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

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.