PROPOSAL FOR A EUCLIDEAN APPROACH TO INVESTIGATE RELATIVISTIC DYNAMICS
The Minkowski Space-Time (MST) diagram emerged as the dominant geometrical tool to investigate the Lorentz transformation as a consequence of the introduction of special relativity. The diagram's non-euclidean (+++−) metric is governed by the functions of a hyperbola. Arguing a case for a euclidean interpretation of special relativity, (a) the fourth axis coordinate time parameter is replaced with proper time and (b) the second postulate's invariant coordinate speed c of photon (light) particles is replaced with an invariant space-time speed c of all particles. Adopting this procedure, an alternative euclidean (++++) metric model called the Euclidean Space-Time (EST) diagram is recovered. The transformations are governed by the functions of a circle expressed in terms of a real spacetime angle phi in trigonometric form. [PAPER 1(New)] [PAPER 1 (Old)].
An argument is given to recover a 4-Euclidean Space (ES) analogue of a moving body by adopting a procedure that transforms the fourth displacement in time in the EST diagram analogous to a displacement in space. The ES diagram offers to serve as a convenient tool to investigate relativistic dynamics in close correspondence to classical physics.[PAPER 2]. Applying this model the relativistic momentum and energy variation equation are derived without invoking the problematic relativistic mass concept expressed as a function of phi in trigonometric form.[PAPER 3]. Also the relativistic frequency equation is expressed in trigonometric form offering a unique approach to investigate the variation.[PAPER 4].
Next the velocity addition formula as deduced from the euclidean space analogue is presented. The characteristics of the velocity transformation graph extracted from euclidean space is identical with rapidity space and fulfills the conditions to satisfy the relativistic requirements.However the deduced formula slightly deviates from the standard one and the interpretation problems in verifying it as a tested formula is discussed[PAPER 5]. (Appendix to Paper 5). Finally the possible advantages of this euclidean approach in modeling relativistic dynamics in comparison with the standard non-euclidean approach is presented.[PAPER 6] ( Appendix to Paper 6 )
PAPER 1 (New): A proposed Euclidean alternative to Minkowski space-time diagram.PAPER 1 (Old) A Euclidean alternative to Minkowski space-time diagram
PAPER 2: A Euclidean space analogue of a moving body.
PAPER 3: Momentum and energy equation from Euclidean space analogue.
PAPER 4: Relativistic frequency variation in trigonometric terms.
PAPER 5 : Velocity addition formula from Euclidean space analogue. ( Appendix to Paper 5 ).
PAPER 6 : The advantage of Euclidean interpretation of relativity. ( Appendix to Paper 6 ).
The above paper versions are as originally published. Revised versions are intended to be included at this site appropriately. In line with this, the revised version of [Paper 1(New)] supercedes [Paper 1(Old)].
An informative site on Euclidean interpretation of relativity is available at Euclideanrelativity.com
Copyright: S. Kanagaraj ; s.kana.raj@gmail.com ; (About the author)
8th Oct 2009 - 27th July 2018