118
DOC.
2
RELATIVITY AND
ITS CONSEQUENCES
rays
should be considered
totally empty,
while
according
to
the
mechanical and
[1]
electromagnetic
theories
such
a
space
should be considered
as
filled
by
ether.
[2]
§2.
The
Optics
of
Moving
Bodies
and
the
Ether
Once
one accepts
the ether
hypothesis,
one
faces
the
question
as
to
the
kind
of
mechanical
bonds that
link
ether
to matter.
When
matter is
in
motion,
does
the ether
participate
in this
motion
completely, or
is
it
only
partly
carried
along, or else,
is
the
ether
completely stationary?
These
questions are
fundamental for the
optics
and
electrodynamics
of
moving
bodies.
The
simplest hypothesis
is
to
assume
that
moving
bodies
carry along completely
the
ether
they
contain.
It
is
on
the
basis
of
this
hypothesis
that Hertz
developed
an
[3]
electrodynamics
of
moving
bodies
that
is
free of
contradictions.
However,
it
follows from
[4]
a
famous
experiment
by
Fizeau that
this
hypothesis
is
not
acceptable.
This
experiment,
which
can
be considered
an
experimentum
crucis,
is
based
on
the
following
consider-
ations:
Let
u'
be
the
velocity
of
propagation
of
light
in
a transparent
and immobile
medium.
Suppose
we
impart
to this
medium
a
uniform translational motion of
velocity
v.
If the medium
completely
carries
along
the ether
it
contains,
then the
light
will
propagate
with
respect
to
the medium in
the
same
way
as
if
the medium
were
at rest.
In
other
words,
u'
will also
be the
velocity
of
propagation
of the
light
with
respect to
the
moving
medium. To
find
the
velocity
with
respect
to
an
observer
not
taking part
in
the
motion of the
medium,
it
suffices, according
to
the rule of addition of
velocities,
to
add
vectorially
the
velocity
v
to
the
velocity
u'. In the
special case
when
u'
and
v
have
the
same
direction,
one
obtains
either u'
+
v or
u'
-
v
for the desired
sum,
depending
on
whether u' and
v
are
in
the
same
or
the
opposite
direction. But
even
the
greatest
velocities
that
could be
imparted
to
a body are very
small
compared
with
the
velocity
of
light;
a
very
sensitive
method
is
therefore needed
in
order
to
demonstrate the
effect
of the motion of the medium
on
this
velocity.
Fizeau devised
the
following
experiment:
We
consider
two
light rays
capable
of
interfering
with
each
other,
and
two
tubes
filled with
the
same liquid.
We
pass one
of the
rays axially
through
each tube
in
such
a way
that each
ray
will
interfere
with
the other after both
exit
from the
tubes:
the
position
of the
fringes
will
be
changed
if
the
liquid
moves
axially
in
the
tube.
From the different
positions
of
the
fringes
when
the
velocity
of
the flow
is varied,
one
can
determine the
propagation
velocity
of the
light1
in
the
moving liquid,
i.e.,
in
the
medium,
with
respect
to
the
walls
of the tube.
Proceeding
in this
way,
Fizeau
did not
obtain the
value
u'
±
v,
as
had
to be
expected
from what
we
have said
above,
but the
value
u'
±
av,
where
a
is
a
number between
0 and
1
that
depends
on
the
refractive
index
n:
1More
exactly,
the
propagation
velocity
of the
planes
of
equal
phase
of
the
light
beam.
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