Wikipedia article: No time in General Relativity

[Nick666]

"In quantum gravity, the problem of time is a conceptual conflict between general relativity and quantum mechanics. Roughly speaking, the problem of time is that there is none in general relativity. This is because in general relativity, the Hamiltonian is a constraint that must vanish. However, in theories of quantum mechanics, the Hamiltonian generates the time evolution of quantum states. Therefore we arrive at the conclusion that "nothing moves" ("there is no time") in general relativity. Since "there is no time", the usual interpretation of quantum mechanics measurements at given moments of time breaks down. This problem of time is the broad banner for all interpretational problems of the formalism."

http://en.wikipedia.org/wiki/Problem_of_time

Could you shed some light on this for me ? Is this another way of saying there's no time, only spacetime in GR ?

 

[PAllen]

I think the summary statements in this article are just wrong. Some of the more detailed explanations are ok, but still tend to overstate the case. Solutions considered physically plausible (e.g. FLRW) have a globally well defined time. I have usually seen this discussed more in terms of:

- you want to quantize gravity
- but gravity = curvature = the relation of space and time
- so you suddenly need to have time itself subject to non-determinism

and nobody knows how to do this yet.

 

[PeterDonis]

Solutions considered physically plausible (e.g. FLRW) have a globally well defined time.

The "time" in these spacetimes is a geometric property of the solution (in FRW solutions, for example, it's the "time" defined by the set of "comoving" worldlines and the spacelike hypersurfaces orthogonal to them). But this property in itself does not give you "time evolution" in the sense of QM.

Another way of stating the problem is that, in order to have a Hamiltonian operator that can generate time evolution in the sense of QM, you need a well-defined global notion of energy. But there isn't one in a general spacetime in GR. The best you can do in the general case is to construct an expression that looks like a "Hamiltonian", but vanishes identically (this is the "Hamiltonian constraint"), so it can't act as a generator of anything.

 

[bcrowell]

This part of the article sounds like total nonsense to me:

The theory that combines general relativity and quantum mechanics, Many worlds interpretation is called Wheeler–DeWitt equation. Wheeler–DeWitt equation says there is no time at all.

 

[PeterDonis]

Well, the Wheeler-DeWitt equation does say $\hat{H} \vert \psi \gt = 0$, which basically amounts to "the wave function of the universe doesn't change". At least, to the extent you can express what it's saying in a short sentence of ordinary language.