One hundred years of Weyl's (unfinished) unified field theory. (May 2019) - Romero, C.; Lima, R.G.; Sanomiya, T.A.T.
Abstract: In 1918, H. Weyl proposed a unified theory of gravity and electromagnetism based on a generalization of Riemannian geometry. In spite of its elegance and beauty, a serious objection was raised by Einstein, who argued that Weyl's theory was not suitable as a physical theory . According to Einstein, the theory led to the prediction of a "second clock effect", which has not been observed by experiments as yet. We briefly revisit this point and argue that a preliminary discussion on the very notion of proper time is needed in order to consider Einstein's critical point of view. We also point out that Weyl theory is basically incomplete in its original version and its completion may lead to a rich and interesting new approach to gravity. Highlights: Weyl's unified theory is the first attempt to geometrize the electromagnetic field together with gravity. The principle of gauge invariance required by Weyl in his unified theory led to modern gauge theories. The need of a notion of an invariant proper time in the original theory led to Perlick's definition of standard clocks. Weyl's unified theory leads to the prediction of the so-called second clock effect.