#
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 v^{2} =
v^{2}, both are written in black, like c and c^{2}; 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 - v^{2}/
c^{2})
^{-1/2}
(x
+ vt)

L(ii)
y = y

L(iii)
z = z

L(iv)
t =
(1 - v^{2}/
c^{2})
^{-1/2}
(t + vx/
c^{2})

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 - v^{2}/
c^{2})
^{-1/2}
(x - vt)

N(ii)
y = y

N(iii)
z = z

N(iv)
t
=
(1 - v^{2}/
c^{2})
^{-1/2}
(t - vx/
c^{2})

v = -v

LN = I

##
Green's Rules

###
(i) Red into Green
(x,y,z,t) = M (x,y,z,t)

Russian-Greek lexicon published in Greece

#
M(i)
x
=
(1 - v^{2}/
c^{2})
^{-1/2}
(x
- vt)

M(ii)
y = y

M(iii)
z = z

M(iv)
t =
(1 - v^{2}/
c^{2})
^{-1/2}
(t - vx/
c^{2})

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 - v^{2}/
c^{2})
^{-1/2}
(x + vt)

K(ii)
y = y

K(iii)
z = z

K(iv)
t
=
(1 - v^{2}/
c^{2})
^{-1/2}
(t + vx/
c^{2})

v = -v

MK = I

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