410 DOC.
401
DECEMBER
1917
For
the
point of
mass (which
is just
located in
the XZ
plane)
rotating
along
with
it,
x
=
z
=
0
y
=
wx.
Hence
d2x/ds2 =
(Cw2x
+
C'w2x)
j
+[. .x,ÿ,z]2.
In order for
this
expression
to
disappear
also in the
limiting
case
of
tiny velocities,
C
=
-C'
must
apply.
In
other
words: the
factors
w2x
in
the
centrifugal
force and
wv
in
the
coriolis
force must
be
numerically equal
to
each other.
But
if
the
T’s
are supposed
to
represent
our
centrifugal
field
in conventional
mechanics,
then
because of
the
formulas mw2r and
2mwv:
2C
=
-C'
would have
to
be
true.[6]
How
can
these differences be
reconciled?
Another
disturbing
two
occurs
elsewhere
as
well.
In
a
stationary gravita-
tional
field in which all guv's
are
independent
of
x4,
the
equations
apply
in
first
approximation[7]
-r144
-
+r4
-
etc
r4
-
o
r
-
-i-J.
14
-
2
q
1
44
-
u-
The
motion
equations
of
a
mass-point
in this
field
are[8]
=
(rLi
+
2(r}4¿
+
v\4y
+
r44¿)}
+
[•
• •
ÿ,
¿]2
d2x4
ds2
=
rj4
+
2(r;4¿
+
q4j
+
q»)
(
^
|
+[...]
Now
d2x4/ds2=d/dt(v2/2),
applies
for
slow
velocities,[9]
whereas
the
highest
ranking
terms
on
the
right-hand
side of
the 4th
equation represent
twice
the
power.[10]
The
energy
balance
thus
is
not correct.
I do not
doubt that this
will be resolvable.
Schrödinger[11]
thought
the
source
of the
error was
that the
field
lost its
stationary
nature through
the motion of
the
mass-point,
thus
that in the
approximation
used,
r444
no longer can
be
set
equal
to
0.
I
replied
to
this that
in
electrodynamics
the
motion of
an
electron also
disturbs the
field,
but
that
there
d2x4/dT2
=
1
.
((Fb)
nonetheless
applies.[12]
Maybe
it
is
only
I who
am now
too
far afield from
the
theory
with
my range
of
thought
to
grasp
the
matter,
but
item,
there
is
nobody
in Vienna who would