DOC. 10 RESEARCH
NOTES
227
[53]The
coordinate
transformation
[eq.
72] sets
Cartesian
axes x, y
into uniform rotation
at
angular speed
co. [Eq. 73]
is
the matrix of
its coefficients,
to
first
order
in
w.
At
t
=
0
the
ma-
trix of deviations from
diag
(1,1,1)
would become
antisymmetric
under the substitutions
[eq.
74]
for the
two
zero-valued
components.
But the substitution
is
"impossible"
("unmöglich"),
since
[eq.
75]
for
the
differential dt' would
no
longer be
exact.
[54][Eq.
76]
and
[eq.
77]
are
the transformation
to
a
uniformly
accelerated
system
as
given
in
Einstein 1912c
(Doc.
3),
p.
359, equation (4),
after the substitution of
eax
for
c.
The
trans-
formation
yields
the differentials dx'
=
dx-atdt
and
dt'
=
-atdx
+
(1
-at)dt.
[p.
22]
Y
Tx
y
d
d
(Y [eq. 79]
Ist dies
ein
Skalar?
[55]
IK*
3jcv
",(Kk)
3
a
S
^nia]nKa2Taia2PiißlPvß2yßiß2TCilcfa
K
"3r
V/''Ei/'KE2
(PizPKeXj
'eie2
[eq.
80]
/
ß,
=
o
art..,
apvß2
[eq.
81]
dxa Yß,ß2
"
5XT
9jc Vß,ß2
~
0
also
7tvT
heraus setzbar
[56]
a a
5
XKia.KKa2TaiaJaxfa
fa
^P^iP™2\eJ
[eq.
82]
[57]
Beschränken
uns
auf infinitesimale Substitution
Dann
muss,
falls
überhaupt
eines der
p
diff
wird,
z.
B.p
l£
k
=
e2
i
= a1
k
=
a2
gesetzt
werden.
+ S
5'
=
-
wobei
p
mindestens einmal
(P
zu
differenzieren ist.