JP Journal of Mathematical Sciences Volume 7 Issues 1 & 013 Pages 41-46 013 Ishaan Publishing House This paper is aailable online at http://www.iphsci.com THE FIFTH DIMENSION EQUATIONS Niittytie 1B16 03100 NUMMELA Finland e-mail: Said_mohamed@hotmail.com Abstract In this presentation we would like to show what happens when we add a new dimension to equation of the Lorentz (see [1]) and found that the conclusions that there are seeral cases including those that could help resole the dispute if there is a moement of the particles faster than the speed of light. We think that we must agree if there is the possibility of the existence of particles that moe faster than the speed of light we hae to be prepared for how to deal with this matter. 0. Introduction The theory of the fifth dimension is not a new innoation. In 197 Kaluza-Klein (see []) for his theory thus there were many scientists who hae tried to build theories to sole new problems in modern physics and cosmology and although it gae answers to some questions that came after the Big Bang Theory. These theories howeer did not answer when the probability that the particle can moe faster than the speed of light or what is the speed of Big Bang? 1. Fifth Dimension Proen According to the foundations established by Lorentz the fourth dimension transformation equation is: 010 Mathematics Subject lassification: 31B99 81V 83E15 85A40. Keywords and phrases: fifth dimension speed of light particles physics cosmology Lorentz big bang. Receied June 13 013
4 The differential of the fourth dimension oer the differential of time is gien by dt 1 (1) c where is speed of particle c is speed of light T is fourth dimension and t is time. This is applied to the supposition that the fastest speed will be the speed of light. The quantity under the square root in equation (1) will be positie when is less than c. How can we explain what happens? When the obserer changes with the speed of light or with a faster than speed of light? According to the fifth dimension and with the same basic in Lorentz transformation equation to proe the four dimensions and adding my assumption to the fifth dimension dimension). INV where I is 1 N is time and V is elocity (the fifth 1. In the case where the compensation of the fifth dimension is by a real alue and the distance is a real alue or the compensation of the fifth dimension is by imaginary alue and the distance is imaginary alue the equation of transformation then becomes: The differential of the pure dimension / the differential of time Speed of light. The transformation equation for fifth dimension ase 1 X 1 X X Y X 3 Z X 4 it X 5 inv [where V is elocity as fifth dimension N is constant time] i 1 and T is time () ds dx + dy + dz N it follows that ds + N dr since S inv we obtain that ds N and that N + N dr.
THE FIFTH DIMENSION EQUATIONS 43 onsequently we obtain dr we conclude that where is speed of light and is speed of a particle.. In the case where the compensation of the fifth dimension is by a real alue and the distance is imaginary the equation of transformation then becomes: The differential of the fifth dimension oer the differential of time is gien by dt K 1 (3) c 13 where ( K ) { 1 : 4.14 10 }. The transformation equation for fifth dimension ase : X 1 X X Y X 3 Z X 4 it X 5 NV [where V is elocity as fifth dimension N is constant time] i 1 and T is time S X + Y + Z T + N V ds dx + dy + dz + N it follows that ds N dr since S inv we obtain ds N N N dr then N dr.
44 onsequently dr N 3 dr N N dr N standard ealuations gie dr 1 N K 1 where K 1 N is the speed of a particle. onsequently K 1 properelocity when K 1 1. N 3. In the case where the compensation of the fifth dimension is by an imaginary alue and the distance is real the equation of transformation then becomes: The differential of the fifth dimension oer the differential of time is gien by K 1. (4) The transformation equation for fifth dimension ase 3: X 1 X X Y X 3 Z X 4 it X 5 inv
THE FIFTH DIMENSION EQUATIONS 45 [where V is elocity as fifth dimension N is constant time] i 1 and T is time S X + Y + Z T + N V ds dx + dy + dz N it follows that ds + N dr since S NV we obtain that ds N and that N + N dr then N dr. onsequently dr N dr N dr N. N Standard ealuations gie N dr 1 K 1.
46 onsequently K 1. Equation (4) is positie when is greater than in case faster speeds than light. The right idea in the situation is if we consider relatiity as a special case inside the general case as fifth dimension theory.. onclusion Equation (3) it can sole the problems of particles in speed under speed of light. Equation (4) it can sole the problems of particles in speed up than speed of light. References [1] A. Einstein Relatiity: The Special and General Theory hapter 17 Bartleby 190. [] Kaluza Klein 5th-dimension http://en.wikipedia.org/wiki/kaluza-klein theory