Lorentz invariance in loop quantum gravity
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Because loop quantum gravity can model universes, space gravity theories are contenders to build and answer unification theory; the Lorentz invariance helps grade the spread of universal features throughout a proposed multiverse in time.
Grand Unification Epoch
The Grand Unification Epoch is the era in time in the
The permanence of Lorentz invariance constants is based on elementary particles and their features. There are eons of time before the Big Bang to build the universe from black holes and older multiverses. There is a selective process that creates features in elementary particles, such as accepting, storing, and giving energy. Lee Smolin's books about loop quantum gravity posit that this theory contains the evolutionary ideas of "reproduction" and "mutation" of universes, and elementary particles, and is formally analogous to models of population biology.[citation needed]
Earlier universes
In the early universes before the Big Bang, there are theories that ''loop quantum gravity loop quantum structures'' formed space. The Lorentz invariance and universal constants describe elementary particles that do not exist yet.
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Minkowski spacetime
Loop quantum gravity (LQG) is a quantization of a classical Lagrangian classical field theory. It is equivalent to the usual Einstein–Cartan theory in that it leads to the same equations of motion describing general relativity with torsion.
Global Lorentz invariance is broken in LQG just like it is broken in general relativity (unless one is dealing with
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. These questions will all remain open as long as the classical limits of various LQG models (see below for the sources of variation) cannot be calculated.
Lie algebras and loop quantum gravity
Mathematically, LQG is local gauge theory of the
One can't distinguish between SO(3) and SU(2) or between SO(3,1) and SL(2,C) at this level: the respective
To make matters more complicated, it can be shown that a positive cosmological constant can be realized in LQG by replacing the Lorentz group with the corresponding quantum group. At the level of the Lie algebra, this corresponds to what is called q-deforming the Lie algebra, and the parameter q is related to the value of the cosmological constant. The effect of replacing a Lie algebra by a q-deformed version is that the series of its representations is truncated (in the case of the rotation group, instead of having representations labelled by all half-integral spins, one is left with all representations with total spin j less than some constant).
It is entirely possible to formulate LQG in terms of q-deformed Lie algebras instead of ordinary Lie algebras, and in the case of the Lorentz group the result would, again, be indistinguishable for sufficiently small velocity parameters.
Spin networks loop quantum gravity
In the spin-foam formalism, the Barrett–Crane model, which was for a while the most promising state-sum model of 4D Lorentzian quantum gravity, was based on representations of the noncompact groups SO(3,1) or SL(2,C), so the spin foam faces (and hence the spin network edges) were labelled by positive real numbers as opposed to the half-integer labels of SU(2) spin networks.
These and other considerations, including difficulties interpreting what it would mean to apply a Lorentz transformation to a spin network state, led
Phenomenological (hence, not specific to LQG) constraints on anomalous dispersion relations can be obtained by considering a variety of astrophysical experimental data, of which high-energy cosmic rays are but one part. Current observations are already able to place exceedingly stringent constraints on these phenomenological parameters.
References
- ^ "So, how did everything start?". European Space Agency. 2003-06-06. Retrieved 2023-10-24.