Dark Matter and Scale Invariance

We point out that the vector meson S first proposed by Weyl on the basis of scale invariance is a candidate for dark matter. As colliders are being built with the creation of dark matters among the stated goals, we wish to point out that one of the possible candidates of dark matter is the vector meson S first conceived by Weyl on the basis of scale invariance. Weyl made the mistake of identifying S with the photon. Also, Weyl’s work is incomplete, as he lacked at his time the framework of the theory of quantum electrodynamics. Our formulation of scale invariance yields results different from those of Weyl’s. For example, we find that S does not couple with the electron. It is well-known that Einstein argued that electrons moving in a background of the S field would produce unobserved broading of the atomic spectral lines. That the electron does not interact with S overrides this objection of Einstein. Since Weyl’s theory was first proposed in 1919, before even the discovery of Dirac’s equation, Weyl did not have the prerequisites which might have led him to conclude that S is a kind of dark matter coupling with neither quarks and leptons, nor any of the gauge mesons. Indeed, in our theory, the only interactions S has are those with the graviton and scalar mesons, the only candidate of which at the moment is the Higgs meson.