238 DOC. 40 ON KOTTLER'S PAPER
being
at
rest,
such that
no
law
of
nature fails to be satisfied
relative to K'.
3.
The
Gravitational Field Not
Only Kinematically
Caused. The
previous
consideration
can
also be inverted. Let the
system
K' with the
gravitational field,
which
we
considered
above,
be the
original system.
One
can
then introduce
a
new
system
K that is accelerated with
respect
to K' such that
(isolated)
masses move
uniformly
in
straight
lines
(within
the domain of
consideration).
But
one
must not
go
beyond
this and
say:
If
K'
is
a
reference
system
with
an
arbitrary
gravitational field,
then
one can always
find
a system
K relative to which isolated
masses move
uniformly
in
straight
lines, i.e.,
relative to which
no gravitational
field exists. The
absurdity
of
such
a hypothesis
is
plainly
obvious.
If
the
gravitational
field relative
to
K'
is,
for
example,
that
of
a mass
point
at
rest,
then
not
even
the most refined trick
of
transformation
can
transform the field
away
in the entire
neighborhood
of
the
mass
point.
Therefore,
one
may
never
maintain that
a gravitational
field could be
explained, so
to
speak, by pure kinematics;
a
"kinematic, nondynamic interpretation
[4]
of
gravitation"
is
not
possible. By mere
transformation from
a
Galilean
system
into
[p.
641]
another
one by means
of
an
acceleration
transformation,
we
do not learn about
arbitrary
gravitational
fields
but
only
about
some
of
a very special
kind;
but these
too
must-of
course-obey
the
same
laws
as
all other fields of
gravitation.
This is
again
just
another formulation
of
the
principle
of
equivalence (specialized
in its
application
to
gravitation).
A
theory
of
gravitation
violates the
principle
of
equivalence-in
the
sense
as
I
understand
it-only if
the
equations
of
gravitation are
not
satisfied
in
any system
K'
of
reference which
moves nonuniformly
relative
to
a
Galilean
system.
It is
evident
that this accusation cannot be raised
against my theory
of
generally
covariant
equations,
because the
equations
are
here satisfied in
every system
of
reference.
The
postulate
for
general
covariance
of
the
equations
embraces the
principle of
equivalence as
a
special
case.
4.
Are
the
Forces
of
a
Field
of
Gravitation "Real" Forces?
Kottler
censures
that I
interpret
the second term in the
equations
of motion
d2xv +
E
aB
dXa
dxB
=0
aBdS
ds
as
an expression
of
the influence
of
the
gravitational
field
upon
the
mass point,
and
the first
term
more
or
less
as
the
expression
of
the Galilean inertia.
Allegedly
this
would introduce "real forces
of
the
gravitational
field" and this would not
comply
with the
spirit
of
the
principle
of
equivalence. My answer
to this is that this
equation
as a
whole is
generally
covariant,
and therefore is
quite
in
compliance
with the
hypothesis
of
equivalence.
The
naming
of the
parts,
which I have
introduced,
is in
principle meaningless
and
only
meant to
appeal
to
our physical
habit
of
thinking.