The Principle of Relativity

by Albert Einstein; H. Minkowski

and according to 83), T_t > 0. In special cases, where ω vanishes it follows from 81) that

X_x² = Y_y² = Z_z² = T_t², = (Det^1/4 S)²,

and if T, and one of the three magnitudes X_x, Y_y, Z_z are = ±Det^1/4 S, the two others = -Det^1/4 S. If Ω does not vanish let Ω ≠ 0, then we have in particular from 80)

T_z X_t = 0, T_z Y_t = 0, Z_z T_z + T_z T_t = 0,

and if Ω₁ = 0, Ω₂ = 0, Z_z = -T_t It follows from (81), (see also 83) that

X_x = -Y_y = ±Det^1/4 S,

and -Z_z = T_t = √(Det^½ S + εμΩ₃²) > Det^1/4S.

The space-time vector of the first kind

(89) K = lor S,

is of very great importance for which we now want to demonstrate a very important transformation