DOC. 9 FORMAL FOUNDATION OF RELATIVITY
31
do not have the
slightest
indication that the earth
moves
around the
sun
with
a
considerable
velocity.
But the confidence
we
have in
relativity theory
also has another root. One cannot
easily
close one's mind to the
following
consideration. When K' and K
are
two
coordinate
systems
in
relative uniform
translatory
motion to each
other,
then these
systems
are
completely
equivalent
from
a
kinematic
point
of
view.
We, therefore,
look in vain to find
a
sufficient
reason why one system
should be
more
suitable
as
a
system
of
reference for the formulation
of
laws
of
nature than another.
Instead,
we
feel
urged
to
postulate
the
equivalence
of
both
systems.
But this
argument immediately spawns
a
counterargument.
The kinematic
equivalence
of
these two coordinate
systems
is
by no means
limited to the
case
where
the two
systems
K and K'
are
in
uniform translatory
motion to each other.
From
the
kinematic
aspect,
this
equivalence
also
obtains, i.e.,
just
as well,
when both
systems
rotate
uniformly
relative to each other. One feels
pressed
toward the idea that the
existing theory
of
relativity
is in need
of
a
considerable
generalization
such that the
apparently unjust preference
for uniform
translatory
motion
over
other relative
motions has
to
be eliminated from the
theory. Everyone
who studied this
subject
in
detail must feel the desire for such
an
extension of the
theory.
[3]
At first
glance
it
appears
that such extension
of
the
theory
of
relativity
would
have to be
rejected on physical grounds.
Because: let there be
a
coordinate
system
K that is admissible
in
the
sense
of
Galilei-Newton,
and another
system
K' which is
in uniform rotation relative to
K; centrifugal
forces will then
act
on masses
which
are
at rest relative to
K' while
the
masses
which
are
at rest
relative
to K do
not suffer
such forces.
Already
Newton viewed this
as
proof
that the rotation
of
K' had to be
interpreted as
"absolute";
in other
words,
that K' cannot claim the
same right as
K
to
be considered
"at
rest." This
argument, however,
is-as
especially
E. Mach has
shown-not
cogent.
This is because
we
need not
necessarily
derive the existence
of
[4]
centrifugal
forces
from
a
motion of
K'; instead,
we can
just
as
well derive them from
the
averaged
rotational movement
of
distant
ponderable
masses
in the
environment,
but
relative
to
K',
thereby treating
K'
as
"at rest."
If
the Newtonian laws
of
[p.
1032]
mechanics and
gravitation
do not allow for such
interpretation,
it
may
well be
founded
in
deficiencies
of
this
theory.
The
following important
argument
also
speaks
in favor
of
a
relativistic
interpretation.
The
centrifugal
force which
acts
under
given
conditions
upon
a
body
is determined
by precisely
the
same
natural constant that
also
gives
its action in
a
gravitational
field. In
fact,
we
have
no means
to
distinguish
a
"centrifugal
field" from
a gravitational
field.
We
thus
always measure as
the
weight
of
a
body
on
the surface
of
the earth the
superposed
action
of
both fields named
above;
and
we
cannot
separate
their actions. In this
manner,
the
point
of
view to
interpret
the
rotating system
K'
as
at rest
and the
centrifugal
field
as
a
gravitational