DOC.
21
THEORY OF RELATIVITY 259
magnitude
Mc2.
We do
not
yet
have
a
direct
experimental
confirmation of this
[15]
important
result;
but
we
do know
special
cases
for which the
validity
of
the "law of
the inertia of
energy"
can
be deduced
even
without the
theory
of
relativity.
[16]
Minkowski's Mathematical Treatment
of the
Theory
of
Relativity
The
development
of the
theory
of
relativity
was
furthered
greatly by
H.
Minkowski's
mathematical formulation of
its
foundations. Minkowski started
out
from the
premise
[17]
that the "time coordinate"
enters
the fundamental
equations
of
the
theory
of
relativity
in
exactly
the
same
way
as
the
spatial
coordinates if
t is
replaced by
the
imaginary
quantity
V-1ct,
which
is
proportional
to
it.
The
equations
of the
theory
of
relativity
thereby
become
equations
in
a
four-dimensional
space;
and
only
in
the number of
dimensions
are
the formal
properties
of this four-dimensional
space distinguished
from the formal
properties
of the
space
of Euclidean
geometry.
Remark
on
the
Presumptive
Limit
of
the
Range
of
Validity
of the
Theory
Finally,
one more
important question:
Does the
theory
of
relativity possess
unlimited
[18]
validity?
Even the
supporters
of the
theory
of
relativity
have different views
on
this
question.
The
majority
are
of the
opinion
that the
propositions
of
the
theory
of
relativity-especially
its
conception
of time and
space-can
claim unlimited
validity.
However,
the writer of these lines
is
of the
opinion
that the
theory
of
relativity
is
still
in
need of
a generalization,
in
the
sense
that the
principle
of the
constancy
of
the
velocity
of
light
is to
be abandoned.
According
to
this
opinion,
this
principle
is
[19]
to
be retained
only
for
regions
of
practically
constant
gravitational potential.
The
future
must
show whether this
view,
which
is
based
mainly
on
epistemological
grounds,
will
prove
to
be
right.
Literature
An excellent
presentation
of this
subject
is
contained
in
Physikalisches
über
Raum
und Zeit
by
E.
Cohn,
2d
ed.
(B.
G. Teubner,
1913).
[20]