192
DOC.
16 FOUNDATIONS
OF GRAVITATION
Doc.
16
Physical
Foundations of
a
Theory
of Gravitation1
by
Albert Einstein
[Naturforschende Gesellschaft
in
58
(1914):
284-290]
By
the word
"mass" of
a
body one
denotes
two
things
that
are
very
different
according
to
their
definitions:
on
the
one
hand,
the inertial resistance
of
the
body
and,
on
the other
hand,
the characteristic
constant
that is the
determining
factor for the
effect of the
gravitational
field
on
the
body.
It is
one
of the most remarkable
empirical
facts of
physics
that these two
masses,
the inertial and the
gravitational,
agree exactly
with each other
as
regards
their
magnitude.
This
agreement was proved
most
exactly by
Eötvös's
experiments.
A
body
on
the surface
of
the Earth is acted
upon by
two
generally differently
directed
forces,
which
together
constitute the
apparent gravity
of
the
body: one
of these
forces,
the
gravitation proper, depends
on
the
gravitational
mass,
while the
other,
the
centrifugal force, depends
on
the inertial
mass.
By experiments
with the
torsion
balance,
Eötvös established that the ratio of
these
two
forces is
independent
of the
nature of the
material;
in that
way
he
proved
the
agreement
of
the two
masses
of
a
body
with
an
accuracy
that rules
out
deviations
[2]
of
the relative
magnitude
of
10-7.
This
empirical
law
can
also be
expressed
in the
following way.
In
a gravitational
field all
bodies fall with the
same
acceleration. This
suggests
the view
that,
with
regard
to
its influence
on
mechanical and other
physical processes,
a
gravitational
field
may
be
replaced by
a
state of acceleration of the
reference
body
(coordinate
system).
This
conception
does
not
necessity
from the
experiments
mentioned,
but it
is
of
great
heuristic interest all the
same.
For,
since the
course
of
physical processes
relative
to
an
accelerated reference
system
can
be determined
theoretically,
this
equivalence hypothesis
permits us
to
predict
the influence of
a
[3] gravitational
field
on
physical processes
of
every
kind. The
experimental
test
of
the
conclusions
so
reached
must
then show whether the
underlying hypothesis
was
correct.
In the
way
indicated,
one
comes
to the conclusion that the
speed
with which
a
physical
process occurs
in
a
gravitational
field is
greater
the
greater
the
gravitational
potential
at
the location where the
physical system
in
question
is situated. For that
reason,
the
spectral
lines
of
solar
light
should,
for
example, experience
a
small shift
toward the red end of
the
spectrum
as
compared
with the
corresponding
spectral
lines
1Based
on a
lecture delivered
on
9
September
1913 at the annual
meeting
of
the
[1]
Schweizer Naturforschende Gesellschaft in
Frauenfeld.
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