350
DOC.
17
THE THEORY OF RELATIVITY
it with
the
principle
of the conservation of
energy
into
a
single
principle.
However odd
this
result
might seem, still,
in
a
few
special
cases,
one can unequivocally
conclude from
empirically
known
facts,
and
even
without the
theory
of
relativity,
that the inertial
mass
[10]
increases
with
energy
content.
And
now
let
me say
just
a
few words
about the
highly
interesting
mathematical
elaboration that the
theory
has
undergone, thanks,
mainly,
to the
sadly so
prematurely
[11]
deceased mathematician
Minkowski.
The transformation
equations
of the
theory
of
relativity are so
constituted that
they
possess
the
expression
x2
+
y2
+
z2

c2t2
as an
invariant.
If
we
introduce the
imaginary
variable
ct
.
x
as
the
time variable
instead of the
time
t,
then
this
invariant
will
assume
the
form
x2
+
y2
+
z2 +
x2.
Here the
spatial
coordinates
and
the
temporal
coordinate
play
the
same
role.
The
further
pursuance
of
this formal
equivalence
of the
space
and time coordinates
in
the
theory
of
relativity
led
to
a very
perspicuous representation
of the
theory,
which makes
its
application
substantially
easier.
Physical
events
are
represented
in
a
4dimensional
space,
and the
spatiotemporal
relations of
what
results
appear as geometrical
theorems
[12]
in this 4dimensional
space.