THE FIELD EQUATIONS OF GRAVITATION 253
He writes the gravitational equations in the form
where R^ is the full Ricci tensor. However, Eqs. 14.7 and 14.12 imply that s^
= 0. Thus Eqs. 14.4 and 14.13 give once again Eq. 14.8, the gravitational equa-
tions of November 4.
Though not compelling, this new idea may seem simple. It is in fact quite mad.
Equation 14.12 together with Eq. 14.9 implies that T = 0. The trace of the
energy momentum tensor does vanish for electromagnetic fields but not for matter.
Thus there seems to be a contradiction, which Einstein proposed to resolve by
means of 'the hypothesis that molecular gravitational fields constitute an essential
part of matter.' The trace density we 'see' in matter, he suggests, is actually the
sum T' of T and the trace of the gravitational field. Then T' can be positive and
yet T = 0. 'We assume in what follows that the condition T = 0 is actually
fulfilled.'
During the next two weeks, Einstein believed that his new equation (Eq. 14.12)
had brought him closer to general covariance. He expressed this opinion to Hilbert
on November 12. 'Meanwhile, the problem has been brought one step forward.
Namely, the postulate \/g = 1 enforces general covariance; the Riemann tensor
yields directly the gravitational equations. If my current modification ... is justi-
fied, then gravitation must play a fundamental role in the structure of matter.
Curiosity makes it hard to work!' [E47].
One week later, he remarked that 'no objections of principle' can be raised
against Eq. 14.12 [E48]. Two weeks later, he declared that 'my recently stated
opinion on this subject was erroneous' [El].
- November the Eighteenth. Einstein still subscribes to the demands of
unimodular invariance and \/g = 1 • On the basis of this 'most radical relativity
theory,' he presents two of his greatest discoveries [E48]. Each of these changed
his life.
The first result was that his theory 'explains ... quantitatively ... the secular
rotation of the orbit of Mercury, discovered by Le Verrier,... without the need
of any special hypothesis.' This discovery was, I believe, by far the strongest emo-
tional experience in Einstein's scientific life, perhaps in all his life. Nature had
spoken to him. He had to be right. 'For a few days, I was beside myself with
joyous excitement' [E49]. Later, he told Fokker that his discovery had given him
palpitations of the heart [F2]. What he told de Haas [F2] is even more profoundly
significant: when he saw that his calculations agreed with the unexplained astro-
nomical observations, he had the feeling that something actually snapped in
him. ...
Einstein's discovery resolved a difficulty that was known for more than sixty
years. Urbain Jean Joseph Le Verrier had been the first to find evidence for an
anomaly in the orbit of Mercury and also the first to attempt to explain this effect.
On September 12, 1859, he submitted to the Academy of Sciences in Paris the text
