Well, in some sense, the Wheeler-DeWitt equation is nothing else than Einstein’s equations that you encountered elsewhere – potentially simplified and reduced in a minisuperspace formulation.

But if something like the Wheeler-DeWitt equation is the only equation that defines what can happen in a quantum gravity system, your task actually becomes harder, not easier. You must artificially reparameterize your physical states according to a new observable (e.g. the total volume of the Universe at some “moment”) that will play the role of your time (recall that there’s no preferred choice of coordinates in general relativity) – and with this new “gauge-fixed” choice of your time, you will find out that the Wheeler-DeWitt “H=0” equation becomes non-trivial.

— Why and how energy is not conserved in cosmology

— Lubos Motl

Bryce DeWitt first published this equation in 1967 under the name “Einstein–Schrodinger equation”; it was later renamed the “Wheeler–DeWitt equation”.

…

Solutions to the Wheeler-DeWitt equation have therefore been interpreted as the Universal wave function.

This property is known as timelessness [disambiguation needed]. The reemergence of time requires the tools of decoherence and clock operators.

— Wikipedia on Wheeler–DeWitt equation

Timelessness is a property of the Wheeler-deWitt equation in canonical quantum gravity.

— Wikipedia on Timeless

2012.03.08 Thursday ACHK