Volume 2: The Swiss Years: Writings, 1900-1909 Page 486 (522 of 692)

486 DOC. 47 THE RELATIVITY
PRINCIPLE
identical to that
of
the last
paragraph on p.
911
of
Einstein
1905r
(Doc. 23).
[32]
See the
corresponding paragraph on
aber-
ration in
Einstein 1905r
(Doc. 23),
p.
912,
and
note 29 to that
paper.
[33]
Laue
1907.
[34]
In
a
reprint
copy
in the Holton collection
of Einstein's
reprints
(see
the
Acknowledg-
ments,
p.
xxxiv),
Einstein
changed
this formula
to:
V'
G'
=
'w'
dV'
1
+
V
da)'
The
plus sign
in the denominator
should be
a
minus
sign.
[35]
Einstein here combined the treatment of
what,
in
Einstein
1905r
(Doc. 23),
he called the
Maxwell-Hertz
equations
for
empty space
(see
ibid.,
§
6)
and the Maxwell-Hertz
equations
with convection
currents (see
ibid.,
§
9).
This
section also includes
some
material treated in
§
7 and
§
8
of
the 1905
paper.
[36]
See Einstein 1905r
(Doc. 23),
pp.
908-
909,
for
the
proof.
[37]
The discussion in the
following
two
para-
graphs corresponds
to
that in Einstein
1905r
(Doc.
23),
last
portion
of
§
6,
pp.
909-910.
[38]
The
following paragraph proves an
asser-
tion in Einstein
1905r
(Doc.
23),
final
paragraph
of
§
9, p.
917.
[39]
In
the
equation
for
4,
"w"
should be
"w".
[40]
The
"w'"
should be
"w'."
[41]
This section
presents a
modified treatment
of
the material in
§
10
of
Einstein 1905r
(Doc.
23), largely
based
on
the
work of
Planck
(see
Planck
1906a).
[42]
In the first
denominator,
"x'"
should be
"x0."
In the second
denominator,
the
paren-
thesis should be raised
to
the third
power.
[43]
This form
of
the the
equations
of
motion
and the
corresponding
definition
of
the relativ-
istic
force
differ from those
given
in Einstein
1905r
(Doc. 23),
§
10.
Einstein followed Planck
here
(see
Planck
1906a).
[44]
The "x,
y,
z"
should be "x,
y,
z."
[45]
In
a reprint
of
this
paper
(see
note
34),
Einstein indicated that the
square
bracket after
"2"
should be
deleted,
and
a square
bracket
placed
after
"-ZM)."
An
open parenthesis
should also be inserted before
"YN."
See also
Einstein
1908b
(Doc. 49).
[46]
Einstein here followed Planck in the defi-
nition
of
the relativistic
momentum
of
a particle
(see
Planck
1906a).
[47]
In this
expression
for the relativistic La-
grangian,
as
in
the rest
of
this
paragraph,
Ein-
stein
followed
Planck's
treatment
(see
Planck
1906a).
[48]
In the final
term,
"x"
should be
"x."
[49]
Einstein did not introduce the
concepts
of
longitudinal
and transverse
mass,
which he had
used in earlier discussions
of
this
topic.
See Ein-
stein
1905r
(Doc. 23),
pp.
918-921, and Ein-
stein
1906g (Doc. 36).
[50]
The
c2
inside the brackets should be
placed
outside.
[51]
Starke
1903, e.g.,
indicates that it
was
dif-
ficult to exceed
discharge potentials
of
38,000
volts,
corresponding
to velocities
of
1.17
x 1010
cm/sec
for
cathode
rays.
[52]
Kaufmann
1906a. This
paper
cites Kauf-
mann's earlier
papers on
his
experiments, start-
ing
with
Kaufmann
1901.
[53]
The
drawing
of Kaufmann's
apparatus on
p.
438 is
reproduced
from
Kaufmann
1906a,
p.
496.
[54]
The
figure on p.
439 is based
on fig.
11,
table
IV
of
Kaufmann
1906a.
[55]
That
is,
the
curve was
calculated
on
the
as-
sumption
that the deviations
are negligibly
small
compared
to the dimensions
of
the
apparatus
(see
Kaufmann
1906a,
p. 524).
[56]
This is the value calculated
by
Kaufmann
(see Kaufmann
1906a,
p. 551).
[57]
Planck
1906b,
1907b.
