DOC.
31
ON
THE RELATIVITY PROBLEM
313
by a comparison
which
I
owe
to
my
friend Besso. Let
us
think back
to
an
earlier
era,
when
one
assumed that the Earth
was
approximately flat. Imagine
that the
following
view
prevailed among
the learned. There is
a
physically privileged
direction in the
world,
the vertical. All bodies fall
in
this direction unless
they
are
supported.
This
is
the
reason why
the surface of the Earth
is
essentially
perpendicular
to
this
direction,
and thus
why
it tends
to
assume a
flat form. If the
error
in this
case
consists in
privileging
one
direction above all others without
any
supporting
reason
(fictitious
cause),
instead of
simply considering
the Earth
as
the
cause
of the
falling,
then the
error
in
our
physics
consists in the introduction of
privileged systems
as
fictitious
causes
without
any supporting
reason;
both
cases are
characterized
by forgoing
the
establishment of
a
sufficient
reason.
Since
not
only
classical
mechanics,
but also the
theory
of
relativity
in the
narrower
sense
manifests the
just-explained
fundamental
deficiency,
I
have
set
myself
the
goal
of
generalizing
the
theory
of
relativity
in such
a
way
that this
imperfection
will be avoided. To
start
with, I
recognized
that
gravitation
in
general
will have
to
be
assigned
a
most
fundamental role in such
a
theory.
For it
already
follows from
what has been said before that
every physical process
must
also
generate
a
gravitational
field,
because
quantities
of
energy correspond
to it.
On the other
hand,
the
empirical
fact that
all
bodies fall
equally
fast
in
a gravitational
field
suggests
the
idea that
physical processes
occur
in
exactly
the
same
way
in
a
gravitational
field
as
they
do
relative
to
an
accelerated reference
system (equivalence hypothesis). Having
taken this idea
as a
basis,
I
arrived
at
the result that the
velocity
of
light
is not to
be
regarded as independent
of the
gravitational potential.
Thus,
the
principle
of the
[21]
constancy
of the
velocity
of
light
is
incompatible
with the
equivalence
hypothesis;
for
this
reason,
the
theory
of
relativity
in the
narrower sense
cannot
be
brought
into
agreement
with the
latter. In
this
way I was
led
to
view the
theory
of
relativity
in
the
narrower sense as
valid
only
for
regions
within which there
are no
noticeable
differences in the
gravitational potential.
The
theory
of
relativity
(in
the
narrower
sense)
had
to be
replaced
by a more general
theory
that contains the former
as a
limiting case.
The
path
leading
to
this
theory
can
only very
incompletely
be described
in
words.3
The
equation
of motion of
a mass
point
in
a
gravitational
field that follows
from the
equivalence hypothesis
can
easily
be written down
in
a
form
in
which this
law
is
totally independent
of the choice
of
the variables that determine
place
and
time.
By leaving
the choice of these variables
a
priori
totally arbitrary,
and thus
not
privileging any specific spatio-temporal systems,
one
avoids the
epistemological
objection explained
above. In that law of motion there
apears
a
quantity
3Cf. A.
Einstein and
M.
Grossmann, Zeitschrift
f.
Math.
&
Physik
62
(1914):
225.
[22]