106
DOC.
1
MANUSCRIPT ON SPECIAL
RELATIVITY
[73]See §9.
[74]The argument
of
this
paragraph
follows Einstein
1905s
(Vol. 2,
Doc.
24).
[75]At
this
point
in the
original text
Einstein indicates
a
note
he has
appended at
the foot of
the
page: "Inbezug
auf E' verschwindet die Summe der
Impulse
beider
Wellenzüge."
[76]See
Einstein
1907j
(Vol.
2,
Doc.
47),
pp.
442-443,
for similar
calculations.
[77]In
a
letter
to
Wilhelm
Wien
of
10
July 1912
(Vol. 5,
Doc. 413)
Einstein
inquired
whether
a test
of
the proportionality
of inertial
and gravitational
mass
for radioactive bodies
was
exper-
imentally
feasible. The
importance
of such
a
test is
also
emphasized
in
Einstein
1912h
(Doc.
8), p.
1062.
[78]See
the historical discussion of
contemporary experiments
in Vol.
2,
the
editorial
note,
"Einstein
on
the
Theory
of
Relativity,"
pp.
270-271.
[79]Beginning
with
the words "Vektor- und
Tensoren-Theorie," the
remainder of
this
head-
ing
is
written
in
dark
ink
and
replaces
the
deleted
word "Geometrie." For
a
discussion of the
relationship
between
geometry
and
tensor
calculus
as
tools for
Einstein's
development
of
a
generalized theory
of
relativity,
see
the
editorial note, "Einstein
on
Gravitation
and Relativity:
The
Collaboration
with Marcel Grossmann."
[80]"a31y" in the
third
equation
below should
be
"a32y."
[81]See,
e.g.,
the
discussion
in Minkowski 1909.
[82]These
questions
are
not
literal
quotations
from Minkowski's
writings.
[83]For
Minkowski's characterization of
the
laws of
physics in
a
four-dimensional world,
see
Minkowski
1908,
p.
57,
where
he
states:
"The entire world
appears to be
resolved into such
world
lines, and
I
would like
to state at
the
outset
that
in
my
view the
physical
laws should
find
their
most perfect expression
in the
interrelations
among
these world lines"
("Die ganze
Welt
erscheint
aufgelöst
in
solche
Weltlinien, und ich möchte
sogleich vorwegnehmen,
dass meiner
Meinung
nach
die
physikalischen
Gesetze
ihren
vollkommensten
Ausdruck
als
Wechselbezie-
hungen
unter
diesen Weltlinien
finden
dürften").
[84]See Einstein
and
Grossmann 1913 (Doc.
13),
part 2,
for
a
systematic treatment
of
tensor
calculus. For
a
brief discussion of
the
contemporary understanding
of
tensors
as
well
as
of Ein-
stein's
and
Grossmann's contribution
to tensor
calculus,
see
the
editorial note, "Einstein's
Research Notes
on
a
Generalized
Theory
of
Relativity,"
secs.
II and III.
[85]Einstein
follows
Sommerfeld's rather than Minkowski's
terminology (see Sommerfeld
1910a,
p.
750).
This
terminology
is
also used
in
Laue
1911a.
[86]For
Sommerfeld's
definition of
an
axial
vector,
see
Sommerfeld
1910a,
p.
750;
for
Laue's
definition,
see
Laue
1911a,
p.
60.
[87]At this
point in
the
original text
Einstein indicates
a
note
he has
appended at
the foot of
the
page:
"Wir wollen solche Vierervektoren wie Laue mit
den grossen
Buchstaben
des
griechischen Alphabeths
bezeichnen."
See
Laue
1911a,
p.
61.
[88]From
this
point
on
the
manuscript is
written
on
paper
of Swiss manufacture.
[89]Einstein's
use
of
parentheses to distinguish
between
vectors
(or tensors) and
their
com-
ponents
is
not
common
in
the
contemporary
literature,
including
Einstein's
own
writings.
For
exceptions,
see
Einstein and Fokker
1914 (Doc.
28),
pp.
322-323, and
Einstein's lecture
notes
for
his
course on
electricity
and
magnetism at
the ETH
in
winter
semester
1913/1914
(Doc.
19).
[90]Einstein's
general
definition of
a
tensor implies
the
existence of sixteen rather than of
ten independent components.
It
was,
however,
customary at
the time
to
restrict
the
notion of
a
tensor to
what
are now
called
symmetric,
second-rank
tensors (see Sommerfeld
1910a,
p.
767).
[91]Neither
Minkowski,
nor
Sommerfeld,
nor
Laue makes
use
of
a
general tensor concept
as
it
is
defined here.
[92]This
notation is
neither
common
in the
literature of the time
nor
is
it
found
in
other
con-
temporary
writings
by
Einstein.
[93]For
a
systematic
discussion
of
vectors
as
second-rank,
antisymmetric
tensors,
see
Ein-
stein and Grossmann
1913 (Doc.
13),
part 2,
§3.
[94]"ein
Tensor" should
be
"eines Tensors."
[95]See
Sommerfeld
1910a,
p.
753.