196 RELATIVITY, THE GENERAL THEORYtional field by a state of motion without gravitational field, as little as one can
transform to rest by means of a relativity transformation all points of an arbitrarily
moving medium.' This statement would continue to be true in the ultimate general
theory of relativity.
Einstein concluded his comments on the equivalence principle by stressing
again the great heuristic significance of the assumption that it is true for all phys-
ical phenomena rather than for point mechanics only.THE GRAVITY OF ENERGY; THE RED SHIFT
In 1907 Einstein had noted that an electromagnetic field is the source not only of
inertial energy but also of an equal amount of gravitational energy (Chapter 9).
He had reached this conclusion by studying the structure of the Maxwell equa-
tions in the frame E. He was now ready to elaborate on this result, but without
recourse to anything as specific as the electromagnetic origins of the energy in
question. His new and broader view was based on general considerations regard-
ing conservation laws. Consider (he said) the energy increase by an amount E of
an arbitrary body. According to the special theory, there is a corresponding
increase E/c^2 of its inertial mass. This leads to the 'so satisfactory' conclusion that
the law of conservation of mass merges with the law of conservation of energy.
Suppose now (he continues) that there were no corresponding increase of the grav-
itational mass of the body. Then one would have to maintain a separate conser-
vation law of gravitational mass while, at the same time, there would no longer
exist a separate conservation law for inertial mass. 'This must be considered as
very improbable.' Not only the very existence of the equivalence principle but also
the gravitational properties of energy point to the incompleteness of the special
theory: 'The usual relativity theory [by itself] yields no argument from which we
might conclude that the weight of a body depends on its energy content.' However,
this dependence on energy can be derived in a rather general way if, in addition,
we invoke the equivalence principle. 'We shall show. .. that the hypothesis of the
equivalence of the systems [S and E] yields the gravity of energy as a necessary
consequence. Then he gives the following argument. (At this point the reader may
like to refresh his memory concerning the coordinate systems described in Chapter
9.)
Let there be a light receiver S, in the origin of the frame E and an emitter at a
distance h along the positive z axis, also in E. The emitter S 2 emits an amount £ 2
of radiation energy at just that moment in which the frame S' is coincident with
E. The radiation will arrive at S, approximately after a time h/c. At that time,
S, has the velocity yh/c relative to S', 7 being the acceleration of E. Recall that
clocks in E are judged by using the inertial frame S'. Einstein could therefore use
a result of his 1905 paper on special relativity [E10]: the energy £, arriving at S,
is larger than E 2 :