## F6     How To Continue?

If we just want to show the main results of the STR, then the next chapter should continue as follows:

• A preliminary section, in which we work out how to transform forces and accelerations. We have provided all of the prerequisites.

• A second section, in which we examine what happens to the Lorentz force, which acts on moving electrons, when represented in the system of the moving electrons itself.

• Then we should in general derive how electric and magnetic fields transform in the STR.

These three points are essential. Only then can we achieve the goal of Einstein - to explain the “asymmetries which do not seem to be inherent in the phenomena”. Perhaps in time an expanded edition of this book will appear – but for the moment, I would simply like to reference the following works of other authors:

• Michael Fowler, in his Internet accessible script [24], gives a basic introduction to the frame dependence of the electromagnetic field. [24] is in general a very nice elementary presentation of the STR and the only other one that I found which also quantitatively presents de-synchronization as a basis phenomenon!

• Roman Sexl and Herbert K. Schmidt present in chapter 16 of [25] a derivation of the transformation of the electromagnetic quantities without the use of higher mathematics. They employ four component vectors in their calculations. This elegant mathematical representation of the STR is introduced in an easily comprehensible fashion.

• Jürgen Freund's book [26] presents in Part IV an introduction to computing with four component vectors. Using this he then derives the transformation of the electric and magnetic field in the STR in a way similar to Sexl et al. [25].

• Anyone with an elementary knowledge in matrix calculations may enjoy a visit to the section Maxwell of this site !

Some other topics we have treated could also be investigated in more detail:

• Transformation and the addition of arbitrary speeds. We have only considered velocities parallel and perpendicular to v. One could also derive the general formula for aberration.

• General Doppler formula. We have investigated only frequency changes in motion in the radial direction (the ‘longitudinal’ Doppler effect)

• Transformation of the quantities of thermodynamics. Some hints to this are given in problem 11 of E6.

Several additions and suggestions will be presented in chapter K. But for now I would like to maintain our momentum and leap into an introduction of the general theory of relativity. I will continue to make use of Epstein's presentation in [15], as well as the beautiful, but long out of print book [27] by Horst Melcher, published in 1968 in the former GDR, and which therefore perhaps has not experienced in the ‘West’ the renown it deserves.