On the History of Unified Field Theories

Abstract

This article is intended to give a review of the history of the classical aspects of unified field theories in the 20th century. It includes brief technical descriptions of the theories suggested, short biographical notes concerning the scientists involved, and an extensive bibliography. The present first installment covers the time span between 1914 and 1933, i.e., when Einstein was living and working in Berlin — with occasional digressions into other periods. Thus, the main theme is the unification of the electromagnetic and gravitational fields augmented by short-lived attempts to include the matter field described by Schrödinger’s or Dirac’s equations. While my focus lies on the conceptual development of the field, by also paying attention to the interaction of various schools of mathematicians with the research done by physicists, some prosopocraphical remarks are included.

Towards a Unified Theory of Health-Disease: I. Health as a complex model-object

“…Unifi ed theories address the plurality of facets of complex objects, thus harmonizing special theories, or different scientifi c approaches, into a given interdisciplinary problem. These terms were introduced along the debate on the validity of relativity theory in Physics 46 and later on adopted for defi ning the general systems theory. 35,51…”

Tuning up mind's pattern to nature's own idea: Eddington's early twenties case for variational derivatives

“…Hilbert thence claimed that "the electrodynamic phenomena are an effect of gravitation" 20 inasmuch as he erroneously inferred that the electrodynamic equations [ √ gH] h = 0 were a mere consequence of the gravitational ones [ √ gH] µν = 0, the latter being tacitly identified as a whole with the independent equations. Though generally covariant and as such very much akin to the equations Einstein obtained at about the same time, these gravitational field equations did not yet constitute the fundamental equations of physics in Hilbert's view, since four supplementary non generally covariant energy equations were then required so as to restore causality 21 . Within such an axiomatic setting, Hilbert still worked out the theory further by postulating that the Hamiltonian function be of a certain form, namely that it should be composed of a gravitational and an electromagnetic part…”

“…20 [23, p. 397]. 21 In this respect, Einstein and Hilbert went reverse ways, insofar as the former doggedly strove for general covariance while not taking it for granted, whereas the latter was eventually led to counterbalance the so-called "axiom of general invariance" by the need to guarantee determinism for the equations of physics. Cf.…”

“…The "axiomatic method" can be of little use here, though. 30 In about the same vein, Weyl would later emphasize "the maze of experimental facts which the physicist has to take into account [being] too manifold, their expansion too fast, and their aspect and relative weight too changeable for the axiomatic method to find a firm enough foothold, except in the thoroughly consolidated parts of our physical knowledge", thus favouring Einstein's way of "grop[ing his] way in the dark" as more appropriate to physical theory inasmuch as requiring "another type of experience and imagination than those of the mathematician" 31 an intertwining of gravitational and electromagnetic fields that would allegedly be more in agreement with experimental facts than mere Göttingen variational virtuosity, still Weyl himself persistently claimed that "the whole of physical phenomena may be derived from one single world-law of mathematical simplicity" 33 , namely from a suitable action principle, whatever be the difficulties, stressed by [21], that were to be encountered so as to find "a satisfactory Lagrangian from which the field equations of Weyl's theory can be derived" 34 . Reversely, by contrast with Einstein whose well-known objection to Weyl's theory did not prevent him though from deeming it a valuable attempt 35 , Hilbert would later judge it rather harshly as ill-conceived immoderate idealizing for which he coined the term "Hegelian physics" 36 , though claiming at the same time the paternity for most of the building blocks that Weyl used :…”

“…abnormally large] curvature" 44 was thought of as an open problem undetermined by the theory as it were. Whereas acknowledging Eddington's distinction between "world geometry" and "natural geometry", Pauli for instance, as recalled by [21], conceded the union of gravitational and electromagnetic fields as only a phenomenological one, involving as such no recourse to the nature of the charged elementary particles 45 .…”