Special relativity asserts that physical phenomena appear the same to all unaccelerated observers. This is called Lorentz symmetry and relates long wavelengths to short ones: if the symmetry is exact it implies that space-time must look the same at all length scales. Several approaches to quantum gravity, however, suggest that there may be a microscopic structure of space-time that leads to a violation of Lorentz symmetry. This might arise because of the discreteness or non-commutivity of space-time.....
The constraint reported here on a possible maximal electron speed less than the speed of light is more than seven orders of magnitude better than previous limits. This limit is strong enough to conclude that quantum gravity scenarios postulating or implying this sort of Lorentz violation are not viable.
The type of Lorentz violation that we have considered also violates CPT symmetry, the symmetry under combined charge conjugation, space inversion, and time reversal. The fact that it is ruled out might therefore be a consequence of CPT symmetry, rather than Lorentz symmetry. It thus makes sense to think seriously about constraining Lorentz violation suppressed by the second power, (E/E Planck).
Carroll, S. M., Harvey, J. A., Kostelecky, V. A., Lane, C. D. & Okamoto, T. Noncommutative field
theory and Lorentz violation. Phys. Rev. Lett. 87, 141601 (2001).
For example, string theory predicts that we may live in a universe with non-commutative coordinates [2], leading to a violation of Lorentz invariance [3].
https://arxiv.org/pdf/hep-th/0407149
https://link.springer.com/content/pdf/10.1140/epjc/s10052-011-1653-y.pdf
in the noncommutative generalization of electrodynamics the interplay be-
tween a nonzero noncommutative parameter and an external
magnetic field leads us to predict the production of lepton
pairs of low invariant mass by free photons (an event for-
bidden by Lorentz invariant electrodynamics) in relativistic
heavy ion collisions at present and future available energies.
This unique channel can be clearly considered as a signature
of noncommutativity.
, in the framework of NCED, the effects of a noncommutative
spacetime can be detected in relativistic heavy ion collisions
by the grid of the following experimental signatures/filtering
procedures:
the decay of a single noncommutative photon
Bremsstrahlung is the electromagnetic radiation produced when a fast-moving charged particle—such as an electron—slows down, speeds up, or changes direction upon interacting with the electric field of an atomic nucleus. The word comes from German, meaning "braking radiation"
Freeman Dyson in 2002, meeting one of us (A.I.) among researchers
at MIT to hear about their work, defined as “radical” the hypothesis of
a noncommutative spacetime.
https://www.mdpi.com/2073-8994/17/6/923
The non-commutativity of the modified
position operators provides a link between GUP models and non-commutative geometry
models [31,32]. Consequently, the related uncertainty relationships are ∆Xi∆Xj ∝ ϵijk⟨ˆlk⟩
and the uncertainty of the cross-sectional area is connected to the expectation of the angular
momentum operator. This provides a potentially dynamic non-commutative geometry that
warrants further study. Moreover, this provides another connection between the 3D GUP
models in this work and spin foam models [33,34].
We leave these questions—the modification of the Lorentz algebra and the connection
of 3D GUP models to non-commutative geometry and spin foam models—for future work.
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