Wheeler–DeWitt equation

The Wheeler–DeWitt equation is a field equation. It is part of a theory that attempts to combine mathematically the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called 'problem of time'. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar 'group' (which is the diffeomorphism group on-shell). H ^ ( x ) | ψ ⟩ = 0 {displaystyle {hat {H}}(x)|psi angle =0} The Wheeler–DeWitt equation is a field equation. It is part of a theory that attempts to combine mathematically the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called 'problem of time'. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar 'group' (which is the diffeomorphism group on-shell). All defined and understood descriptions of string/M-theory deal with fixed asymptotic conditions on the background spacetime. At infinity, the 'right' choice of the time coordinate 't' is determined (because the space-time is asymptotic to some fixed space-time) in every description, so there is a preferred definition of the Hamiltonian (with nonzero eigenvalues) to evolve states of the system forwards in time. This avoids all the need to dynamically generate a time dimension using the Wheeler–DeWitt equation. Thus, the equation has not played a role in string theory thus far.