9780192806727.pdf

THE PRAGUE PAPERS 203

is valid in every mass-free static gravitational field.' The next assumption concerns

the modification of this equation in the presence of a density of matter p:

where k is a constant. The source must be static: 'The equations found by me

shall refer only to the static case of masses at rest' [El8].

This last remark, referring to the gravitational field equation, does not preclude

the study of the motion of a mass point under the action of the external static field

c. This motion (Einstein finds) is given by

where v^2 = ~x^2. For what follows, it is important to note in what sense this equa-

tion satisfies the equivalence principle: if c is given by Eq. 11.9, then Eq. 11.11

can be transformed to a force-free equation in the accelerated frame Z.

Einstein derived Eq. 11.11 in I by a method which need not concern us. It is

quite important, on the other hand, to note a comment he made about Eq. 11.11

in a note added in proof to paper II. There he showed that this equation can be

derived from the variational principle:

Earlier, Planck had applied Eq. 11.12 to special relativistic point mechanics [P3],
where, of course, c in Eq. 11.13 is the usual constant light velocity in vacuum.
Einstein was stirred by the fact that Eqs. 11.12 and 11.13 still apply if c is a static
field!
C. 'Also, here it is seen—as was shown for the usual relativity theory by
Planck—that the equations of analytical mechanics have a significance which far
exceeds that of the Newtonian mechanics.'
It is hard to doubt that this insight guided Einstein to the ultimate form of the
mechanical equations of general relativity, in which Eq. 11.12 survives, while Eq.
11.13 is generalized further.
Paper II is largely devoted to the question of how the electromagnetic field
equations are affected by the hypothesis that c is a field satisfying Eq. 11.6. The
details are of no great interest except for one remark. The field c, of course, enters
into the Maxwell equations. Hence, there is a coupling between the gravitational
field and the electromagnetic field. However, the latter is not static in general,
whereas the gravitational field is static by assumption. Therefore '[the equations]
might be inexact... since the electromagnetic field might be able to influence the
gravitational field in such a way that the latter is no longer a static field.'
It is conceivable that some of my readers, upon reflecting on this last statement,
may ask the same question I did when I first read paper II. What possessed Ein-