DOC.
411
JUNE
1912
313
requirement
[A]
with
requirement
[C]
(ascertainability
of
a
wall-clock
time) or,
still
further,
with
requirement
[D]
(temporal
constancy
of
the
velocity
of
light
from
a
wall
lamp
for
each
laboratory
point).
But
I do
not
want to
talk about that
now
because
it
would be
very
tiresome.
So,
we
impose
on
the world
lines in
the
x,
y,
t
space
the
requirements
[A] (optical
conservativeness)
and
[B]
optical
reversibility).
From
this
one can
obtain the
following
propositions
by
purely geometrical
means:
1.
These
world lines
are necessarily
hyperbolas
or
straight
lines.
2.
If
two
of them
are
straight
lines
that
do not form
an
angle
of
45°
with
the
t-axis,
then
this
is
true
of
all
of
them, and all
then
pass
through
one
point
(possibly
an
oo
distant
one:
uniform
motion.)
3.
In
any
other
case
the
field
of
world lines consists
of
oo2
hyperbolas
for
which the
following
propositions
hold
true:
a.
Their
asymptotes
form
an
angle
of
45°
with
the
t-axis.
b. All of the
planes
Ea,
Eb,
Ec .....
of
all the
different
world lines
(hyperbolas)
a,
b,
c,
....
pass
through one
and
the
same
straight
line
T.
By means
of
a
Lorentz
transformation,
one can
always arrange
for
this
straight
line
T to
have
one
of the
following 3
positions
(I)
T
coincides with
the
t-axis
(II) T
coincides with the x-axis
(III)
T forms
an angle
of
45°
with
the
t
and
x
axes.[11]
Dear
Mr.
Einstein:
Thank
you
so
much for
your
kind
letter.
I
needed
it
badly.
I
am
in
a
very
warped
mental
state:
I've
not
heard
a
word from
Lorentz
in
four
weeks.[12] Thus,
it
appears
that
the
whole
bubble
has
burst
again
after
it
had
glittered
so nicely.
o
I
received the
reprints
only today
(great
delay
in
comparison
with
letters because
all
printed
matter
goes through
the
censor!)[13]
o
You
say
in
your
letter
and
refer
in this
regard
to
your
papers:
"It
appears
that the
equivalence
principle
can
be valid
only
for
infinitely
small fields"
(Conjecture
I)
"that,
therefore,
Born's
accel.
finite system
cannot be
considered
a
static
gravit.
field"
(Conjecture II).