Of interest in this connection would be to see whether the LQG analogue of Minkowski spacetime breaks or preserves global Lorentz invariance, and Carlo Rovelli and coworkers have recently been investigating the Minkowski state of LQG using spin-foam techniques.
A possible solution to this problem has been put forward by Carlo Rovelli and Alain Connes, both in the classical and quantum theory, and goes by the name of the thermal time hypothesis.
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