Question

According to the argument, a theory of Quantum Gravity should not be compatible with the notion of time evolution. This is also called The Problem of time.

However, the target spacetime formulation of string theory does have a notion of universal background time given by the target spacetime. So it seems like it does not address the problem of time. The CFT part of AdS/CFT is also a QFT with a well-defined universal time.

So does String theory not address this problem? If no, then what does it say about it?

Answer 1

String theory addresses the problem of time in different ways depending on the context. The target spacetime formulation of string theory has a concept of universal background time, but it does not fully resolve the problem of time in the context of quantum gravity. The CFT part of the AdS/CFT correspondence, however, does have a well-defined universal time.

Step-by-step explanation:

In string theory, the notion of time evolution is addressed differently depending on the context.

While the target spacetime formulation of string theory does have a concept of universal background time given by the target spacetime, it does not fully resolve the problem of time in the sense that it does not establish a fundamental theory of time evolution compatible with quantum gravity.

On the other hand, in the context of the AdS/CFT correspondence, which relates string theory to a conformal field theory (CFT), the CFT part of the correspondence does have a well-defined universal time.

However, it is important to note that the AdS/CFT correspondence is a conjectured duality and not a complete theory of quantum gravity on its own.