DOC.
17
THE THEORY OF RELATIVITY
349
systems
of
any
other constitution. Were
we,
for
example,
to place
a
living
organism
in
a
box
and
make
it
perform
the
same
to-and-fro motion
as
the
clock discussed
above,
it
would
be
possible
to have this
organism
return to its
original
starting point
after
an
arbitrarily long flight having
undergone
an
arbitrarily
small
change,
while
identically
constituted
organisms
that remained
at rest at
the
point
of
origin
have
long
since
given
way
to
new
generations.
The
long
time
spent
on
the
trip represented
only an
instant for
the
moving
organism
if
the motion occurred
with
approximately
the
velocity
of
light!
[7]
This
is
an
inevitable
consequence
of
our
fundamental
principles,
imposed
on us by experi-
ence.
And
now
a
few
more
words
on
the
significance
of the
theory
of
relativity
for
physics.
This
theory
demands that the mathematical
expression
of
a
law
of
nature valid
for
arbitrary
velocities does not
change
its
form
if
one
introduces
with
the
help
of
transformation
equations new
space-time
coordinates into the
formulas
that
express
that
law.
This
substantially
narrows
the
manifoldness
of
possibilities. By
means
of
a
simple
transformation
it
is
possible
to derive laws
for bodies
moving
arbitrarily
fast
from the
laws
that
are
already
known
for bodies
at
rest
or
in slow motion. In this
way one can
derive,
for
example,
the
laws
of motion for
fast
cathode
rays.
At the
same
time it
turned
out
that Newton's
equations
do not
hold for material
points
moving
with
arbitrarily great
velocity,
but
have to be
replaced
by
equations
of
motion
of
a
somewhat
more
complicated
structure.
These
laws
of cathode
ray
deflection turned out to be
in
quite
satisfactory
agreement
with
experience.
[8]
Of the
physically
important consequences
of
the
theory
of
relativity we
ought
to
mention the
following.
We
saw
earlier
that,
according
to
the
theory
of
relativity,
a
moving
clock
runs more slowly
than does the
same
clock in
the
state
of
rest.
It
will
probably
never
be
possible
to
verify
this
by
experiments
with
a
pocket
watch,
because the
velocities
we
can impart
to
the latter
are vanishingly
small
compared
with
the
velocity
of
light.
But nature
provides us
with
objects
that
have
quite
the
same
character
as
clocks
and
can
be
moved
exceedingly
fast.
These
are
atoms which emit
spectral lines,
and to
which
we can impart
velocities
of
several
thousand kilometers
per
second
by
means
of
electric
fields
(canal rays).
In accordance
with
theory,
it
is
to
be
expected
that the
oscillation
frequencies
of these
atoms
should
appear
to
be affected
by
their motions
in
exactly
the
same way
in which this
is
to
be deduced for
moving
clocks. Even
though
the
experiments
in
question
face
great
difficulties, we
do
hope
that
in
the
next few
decades
we
will
obtain
an important
confirmation
or
refutation of the
theory
of
relativity
in this
way.
[9]
The
theory
further
leads to
the
important
result that the inertial
mass
of
a body
depends on
its
energy
content,
though
to such
a
small extent
that
a
direct
proof seems
absolutely
hopeless.
If the
energy
of
a body
increases
by
E,
the inertial
mass
increases
E
by
-.
This
theorem
overturns
the
principle
of
the
conservation of
mass, or,
rather,
fuses
c2
Previous Page Next Page