218 DOC.
225
JUNE
1916
225.
From Hendrik
A.
Lorentz
Haarlem, 6
June
1916
Dear
Colleague,
In
recent months
I
have been
occupying myself
much with
your
gravitation
theory
and
general
theory of relativity
and have also lectured
on
it,
which
was
very
useful to
me.[1]
Now I
believe
I
understand
the
theory
in its full
glory; every
difficulty
I
encountered
I
was
able
to
overcome upon
closer consideration.
I
have
also succeeded in
deriving your
field
equations
Gim
-
K\Tir
-
~gj~T)
out
of
the variation
principle;
at
least,
but
a
minor detail
is
still
lacking
in
this
derivation,
which
required
what
I consider
long
calculations.[2]
But
now
I
have
come across a
consideration I would
like
to
present to
you
and which
is
based
upon
the
examination of
a
fictitious
experiment.
We
can
imagine
that
Lecher’s
experiment
is
done with
two
completely
conductive wires
which
are
stretched around the Earth
along
the
equator
and each of which
is
self–
contained.[3] In order
to
avoid
the
danger
of
a “derailing”
by
the
electromagnetic
waves (owing
to
the Earth’s
curvature),
we can
also
use
instead
of
the
two
wires
a
single
wire
enveloped
concentrically by
an
entirely
conductive
sheath.
At
a
particular point A
on
this
self-contained
“cable”[4]
[space
between
the
conductors
void of
air]
let
there
be
a
device
that
permits
the
excitation of
waves
and
a
detector with which
we
can
observe
at A
the
returning
waves
after their
having
gone
through
the
circuit. The cable
as
well
as
point
A
are
firmly
affixed
to
the
Earth.
From
all
that
we
know,
we can probably
say
with
certainty
what
we
would
observe with
adequately
refined
means.
Waves
produced
at
the
same
moment
at
A
and
that
go
through
the
circuit in
opposite
directions
will not return to A at
the
same
instant.
Among
the
various
ways
in which
we can
describe
this
result, only
two
exist
that
are
particularly simple.
a.
We
can
choose coordinate
system
I,
OX
OY
(OZ
coincides
with the Earth’s
axis),
such
that
in
this
system
the
propagation velocity
of
the
waves
is
the
same
for
both
directions
around the
cycle.
We
then
find
that
the Earth
rotates
in
this
coordinate
system.
b. We
introduce
coordinate
system II,
which
is
firmly
attached
to
the Earth.
In
this
one,
unequal
propagation
velocities
c1
and
c2
exist for
both
directions
around
the
cycle.