DOC.
628
SEPTEMBER
1918 659
You
unjustifiably
contest
the
accuracy
of
my
rod consideration.
It
is
com-
pletely
correct when
the
two
assumptions
1)
principle
of
relativity
2)
isotropy
of
the
physical space
are
taken
as a
basis.
I
do
seem
to have
forgotten, though,
to
emphasize
in
the
first
explanation
that
the
principle
of
relativity
must be
applied
again
at
this
place.
The
consideration
is
best
clothed in this form:
A
sphere
that
when measured at
rest
has
the
radius R
must
always
have
the
same
shape
&
size,
measured from
a
coordinate
system
K
relative to which it is
moving
at
the
velocity u, independently
of
the
choice of
system
K.
The
static
sphere
relative
to
K'
with
the
equation
x'2
+
y'2
+
Y2
=
R2
must
therefore have
the
same
shape
and
size, seen
from
K,
as
the
sphere
at
relative rest
to
K with the
equation
x2
+
y2
+
z2
=
R2,
seen
from
K'.
This,
translated
into formulas with
the
aid of
equations (1),
nec-
essarily requires l
=
1.
The consid.
yields
l2
=
1/l2,
whereby
l
should be
positive.)
The situation
naturally is
different
if
you
do
not
want to
presuppose
the
principle
of relativity
or
the
law of
isotropy.
Then the
problem
reads
as
follows:
Are
there
known
observations,
or are
observations
conceivable
that
can
clarify
this? In
any
event
it
is
clear
that
the
choice
of
l
is
not
merely
a
matter of formal
convention but
is
a
realistic
hypothesis.
This
hypothesis
determines,
for
ex.,
the
form of the electron in connection with
velocity
and
thus
also
the
dependence
of
electromagnetic
mass on velocity.
Thus,
for
instance,
for
a
while Bucherer
advocated
a
theory
that
boils down
to
another
choice of
l.[4]
But
now
that the
laws of motion of
the
electron have been verified with
great precision,
a
different
choice
of
l
is out of
the
question
today.[5]
A
decision between
Lorentz and Einstein
is
impossible,
anyway,
since
factually
Lorentz’s
theory agrees entirely
with
the
special
th.
of
rel.;
it
is just
a more
specialized
(exclusively
electromagnetic)
theory.-
Now to
the
clock
problem.
This
paradox
is
solved,
from
the
point
of view
of
special
relativity
theory,
as
follows.
If
U is
permanently
at rest relative to
a
Galilean reference
system
while U'
is
describing a
circle relative to
it,
then
U'
lapses
behind
U
even
though
the
clocks
are
of
the
same
construction and
even
though-looked
at
kinematically-U
thus
likewise
describes
a
circle relative to
a