[58]
See
Laub
1910 for
a contemporary
review
of
experiments by
Kaufmann and others
on
the
dependence
of
electron
mass on
velocity.
For
a
discussion
of
these
experiments, see
the editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
pp.
270-272.
[59]
Abraham
1902a.
[60]
Bucherer
1904. See also
Langevin
1905c.
[61]
Einstein had
previously
discussed this
topic
in Einstein 1905v
(Doc. 27)
and Einstein
1906e
(Doc. 35).
His treatment here is similar to
that in
Einstein
1907h
(Doc.
45),
§
1
and
§
2.
[62]
The
"E"
on
the
right-hand
side
of
this
equation
should be "E0."
[63]
The
quotation
is
from
Planck
1907a,
§
18,
p.
568.
Planck's
text
has
"1
gr
Atom"
where
Einstein's
text has
"ein Grammatom."
[64]
Precht
1906.
[65]
In
Planck's
text (see note 63),
the refer-
ence
is
to
eq.
(48)
on p.
564
of Planck
1907a,
which differs from
Einstein's
eq.
(17).
Planck

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Extracted Text (may have errors)

486 DOC. 47 THE RELATIVITY
PRINCIPLE
identical to that
of
the last
paragraph on p.
911
of
Einstein
1905r
(Doc. 23).
[32]
See the
corresponding paragraph on
aber-
ration in
Einstein 1905r
(Doc. 23),
p.
912,
and
note 29 to that
paper.
[33]
Laue
1907.
[34]
In
a
reprint
copy
in the Holton collection
of Einstein's
reprints
(see
the
Acknowledg-
ments,
p.
xxxiv),
Einstein
changed
this formula
to:
V'
G'
=
'w'
dV'
1
+
V
da)'
The
plus sign
in the denominator
should be
a
minus
sign.
[35]
Einstein here combined the treatment of
what,
in
Einstein
1905r
(Doc. 23),
he called the
Maxwell-Hertz
equations
for
empty space
(see
ibid.,
§
6)
and the Maxwell-Hertz
equations
with convection
currents (see
ibid.,
§
9).
This
section also includes
some
material treated in
§
7 and
§
8
of
the 1905
paper.
[36]
See Einstein 1905r
(Doc. 23),
pp.
908-
909,
for
the
proof.
[37]
The discussion in the
following
two
para-
graphs corresponds
to
that in Einstein
1905r
(Doc.
23),
last
portion
of
§
6,
pp.
909-910.
[38]
The
following paragraph proves an
asser-
tion in Einstein
1905r
(Doc.
23),
final
paragraph
of
§
9, p.
917.
[39]
In
the
equation
for
4,
"w"
should be
"w".
[40]
The
"w'"
should be
"w'."
[41]
This section
presents a
modified treatment
of
the material in
§
10
of
Einstein 1905r
(Doc.
23), largely
based
on
the
work of
Planck
(see
Planck
1906a).
[42]
In the first
denominator,
"x'"
should be
"x0."
In the second
denominator,
the
paren-
thesis should be raised
to
the third
power.
[43]
This form
of
the the
equations
of
motion
and the
corresponding
definition
of
the relativ-
istic
force
differ from those
given
in Einstein
1905r
(Doc. 23),
§
10.
Einstein followed Planck
here
(see
Planck
1906a).
[44]
The "x,
y,
z"
should be "x,
y,
z."
[45]
In
a reprint
of
this
paper
(see
note
34),
Einstein indicated that the
square
bracket after
"2"
should be
deleted,
and
a square
bracket
placed
after
"-ZM)."
An
open parenthesis
should also be inserted before
"YN."
See also
Einstein
1908b
(Doc. 49).
[46]
Einstein here followed Planck in the defi-
nition
of
the relativistic
momentum
of
a particle
(see
Planck
1906a).
[47]
In this
expression
for the relativistic La-
grangian,
as
in
the rest
of
this
paragraph,
Ein-
stein
followed
Planck's
treatment
(see
Planck
1906a).
[48]
In the final
term,
"x"
should be
"x."
[49]
Einstein did not introduce the
concepts
of
longitudinal
and transverse
mass,
which he had
used in earlier discussions
of
this
topic.
See Ein-
stein
1905r
(Doc. 23),
pp.
918-921, and Ein-
stein
1906g (Doc. 36).
[50]
The
c2
inside the brackets should be
placed
outside.
