“Now, these objects are tremendous
concentrations of energy in the smallest place; therefore, they
will house huge curvatures of space or, in other words,
gravitational fields. The idea that they keep together the
dispersing electrical charges lies close at hand.” 52
([19
], p. 235)
Thus, the idea of a program for building the extended constituents of matter from the fields the source of which they are, was very much alive around 1920. However, Pauli’s remark after Weyl’s lecture in Bad Nauheim (86. Naturforscherversammlung, 19-25 September 1920) [245] showed that not everybody was a believer in it. He claimed that in bodies smaller than those carrying the elementary charge (electrons), an electric field could not be measured. There was no point of creating the “interior” of such bodies with the help of an electric field. Pauli:
“None of the present theories of the electron,
also not Einstein’s (Einstein 1919 [70]), up to now did
achieve solving satisfactorily the problem of the electrical
elementary quanta; it seems obvious to look for a deeper reason for
this failure. I wish to see this reason in the fact that it is
altogether not permitted to describe the electromagnetic field in
the interior of an electron as a continuous space function. The
electrical field is defined as the force on a charged test
particle, and if no smaller test particles exist than the electron
(vice versa the nucleus), the concept of electrical field at a
certain point in the interior of the electron - with which all
continuum theories are working - seems to be an empty fiction,
because there are no arbitrarily small measures. Therefore, I’d
like to ask Mr. Einstein whether he approves of
the opinion that a solution of the problem of matter may be
expected only from a modification of our perception of space
(perhaps also of time) and of electricity in the sense of atomism,
or whether he thinks that the mentioned reservations are
unconvincing and is of the opinion that the fundaments of continuum
theory must be upheld.” 53
Pauli referred to Einstein’s paper about elementary particles and field theory in which he had exchanged his famous field equations for traceless equations with the electromagnetic field tensor as a source. Einstein’s answer is tentative and evasive: We just don’t know yet54 .
“With the progressing refinement of scientific
concepts, the manner by which concepts are related to (physical)
events becomes ever more complicated. If, in a certain stage of
scientific investigation, it is seen that a concept can no longer
be linked with a certain event, there is a choice to let the
concept go, or to keep it; in the latter case, we are forced to
replace the system of relations among concepts and events by a more
complicated one. The same alternative obtains with respect to the
concepts of time- and space-distances. In my opinion, an answer can
be given only under the aspect of feasibility; the outcome appears
dubious to me.” 55
In the same discussion Gustav Mie came back to Förster’s idea of an asymmetric metric but did not like it
“[...] that an antisymmetric tensor was added
to the symmetric tensor of the gravitational potential, which
represented the six-vector of the electromagnetic field. But a more
precise reasoning shows that in this way no reasonable world
function is obtained.” 56
It is to be noted that Weyl, at the end of 1920, already had given up on a possible field theory of matter:
“Finally I cut loose firmly from Mie’s theory
and arrived at another position with regard to the problem of
matter. To me, field physics no longer appears as the key to
reality; in contrary, the field, the ether, for me simply is the
totally powerless transmitter of
causations, yet matter is a reality beyond the field and causes its
states.” 57
(letter of Weyl to F. Klein on 28
December 1920, see [292],
p. 83)
In the next year, Einstein had partially absorbed Pauli’s view but still thought it to be useful to apply field theory to the constituents of matter:
“The physical interpretation of geometry
(theory of the continuum) presented here, fails in its direct
application to spaces of submolecular scale. Yet it retains part of
its meaning also with regard to questions concerning the
constitution of elementary particles. Because one may try to
ascribe to these field concepts [...] a physical meaning even if a
description of the electrical elementary particles which constitute
matter is to be made. Only success can decide whether such a
procedure finds its justification [...].” 58
[72
]
During the twenties Einstein changed his mind and looked for solutions of his field equations which were everywhere regular to represent matter particles:
“In the program, Mr. Einstein expressed during his two
talks given in November 1929 at the Institut Henri Poincaré, he
wished to search for the physical laws in solutions of his
equations without singularities - with
matter and the electromagnetic field thus being continuous. Let us
move into the field chosen by him without too much surprise to see
him apparently follow a road opposed to the one successfully walked
by the contemporary physicists.” 59
([36
], p. 17
(1178))