282
DOC.
42
SPECIAL AND GENERAL RELATIVITY
The
Lorentz
Transformation
37
every ray)
with
respect to
K
and
K'.
For
the
relative orienta-
tion
in
space
of the co-ordinate
systems
indicated in the dia-
gram (Fig. 2),
this
problem
is
solved
by
means
of
the
equations:
x'
=
x- vt/1-v2/c2
y'
=
y
z'
=
Z
This
system
of
equations
is
known
as
the
“Lorentz
transfor-
[15]
mation.”1
If
in
place
of the
law
of
transmission
of
light
we
had
taken
as our
basis
the tacit
assumptions
of the older mechanics
as
to
the absolute
character of
times and
lengths,
then
instead of
the above
we
should have obtained the
following equations:
x'
=
x
-
vt
y'
=
y
z'
=
z
t'
=
t.
1
A
simple
derivation of the Lorentz transformation
is
given
in
Appendix 1.
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