THE PRAGUE PAPERS 197Now go to the frame S with its gravitational field. In that frame, we install the
same equipment S, and S 2 in the same relative positions as in E. Then Eq. 11.1
and the equivalence principle yieldwhere 0, and 02 are tne gravitational potential at positions 1 and 2, respectively.
This is the energy conservation law for the transmission process. It implies that
to an energy E there corresponds a gravitational mass E/c^2 , the desired result.
Next Einstein treated the red shift in a similar way. First work in E. Let the
light emitted at S 2 have the frequency v 2. After having traveled the approximate
time h/c, this light is received at S, with frequency i>,. To find the connection
between v 2 and c,, work in S'. Then the well-known linear Doppler effect formula
gives
The equivalence principle tells us what happens in S:Assume that this equation also holds for inhomogeneous fields. Let 2 be the sun
and 1 the earth. Then 4> is negative. A red shift is seen on earth such that &v/v
« 1(T^6.
I next interrupt the discussion of the Prague paper in order to make two com-
ments. First, Einstein derives Eq. 11.2 for the energy shift; then he starts 'all over
again' and derives the frequency shift (Eq. 11.4). It is no accident, I am sure, that
he did not derive only one of these equations and from there go to the other one
with the help of
He had had something to do with Eq. 11.5. It cannot have slipped his mind; the
quantum theory never slipped his mind. However, it was Einstein's style forever
to avoid the quantum theory if he could help it—as in the present case of the
energy and the frequency shift. In Chapter 26 I shall come back to discuss at some
length this attitude of his, a main clue to the understanding of his destiny as a
physicist.
Second, in good texts on general relativity the red shift is taught twice. In a first
go-around, it is noted that the red shift follows from special relativity and the