Dimensionless Physics

We discuss two scenarios of emergent gravity. In one them the quantum vacuum is considered as superplastic crystal, and effective gravity describes dynamical elastic deformations this crystal. other gravitational tetrads emerge bilinear form fermionic fields. spite essentially different mechanisms gravity, these have important common property: metric field has dimension inverse square length [g??] = 1/[l]2, distinct from conventional dimensionless metric, 1, in general relativity. As a result physical quantities, which obey diffeomorphism invariance, become dimensionless. This takes place for such quantities Newton constant, scalar curvature, cosmological particle masses, bosonic fields, etc. may suggest that physics can be natural consequence thus property any emerges vacuum. One nontrivial consequences shift dimensions related to topology. Due some operators topological, contain integer or fractional prefactors action. particular concerns intrinsic 3+1 Hall effect Nieh–Yan anomaly terms torsion.