Discreteness without symmetry breaking: A Theorem

This paper concerns sprinklings into Minkowski space (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.

Causal sets
Lorentz symmetry
spacetime discreteness
causal set
invariance: Lorentz
space-time: discrete

References(5)

Figures(0)

Space-Time as a Causal Set

Luca Bombelli
(
- Syracuse U.
)
,
Joohan Lee
(
- Syracuse U.
)
,
David Meyer
(
- Syracuse U.
)
,
Rafael Sorkin
(
- Syracuse U. and
- Princeton, Inst. Advanced Study
)

- Phys.Rev.Lett. 59 (1987) 521-524
•
DOI:
- 10.1103/PhysRevLett.59.521

Causal sets: Discrete gravity

Rafael D. Sorkin
(
- Syracuse U. and
- Queen Mary, U. of London
)

The Causal set approach to quantum gravity

Joe Henson
(
- Utrecht U.
)

•
e-Print:
- gr-qc/0601121

Semiclassical quantum gravity: Statistics of combinatorial Riemannian geometries

Luca Bombelli
(
- Mississippi U. and
- Perimeter Inst. Theor. Phys.
)
,
Alejandro Corichi
(
- Mississippi U. and
- Mexico U., ICN
)
,
Oliver Winkler
(
- Perimeter Inst. Theor. Phys.
)

- Annalen Phys. 14 (2005) 499-519
•
e-Print:
- gr-qc/0409006
•
DOI:
- 10.1002/andp.200410144

Quantum gravity phenomenology, Lorentz invariance and discreteness

Fay Dowker
(
- Imperial Coll., London and
- Perimeter Inst. Theor. Phys.
)
,
Joe Henson
(
- UC, San Diego
)
,
Rafael D. Sorkin
(
- Syracuse U.
)

- Mod.Phys.Lett.A 19 (2004) 1829-1840
•
e-Print:
- gr-qc/0311055
•
DOI:
- 10.1142/S0217732304015026