  When  quantum theory was developed a few years later it became clear that  Weyl’s theory was in conflict with experience in an even more  fundamental way since there is a direct relation between clock rates  and masses of particles in quantum theory. A particle with a certain  rest mass \(m\) possesses a natural frequency which is a function  of its rest mass, the speed of light \(c\), and Planck’s constant  \(h\). This means that in a Weyl geometry not only clocks would  depend on their histories but also the masses of particles. For  example, if two protons have different histories then they would also have different masses in a Weyl geometry. But this violates the  quantum mechanical principle that particles of the same kind—in this case, protons—have to be exactly identical. 