258 DOC.
21
THEORY OF RELATIVITY
Heuristic
Value of the
Theory
of
Relativity
Is
the
theory
of
relativity
of
significance
for the further
development
of
physics apart
from
the fact that
it solves
the dilemma
analyzed
above? This
question must
be
answered in the affirmative for the
following
reason:
According
to
the
theory
of
relativity,
the
systems
K and K'
are
equivalent,
and
the
coordinates and time values
of the
two
systems
are
connected
by
the
equations presented
above. If
a
general
physical theory
is
formulated with
respect
to
K,
then,
with the
help
of the transforma-
tion
equations t,
one can
introduce the
quantities
x',
y',
z', t' into the
equations
instead of the
quantities
x,
y, z,
t.
This results
in
a
system
of formulas referred
to
K'.
According
to
the
relativity principle,
the latter
must
coincide
exactly
with the
system
of
formulas formulated with
respect
to
K,
the
only
difference
being
that
x,
y,
z,
t
are
replaced by
x',
y',
z',
t'.
Thus,
the
theory
of
relativity provides
a
general
criterion of
[13]
admissibility
for
a
physical theory.
Some
Accomplishments
of the
Theory
of
Relativity
Let
us
briefly
enumerate
the individual results owed
so
far
to
the
theory
of
relativity.
It
yields
a
simple theory
of the
Doppler principle,
of
aberration,
of Fizeau's
experiment.
It
proves
that the Maxwell-Lorentz field
equations
are
also admissible in
the
electrodynamics
of
moving
bodies. The laws of deflection of fast cathode
rays
and of the
ß-rays
of radioactive
substances,
which
are
essentially
identical with the
former,
in fact the laws of motion of
rapidly moving
material
points
in
general,
can
be established with the
help
of the
theory
of
relativity
without
invoking special
[14]
hypotheses.
Inertia
and
Energy
But the
most
important
result
produced by
the
theory
of
relativity
thus far is
a
relation between the inertial
mass
of
physical systems
and their
energy
content.
Let
a
body
in
a
certain
state
possess
the inertial
mass
M.
If the
quantity
of
energy
E
is
supplied
to it
in
any way whatsoever, then,
according
to
the
theory
of
relativity,
its
E
inertial
mass
increases
thereby
to
M
+
E/c2,
where
c
denotes the
velocity
of
light.
The
the
law
of conservation
of
mass
that
we
have retained
up
to
now
is
thereby
modified
and
merged
with the
energy principle
into
one
law.
The result
suggests
that the
inertial
mass
M
of
a body
is to
be conceived of
as
an energy
content
of the