382
DOC. 514
MARCH
1914
The
novelty
in
the
gravitation theory
is
as
follows.
From the
gravitation
equations[5]
V
3
(J~g
i- ^
3F
YŦß
IhT
=K(T
+
aßja
a
V
öxß
J
and from
the conservation
law it follows
that
d
d
(
r~
aßjiv^v
^a
S..dx.3jc
''
8
YŦß
^
dxa
0.
V
These
are
4
third-order
equations
for
the
gßv
(or
y^v),
which
can
be conceived
as
the
conditions
for
the
special
choice of the
reference
system.
For
brevity,
let
us
call
them
Bo =
0
By means
of
a simple
calculation
I
have
been
able
to
prove
that
the
gravitation
equations
hold
for
every
reference system
that
is
adapted
to
this condition.
From
this it
follows
that there
exist
acceleration transformations
of the
most
varied
kind
that
transform the
equations to
themselves
(e.g.,
also
rotation),
so
that the
equivalence
hypothesis
is
preserved
in its
original
form,
even
to
an unexpectedly
large
extent.
The
strict
equivalence
of
the
gravitational
and
the inertial
mass,
and
also
of
the
gravitational field,
I
had
already proved, I think,
by
the
time
of
your visit.[7]
Now I
am
completely
satisfied and
no
longer
doubt the
correctness
of the
whole
system,
regardless
of whether the observation of
the solar
eclipse
will succeed
or
not.[8]
The
logic
of the
thing
is too evident.
So,
I
am
going
to
live
in
Dahlem and
have
a room
in
Haber's
institute.[9]
I
hope very
much
that
you
will visit
me soon.
No doubt, it will be
very
interesting
in
Berlin,
even
just
to watch. At
the
moment
I do
not
especially
feel like
working,
for
I
had
to
struggle
horribly
to
discover
what
I
described
above.
The
general theory
of invariants
was
only
an
impediment.
The direct
route
proved to
be the
only
feasible
one.
It
is just
difficult
to
understand
why
I
had
to grope
around
so long
before
I
found what
was so near
at
hand.
Cordial
greetings,
also
to
Anna and
Vero,
from
your
Albert
[...][10]