74 DOCUMENT
43 JANUARY 1915
Hiermit
bin
ich
am
Ende. Es wird
mir
sehr wertvoll
sein,
einmal
von
Ihnen
zu
hören,
was
Ihre
Meinung
über die
besprochenen
Fragen
ist.
ADft
(NeHR,
Archief
H.
A.
Lorentz, 270). [70 398].
At the head
of
the
draft,
which is in
one
of
his
notebooks,
Lorentz noted: “Aan Einstein.
Januari
1915.
Naar
aanleiding
van:
Die formale
Grundlage
der
allgemeinen
Relativitätstheorie.”
(“To
Einstein.
January
1915. In
connection
with: Die formale
Grundlage
der
allgemeinen
Relativitätstheorie.”)
[1]This
letter
is
dated
on
the
assumption
that
it
was
written
during
the month
provided
by
the author
in his notebook
(see
descriptive note)
and
before
Einstein’s
response (Doc. 47).
[2]Here
and in
the
following,
references to
sections, pages
and
numbered
equations are
to Einstein
1914o
(Vol.
6,
Doc.
9).
In
sec.
12,
Einstein
presents
his “hole
argument” against
generally
covariant
gravitational
field
equations.
He considers
coordinate
transformations
from
a
coordinate
system
K to
a
coordinate
system
K',
which
only
differs
from K
inside
some
“hole”
Z,
a
finite source-free
region
of
the
four-dimensional
continuum.
He
argues
that
the field
equations
cannot
be
covariant under such
transformations. The
problem
is
not,
as
is
suggested by
Lorentz’s
comments here,
that
g'uv(x')
in
K'
or
its derivatives have
discontinuities,
but
that if
the field
equations were
covariant under this
transformation,
both
guv(x)
and g'uv(x)
would be
solutions in K
for the
same configuration
of
sources.
The
sources,
Einstein
thought,
would
then
fail
to
determine the field
uniquely.
See Norton
1984,
sec.
5,
Stachel
1989, sec. 3,
and
Vol. 4,
the editorial
note,
“Einstein
on
Gravitation
and Relativ-
ity:
The Collaboration with Marcel
Grossmann,”
pp.
297-298, for discussions
of
the “hole
argument.”
[3]For
the definition
of
“adapted”
coordinate
systems,
see
Doc.
18,
note 5.
[4]Lorentz
has
misunderstood
Einstein’s
argument
on p.
1070
of
Einstein 1914o
(Vol.
6,
Doc.
9)
(see
Einstein’s
response
in Doc.
47).
[5]At
this
point
in
the
original
text,
Lorentz indicates
a
note
that he has
appended:
“wenn
es
sich
nur um
diese
Ableitung
handelt, so
können
wir
uns
auf
das
Innere eines
endlichen
Gebietes be-
schränken,
und
brauchen
uns
um
die
Diskontinuitäten
an
der
Grenze
nicht
zu
kümmern.”
[6]At
this
point
in the
original
text,
Lorentz
indicates
a
note that he has
appended:
“Man
wird
sich
in vielen Fällen
über
die
Frage was
mehr und
was
weniger einfach ist, leicht
einigen. Übrigens
hält
die
Gleichberechtigung
der
beiden
Systeme
schon
auf,
wenn nur
die
Beschreibung
bei
Benutzung
des
einen oder
des
anderen
verschieden aussieht.”
[7]See
Einstein 1914o
(Vol. 6,
Doc.
9),
pp.
1031-1032.
[8]At
this
point
in
the
original
text,
Lorentz indicates
a
note that he has
appended:
“Ich denke hier
an
Mach’s
"Körper
des Weltraumes“ und
an
die
"durchschnittliche Rotationsbewegung
der
pondera-
blen fernen Massen
der
Umgebung“ von
der
Sie
sprechen.”
(See
Einstein 1914o
[Vol.
6,
Doc.
9],
p.
1031.)
[9]The
quotation
is
from
Einstein 1915b
(Vol. 4,
Doc.
21),
p.
707.
[10]Henri
Poincaré
(1854-1912) had been
Professor of
Mathematics at the Sorbonne. See
Poincaré
1902,
pp.
201-202,
for
his criticism
of
the
contraction
hypothesis.
[11]See Lorentz 1904a,
written in
part
in
response
to Poincaré’s criticism
(see
the
preceding note),
as
Lorentz
explicitly
states in
sec.
2
of
the
paper.
[12]See Lorentz
1892b.
[13]At
this
point
in
the
original
text,
Lorentz
indicates
a
note that he has
appended: “1)
Ich
muss
indes
gestehen,
dass ich diese
Bemerkung
erst gemacht habe,
nachdem
ich
die
Hypothese gefunden
hatte.”
[14]At
this
point
in
the
original
text,
Lorentz indicates
a
note
that he has
appended: “2)
Ob
es
sich
um
die
Erklärung
eines
negativen
oder eines
positiven
Resultats
handelt,
scheint mir
kaum einen
Unterschied
zu
machen.”
[15]The same analogy
is used in
Lorentz
1909, p.
196.
[16]At
this
point
in
the
original
text,
Lorentz
indicates
a
note
that
he has
appended:
“Selbstver-
ständlich kann
man sich,
ohne
diese
Änderungen
im Einzelnen
zu
verfolgen
mit
der
Aussage
begnü-
gen,
dass alle
Kraftwirkungen
derart sein
müssen, dass sie sich dem
Relativitätsprinzip
fügen.”
[17]At
this
point
in
the
original text,
Lorentz indicates
a
note that he has
appended:
“1)
Vergl.
Ihre
Überlegungen
auf
S.”
The
unspecified
page
reference
is to Einstein’s discussion
of
the formal
equiv-
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