2l6 RELATIVITY, THE GENERAL THEORYlem of the rigid body until 1916 [E27]. Could it be, however, that Horn's formal-
ism had given him the inspiration for general covariance?
However this may be, after his first dicussions with Grossmann, Einstein had
found the correct starting point for general relativity. The real work could now
begin. Hard days lay ahead. In October Einstein wrote to Sommerfeld:
At present I occupy myself exclusively with the problem of gravitation and now
believe that I shall master all difficulties with the help of a friendly mathema-
tician here. But one thing is certain, in all my life I have labored not nearly as
hard, and I have become imbued with great respect for mathematics, the subtler
part of which I had in my simple-mindedness regarded as pure luxury until
now. Compared with this problem, the original relativity is child's play. [E28]12c. The collaboration
The Einstein-Grossmann paper (referred to here as EG), published in 1913
[E29], contains profound physical insight into the nature of measurement, some
correct general relativistic equations, some faulty reasoning, and clumsy notation.
First some remarks about the notation. The concepts of covariant and contra-
variant tensors are introduced, but all tensor indices are written as subscripts. For
example, the covariant metric tensor is denoted by g^, its contravariant counter-
part by 7^. In 1914 Einstein abandoned this miserable notation. 'Following Ricci
and Levi-Civita, we denote the contravariant character in such a way that we
place the index in the upper position' [E30]. Even then he excluded the coordinate
differentials dx* from this rule. Nor does EG contain the modern convention that
summation over repeated indices is automatically understood. This rule was intro-
duced in 1916—by none other than Einstein himself [E31]. Later he said in jest
to a friend, 'I have made a great discovery in mathematics; I have suppressed the
summation sign every time that the summation must be made over an index which
occurs twice.. ..' [K2]. I do not believe it will serve the reader if I push historical
accuracy to the point of adhering to the EG notations. Instead, I shall transcribe
the EG equations into their modern form by adopting the notations and conven-
tions of Weinberg's book on gravitation and cosmology [Wl]. All technicalities
that can be covered by a reference to that text will be omitted.
In EG, Einstein expresses his indebtedness to Mach for inspiring some of his
ideas. Comments on the influence of Mach on Einstein, an important subject in
its own right, will be deferred till Chapter 15.
As we have seen, the equivalence principle in its primitive form (equality of
gravitational and inertial mass for a material object) was Einstein's guide ever
since 1907. It is characteristic, -because of his limited acquaintance with the liter-
ature, that only five years later would he become aware of the precision measure-
ments of Roland the Baron Eotvos of Vasarosnameny that showed the high degree
of accuracy of the equality of inertial and gravitational mass. He discussed the