DOC.
18
DISCUSSION OF DOC.
16 223
Doc.
18
"Discussion"
Following
Lecture Version of
"On the
Present State of the Problem of Gravitation"
[Physikalische Zeitschrift
14
(1913):
1262-1266]
Mie:
First
of
all,
I would like
to
round
out
Mr. Einstein's
interesting
lecture
a
few words
on
the historical
development
of the
theory.
Mr.
Einstein
passed over
this
very
briefly.
Nordström's
theory
takes off from Abraham's
investigations.
I
find
it
necessary
to
have it said here
that Abraham
was
the first
to
set
up
somewhat
reasonable
equations
for
gravitation.
While scientists before
him-after
all,
there do
exist several older
theories of
gravitation-always
tried
to
represent
the
gravitational
field much like the
electromagnetic
one,
Abraham found
a new
possibility.
For the
older
attempts
are
impossible
to
reconcile with the
principle
of
relativity;
because
if
the
principle
of
equality
of inertial and
gravitational mass
is to
be satisfied with
sufficient
exactness,
then the
gravitational
field
cannot
be
represented by a
six-vector.
For that
reason
Abraham first
put
forth
a
theory
with
a
scalar
gravitational potential.
I
would like
to write down the field
equations
with the scalar
potential
in the
somewhat
simplified
form that
I gave
them later. The
gravitational
field is described
with the aid
of
a
four-vector
(gx, gy, gz,
i

u),
which
one
can, however,
as
well
replace
by
another
one
(kx,
ky,
kv
i.w).
These
two
four-vectors
are
related
to
one
another in
a
fashion similar
to,
say,
the relation between the field
strength
and the electric
displacement
in the electric
field,
or
between the
stress
and deformation in
an
elastic
body.
In
the
description
of the
gravitational
field also includes
a
four-dimensional scalar
w,
which
may
be called the
gravitational potential.
The field
equations
then
appear
as
follows:
dtta_dw
_3G
*x=
dx'*y
dy'*z
dz'
dx'
dkx
^
dky
^
dkz
,
dw
=
"VP
dx
dy
dz
dt
where
y
denotes
a
universal
constant
and
p
the
density
of
the
gravitational
mass.
If
one
identifies
the two
vectors
(g,
i

u)
and
(k,
i

w),
one gets
the
equations
that
Abraham has
been
using. However,
of
setting p
identical with the
density
of
the inertial
mass,
which, according
to the
theory
of
relativity is,
in
turn,
identical with the
energy density. However,
the left-hand side
of
the last
equation
is
a
four-dimensional
scalar,
an
invariant for the Lorentz transforma-
tion,
whereas
the
energy density
is
not
an
invariant, so,
of
course,
the
principle
of
relativity
cannot
be
satisfied in this
manner.
Nordström
improved
on
this
theory by substituting
for
p
a
quantity
that
is
invariant for the Lorentz transformation. At
the
same
time
as
he
did
so,
I also
[1]
[2]
[3]
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