Page:Grundgleichungen (Minkowski).djvu/43



an alternating matrix, and denotes a space-time vector of the second kind. From the expressions (83), we obtain,

from which we deduce that [see (57), (58)].

When the matter is at rest at a space-time point, $$\mathfrak{w}=0$$, then the equation 86) denotes the existence of the following equations

and from 83),

Now by means of a rotation of the space co-ordinate system round the null-point, we can make,

According to 71), we have

and according to 83), $$T_{t} > 0$$. In special eases, where $$\Omega$$ vanishes it follows from 81) that

and if $$T_{t}$$ and one of the three magnitudes $$X_{x},\ Y_{y},\ Z_{z}$$ are $$=+Det^{\frac{1}{4}}S$$, the two others $$=-Det^{\frac{1}{4}}S$$. If $$\Omega$$ does not vanish let $$\Omega_{3} \ne 0$$, then we have in particular from 80)

and if $$\Omega_{1} = 0,\ \Omega_{1} = 0,\ Z_{z} = -T_{t}$$. It follows from (81), (see also 88) that