Dimensionless Physics: Planck Constant as an Element of the Minkowski Metric

Diakonov theory of quantum gravity, in which tetrads emerge as the bilinear combinations fermionis fields,\cite{Diakonov2011} suggests that general relativity metric may have dimension 2, i.e. $[g_{\mu\nu}]=1/[L]^2$. Several other approaches to including model superplastic vacuum and $BF$-theories gravity support this suggesuion. The important consequence such is all diffeomorphism invariant quantities are dimensionless for any spacetime. These include action $S$, interval $s$, cosmological constant $\Lambda$, scalar curvature $R$, field $\Phi$, etc. Here we trying further exploit idea, consider Planck constant. application $\hbar$ parameter Minkowski metric. only under Lorentz transformations, not invariant. As a result has nonzero -- length [L]. Whether related scale, an open question. In principle there can be different vacua with their own values $\hbar$. Then thermal contact between two temperatures obey analog Tolman law: $\hbar_1/T_1= \hbar_2/T_2$.