THE NEW DYNAMICS 289interlude) what the answer to this question was: singularities are anathema. His
belief in the inadmissibility of singularities was so deeply rooted that it drove him
to publish a paper purporting to show that 'the "Schwarzschild singularity" [at
r = 2GM/C^2 ] does not appear [in nature] for the reason that matter cannot be
concentrated arbitrarily ... because otherwise the constituting particles would
reach the velocity of light' [E53].* This paper was submitted in 1939, two months
before Oppenheimer and Snyder submitted theirs on stellar collapse [O3]. Unfor-
tunately, I do not know how Einstein reacted to that paper. As to the big bang,
Einstein's last words on that subject were, 'One may ... not assume the validity
of the equations for very high density of field and matter, and one may not con-
clude that the "beginning of expansion" must mean a singularity in the mathe-
matical sense' [E54]. He may very well be right in this.
The scientific task which Einstein set himself in his later years is based on three
desiderata, all of them vitally important to him: to unify gravitation and electro-
magnetism, to derive quantum physics from an underlying causal theory, and to
describe particles as singularity-free solutions of continuous fields. I add a com-
ment on this last point (unified field theory and quantum theory will be discussed
in later chapters). As Einstein saw it, Maxwell's introduction of the field concept
was a revolutionary advance which, however, did not go far enough. It was his
belief that, also, in the description of the sources of the electromagnetic field, and
other fields, all reference to the Newtonian mechanical world picture should be
eradicated. In 1931 he expressed this view in these words:
In [electrodynamics], the continuous field [appears] side by side with the mate-
rial particle [the source] as the representative of physical reality. This dualism,
though disturbing to any systematic mind, has today not yet disappeared. Since
Maxwell's time, physical reality has been thought of as [being] represented by
continuous fields, governed by partial differential equations, and not capable of
any mechanical interpretation. ... It must be confessed that the complete real-
ization of the program contained in this idea has so far by no means been
attained. The successful physical systems that have been set up since then rep-
resent rather a compromise between these two programs [Newton's and
Maxwell's], and it is precisely this character of compromise that stamps them
as temporary and logically incomplete, even though in their separate domains
they have led to great advances. [E55]That is the clearest expression I know of Einstein's profound belief in a descrip-
tion of the world exclusively in terms of everywhere-continuous fields.
There was a brief period, however, during which Einstein thought that singu-
larities might be inevitable. That was around 1927, when he wrote, 'All attempts
'Actually, the singularity at the Schwarzschild radius is not an intrinsic singularity. It was shown
later that the Schwarzschild solution is a two-sheeted manifold that is analytically complete except
at r = 0. Two-sheetedness was first introduced in 1935 by Einstein and Rosen [E53a], who believed,
however, that the singularity at r = 2GM/C^2 is intrinsic.