Remarks on the issue of time and complex numbers in canonical quantum gravity

Abstract

Upon using some special example in the homogeneous cosmological model we develop the idea that, as a result of the arbitrariness of the factor ordering in Wheeler-DeWitt equation, gauge phases can not, in general, being completely removed from the wave functional in quantum gravity. The latter may be conveniently described by means of a remnant complex term in WDW equation depending on the factor ordering. Taking this equation for granted we can obtain WKB complex solutions and, therefore, we should be able to derive a semiclassical time parameter for the Schrödinger equation corresponding to matter fields in a given classical curved space. 4.60.+n,03.65Bz,04.20.Fy

The Final Theory of Physics - a Tautology?

“…The intransparent mixture of quantity and structure however may lead to confusion about the meaning and role of complex numbers in quantum mechanics and physics in general. This is indicated by the discussion about the meaning of complex numbers in QM that is ongoing for decades [22][23][24][25][26][27][28][29][30][31][32][33][34] .…”

Vacuum Decay via Lorentzian Wormholes

“…In other words, the reality of the wave function implies that the asymptotically flat spacetime is just the extreme Reissner-Nordström black hole. Since time is absent from this quantum theory , such a complex conjugation invariance could be required by the consistence of the quantisation procedure (although, quantum gravity might not satisfy this requirement strictly 11 ). On the other hand, the existence of a finite differences equation seems to be a fact related with the speculations of Wheeler 1 in the sense that spacetime might not be considered as classical on scales of the order of the Planck length (a ∼ M −1 ), i.e., in our terms, that the continuous character of spacetime can only be recovered, we will see, as an approximated phenomenon having a semiclassical meaning.…”