and Almeida [4] (for references see second attachment), have paved the way. Its history goes further back, as early as 1963 when Robert d'E Atkinson [5] first proposed Euclidean general relativity.
The version in the present paper emphasizes extending the notion of velocity to the time dimension. Next, the consistency of this concept in 4D Euclidean space is shown with the classical Lorentz transformations, after which the major inconsistency with classical special relativity, the velocity addition formula, is addressed. Following paragraphs treat energy and momentum in 4D Euclidean space, partly using methods of relativistic Lagrangian formalism already explored by others after which some Euclidean 4vectors are established.
With permission of the moderator, I refer to the attached document parts for the remaining sections. Each attachment contains 5 pages of the article.
The article has been accepted for publication in Galilean Electrodynamics and is copied here with permission.
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