THE PRAGUE PAPERS 195
touch and this element of closure is missing. His style of writing changes. Instead
of statements made with characteristic finality, we find reports on work in
progress.
Turning to the first of the Prague papers, I should evidently begin with the
approximations to which Einstein referred. His problem was and remained to find
a way to give meaning to simultaneity for the case of uniformly accelerated sys-
tems. To this end, he used once again the approximate methods of 1907. Thus in
1911 the three coordinate systems S, Z, and S' discussed in Chapter 9 reappear.*
Recall that Z is in constant acceleration relative to S and that the inertial frame
S' is at one, and only one, time coincident with Z. As indicated earlier, the strategy
was to relate the clocks in S' to those in S by a Lorentz transformation and then,
for a tiny time interval, to identify the clock readings in S' with those in Z. This
is not a rigorous procedure, as we saw in Chapter 9. The approximations
explained there are the ones that also apply to the paper now under consideration.
In 1911 the four main issues were the same as in 1907: the equivalence prin-
ciple, the gravity of energy, the red shift, and the bending of light. The main
equations in these two papers are also nearly all identical. However, Einstein now
had new thoughts about each one of these four questions.
THE EQUIVALENCE PRINCIPLE
Let the frame S be at rest and let it carry a homogeneous gravitational field in the
negative z direction. Z is a field-free frame that moves with a constant acceleration
relative to S in the positive z direction. Einstein first reminds the reader of the
equivalence of Newton's mechanical laws in both frames. Then he rephrases this
principle as follows. 'One can speak as little of the absolute acceleration of the
reference frame as one can of the absolute velocity in the ordinary [special] rela-
tivity theory' (his italics). From this he concludes that 'according to this theory,
the equal fall of all bodies in a gravitational field is self-evident^1 (my italics).
This seemingly innocent new twist is typical. Einstein had the gift of learning
something new from ancient wisdom by turning it around. In the present instance,
instead of following the reasoning—experimentally known equal time of fall —*•
meaninglessness of constant absolute acceleration—he reverses the direction of the
arrow of logic. Thus in 1911 we discern the first glimpses of the new Einstein
program: to derive the equivalence principle from a new theory of gravitation.
This cannot be achieved within the framework of what he called the ordinary
relativity theory, the special theory. Therefore one must look for a new theory not
only of gravitation but also of relativity. Another point made in this paper likewise
bears on that new program. 'Of course, one cannot replace an arbitrary gravita-
*In the 1911 paper, Einstein denotes the frames S, E, and S' by K, K', and K 0 , respectively. For
ease of presentation, I continue to use his earlier notation.