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Modern tests of Lorentz invariance

David Mattingly

TL;DR

The paper surveys theoretical frameworks and experimental searches for Lorentz invariance violation (LV) motivated by quantum gravity, organizing LV models into kinematic (modified dispersion, RMS, c^2, DSR, non-systematic) and dynamic (effective field theory, non-commutative spacetime, gravity-coupled LV) categories. It compiles terrestrial and astrophysical constraints, highlighting precision tests from Penning traps, clock comparisons, cavities, torsion balances, meson systems, Doppler experiments, muons, and collider-like settings, as well as high-energy astrophysical probes (time-of-flight, birefringence, threshold reactions, GZK, synchrotron, neutrinos, and phase coherence). The review shows that current limits on LV operators, including those up to dimension-6 in EFT, are extremely stringent, constraining Planck-scale LV to be highly suppressed in low-energy physics and guiding models of quantum gravity. It also discusses potential future tests, including space-based experiments, gravitational wave observations, and high-energy astrophysical facilities, which could further illuminate or constrain LV scenarios. Overall, the work clarifies how different LV frameworks map to observable signatures and emphasizes that, to date, Lorentz invariance remains an extraordinarily robust symmetry across a wide range of energies and experimental contexts.

Abstract

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

Modern tests of Lorentz invariance

TL;DR

The paper surveys theoretical frameworks and experimental searches for Lorentz invariance violation (LV) motivated by quantum gravity, organizing LV models into kinematic (modified dispersion, RMS, c^2, DSR, non-systematic) and dynamic (effective field theory, non-commutative spacetime, gravity-coupled LV) categories. It compiles terrestrial and astrophysical constraints, highlighting precision tests from Penning traps, clock comparisons, cavities, torsion balances, meson systems, Doppler experiments, muons, and collider-like settings, as well as high-energy astrophysical probes (time-of-flight, birefringence, threshold reactions, GZK, synchrotron, neutrinos, and phase coherence). The review shows that current limits on LV operators, including those up to dimension-6 in EFT, are extremely stringent, constraining Planck-scale LV to be highly suppressed in low-energy physics and guiding models of quantum gravity. It also discusses potential future tests, including space-based experiments, gravitational wave observations, and high-energy astrophysical facilities, which could further illuminate or constrain LV scenarios. Overall, the work clarifies how different LV frameworks map to observable signatures and emphasizes that, to date, Lorentz invariance remains an extraordinarily robust symmetry across a wide range of energies and experimental contexts.

Abstract

Motivated by ideas about quantum gravity, a tremendous amount of effort over the past decade has gone into testing Lorentz invariance in various regimes. This review summarizes both the theoretical frameworks for tests of Lorentz invariance and experimental advances that have made new high precision tests possible. The current constraints on Lorentz violating effects from both terrestrial experiments and astrophysical observations are presented.

Paper Structure

This paper contains 73 sections, 98 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. General Considerations
  3. Defining Lorentz violation
  4. Lorentz violation in field theory
  5. Modified Lorentz groups
  6. Kinematics vs. dynamics
  7. The role of other symmetries
  8. CPT Invariance
  9. Supersymmetry
  10. Poincaré Invariance
  11. Diffeomorphism invariance and prior geometry
  12. Lorentz violation and the equivalence principle
  13. Systematic vs. Non-systematic violations
  14. Causality and stability
  15. Causality
  16. ...and 58 more sections

Figures (4)

  • Figure 1: Elements involved in threshold constraints.
  • Figure 2: Total outgoing particle energy in symmetric and asymmetric configurations.
  • Figure 3: An example of an upper and lower threshold. R is the region spanned by all $X_k$ and $E_1(p_1)$ is the energy of the incoming particle. Where $E_1(p_1)$ enters and leaves R are lower and upper thresholds, respectively.
  • Figure 4: Constraints on LV in QED at $n=3$ on a log-log plot. For negative parameters minus the logarithm of the absolute value is plotted, and region of width $10^{-10}$ is excised around each axis. The constraints in solid lines apply to $\xi$ and both $\eta_\pm$, and are symmetric about both the $\xi$ and the $\eta$ axis. At least one of the two pairs $(\eta_\pm,\xi)$ must lie within the union of the dashed bell-shaped region and its reflection about the $\xi$ axis. Intersecting lines are truncated where they cross.