[51]
Starke
1903, e.g.,
indicates that it
was
dif-
ficult to exceed
discharge potentials
of
38,000
volts,
corresponding
to velocities
of
1.17
x 1010
cm/sec
for
cathode
rays.
[52]
Kaufmann
1906a. This
paper
cites Kauf-
mann's earlier
papers on
his
experiments, start-
ing
with
Kaufmann
1901.
[53]
The
drawing
of Kaufmann's
apparatus on
p.
438 is
reproduced
from
Kaufmann
1906a,
p.
496.
[54]
The
figure on p.
439 is based
on fig.
11,
table
IV
of
Kaufmann
1906a.
[55]
That
is,
the
curve was
calculated
on
the
as-
sumption
that the deviations
are negligibly
small
compared
to the dimensions
of
the
apparatus
(see
Kaufmann
1906a,
p. 524).
[56]
This is the value calculated
by
Kaufmann
(see Kaufmann
1906a,
p. 551).
[57]
Planck
1906b,
1907b.
[58]
See
Laub
1910 for
a contemporary
review
of
experiments by
Kaufmann and others
on
the
dependence
of
electron
mass on
velocity.
For
a
discussion
of
these
experiments, see
the editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
pp.
270-272.
[59]
Abraham
1902a.
[60]
Bucherer
1904. See also
Langevin
1905c.
[61]
Einstein had
previously
discussed this
topic
in Einstein 1905v
(Doc. 27)
and Einstein
1906e
(Doc. 35).
His treatment here is similar to
that in
Einstein
1907h
(Doc.
45),
§
1
and
§
2.
[62]
The
"E"
on
the
right-hand
side
of
this
equation
should be "E0."
[63]
The
quotation
is
from
Planck
1907a,
§
18,
p.
568.
Planck's
text
has
"1
gr
Atom"
where
Einstein's
text has
"ein Grammatom."
[64]
Precht
1906.
[65]
In
Planck's
text (see note 63),
the refer-
ence
is
to
eq.
(48)
on p.
564
of Planck
1907a,
which differs from
Einstein's
eq.
(17).
Planck

Help

DOC.
47 THE RELATIVITY
PRINCIPLE 487
defines the
mass
M
of
a body as
the limit
of
its
momentum divided
by
its
velocity as
the veloc-
ity approaches zero
(see
ibid.,
p.
564).
Applied
to
black-body
radiation, this
gives
M
=
(E0
+
pV0)/c2,
which
is
Planck's
eq. (48).
[66]
See
Cockcroft
and
Walton 1932 for the
first
reported
verification
of
the
mass-energy re-
lationship
in
a
nuclear reaction.
[67]
See
Planck
1907a,
§
18,
pp.
568-569, for
a
discussion
of
the
relationship
of
inertial and
gravitational mass.
[68]
See Eötvös 1890 for
a report
of
the most
accurate tests
of
this
proportionality
then avail-
able.
[69]
The
"Xa" should
be
"X'a."
[70]
The
"e2"
should
be
"c2."
[71]
The
following
discussion
is based
on
Ein-
stein 1907h
(Doc.
45),
§
1.
[72]
Einstein
1907h
(Doc. 45);
the reference
should be
to
§
1.
[73]
The
"q"
on
the
left-hand side
of
this
equa-
tion should be
"G."
[74]
Planck derived results
equivalent
to the
following
two
equations
from
a
variational
prin-
ciple
in
Planck
1907a,
§ 11
and
§
12.
[75]
Planck derived transformation
equations
for volume and
pressure by
different methods in
Planck
1907a,
§
5
and
§
6.
[76]
The
u
should be omitted from this
equa-
tion.
[77]
See
Mosengeil
1907 for
a
discussion
of
this
system
not
involving
the
theory
of
relativity.
Planck
1907a,
§
1,
summarizes
Mosengeil's
re-
sults;
§
15
shows how
to
obtain them with the
help
of
the relativistic transformation laws.
[78] The
"E0"
should be "E0/c2."
[79]
The
"c2"
should be "V0."
[80]
In
a
reprint
copy
(see note 34),
Einstein
crossed out the factor
"4/3"
in this
equation.
See also
Einstein
1908b
(Doc. 49).
[81]
Einstein
1907h
(Doc. 45).
[82]
In
a
reprint
copy
(see note 34),
Einstein
corrected the term "-
q
dQ" to
"-
q
dG."
