Speaker
Description
I discuss the simplest solution of the covariant Schroedinger equation of
quantum gravitational field derived using precanonical quantization,
a quantization based on the De Donder-Weyl Hamiltonian theory which
requires no space-time decomposition. This is a second-order PDE for
a Clifford algebra valued wave function on the space of space-time and spin-connection variables which reproduces the Einstein field equations on average in the sense of the Ehrenfest theorem. The quantum-gravitational geometry is
described by a probability amplitude of having some value of spin
connection at one point and another value of spin connection at
another point. A simple solution can be found when the expectation
value of spin-connection equals zero, which corresponds to a quantum
state associated with the Minkowski space-time in Cartesian
coordinates. The solution shows that the scale when quantum
fluctuations of space-time are noticeable can be several orders of
magnitude above the Planck scale. We show that this scale actually
depends on G, $\hbar$, c, and also on the scale $\varkappa$ which is
introduced in precanonical quantization and has been shown to be associated
(surprisingly) to the scale of the mass gap in quantum gauge theories. This is the reason why, in precanonical quantization, the space-time seems to foam at
much lower energies in precanonical quantum gravity than the estimations
in LQG or string theory usually expect. Potentially, it opens an opportunity
for experimental testing and falsifying some of the competing theories.
