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290 RELATIVITY, THE GENERAL THEORY


of recent years to explain the elementary particles of nature by means of contin-
uous fields have failed. The suspicion that this is not the correct way of conceiving
material particles has become very strong in us after very many failed attempts,
about which we do not wish to speak here. Thus, one is forced into the direction
of conceiving of elementary particles as singular points or world lines.... We are
led to a way of thinking in which it is supposed that there are no field variables
other than the gravitational and the electromagnetic field (with the possible excep-
tion of the 'cosmological term' [!]); instead one assumes that singular world lines
exist' [E56]. These phrases are found in a paper, prepared with Jacob Grommer,
in which Einstein made his first contribution to the problem of motion. Let us
recall what that problem is.
Our knowledge of the left-hand side of the gravitational equations (Eq. 15.20)
is complete: R^ and R are known functions of the g^ and their derivatives and
of nothing else. To this day, our knowledge of the right-hand side, the source
7^, is flimsy. However, the left-hand side satisfies the identities Eq. 15.4. This
piece of purely gravitational information implies that 7^ = 0. Thus general rel-
ativity brings a new perspective to energy-momentum conservation: gravitation
alone constrains its own sources to satisfy these laws. Consider now, as the sim-
plest instance of such a source, a structureless point particle, a gravitational mono-
pole. Its motion is necessarily constrained by T% = 0. Question: In view of these
constraints, which are of gravitational origin, does the equation of motion of the
source follow from the gravitational field equations alone? In other words, was
the separate postulate of geodesic motion, already introduced by Einstein in 1914,
unnecessary? Einstein and Grommer showed that this is indeed true for the case
of a weak external gravitational field.
A few weeks later, Weyl wrote to Einstein, thanking him for the opportunity
to see the galley proofs of his new paper and 'for the support [this paper] gives to
my old idea about matter' [W20], adding a reference to an article he had written
in 1922 [W21] in which similar conclusions had been reached. Indeed, as was
discussed in particular by Havas [HI2],* Einstein was one of the independent
originators of the problem of motion, but neither the only nor the first one.
Einstein's reply to Weyl is especially interesting because it adds to our under-
standing of his interest in this problem at that time. 'I attach so much value to the
whole business because it would be very important to know whether or not the
field equations as such are disproved by the established facts about the quanta
[Quantenthatsachen]' [E58]. Recall that we are in 1927, shortly after the discov-
eries by Heisenberg and Schroedinger.
Einstein's last important contribution to general relativity deals again with the
problem of motion. It is the work done with Leopold Infeld and Banesh Hoffmann


"Havas's paper, which also contains a simple derivation of the Einstein-Grommer result, is one of
several important articles on the problem of motion in modern guise found in a volume edited by J.
Ehlers [E57].

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