Reconcile Planck scale discreteness and the Lorentz-Fitzgerald contraction

By Carlo Rovelli, Simone Speziale. 2002

141 citations recorded by the source corpus.

A Planck-scale minimal observable length appears in many approaches to quantum gravity. It is sometimes argued that this minimal length might conflict with Lorentz invariance, because a boosted observer could see the minimal length further Lorentz contracted. We show that this is not the case within loop quantum gravity. In loop quantum gravity the minimal length (more precisely, minimal area) does not appear as a fixed property of geometry, but rather as the minimal (nonzero) eigenvalue of a quantum observable. The boosted observer can see the same observable spectrum, with the same minimal area. What changes continuously in the boost transformation is not the value of the minimal length: it is the probability distribution of seeing one or the other of the discrete eigenvalues of the area. We discuss several difficulties associated with boosts and area measurement in quantum gravity. We compute the transformation of the area operator under a local boost, propose an explicit expression for the generator of local boosts and give the conditions under which its action is unitary.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c3ebd4ed5ac833f55d5c51fcf62ff9746b8f7f7f

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

Quantum-Spacetime Phenomenology (2008, background): “[478, 479]) have observed that there could be ways to reconcile what is presently known about LQG with the presence of exact Lorentz symmetry in the quasi-Minkowski limit.”
Tests of Lorentz invariance: a 2013 update (2013, background): “3 See however [111] for an example where (coarse grained) boost invariance is preserved in a discrete model, and [112, 113] for a study of how discreteness may be compatible with Lorentz symmetry in a quantum setting.”
Loop Quantum Gravity (2003, background): “For a complete discussion of this point, see [156].”
SU(2) loop quantum gravity seen from covariant theory (2002, background): “It turns out that this result matches exactly what comes out of the direct covariant canonical analysis as described in section 2: b = x(∂x−1) coincides with the function Λ( ∼ Q) and iχa should be identified with A(ash) (77).”
The Spin-Foam Approach to Quantum Gravity (2012, background): “The LIV effects obtained in LQG so far promote by assumption the kinematical discreteness of quantum geometry to discreteness of the physical background in a literal fashion (on the one hand, discreteness of geometry can coexist with Lorentz invariance [331], on the other, at the level of gauge-inva”