The Lorentz Transformations

There are four versions, each consisting of four equations for the 3+1 dimensions of Minkowski spacetime X,Y,Z,T. There are four versions, because there are two directions of translation and two possible frames of reference. We have a Russian-Greek dictionary published in Russia, a Greek-Russian dictionary published in Russia, a Greek-Russian lexicon published in Greece, and a Russian-Greek lexicon published in Greece. Since v² = v², both are written in black, like c and c²; but the other brackets and symbols are in local colours.

Red's Rules

(i) Red into Green (x,y,z,t) = L(x,y,z,t)
Russian-Greek dictionary published in Russia

L(i) x = (1 - v²/ c²) ^-1/2 (x + vt)
L(ii) y = y
L(iii) z = z
L(iv) t = (1 - v²/ c²) ^-1/2 (t + vx/ c²)
v = -v

(ii) Green into Red (x,y,z,t) = N(x,y,z,t)
Greek-Russian dictionary published in Russia

N(i) x = (1 - v²/ c²) ^-1/2 (x - vt)
N(ii) y = y
N(iii) z = z
N(iv) t = (1 - v²/ c²) ^-1/2 (t - vx/ c²)
v = -v
LN = I

Green's Rules

M(i) x = (1 - v²/ c²) ^-1/2 (x - vt)
M(ii) y = y
M(iii) z = z
M(iv) t = (1 - v²/ c²) ^-1/2 (t - vx/ c²)
v = -v

(ii) Green into Red (x,y,z,t) = K(x,y,z,t)
Greek-Russian lexicon published in Greece

K(i) x = (1 - v²/ c²) ^-1/2 (x + vt)
K(ii) y = y
K(iii) z = z
K(iv) t = (1 - v²/ c²) ^-1/2 (t + vx/ c²)
v = -v
MK = I

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