The discussion revolves around the nature of time in Loop Quantum Gravity (LQG) and string theory, particularly in the context of singularities within black holes. Participants explore whether time is absolute or dynamical and how these theories address time-related issues in quantum gravity.
Participants express differing views on the nature of time in LQG and string theory, with no consensus reached on whether time is absolute or dynamical. The discussion includes multiple competing perspectives and remains unresolved on several points.
Some claims rely on specific assumptions about the nature of time and the mathematical framework of the theories discussed. The implications of these assumptions and the validity of the models presented are not fully resolved.
ensabah6 said:How does LQG and string theory deal with time in singularities in the center of black holes?
marcus said:In LQC they typically include a matter field whose evolution can serve as clock. Time is not absolute. It is relational. The theory deals with correlations between observables---one of the observables is chosen to serve as clock.
In other words, no time without some real clock, there must be some process.
Black hole collapse has been studied in LQG by various people, look up Leonardo Modesto, Dah-wei Chiou, Kevin Vandersloot.
As I recall those particular researchers find no singularity.
Because of quantum corrections gravity becomes repellent at near Planckian density and the collapsing spacetime region re-expands out the bottom--a socalled "bounce".
However the issue is not settled. All the work so far has involved simplifying assumptions. Can't be sure yet what happens. I have to go. There is more to say and other researchers' work to mention. Maybe someone will, or i will get to it when I return.
marcus said:You are talking about canonical quantization but what you are describing is the wrong way to conceptualize it. With canonical quantization of GR, what you get is essentially timeless*. The Hamiltonian is a constraint. This is why in a canonical quantization of GR something be chosen to serve as clock, like i said. Observables which depend on time are treated as correlations with the clock observable.
Instead of saying "But I thought that..." and contradicting, maybe could you go back and try to understand what I said?
Another thing to realize that LQG is not now presented as a quantization of GR. All that canonical quantization stuff from years back was basically heuristics. Read Rovelli's April paper to get an up-to-date perspective.
It is really crucial that people who want to ask and talk about LQG should have examined that April paper:
http://arxiv.org/abs/1004.1780
and understood as much of it as they can.
It is essentially a complete reformulation of LQG, with a lot of insight and perspective expressed in ordinary words, as well as equations. A major effort to communicate a new perspective. I don't understand all of it by a long shot, but there are easy parts and I'm slowly struggling through the hard parts.
*so-called "frozen time" formalism. Introducing real clocks and treating time relationally was the response adopted, some 10 years ago I guess.
The situation could not be worse! We have a quantum theory in which the main dynamical equation can be solved without considering the evolution in time.
tom.stoer said:The slicing of spacetime M4 into time * space R * M3 assumes a certain topological structure of spacetime.
This slicing does however not introduce any absolute time. This can be understood as follows: in canonical quantum gravity one expresses the local Lorentz symmetry plus 4-dim. diffeomorphism invariance in terms of certain operators forming an algebra. If this algebra stays intact after quantization (w/o anomaly) and can be implemented on the physical states the theory still has this symmetry even if it is not visible.
The residue of the 4-dim. diff. inv.is just the Hamiltonian with H |phys> = 0.
Look at angular momentum; you know the su(2) algebra as defined by the Pauli matrices. The angular momentum operators have the same commutation relations. No as you write down the angular momentum operators in cylinder coordinates it looks like as the z-coordinate has been singled out and is something special; this corresponds to the fact that m is always identified with Lz. Anyway - if you calculate the commutation relations you find that it's still su(2) and that the algebra stays intact; that is all what you need. Cylinder coordinates do not break the symmetry.