Time and space in Quantum gravity

  • #1
In Einstein equation of general relativity, one side is stress-energy tensor and the other side is the Einstein tensor (functions of metric tensor). But the problem is in order to describe the matter field/stress-energy tensor, we have to use the space and time, which are determined by the metric tensor. So there is some circular reasoning here. Is the spacetime just some geometry or a real field carrying energy?
In the string theory, a string exists in a 26 or 11 or 10 dimensional spacetime. But could the spacetime exists as some kind of container for the string?
Is spacetime some kind of material or a priori notion of physics?

Answers and Replies

  • #2
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One should distinguish between spacetime topology and spacetime metric. The former may be defined even without the latter. Only the latter is explicitly dynamical in general relativity (GR), including the most of quantum versions of GR.
  • #3
Is spacetime some kind of material or a priori notion of physics?

Time is ticks on the observer's clock.
  • #4
You may be interested to know that one of the endpoints (I hesitate to say conclusions) of the mini-program on singularity resolution at the Kavli Institute of Theoretical Physics (Jan. 2007) was that a new view of space-time is needed by both the Loop Quantum Gravity approach and the String Theory approach to understand what happens physically at or near black holes and/or the Big Bang.

In Thomas Thielmann's first seminar at the mini-program, he considers the problem of time to be 1. the lack of a canonical Hamiltonian in generally covarient theories, and 2. there is no time evolution of observables, resulting in a frozen picture.

More simply, I should say your question is an open problem of some importance in the theoretical physics community.

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  • #5
I don't think it is too unexpected/freak to discard the present concept of space and time. The question is what spacetime is. Could we think/experiment withouth the concept of spacetime? Loop quantum gravity attacks the problem mainly from GR viewpoint, while string theory attacks the problem from QM viewpoint. But I am not sure whether the last winner will be either of the two. Without attacking at the spacetime problem directly there will be no real results of the physics concerning the world.
Many results from the string theory are beautiful and have a clear brand of Ed Witten's influence. But I guess to distinguish physics and mathematics is a necessary job we need to do. Compared with the era of Newton, Newton needed to develop the necessary mathematics calculus to describe his mechanics. Einstein didn't need to develop Riemann geometry to write the equation of GR. Heisenberg didn't need to invent the matrix and spectral theory to develop the Matrix mechanics. But today we even don't know what kinds of basic mathematics tools we need. String theoreticians are just speculating on every kind of physics/mathematics.

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