Page:Grundgleichungen (Minkowski).djvu/33

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and further

(48) ,

Because F is an alternating matrix,

(49) ,

i.e. is perpendicular to the vector to w; we can also write

(50) ,

I shall call the space-time vector of the first kind as the Electric Rest Force.

Relations analogous to those holding between , hold amongst , and in particular -wf is normal to w. The relation (C) can be written as


The expression (wf) gives four components, but the fourth can be derived from the first three.

Let us now form the time-space vector 1st kind , whose components are

Of these, the first three are the x-, y-, z-components of the space-vector

(51) ,

and further

(52) ;

Among these there is the relation

(53) ,

which can also be written as