[83]
Planck
1907a. The
quotation
is
from
p.
552. Planck used S
as
a symbol
for the
entropy
throughout
his text.
[84]
Planck's
text
(see
note 81)
has
"dasje-
nige"
where
Einstein's
quotation
has
"das."
[85]
Planck's
text
(see
note
81)
has
"Bezugs-
system"
following
"ungestrichene."
[86]
Planck's
text
(see
note 81)
has
"S'1S1,"
where
Einstein's
quotation
has
"n'1n1."
[87]
The "T"
in this
equation
should be
"T0."
[88]
Planck
gave a
different derivation
of
this
result in
Planck
1907a,
§
6. Einstein returned to
the
question
of
the transformation law for
tem-
perature
many years
later,
and arrived
at
a
dif-
ferent result:
-
T/T0
=
Vl
-
v2/c2
(see
Einstein
to
Max
von
Laue,
27
January
1952).
[89]
Planck
1907a.
[90]
In
a
reprint
copy
(see note 34),
Einstein
corrected
the coefficient
of
dz to
Fz,
and the
coefficient
of
T to
dn.
See also Einstein 1908b
(Doc. 49).
[91]
In
a reprint copy (see
note
34),
Einstein
corrected
the term
"x dG"
to
"x
dGx."
See also
Einstein 1908b
(Doc. 49).
[92]
See
Planck
1907a,
§
2. The definition
of
the kinetic
potential
H
is
given on p.
549,
and its
relationship
to the
energy
E
on p.
550.
[93]
See
Einstein
1908b
(Doc. 49),
p.
99, for
a
clarification
of
the
meaning
of
constant acceler-
ation.
[94]
This
paragraph
contains
Einstein's
first
formulation
of
what he later termed the
equiva-
lence
principle
(see
Einstein
1912b,
p.
365).
[95]
In
a reprint copy
(see
note
34),
Einstein
crossed
out
"nutzbar"
and
wrote
"ersetzbar."
See also
Einstein
1908b
(Doc. 49).
[96]
See
p.
413
of
the text
above,
and note
6.
The first
equation on p.
457
corresponds
to Lo-
rentz's
original
definition
of
the local time
("Ortszeit").
[97]
In
a reprint copy (see
note
34),
Einstein
corrected
"gleichen" to "gleicher."
[98]
The reference
to
eq.
(29)
should
be to
eq.
(12).
[99]
See
Einstein
1908b
(Doc. 49), p. 99,
for
a
comment
on
this
equation.
[100]
Einstein
evidently
calculated the
gravita-
tional
potential
at the surface
of
the
sun
and
di-
vided it
by c2.
This is
Einstein's
first
prediction
of
what
came
to
be known
as
the
gravitational
red shift
of
spectral
lines.
His next
paper
on
gravitation
contains
a
discussion
of
this effect
that differs
from the
one given
here
(see
Einstein
1911g,
p.
905).
[101]
In
a reprint copy (see
note
34),
Einstein
corrected
"d/dt" on
the
right-hand
side
of
this
equation to
"d/da"
See also
Einstein
1908b
(Doc. 49),
p.
99.
[102]
In
a
reprint
copy
(see
note
34),
Einstein
added
"u"
following
the
closing parenthesis
in

Previous Page Next Page

DOC. 47 THE RELATIVITY PRINCIPLE
485
Published in
Jahrbuch der Radioaktivität
und
Elektronik
4
(1907):
411-462.
Received 4 De-
cember
1907, published
22
January
1908.
[1]
Lorentz 1895.
[2]
See Lorentz
1895,
§
V.
[3]
Michelson
and
Morley
1887,
which
gives
the results
of
a more
precise
repetition
of
the
ex-
periment reported
in Michelson 1881. This
is
Einstein's first
known reference to
the Michel-
son-Morley experiment.
[4]
See
FitzGerald
1889
and Lorentz
1892b.
[5]
This
may
be
an
allusion
to attempts to set
up an
emission
theory
of
light.
For
evidence
of
an
attempt
by
Einstein before
1905,
see
the edi-
torial
note,
"Einstein
on
the
Theory
of
Relativ-
ity,"
pp.
263-264.
[6]
Lorentz
1895,
pp.
