Fünfdimensionale Physik

Why the Speed of Light Is the Maximum Speed



Spacetime is regarded as a medium consisting of spacetime quanta. Similar to the speed of sound in air or water, the vacuum speed of light is the intrinsic speed of spacetime. Because moving inertial systems are rotated into a fifth dimension, the speed of light is the same in all of them, and the principle of relativity holds.


1. Introduction
 
The script “Relativistic Dynamics and Energy in R5” [1] demonstrate and explain that the limitation of all effective velocities to the vacuum speed of light for bodies results in their having a velocity component in the fourth spatial dimension introduced there, which absorbs more and more energy during acceleration. The aim here is to answer the question of why such a limiting speed exists in the theory of relativity.
According to [1], the rest mass of a body remains constant even at relativistic speeds; therefore, it does not differ from its dynamic mass and, like the latter, will hereafter be referred to simply as mass m. It is equivalent to its kinetic energy E, which results from the translation of four-dimensional space in the direction of time at the speed of light. For a body at rest in three-dimensional space, E = m c². If a body moves with velocity vx in the x-direction, then according to [1], it has the four-dimensional velocity v given by

                                                                                          v2 = vx2 + vw2            ,                                                                                (1)

where, for its component vw2 in the direction of the fourth dimension w, the following holds:

                                                                                         vw = (γ / c) vx2 = vx2 / √ (c2 - vx2)         .                                                        (2)

For the angle ψ between vector v and the x-axis, the following holds:
 
                                                                                          cos⁡ ψ = √ (1 - vx2 / c2) = 1 / γ          .                                                         (3)

A moving body has the energy                                         E = m c √ (c2 + v2) = m c vE                                                                     (4)                                                                          
with the five-dimensional velocity                                     vE = √ (c2 + v2)         .                                                                                 (5)
 

                                               
Fig. 1: Motion of a body with vx = 0.5 c and four-dimensional velocity v, with the x-w-plane moving in the direction of time at the speed of light; resulting velocity vector vE ; worldlines in R4 and R5 shown in blue; rest energy E0 and total energy E as red lines, in the chosen unit of measurement m0c, with magnitudes equal to those of the velocity vectors c and vE .