308
DOC.
23 ELECTRODYNAMICS OF MOVING BODIES
this in
an
article
entitled "The
Measurement
of
Time [Poincare 1898]" ("Non seulement
nous
n'avons
pas
l'intuition
directe de l'egalite de
deux
durees,
mais
nous
n'avons
meme pas
celle
de la simultaneite de deux evenements
qui
se
produisent
sur
des theatres
differents;
c'est
ce
que
j'ai
explique
dans
un
article
intitule la Me-
sure
du temps").
In the German translation
of
Poincare's
book, the
relevant
passage
of Poin-
care
1898 is translated in
an
editorial
note
to
this
paragraph,
which includes
a lengthy
discus-
sion
of Poincare's
comments
on simultaneity
(see
Poincare
1904a,
pp.
286-289).
[10]
Poincare
1900,
p.
272, gives a physical
interpretation
of Lorentz's
concept
of
local time
(see
Lorentz
1895,
pp.
49-50;
see
also Einstein
1907j
[Doc.
47], note
6).
This
interpretation
is
based
on
a
clock-setting procedure, to
which
Einstein's
is
quite
similar.
Poincare
1900
is
cited in
Einstein 1906e
(Doc. 35), p.
627;
there
is
no
evidence to indicate
when Einstein first
read it.
[11]
For
a
discussion
of
the
role
of
such
princi-
ples
in
Einstein's
research,
see
the Introduction,
pp.
xxi-xxii, xvi.
[12]
Poincare 1902
formulates
"le
principe
du
mouvement
relatif"
in similar words:
"The
mo-
tion
of
an
arbitrary system
must
obey
the
same
laws,
whether referred
to
fixed
axes or
to mov-
ing axes
undergoing
a
uniform rectilinear
mo-
tion" ("Le
mouvement
d'un
systeme
quel-
conque
doit obeir
aux
memes
lois, qu'on le
rapporte
a des
axes
fixes,
ou
a des
axes
mobiles
entraines
dans
un
mouvement
rectiligne
et
uni-
forme")
(p.
135).
[13]
See note 5.
[14]
Einstein
evidently was attempting
to as-
sure
that
initially
identical
measuring
rods and
clocks in the two inertial frames
measure equal
spatial
and
temporal
intervals, respectively,
once
the two
frames
are
in relative motion. He
did not
consider
dynamical problems
that arise
in
accelerating
measuring
rods and clocks in
or-
der
to
transfer
them from
one
inertial frame to
the other. The
corresponding
discussion in Ein-
stein
1907j
(Doc.
47),
p.
418,
is
more
cautious.
For
Einstein's
first discussion
of
the relativistic
dynamics
of
a rigid body,
see
Einstein 1907h
(Doc.
45),
§
3,
pp.
379-382.
[15]
In the 1913
reprint,
the
following
note is
appended
to the end
of
this line:
"The
Lorentz
transformation
equations
are
more simply
deriv-
able
directly
from
the condition
that,
as a
con-
sequence
of
these
equations,
the relation
£2
+
t]2
+
c2 -
V2t2
=
0 shall have the other
x2
+
y2
+
z2
-
V2t2
=
0
as a
consequence"
("Die
Gleichungen
der
Lorentz-Transformation sind
einfacher
direkt
aus
der
Bedingung
abzuleiten,
daß
vermöge
jener
Gleichungen
die
Beziehung
£2
+
t|2
+
t2
-
V2t2
=
0 die andere
x2
+
y2
+
z2
-
V2t2
=
0
zur Folge
haben soll")
(Blumen-
thal
1913,
p.
35).
Einstein
1907j (Doc. 47), pp.
418-420,
gives
such
a
derivation.
[16]
Mathematically
similar transformation
equations
are
introduced in
Larmor 1900 and
Lorentz 1904a.
Voigt
1887 utilizes transforma-
tions
differing only by a
scale factor. Wien
1904
introduces
a
different set
of
linear transforma-
tions
on
the
x
and
t
variables in
Maxwell's
equa-
tions in order to demonstrate that
Lorentz's
the-
ory gives
the
same
result whether
an
electron
is
taken
to
be at
rest,
with the
ether
flowing past
it
at
a
constant
velocity;
or
the
ether is taken
to
be
at rest, with the
electron moved
through
it at the
same speed
in the
opposite
direction.
[17]
Einstein
may
have considered
the kine-
matics
of
a
rigid
sphere
because of
Abraham's
use
of
such
a
model
of
the electron. See, e.g.,
Abraham
1903,
pp.
107-109.
[18]
This
result later became known
as
"the
clock
paradox." Langevin
1911
seems
to
have
first introduced human
travelers,
leading
to the
alternate
name,
"the
twin
paradox."
[19]
In the 1913
reprint,
the
following note is
appended
to
the
word
"Unruhuhr": "In
contrast
to the
'pendulum
clock,'
which-from
the
phys-
ical
standpoint-is
a system,
to
which the earth
belongs;
this had to be
excluded" ("Im
Gegen-
satz
zu
"Pendeluhr",
welche-physikalisch
be-
trachtet-ein
System ist,
zu
welchem
der
Erd-
körper
gehört;
dies mußte
ausgeschlossen
werden")
(Blumenthal
1913,
p.
38).
[20]
The fraction should be "Wn/We."
[21]
Poincare 1905b
notes
that these transfor-
mations, together
with the
spatial
rotations,
form
a group
(see p. 1505).
[22]
See Hertz,
H.
1890a, as reprinted
in
Hertz,
H.
1892, p. 214,
for Hertz's
form
of
Maxwell's
equations (see
Einstein
to
Mileva
Maric,
10
August
1899,
Vol.
1,
Doc.
52,
for
evidence that Einstein read
Hertz,
H.
1892).
Hertz first
gave
this formulation
of Maxwell's
theory
in
Hertz,
H.
1884. Einstein used
Hertz's
notation for
the field
components,
but Lorentz's
notation
for
the
speed
of
light.
[23]
See
Einstein
1907j
(Doc.
47),
p.
429, for
a
fuller discussion
of
the invariance
of
electric
charge.