DOCUMENT 508 APRIL 1918 721
Denke ich
mir
zwei Punkte
P1
&
P2,
die durch eine zeitar-
tige
Linie verbunden werden können. Die
an P1
&
P2
anlie-
genden zeitartigen
Elemente
ds1
und
ds2
können
dann durch
mehrere
zeitartige
Linien verbunden
werden,
auf
denen sie
liegen[5]
Auf
diesen laufende Uhren werden ein Verhältnis
ds1
:
ds2
liefern,
welches
von
der Wahl
der
verbindenden Kur-
ven unabhängig
ist.-Lässt
man
den
Zusamenhang
des ds mit
Massstab- und
Uhr-Messungen
fallen,
so
verliert die Rel.
Theorie
überhaupt
ihre
empirische
Basis.
Beste Grüsse
von
Ihrem
Einstein.
ds1/P2
ds2/
P1
AKS
(SzZE Bibliothek,
Hs.
91:541). [24 020].
The
verso
is addressed "Herrn Prof. Dr. H.
Weyl
Schmelzbergweg
Zürich
(Schweiz),"
with
return
address "Abs. A. Einstein Haberlandstr.
5 Berlin.,"
and
postmarked
"Berlin W 30 15.4.18.
8-9N[achmittags]."
[1]The
manuscript
of
Weyl
1918b. For
a
brief
characterization
of
the
theory presented
in this
paper,
see
Doc.
472, note 3.
[2]Weyl
had been
out
of
town
and found the
postcard
(Doc. 499)
upon
his
return to
Zurich
(see
Doc.
509).
[3]Einstein had
already
voiced such reservations in Docs. 498 and 499. The
following
consider-
ations
appear to
be
an
elaboration
of
what he referred
to
in Doc. 498
as
his
"measuring
rod
objection"
("Massstab-Einwand").
Einstein
also
explained
his
objection
when
submitting Weyl’s paper
to the
Prussian
Academy
and,
as a
result,
had trouble
getting
the
paper accepted
for
publication (see
Doc. 512
for
more details).
[4]In
Weyl’s "truly
local
geometry"
("wahrhafte Nahe-Geometrie,"
Weyl
1918b, p. 466),
the line
element ds2
= guvdxudxv
is determined
only up
to
a gauge
factor
y,
some arbitrary
continuous
function
of
the
space-time
coordinates. In
support
of
this
departure
from standard Riemannian
geom-
etry, Weyl
offered the
physical argument
that
only
the ratios
of
the
components
of
the metric
tensor
guv
have "an immediate intuitive
significance
...
from
a physical point
of
view"
("physikalisch
...
eine
unmittelbar
anschauliche
Bedeutung,"
Weyl
1918b,
p.
468),
since it is
only
these ratios that
enter
into the fundamental
equation
for the
light
cones,
ds2
=
0.
In
general relativity,
ds2,
and thus
guv,
have
a
direct
physical significance
themselves
as
the
quantities
measured
by
rods and clocks
(al-
though
Einstein had conceded
to
Weyl’s
student Walter Dällenbach the
previous
year
that
strictly
speaking
this is
not true [see
Doc.
299]).
In
that
case,
as
Einstein
proceeds to argue,
the fundamental
feature
of
Weyl’s
theory-that the
transport
of standards
of
lengths
from
one point
to
another is
path-
dependent (see
Doc.
472, note
3)-appears
to
be
at
odds with the observed behavior
of
rods and
clocks.
[5]In
the
diagram,
the labels ds1 and
ds2
should be
interchanged.
508.
From
Hugo
A.
Kruss
Berlin
W
8, 15.
April
1918.
An Hrn. Prof.
Dr. Einstein,
Hochw. Berlin. Haberlandstrasse
5.
Sehr verehrter
Herr
Professor:
Es
tut
mir herzlich
leid,
Ihnen
auf
Ihre
Anfrage
keine
günstige
Antwort
geben
zu
können.[1]
Die
Regelung
der
Wittwenpensionen
ruht auf
allgemeinen gesetzli–