Volume 6: The Berlin Years: Writings, 1914-1917 (English translation supplement) Page 351 (363 of 462)

DOC.
42
SPECIAL AND GENERAL RELATIVITY
351
Space-Time
Continuum
of
the
General
Theory
107
x1, x2, x3, x4.
Thus
in
reality,
the
description
of the
time-space
continuum
by
means
of Gauss co-ordinates
completely
re-
places
the
description
with
the
aid
of
a
body
of
reference,
without
suffering
from the defects
of the
latter mode of de-
scription;
it
is
not
tied down
to
the Euclidean character of the
continuum
which
has
to
be
represented.

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DOC.
42
SPECIAL AND GENERAL RELATIVITY
351
Space-Time
Continuum
of
the
General
Theory
107
x1, x2, x3, x4.
Thus
in
reality,
the
description
of the
time-space
continuum
by
means
of Gauss co-ordinates
completely
re-
places
the
description
with
the
aid
of
a
body
of
reference,
without
suffering
from the defects
of the
latter mode of de-
scription;
it
is
not
tied down
to
the Euclidean character of the
continuum
which
has
to
be
represented.

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352
DOC. 42 SPECIAL AND GENERAL RELATIVITY
TWENTY-EIGHT
Exact Formulation
of
the
General
Principle
of
Relativity
We
are
now
in
a
position to replace
the
provisional
formulation of the
general principle
of
relativity
given
in
Section
18
by
an
exact
formulation.
The
form
there
used, "All
bodies of reference
K,
K',
etc.,
are
equivalent
for
the
description
of natural
phenomena
(formu-
lation of the
general
laws
of
nature),
whatever
may
be their
state
of
motion," cannot
be
maintained,
because the
use
of
rigid
reference-bodies, in
the
sense
of the method followed
in the
special theory
of
relativity, is
in
general
not
possible
in
space-time description.
The
Gauss
co-ordinate
system
has
to
take the
place
of the
body
of reference. The
following
statement
corresponds to
the fundamental idea of the
gen-
eral
principle
of
relativity: "All
Gaussian co-ordinate
systems
are essentially
equivalent
for the
formulation
of
the general
laws
of
nature."
We
can
state
this
general principle
of
relativity
in still
an-
other
form,
which
renders it
yet
more
clearly intelligible
than
it
is
when in the
form
of
the natural extension of the
special
108

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350
DOC.
42
SPECIAL AND GENERAL
RELATIVITY
106
Relativity
systems
of
values,
the co-ordinate values of
which
are so
close
together
as
to give continuity; corresponding to
the material
point,
we
thus have
a
(uni-dimensional)
line in the four-
dimensional continuum. In the
same way,
any
such lines in
our
continuum
correspond to many
points
in motion.
The
only
statements having regard to
these
points
which
can
claim
a
physical
existence
are
in
reality
the
statements
about their
encounters.
In
our
mathematical
treatment,
such
an
encounter
is expressed
in
the
fact
that
the
two
lines which
represent
the
motions
of
the
points
in
question
have
a
particular
system
of
co-ordinate
values,
x1,
x2, x3, x4,
in
common.
After
mature
consideration the reader
will doubtless
admit
that
in
reality
such
encounters
constitute the
only
actual evidence of
a
time-
space nature
with which
we
meet
in
physical statements.
When
we
were
describing
the motion of
a
material
point
relative
to
a
body
of
reference,
we
stated
nothing
more
than
the
encounters
of this
point
with
particular
points
of the
reference-body.
We
can
also
determine the
corresponding
val-
ues
of
the time
by
the
observation of
encounters
of the
body
with
clocks,
in
conjunction
with the observation of the
en-
counter
of the hands of
clocks
with
particular
points
on
the
dials.
It
is
just
the
same
in the
case
of
space-measurements by
means
of
measuring-rods,
as
a
little consideration
will
show.
[57]
The
following
statements
hold
generally: Every physical
description
resolves itself
into
a
number of
statements,
each of
which
refers
to
the
space-time
coincidence of
two events
A
and
B.
In
terms
of Gaussian
co-ordinates,
every
such
state-
ment is expressed by
the
agreement
of
their four co-ordinates

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