Page:Grundgleichungen (Minkowski).djvu/4

In an appendix, I have gone into discussion of the position of Classical Mechanics with respect to the relativity postulate. Any easily perceivable modification of mechanics for satisfying the requirements of the Relativity theory would hardly afford any noticeable difference in observable processes; but would lead to very surprising consequences. By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy (and statements concerning the form of the energy) alone.

§ 1. NOTATIONS.

Let a rectangular system (x, y, z, t,) of reference be given in space and time. The unit of time shall be chosen in such a manner with reference to the unit of length that the velocity of light in space becomes unity.

Although I would prefer not to change the notations used by Lorentz, it appears important to me to use a different selection of symbols, for thereby certain homogeneity will appear from the very beginning. I shall denote the vector

electric force by ${\mathfrak {E}}$, the magnetic induction by ${\mathfrak {M}}$, the electric induction by ${\mathfrak {e}}$ and the magnetic force by ${\mathfrak {m}}$,

so that ${\mathfrak {E,M,e,m}}$ are used instead of Lorentz's ${\mathfrak {E,B,D,H}}$ respectively.

I shall further make use of complex magnitudes in a way which is not yet current in physical investigations, i.e., instead of operating with t, I shall operate with it, where i denotes ${\sqrt {-1}}$. If now instead of (x, y, z, it), I use the method of writing with indices, certain essential circumstances will come into evidence; on this will be based a general use of the suffixes (1, 2, 3, 4). The advantage of this method will be, as I expressly emphasize here, that we shall have to handle symbols which have a purely real appearance; we can however at any moment pass to real equations