Continuous symmetries in discrete space?

Martin Bojowald

Martin Bojowald is a Professor of Physics at Pennsylvania State University, PA,

Violating Lorentz symmetries can be dangerous. A new model assesses this threat in loop quantum gravity.

Discrete space is attractive in quantization attempts of gravity, but it implies the great danger of violating Lorentz transformations. Any approach must show that modifications of symmetries by discrete space are tame enough for predictions to be consistent with continuum low-energy physics. In the CQG paper, Sandipan Sengupta constructs an encouraging model using methods of loop quantum gravity.

About 25 years ago, the originators of loop quantum gravity made the intellectual bet that discrete space can be meaningful. Since then, there has not been much interest in validating the claim. But recently, Tim Koslowski and Hanno Sahlmann introduced a new class of states that show promise in bringing the theory closer to this aim. Sengupta, building on their work, studies a simplified model in which symmetry operators can be analyzed explicitly. He does not derive a continuum from discrete space, but makes use of a built-in background. From the microscopic viewpoint, he assumes that some coarse graining has already been performed, and then looks at possible remnants of discreteness.

The result is encouraging but also confirms potential dangers of discreteness. Sengupta is able to show that states exist which describe discrete space and approach flat space-time. Lorentz symmetries are realized approximately. The fact that they can be represented at all is encouraging, but future research must answer whether the  approximation is sufficient: Even small violations could lead to inconsistencies. Whether loop quantum gravity can be meaningful remains open. But thanks to work by Sengupta and others, there is hope that the loopy bet may be validated.

Read the full article: Class. Quantum Grav. 31 085005
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