DOC.
270
OCTOBER
1916 257
270. To Michele Besso
[Berlin,]
31
October
1916
Dear
Michele,
In
the
interim,
I
had
a
lovely
time in
Holland.[1] The
general
theory
of rel-
ativity
has
already
come very
much
alive
there. Not
only are
Lorentz
and
the
astronomer de
Sitter
working independently
on
the
theory
but
a
number of
other
young colleagues as
well.[2]
The
theory
has also taken root in
England.[3]
I spent
unforgettable
hours with Ehrenfest and not
only stimulating
but
also
reinvigorat-
ing
ones
with
Lorentz
especially.
In
general,
I feel
incomparably
closer to these
people. Nordstrom,
whom
you
know,
of
course,
was
also there.
Zangger
has been
keeping
me
informed
about
my
wife’s
condition and
my
boys’
welfare. I’m
very
glad
that
she
is
recovering
now
after
all,
if
only
slowly.[4]
I’ll
take
care
that
she
doesn’t
get any more
disturbance
from
me.
I
have abandoned for
good proceeding
with the
divorce.[5] Now
to scientific matters!
The
objective
significance
of
space
and time
is
primarily
that the
four-di-
mensional continuum
is
hyperbolic;
so
from each
point
there
are
“temporal”
and
“spatial”
line
elements,
that
is,
those for which
ds2 0
and those for which
ds2
0.
The
xr
coordinates do not have
a
spatial
or
temporal
character
per
se.
To
preserve
the
habitual
way
of
thinking,
you
can
prefer systems
for which
throughout
g44dx24
0,
g11dx21
+
2g12dx1dx2
...
g33dx23
0.
However,
there
is
no
objective
justification
for such
a
choice.
Thus
the
“spatial”
or
“temporal”
nature
is real.
But
it
is
not “natural” for
one
coordinate
to
be
temporal
and
the
others
spatial.
On Dällenbach:[6] The reduction
of
the Riemann tensor
(single or double)
does
not
result in
the
vanishing
of
the former. For
it
should be
easy
to demonstrate,
in
the
case
of
the
field of
a
mass-point
at rest
(external
to the
latter),
that
the
(ik,
lm)'s
do
not
become infinitesimal
even
though
Yjgk\ik,
lm)
kl
all vanish.
On Grossmann:[7]
He
was
mistaken. The
case
of
normal
relativity is
the
case
of
vanishing
curvature;
more precisely:
all
the
components
of
(ik, lm)
vanish.
Definition of the
tensors:
Not
“objects
that
transform in such
and such
a
way.”
Rather:
“objects
that
may
be
described,
with reference
to
an
(arbitrary)
frame
of
reference, by
a
number of
(Auv)
quantities,
with
a
particular
transformation
law