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.
In both LQG (Loop Quantum Gravity) and string theory, time is considered to be a dynamical concept rather than an absolute one. This means that time is not viewed as a fixed and immutable entity, but rather as a variable that can change and be affected by other factors such as gravity.
In LQG and string theory, time is viewed as a dimension that is intertwined with space, forming a four-dimensional spacetime. This means that time is not considered to be a separate entity, but rather an integral part of the fabric of the universe.
While both LQG and string theory view time as a dynamical concept, they differ in their mathematical frameworks and approaches to understanding it. LQG uses a discrete approach, where time is quantized into tiny units, while string theory uses a continuous approach, where time is viewed as a smooth and continuous variable.
The problem of time refers to the challenge of reconciling the concept of time with the laws of physics, particularly in the context of quantum mechanics and general relativity. LQG and string theory both provide potential solutions to this problem, but it is still an ongoing area of research and debate in both theories.
The concept of time travel is a popular topic in science fiction, but it is still highly debated and remains a hypothetical possibility in both LQG and string theory. While both theories allow for the possibility of warping spacetime, the practicality and feasibility of actually traveling through time are still uncertain and require further research.