49-50, defines the local
time
t' for
a
frame
of
reference
moving through
the
ether
by
the
equation:
t'
=
t
-
px/V2
x
-
py/V2
y
-
pz/V2
z,
where
t
is the
(universal) time, p is
the
velocity
vector
of
the
moving
frame with
respect
to
the
ether
frame,
and
r
=
(x,y,z)
is the
position vec-
tor with
respect
to the ether frame
of
the
point
at
which the local time is calculated. Lorentz
1904a defines the local time
by an
expression
that is
formally equivalent to
Einstein's
expres-
sion for the time relative
to
the
moving
frame
of
reference. Cohn
1904b,
p.
1408,
expresses
a
view similar
to
Einstein's
on
the role
of
the local
time.
[7]
See Einstein 1905s
(Doc. 24),
Einstein
1906e
(Doc. 35),
and Einstein 1907h
(Doc. 45)
for discussions
of
the inertia
of
electromagnetic
energy.
[8]
See Cohn
1900, 1902, 1904a,
1904b.
A
copy
of
Cohn 1904a
is
in
Einstein's
collection
of
reprints, now
in IsReW.
[9]
Lorentz 1904a and Einstein 1905r
(Doc.
23) (the
reference should be
to
vol.
17).
[10]
Laue
1907. A
reprint copy,
dedicated
"To
the
discoverer of
the
relativity principle"
("Dem
Entdecker
des Relativitätsprinzips"),
containing a
short calculation
in Einstein's
hand,
is
in
Einstein's
collection
of
reprints, now
in
IsReW.
[11]
Laub
1907
(the
reference should be
to
vol.
23).
In
a
letter
of
4
September
1907,
Max Laue
informed Einstein that he had discovered
Laub's
paper
after
completing
work
on
Laue
1907.
Since
Laub's
paper
contains several
errors,
Laue
decided not to
withdraw his
paper,
but to inform
Laub
of
his
objections.
[12]
See Einstein 1905r
(Doc.
23),
pp.
917-
920.
[13]
Planck
1906a.
Planck
1907a,
cited below
by
Einstein in connection
with this
topic,
is
Planck's
second
paper
on
the
topic.
[14]
Einstein
1905s
(Doc. 24),
1907h
(Doc.
45),
and
Planck
1907a.
[15]
Mosengeil
1907. The
article,
based
on
Mosengeil's
1906 Berlin doctoral
thesis,
was
prepared
for
publication by
Planck,
his thesis
su-
pervisor,
after
Mosengeil's
death
(see
ibid.,
p.
867).
[16]
The
question
of
rigid
bodies in the
theory
of
relativity was an
unsolved
problem
at
this
time
(see
Einstein 1907h
[Doc. 45],
§
3).
Ein-
stein here noted that
only rigid
motions
of
solid
bodies
are required.
[17]
Lorentz
1895.
[18]
See
Fizeau 1851. For
Lorentz's
explana-
tion
of
the
dragging
coefficient,
see
Lorentz
1895,
pp.
96-99.
[19]
See
note
3.
[20]
Einstein here introduced the
terms "geo-
metrische
Gestalt"
and
"kinematische Gestalt"
to
generalize
what he had earlier called
"the
length
of
the
rod"
("die
Länge
des Stabes") and
"the
length
of
the
(moving)
rod in
a
system at
rest"
("die
Länge
des
(bewegten)
Stabes
im
ru-
henden
System"), respectively (see
Einstein
1905r
[Doc. 23], p. 896).
[21]
The derivation
of
the transformation
equa-
tions
given
in this section differs
substantially
from that
given
in Einstein
1905r
(Doc. 23),
§3.
[22]
This rule had been
given
in
Planck
1907a,
p.
551.
[23]
Stark
1906.
[24]
Einstein discussed this
question
in
more
detail in Einstein 1907e
(Doc. 41).
[25]
The "n'x
"
in the
denominator
should be
"u'x."
[26]
The
c
in the denominator of the last
term
should
not
be
squared.
[27]
The discussion in the remainder
of
this
paragraph
follows Einstein 1907h
(Doc. 45), pp.
381-382.
[28] The
"X"
should be
"l."
[29]
The
topics
that
are
treated
kinematically
in
this section
are
not discussed in Einstein 1905r
(Doc.
23)
until after the introduction
of
Max-
well's
equations
(see
ibid.,
pp.
910-911).
[30]
The
"x"
in the
numerator
should be
"x'."
[31]
The
wording
of
this
paragraph
is
almost

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