DOC.
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141
basis of Maxwell's
theory
for bodies
at rest.
The
introduction of
a
"light
ether"
will
prove
superfluous, inasmuch
as
in accordance with the
concept to
[6]
be developed
here,
no
"space at
absolute
rest"
endowed
with
special properties
will
be introduced,
nor
will
a
velocity
vector be
assigned
to
a
point
of
empty
space
at which electromagnetic
processes are
taking
place. [7]
Like
every
other
electrodynamics,
the
theory
to be
developed
is
based
on
the kinematics of the rigid
body,
since assertions
of
each
and
any
theory
concern
the relations
between
rigid bodies
(coordinate
systems),
clocks,
and
electromagnetic processes.
Insufficient
regard
for this circumstance is
at
the
root
of the difficulties with
which
the
electrodynamics
of
moving
bodies
must presently grapple.
I.
Kinematic
Part
§1.
Definition
of
simultaneity
Consider
a
coordinate
system
in
which
the
Newtonian
mechanical
equations
are
valid.
To
distinguish
it
verbally from
the coordinate
systems
that will
[8]
be
introduced later
on,
and to
visualize it
more
precisely,
we
will designate
this
system
as
the
"system
at
rest."
If
a
material
point
is at rest
relative
to
this coordinate
system,
its
position
relative
to
the latter
can
be
determined
by means
of rigid
measuring
rods
using
the
methods of
Euclidean
geometry
and
can
be
expressed
in
Cartesian
coordinates.
If
we
want
to
describe the
motion
of
a
material point,
we
give
the
values of its coordinates
as a
function of time.
However,
we
should
keep
in
mind
that for
such
a
mathematical description
to
have physical
meaning,
we
first
have to
clarify
what
is
to be
understood here
by
"time."
We
have to
bear in
mind
that all
our
propositions
involving
time
are
always
propositions
about simultaneous
events.
If, for
example,
I
say
that "the train arrives
here
at
7
o'clock,"
that
means,
more or
less,
"the
pointing
of the small
hand
of
my
clock
to
7
and
the arrival of the train
are
simultaneous events."1
1We
shall
not
discuss here the
imprecision
that is inherent in the
concept
of
simultaneity of
two events
taking
place
at
(approximately)
the
same
location
and
that also
must
be
surmounted
by
an
abstraction.