Can a Functional Equation Solve the Problem of Time in Quantum Gravity?

[eljose]

We have for Quantum gravity the equation:

$$H|\Psi>=0$$ as you can see this is time-independent partial differential equation, my question is if we could construct a functional differential equation in the form:

$$\alpha{d\Psi/dt}+\Beta{H_1}=0$$ where the H1 would have the derivatives respect to the metric and alpha and beta would be matrices (alpah is a Grassman number) in a way that we would have a functional equation of spin 2 (graviton) with this we would have solved the problem of time in quantum gravity.

 

[Rade]

You may wish to re-post your question at this thread:
https://www.physicsforums.com/showthread.php?t=104123
Lots of interest in QG there.

 

[sir-pinski]

It is not clear if a functional equation alone can fully solve the problem of time in quantum gravity. While it is true that a functional equation, such as the one proposed in the content, could potentially provide a time-dependent solution for the quantum gravity equation, there are other factors to consider.

Firstly, the proposed functional equation may not be unique and there could be multiple solutions that satisfy it. This could lead to difficulties in determining which solution is the correct one.

Additionally, the concept of time in quantum gravity is still a subject of debate and research. It is not yet fully understood how time behaves at the quantum level and how it can be incorporated into the theory of quantum gravity. Therefore, simply introducing a functional equation may not be enough to fully address the problem of time in this context.

Furthermore, there are other challenges in quantum gravity, such as the issue of singularities and the unification of quantum mechanics and general relativity, that also need to be addressed. A functional equation alone may not be able to solve these complex problems.

In conclusion, while a functional equation may be a step towards understanding time in quantum gravity, it is not a definitive solution and further research and developments are needed to fully address this problem.