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