Fünfdimensionale Physik

Relativistic Dynamics and Energy in R5

Roland Alfred Sprenger                                                                                                  DOI 10.5281/zenodo.20007363
 
                                                                                                                                                   
                                                  
Contents
 
The kinetic energy of the motion of a body moving in a relativistic manner in four-dimensional space is specified, and the relativistic mass increase is replaced by the increase in four-dimensional velocity. The existence of rest mass and the nature of time are explained.
 
Sections:
1. Introduction 
2. Momentum, Mass, and Energy in Four-Dimensional Space
3. The Invariance of Total Energy and Total Momentum
4. Force and Acceleration
5. Energy and Spacetime
6. Summary and Outlook
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1. Introduction
 
The hypothesis presented in [1], that relativistically moving bodies move in a four-dimensional auxiliary space, raises the question of whether energy is also associated with the component of motion in the direction of the fourth dimension. Apparently, no energy has yet been measured that occurs in a fourth dimension. On the other hand, the question arises as to whether the increase in mass with velocity contains the answer to the previous question.
In [1], equations (6) and (7)
                                                            vw = (γ / c) ∙ vx2                                      (1)
 
and                                                             vx2 + vw2 = v2                                                  (2)
 
are derived for the velocity component vw in the direction of the fourth dimension w and for the motion v composed of the components vw and vx . (In [1], v = v´, since this is also the velocity of the inertial frame S´ of the moving body.) Furthermore, according to [1], for the angle ψ at which the body moves relative to the x-axis in the x-w-plane, the following equations (5) hold: 
 
                                                                                        cos⁡ ψ = l / l´ = vx / v , s. Fig. 1

and                                                 cos⁡ ψ = √ (1 -vx2 / c2 ) = 1 / γ .                                              (3)

                                                       
Fig. 1: A rod of length l moves at the relativistic velocity vx in the positive x-direction. In the assumed four-dimensional auxiliary space, according to [1], its rest length l´, and the velocity v (= v´) of its rest frame appear at an angle ψ, and its component vw in the direction of the fourth dimension w.