One hundred years of Weyl’s (unfinished) unified field theory

Double layers in Weyl geometry and some physical implications

“…Previous attempts had been made to achieve the same, specifically Mies attempt [9], from which Weyl drew a lot of his inspiration, albeit his attempt, although ultimately not acceptable because of physical repercussions (the second clock effect and other misgivings as pointed out by Einstein, Pauli and other contemporaries [27]), was mathematically ingenious, indeed. A very brief introduction to the same can be found below (and in detail in [20]), I shall introduce the basic formalism here. Weyl geometry is perhaps one of the simplest generalisations of Riemannian geometry, the only modification being the fact that the covariant derivative isn't metric compatible (i.e the covariant derivative of the metric tensor isn't zero), but instead given by: ∇ α g βλ = σ α g βλ (1.1) Weyl believed that a true unified theory of the present fundamental forces at the time (Gravity and Electromagnetic/Lorentz force(s)), could never be achieved in the framework of Riemannian geometry, which was at the base of GR.…”

“…In the first three chapters 3, 4 and 5, I attempt to describe the developments that took place in the early twentieth century in the realm of Unified Field Theories, focusing especially on Weyls Unification of GR and classical Maxwellian Electrodynamics. The following chapters elucidate upon the same, deriving from a wide range of references [14], [24], [23], [20], [27] and [1] and the reader is directed to them to explore the subject in greater detail. A basic understanding of General Relativity Theory is assumed.…”