×

Discreteness without symmetry breaking: a theorem. (English) Zbl 1179.83012

Summary: This paper concerns random sprinklings of points into Minkowski spacetime (Poisson processes). It proves that there exists no equivariant measurable map from sprinklings to spacetime directions (even locally). Therefore, if a discrete structure is associated to a sprinkling in an intrinsic manner, then the structure will not pick out a preferred frame, locally or globally. This implies that the discreteness of a sprinkled causal set will not give rise to “Lorentz breaking” effects like modified dispersion relations. Another consequence is that there is no way to associate a finite-valency graph to a sprinkling consistently with Lorentz invariance.

MSC:

83A05 Special relativity
83C45 Quantization of the gravitational field
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1103/PhysRevLett.59.521 · doi:10.1103/PhysRevLett.59.521
[2] Sorkin R. D., Lectures on Quantum Gravity (2003)
[3] Henson J., Approaches to Quantum Gravity: Toward a New Understanding of Space, Time and Matter (2009)
[4] DOI: 10.1002/andp.200410144 · Zbl 1080.83008 · doi:10.1002/andp.200410144
[5] DOI: 10.1142/S0217732304015026 · doi:10.1142/S0217732304015026
[6] DOI: 10.1103/PhysRevD.67.064019 · Zbl 1222.83073 · doi:10.1103/PhysRevD.67.064019
[7] Livine E. R., JHEP 06 pp 050–
[8] DOI: 10.1016/0550-3213(82)90222-X · doi:10.1016/0550-3213(82)90222-X
[9] Stoyan D., Stochastic Geometry and Its Applications (1995) · Zbl 0838.60002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.