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How is loop quantum gravity related to the principle of relativity, in particular to the diffeomorphism invariance of general relativity?
the thing to focus on is a relatively recent formulation of Lqg called "covariant Lqg". If I google that, I get:A. Neumaier said:How is loop quantum gravity related to the principle of relativity, in particular to the diffeomorphism invariance of general relativity?
A. Neumaier said:How is loop quantum gravity related to the principle of relativity, in particular to the diffeomorphism invariance of general relativity?
Thanks for that Marcus. I splashed out and ordered a copy and also downloaded it. I really enjoy reading anything by Rovelli.marcus said:thanks!
So it's a Jan 2008 lecture series.
The formulation has changed some since, which could matter. There is EPRL and variations like Jon Engle's.
I don't know if it would make a difference to you but you might be interested in looking at some of the more recent papers I linked to.
e.g. in post #4
http://arxiv.org/abs/1303.4636
Now the standard textbook on LQG is "Covariant LQG" (2014) by Rovelli and Vidotto. There is a free draft version one can download or one can buy the book. I gave a link. It's different from what was current in 2008.
http://www.cambridge.org/us/academi...roduction-quantum-gravity-and-spinfoam-theory
Loop quantum gravity is a theory of quantum gravity that attempts to reconcile the principles of general relativity and quantum mechanics. It suggests that space and time are quantized, meaning they are made up of discrete, indivisible units, rather than being continuous. It also proposes that gravity is a result of the interaction between these quantized units of space and time, rather than being a fundamental force like in classical physics.
The diffeomorphism group in loop quantum gravity refers to the symmetries of space and time that are preserved in the theory. These symmetries involve the ability to smoothly deform or transform space and time without changing the underlying physical laws. In loop quantum gravity, these symmetries are crucial for maintaining the discrete, quantized nature of space and time.
One of the main differences between loop quantum gravity and other theories of quantum gravity, such as string theory, is the way in which it addresses the problem of quantizing gravity. Whereas string theory proposes that particles are made up of tiny strings vibrating in multiple dimensions, loop quantum gravity suggests that space and time themselves are quantized. Additionally, loop quantum gravity does not require the existence of extra dimensions beyond the four dimensions of space and time.
No, loop quantum gravity has not yet been proven experimentally. It is still a theoretical framework and has not yet been tested through experiments. However, there are ongoing efforts to develop experimental tests for loop quantum gravity, such as through studying the cosmic microwave background radiation or the behavior of gravitational waves.
If loop quantum gravity is proven to be a valid theory, it could have significant implications for our understanding of the universe. It could potentially resolve the singularity problem in black holes and provide a better understanding of the Big Bang. It could also have implications for the unification of all fundamental forces, as well as for our understanding of the nature of space and time.