DOC.
2
RELATIVITY
AND
ITS CONSEQUENCES
123
facts,
is
introduced
every
time
one
resorts to
the
presence
of the ether
to
explain
phenomena
caused
by
relative
motions of
two bodies.
§4.
The
Principle
of
Relativity
and
the
Ether
What
is
the
source
of the
difficulties
we
have
just
seen?
Lorentz's
theory
contradicts
the
purely
mechanical models
to which
physicists
hoped
to
reduce
all
the
phenomena
of
the universe.
For
while mechanics in effect admits
of
no
absolute
motion,
but
only
the motions of bodies
relative to
each
other,
there
is
a
particular
state in Lorentz's
theory
that
corresponds
physically
to
the
state
of
absolute
rest:
that
is
the
state
of
a
body
which
is
not in
motion
with
respect
to
the ether.
If the fundamental
equations
of Newtonian
mechanics,
referred
to
a
coordinate
system
that
is
not
undergoing
accelerated
motion,
are
referred
by means
of the relations
t'
=
t
x'
=
x
-
vt
(1)
y'
=
y
z'
=
z
to
a new
coordinate
system
which
is
in uniform
translational motion
with
respect
to
the
first,
one
obtains
equations
in
t',
x', y',
z' that
are
identical
to
the
original
equations
in
t, x, y, z.
In other
words,
the
Newtonian laws
of
motion
transform
to
laws
of
the
same
form when
one passes
from
one
coordinate
system
to
another
one
that
is
in
uniform
translational
motion with
respect
to
the
first. This
is
the
property we
express
when
we
say
that the
principle
of
relativity
is
satisfied in classical mechanics.
More
generally, we
will
state
the
principle
of
relativity
in
the
following
way:
The laws
governing
natural
phenomena
are independent
of
the
state
of
motion
of
the
coordinate
system
with
respect
to
which the
phenomena
are observed, provided
that
this
system
is not
in accelerated motion.6
If
one
transforms the fundamental
equations
of Lorentz's
theory
by means
of
the
transformation
equations
(1), one
obtains
equations
of
another
form,
in which
the
quantities
x',
y',
z'
no
longer
occur symmetrically. Thus,
the
theory
of
Lorentz,
based
on
the ether
hypothesis,
does not
admit of the
principle
of
relativity.
The
difficulties
6In
all
this
we assume
that the notion of
acceleration has
an objective meaning, or
in
other
words,
that
an
observer
attached
to
a
coordinate
system
is
able to
determine
by
experiment
whether the
system
is
or
is not in accelerated motion. From
now on we
will
consider
only
coordinate
systems
in
nonaccelerated motion.
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