298
EINSTEIN
IN
COLLABORATION
WITH
GROSSMANN
of the
relationship
between the coordinate
description
of
a space-time
manifold and
its
physical properties.
The
argument postulates
a
source-free
region
of
space-time
(the
"hole")
and then
proceeds
to
show that
generally
covariant
field
equations
allow
the construction of
two
distinct metrical
tensors
guv
and
g'uv
that
are
the
same
outside
the "hole" but differ within
it,
so
that the
field
inside the "hole"
is
not
uniquely
determined
by
the
field
and the
sources
outside. The traditional
interpretation
of
the
"hole
argument"
assumes
that Einstein confused the
two
metrical
tensors with
two
different coordinate
representations
of the
same
gravitational field.[20]
In
fact,
as
becomes clear from
more
detailed
accounts
of the "hole
argument"
such
as
the
one
given
in
Einstein 1914e
(Doc.
25),
Einstein
uses
the
representation
of
the
same
metric
field
in
two
different coordinate
systems
to construct two
different metric
fields in
the
same
coordinate
system
that both
satisfy
the
field
equations
for
one
and the
same
matter
distribution. Einstein later realized that
his
argument
was
fallacious.
He
never
returned
to it
in
print,
but he did discuss
it with
several of
his
correspondents
after
he
returned
to
general
covariance
in
the
fall
of
1915.[21]
IV
The detailed
exposition
of the "hole
argument"
in
Einstein 1914e
(Doc.
25), men-
tioned
in
the
preceding
section, is
part
of
a
response
to
a
polemical
attack
on
the
"Entwurf"
theory
launched
by
Gustav
Mie.[22]
In late 1913
and
early
1914
Einstein
wrote two
other
papers
in
reaction
to
questions
or
objections
raised
by
colleagues:
Einstein 1914c
(Doc.
24)
and Einstein
1914h
(Doc. 31).
In
Einstein 1914c
(Doc. 24),
Einstein
shows, in
response
to
a
question
raised
at the
meeting
of
the
Gesellschaft
Deutscher Naturforscher
und Ärzte
in
Vienna,[23]
that
the
energetic components
of
the
gravitational
field
contribute
to
the
gravity
and
the
inertia of
a
physical
system
in
the
same
way
as
nongravitational energy.
But
apart
from
this
original contribution,
the
papers
listed above
mostly
aim
to expound
more
clearly
the essential ideas of the
"Entwurf"
theory,
rather than refute
specific objections
or
criticize alternative
theories.[24]
The
only
other
gravitational theory
in
which Einstein became
seriously
interested
was
the
one by
Gunnar
Nordström, the first
version of which had been
published
in
[20]See,
e.g.,
Pais
1982,
p.
222.
[21]See
Einstein
to
Michele
Besso, 3 January 1916,
and
Einstein
to
Paul
Ehrenfest, 26
Decem-
ber
1915
and
5 January
1916. See
also the
secondary
literature cited
in note
19.
[22]See
Mie
1914a,
1914b.
[23]See
Einstein
et
al. 1913 (Doc.
18).
[24]A
sketch of the "Entwurf"
theory is
also
included
in
Walter Dällenbach's
notes
for
Einstein's
lecture
course
on
electricity
and
magnetism, given
at
the ETH
in
winter
semester
1913/1914
(see Appendix A).
For
an
overview of
contemporary
theories of
gravitation, see
Abraham 1915.
For Einstein's views
on
other
gravitational
theories,
see
Einstein
to
Erwin
Freundlich, mid-August
1913
(Vol. 5,
Doc.
468).
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