250 RELATIVITY, THE GENERAL THEORY14c. The Final Steps- The Crisis. On the first of January 1916, when it was all over, Einstein wrote
to Lorentz, 'During the past autumn, the gradually dawning realization of the
incorrectness of the old gravitational equations caused me hard times (bose Zei-
ten)' [E25]. It appears that this crisis occurred between late July and early Octo-
ber 1915. For on July 7, 1915, Einstein described to Zangger the subject of lec-
tures he had just given in Goettingen as 'die nun schon sehr geklarte
Gravitationstheorie,' the by now already quite clarified theory of gravitation
[E38]. A week later, he wrote to Sommerfeld about a tentative plan to write a
short treatise on relativity which was to be oriented toward a general theory of
relativity [E39]. But on November 7 he wrote to Hilbert, 'I realized about four
weeks ago that my methods of proof used until then were deceptive' [E40], and
on October 12, to Lorentz, 'In my paper [of October 1914, [E16]], I carelessly
(leichtsinnig) introduced the assumption that [the gravitational Lagrangian] is an
invariant for linear transformations' [E41]. He abandoned this linear invariance
in a series of papers completed in November 1915, which culminate in the final
form of his gravitational equations, presented on November 25. On November 28
he wrote to Sommerfeld: "During the past month I had one of the most exciting
and strenuous times of my life, but also one of the most successful ones' [E42]. All
these statements taken together convince me that Einstein still believed in the 'old'
theory as late as July 1915, that between July and October he found objections
to that theory, and that his final version was conceived and worked out between
late October and November 25. In December he wrote with irony about his earlier
faith in the old version of the theory. 'That fellow Einstein suits his convenience
(Es ist bequem mil dem E.). Every year he retracts what he wrote the year before
...' [E43].
What made Einstein change his mind between July and October? Letters to
Sommerfeld [E42] and Lorentz [E25] show that he had found at least three objec-
tions against the old theory: (1) its restricted covariance did not include uniform
rotations, (2) the precession of the perihelion of Mercury came out too small by
a factor of about 2, and (3) his proof of October 1914 of the uniqueness of the
gravitational Lagrangian was incorrect. Einstein got rid of all these shortcomings
in a series of four brief articles. 'Unfortunately, I immortalized in [these] academy
papers the last errors made in this struggle' [E42]. - November the Fourth. Einstein presents to the plenary session of the Prus-
sian Academy a new version of general relativity 'based on the postulate of covar-
iance with respect to transformations with determinant 1' [E44]. He began this
paper by stating that he had 'completely lost confidence' in the equations proposed
in October 1914 [El6]. At that time he had given a proof of the uniqueness of the
gravitational Lagrangian. He had realized meanwhile that this proof 'rested on
misconception,' and so, he continued, 'I was led back to a more general covariance
of the field equations, a requirement which I had abandoned only with a heavy