Conformal general relativity contains the quantum

Based on the de Broglie-Bohm relativistic quantum theory of motion we show that the conformal formulation of general relativity, being linked with a Weyl-integrable geometry, may implicitely contain the quantum effects of matter. In this context the Mach's principle is discussed. In recent papers [1,2] the singularity problem has been treated from a point of view that is based upon the conformal transformation technique. Under a conformal transfomation of the spacetime metric ˆ g ab = Ω 2 (x)g ab , (1) where Ω(x) is a non-vanishing smooth function, the spacetime coincidences [coordinates] are unchanged. Correspondingly, the experimental observations [measurements], being nothing but just verifications of these coincidences are unchanged too by this conformal transformation. Dicke showed that the transformation (1) can be interpreted as a point-dependent transformation of the units of length, time and mass [3]. In fact, if one takes the arc-length