Problem of the time and static restriction in quantum gravity

TL;DR

This paper addresses the longstanding problem of defining time in quantum gravity, proposing a method to relate time evolution and static restrictions, with application to the Friedmann universe.

Contribution

It introduces an up-to-down method to clarify the time evolution in quantum gravity and derives related equations, advancing understanding of the problem of time.

Findings

Derived equations linking time and static restrictions in quantum gravity

Applied the method to the Friedmann universe example

Provided insights into the problem of time in canonical quantum gravity

Abstract

The problem of the time is one of the open issues in the quantum gravity. This problem is particular problem in the canonical quantum gravity. Even in the loop gravity the problem of the time remain. Our work is concerning to the problem of the time. The Wheeler-DeWitt itself contains time evolution part, but which part is the time evolution part is open issue. However, we can create a method that seems to solve this problem that is up-to-down method created in the previous works. We can derive equation relating to the time and static restriction in this paper. As a example we treat the problem of the time of the Friedmann universe. And we derive the static restriction in quantum gravity.