9780192806727.pdf

THE PRAGUE PAPERS 205

mechanics. That, too, seens to me to be a naive theory, and I think people should

try to start all over again, first reconsidering the nonrelativistic theory, just as I

did for gravitation in Prague. .. .'*

Here my fabrications end. I now return to the 1912 papers in order to add three

final exhibits.

The inclusion of electromagnetism forced Einstein to generalize the meaning of

p in Eq. 11.10, since the electromagnetic energy has a gravitating mass equivalent:

D. The source of the gravitational field had to be 'the density of ponderable

matter augmented with the [locally measured] energy density.'

Applied to a system of electrically-charged particles and electromagnetic fields,

this would seem to mean that p should be replaced by the sum of a 'mechanical'

and an electromagnetic term. Einstein denoted this sum by the new symbol a.

However, a paradox arose. On closer inspection, he noted that the theory does not

satisfy the conservation laws of energy and momentum, 'a quite serious result

which leads one to entertain doubt about the admissibility of the whole theory

developed here.' However, he found a way in which this paradox could be

resolved.

E. 'If every energy density... generates a (negative) divergence of the lines of

force of gravitation, then this must also hold for the energy density of gravitation

itself.' This led him to the final equation for his field c:

He went on to show that the second term in the brackets is the gravitational field
energy density and that the inclusion of this new term guaranteed validity of the
conservation laws. From then on, he was prepared for a nonlinear theory of the
gravitational field!
It had been a grave decision to make this last modification of the c-field equa-
tion, Einstein wrote, 'since [as a result] I depart from the foundation of the uncon-
ditional equivalence principle.' Recall the discussion following Eq. 11.9: it was
that equation and the equivalence principle which had led him to Ac = 0 in the
source-free case. This same reasoning does not apply to Eq. 11.14 with <r = 0!
What was the moral?

F. It seems that [the equivalence principle] holds only for infinitely small

fields.... Our derivations of the equation of motion of the material point and

of the electromagnetic [field] are not illusory since [Eqs. 11.8 and 11.9 were]

applied only to infinitely small space domains.

This is the dawn of the correct formulation of equivalence as a principle that holds
only locally.

"The references to other physicists in this piece of fiction have their basis in reality, as will become

clear in later chapters.