xviii
INTRODUCTION TO
VOLUME
6
rotations;
and the
perihelion
motion of
Mercury
came
out too
small. For all
three
points some background can
be
given.
The
first
problem,
the realization that Einstein's method for
determining
the form of
the Hamiltonian in
fact
did
no
such
thing, perhaps
has its
roots
in
a
discussion with the Italian mathematician Tullio Levi-Civita
on an
essential
point
in
Einstein's derivation of the
field
equations
in
Einstein 1914o
(Doc.
9).[13]
The second
point
is
connected with Einstein's conviction that the
jus-
tified transformations should include rotations because the
theory
had
to
in-
corporate
Mach's
principle,
understood
as
the
relativity
of rotation
and
the
determination of inertia
by
distant
masses.[14] His
Machian views had
in
fact
guided
him
in
his search for
generally
covariant
field
equations.
A
letter Ein-
stein
wrote to
Erwin Freundlich sheds
some
interesting light
on
the
way
Ein-
stein
came
to
the
conclusion that rotations
were
not
included
in
the allowed
transformations.[15]
The third
problem,
the
theory's
failure
to
account
for the
motion of the
perihelion
of
Mercury,
can
be
connected
to
the
calculations
Einstein had
already
done earlier in collaboration with his friend Michele
Besso
on
this motion of
Mercury
on
the basis of
the
"Entwurf"
theory.
These
calculations,
previously
unknown and
presented
as
Doc.
14
in
Vol.
4,
lead
to
a
result that
is too
small
by
a
factor of
about
two.[16]
Once Einstein had realized the seriousness of the three
flaws,
he decided
to
make
a
fresh
start:
"For
these
reasons
I
completely
lost confidence
in
the
field
equations
drawn
up
by me
and looked for
a
way
to
limit the
possibilities
in
a
natural
manner."[17]
He returned
to general
covariance and in
rapid
suc-
cession
published
the
papers
that contained
the essentials of the
final
theo-
ry.[18]
Initial
errors,
made
in
the
first
two papers concerning
the form of the
field
equations
and the
trace
of the
energy-momentum
tensor,
were
corrected
[13]See
the
correspondence
between Einstein and Levi-Civita
in Vol.
8.
See also Cattani and
De Maria 1989 for
an
analysis.
[14]From
1912
on,
and especially
after the
publication
of
the
"Entwurf"
theory,
the idea of
relativity
of rotation
and its
connection with
Mach's
ideas
had
been
emphasized
by
Einstein
in
his
correspondence
as
well
as
in his
publications (see, e.g.,
Einstein
to
Ernst
Mach, 25
June
1913
[Vol. 5,
Doc.
448],
and also Einstein 1912e
[Vol. 4,
Doc.
7]).
In
later
years,
Einstein's
interpretation
of Mach's
principle
went
through
several
changes. See, e.g.,
Barbour
1992
and
Hoefer
1994;
see
also Einstein's
comments
in
his
obituary
of Ernst Mach
(Einstein
1916c
[Doc.
29]).
[15]See
Einstein
to
Erwin
Freundlich, 30
September
1915.
[16]See
Vol.
4,
the editorial
note,
"The Einstein-Besso
Manuscript
on
the Perihelion Motion
of
Mercury,"
pp.
344-359,
for
a
detailed discussion.
[17]"Aus
diesen Gründen verlor ich das Vertrauen
zu
den
von
mir
aufgestellten Feldglei-
chungen vollständig
und suchte nach einem
Wege,
der die
Möglichkeiten
in
einer natürlichen
Weise
einschränkte." Einstein
1915f
(Doc.
21),
p.
778.
[18]Einstein
1915f,
1915g,
and
1915i
(Docs.
21, 22,
and 25),
which
were
submitted
on
4,
11,
and
25 November,
respectively.