INSIGHTS | BOOKS
1078 6 MARCH 2015 • VOL 347 ISSUE 6226 sciencemag.org SCIENCE
The publication of the field equations of general relativity in November 1915 was the crowning achievement of Albert Einstein’s scientific career. A few years later, he embarked on a quest for a theory that would unify
gravity and electromagnetism. In Einstein’s
Unification, one of the most insightful books
on Einstein of the past decade, Jeroen van
Dongen examines the interplay between this
quest and the evolution of Einstein’s views
on scientific methodology.
In his later years, Einstein routinely
claimed that the way he had found the
field equations of general relativity fundamentally changed his approach to physics. In view of this claim and drawing on
studies brought together in The Genesis of
General Relativity (1), van Dongen begins
by reexamining Einstein’s search for gravitational field equations from 1912 to 1915.
Einstein employed two strategies in this
search: either starting from a mathematically attractive candidate and then checking the physics or starting from a physically
sensible candidate and then checking the
mathematics. Although Einstein scholars
disagree about which of these two strategies brought the decisive breakthrough of
November 1915, they all acknowledge that
both played an essential role in the work
leading up to it. In hindsight, however,
Einstein maintained that his success with
general relativity had been due solely to the
mathematical strategy. It is no coincidence
that this is the approach he adopted in his
search for a unified field theory.
Einstein famously sang the praises of
the mathematical approach in his Herbert
Spencer lecture in Oxford in 1933 (2), citing
general relativity and the unified field theory
he was working on at the time with his assistant, Walther Mayer, among its successes.
The latter seemed to explain why protons
and electrons have opposite charges but
vastly different masses.
Ironically, Einstein’s letters around this
time suggest that his enthusiasm for this
new theory was already waning, and a few
months later a student of his colleague Wolf-
gang Pauli showed that it was mathemati-
cally flawed and did not shed any light on
the mass difference between electrons and
protons (pp. 121–122). The student, Valentin
Bargmann, later collaborated with Einstein
on a different unified field theory. In a letter
recommending him to Einstein, Pauli noted
that Bargmann’s mathematics was stronger
than his physics, adding sarcastically that
Einstein might consider that a point in his
favor (p. 147).
Van Dongen (p. 50) largely avoids and
downplays the importance of Einstein’s oft-cited but contentious distinction between
constructive and principle theories (3). Instead, a diagram from a letter Einstein wrote
to his friend Maurice Solovine in 1952 takes
center stage in van Dongen’s analysis of
Einstein’s methodology (4). This “Solovine
schema,” which seems to privilege principle
theories, consists of three layers, with sensory data at the bottom, fundamental axioms
or principles at the top, and empirical laws
to be derived from these principles and then
compared to the data in the middle. This last
step is represented by an arrow going from
the empirical laws to the data. The first and
most difficult step is represented by an arrow
going directly from the data to the principles.
In the 1910s, Einstein insisted that this key
step requires empirical intuition or, as he put
it, “the intuitive grasp of the essentials of a
large complex of facts” (p. 42). He later came
to believe that it requires mathematical intuition instead.
Unification introduces an additional layer
to the Solovine schema, with the principles of
the unified theory appearing above the prin-
ciples of the nonunified theories for the same
range of data. Einstein considered it highly
improbable that a path could be found from
the data through the empirical laws all the
way up to the principles of the unified theory.
Van Dongen also uses the Solovine schema
to explain why, later in his career, Einstein
suppressed the role of the physical strategy in
his work toward general relativity. The mathematical strategy corresponds to the arrow
directly from data to principles. By contrast,
the physical strategy, which van Dongen also
describes as a constructive or bottom-up approach, would have to be represented by arrows going from data to principles indirectly
through the empirical laws. There are no
such arrows in the Solovine schema. By the
mid-1920s, Einstein had convinced himself
that these indirect paths are unreliable. Van
Dongen suggests that part of the reason for
Einstein’s skepticism about quantum mechanics was that it had been found via such
an indirect path (p. 174).
Another factor accounting for the shift
in Einstein’s methodology was his gradual
loss of confidence in the power of experimentation to settle fundamental issues. Van
Dongen highlights two 1926 experiments,
proposed by Einstein and performed by
Emil Rupp, to probe the nature of light. Despite strong warning signs, Einstein failed to
recognize that Rupp had forged his data to
match Einstein’s expectations. In 1935, Rupp
was forced to retract the results of several
other fraudulent experiments. Even after he
realized that Rupp had fabricated his data,
however, Einstein stood by his theoretical
considerations (p. 87).
Einstein’s Unification weaves together
many threads of the second half of Einstein’s
scientific career. It is based on an impressive
array of challenging primary and secondary
source material, which the author pulled
together in an eminently readable book of
REFERENCES AND NOTES
1. J.Renn,Ed. The Genesis of General Relativity. 4Vols.
(Springer, Berlin, 2007).
2. Reprinted in Einstein, Ideas and Opinions (Crown, New
York, 1954; Reprint: Modern Library, New York, 1994).
3. Einstein made this distinction in 1919 in an article in the
London Times reprinted in Ideas and Opinions [see (2)].
4. Van Dongen here expands on Gerald Holton,
“Constructing a Theory: Einstein’s Model” (1979), revised
and reprinted in The Advancement of Science and Its
Burdens (Harvard Univ. Press, Cambridge, ed. 2, 1998).
Beyond general relativity
By Michel Janssen
The reviewer is at the University of Minnesota and is the
co-editor (with Christoph Lehner) of The Cambridge
Companion to Einstein (2014). E-mail: firstname.lastname@example.org
Jeroen van Dongen
Press, 2010. 223 pp.
Einstein’s quest to discover a unified field theory
Albert Einstein, 1933.