652 DOCUMENT 465 FEBRUARY 1918
[5]Schlick
emphasizes
the word
"willkürlichen"
in the
previous sentence.
[6]See
Doc. 456.
[7]In
the
draft,
there is
a
deleted line
at
this
point repeating
the actual
objection
that Einstein
men-
tioned in Doc. 460: "derselbe
Körper
könne nicht
zugleich
ruhend und
bewegt
sein."
[8]This
example
is also
given
in Mie
1917c,
p.
598.
[9]A
similar
argument
is
put
forward
by
Hendrik A. Lorentz in Doc. 43 and
by
Franz
Selety
in
Doc. 364. See also Einstein’s
response
to
Lorentz in Doc. 47.
[10]The
crucial difference between
going
from rest
to
uniform motion and
going
from
rest to
accel-
erated
motion in Minkowski
space-time
is that the former
case corresponds
to
a symmetry-transfor-
mation
of
the
space-time
metric,
whereas the latter does
not.
Mie would
return to
the
problem
of
an
electron in circular motion in Mie 1920b.
[11]Presumably
the discussion
following one
of
Mie’s Wolfskehl lectures
of
June
1917,
published,
in revised form and without the
discussion,
as
Mie
1917a, 1917b,
and 1917c.
[12]Erich
Justus Kretschmann (1887-1973)
was a
substitute
high
school
teacher
in
Königsberg.
In
Kretschmann
1917,
the author criticizes the notion
of
a relativity principle
used
by
Einstein,
accord-
ing
to
which
a theory
satisfies
a relativity principle
associated with
some group
of
coordinate
trans-
formations
if
its laws
are
covariant
under
those transformations.
Since,
Kretschmann
argues, any
physical
law
can
be stated in
generally
covariant
form,
any theory
can,
in this
sense,
be made to
satisfy
the broadest
possible relativity principle.
Kretschmann
proposes a
different notion
of
a relativity prin-
ciple,
which is
fully independent
of
the form in which the laws
of
a theory are
stated.
Consider
a
theory
in which the
physically possible trajectories are given by
the
geodesics
of
the
space-time
geometries
it
allows;
and consider
symmetries common
to
the
sets
of
all
geodetic trajectories
for all
allowed
space-time geometries. According
to
Kretschmann’s
definition,
the
theory
satisfies
a partic-
ular
relativity principle,
if
and
only
if
the transformations associated with that
relativity principle cor-
respond
to
such
symmetries (Kretschmann
1917,
sec. 26).
Since the set
of
geodesics
of
some
intri-
cately
curved
space-time geometry
allowed
by general relativity
will,
in
general,
have
no
nontrivial
symmetries,
Kretschmann concludes
that,
in this
new
sense,
general relativity
does
not
satisfy any
rel-
ativity principle
at
all. To arrive
at
theories that
do,
he
continues,
one
has
to
add further
requirements
to
the laws
of
general relativity
that restrict the allowed
space-time geometries
to
those with the
appropriate symmetries.
In the
concluding secs.
27-29 of
his
paper,
Kretschmann
argues
that,
in order
to
satisfy a general principle
of
relativity, a theory
would have
to
allow
arbitrary
rather
than
just geo-
detic
trajectories.
Since
such
a theory
would be
highly unrealistic,
Mie
can
refer
to
this
argument as
a
proof
of the
impossibility
of
having a general
principle
of
relativity.
A
large portion
of
Kretschmann’s
paper
(secs. 13-22)
is devoted
to
constructing special
coordi-
nate
systems
in
general relativity.
At the
beginning
of
this
discussion,
Kretschmann
acknowledges a
letter from Mie
of
February
1916 for
a
useful
suggestion
in this
context
(Kretschmann
1917,
p.
592,
fn.
1).
For Einstein’s
response
to
Kretschmann's
paper, see
Einstein
1918f
(Vol.
7,
Doc.
4).
For further
discussion
of
Kretschmann’s
paper, see
Norton
1992a,
sec.
8,
and Norton
1993,
sec.
5.
[13]Mie’s
"axiom
of
the
general relativity
of
the
gravitational
field"
("Axiom
von
der
allgemeinen
Relativität des Gravitationsfeldes"; Mie
1917c,
p.
597),
a generalization
of
his
earlier
principle
of
the
relativity
of
the
gravitational potential (see
Doc.
346,
note 3,
for
further
discussion).
[14]In
the
draft,
Mie deleted the
following passage:
"hoffentlich
...
werde ich Sie dann auch für
diese
Auffassung gewinnen."
[15]The
following part
of
the
text,
which deals with the modified field
equations
and the
cosmolog-
ical model
proposed
in Einstein 1917b
(Vol. 6,
Doc.
43)
departs substantially
from the
draft,
with the
exception
of
the first
two sentences
and the closure.
Following
the
two sentences,
the draft continues:
"Ich bin
nun
aber recht entsetzt
zu
merken,
dass in
der
neuen
Theorie
überhaupt
gar
nichts mehr
von
den
Prinzipien gilt,
die ich
bisher
als die schönsten in
Ihrer
Gravitationstheorie
angesehen
habe. Das
Prinzip
der
Relativität der
Bewegungen gilt
sicherlich nicht
mehr,
weil ja im Weltraum selber die
Zeitaxe eine andere Rolle
spielt
als die drei räumlichen
Axen,
es muss
also Versuche
geben,
die nicht
mehr wie der Michelsonsche Versuch ein
negatives
Resultat
geben, vorausgesetzt,
dass
man
die
Genauigkeit
weit
genug
treiben kann. Vor allem aber
wird,
soviel ich
sehe,
auch das
Prinzip von
der
Relativität des
Gravitationspotentials ungültig,
weil ein Teilchen
nur an
einer
Stelle
existenzfähig
ist,
wo p
und damit
zugleich
das
Gravitationspotential
einen bestimmt
vorgeschriebenen
Wert hat. An