Lorentz invariance and quantum gravity: an additional fine-tuning problem?

TL;DR

The paper argues that Planck-scale space-time granularity can induce Lorentz violation in low-energy physics once standard-model interactions are included, overturning prior expectations of only tiny effects. A renormalization-based analysis shows that Lorentz-violating contributions from self-energy loops arise from dimension-4 (or lower) operators and are not generically suppressed by powers of $E/E_P$, causing different fields to acquire distinct effective speeds $c_i$ with fractional differences $\Delta c/c$ of order $0.1\%$ to $10\%$. Such unsuppressed low-energy Lorentz violation clashes with experimental bounds (e.g., Coleman–Glashow tests requiring $|c_i-c_j|/c \lesssim 10^{-20}$), implying that either the bare parameters must be unnaturally fine-tuned or a mechanism must automatically preserve Lorentz invariance at low energies. The authors discuss related frameworks like non-commutative field theories (NCFT) and potential remedies, emphasizing the need for theoretical mechanisms (e.g., custodial symmetries) to prohibit dangerous dimension-4 Lorentz-violating terms and urging a shift in both experimental searches and theoretical development toward preserving Lorentz invariance rather than merely constraining tiny violations.

Abstract

Trying to combine standard quantum field theories with gravity leads to a breakdown of the usual structure of space-time at around the Planck length, 1.6*10^{-35} m, with possible violations of Lorentz invariance. Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. Here, we explain that combining known elementary particle interactions with a Planck-scale preferred frame gives rise to Lorentz violation at the percent level, some 20 orders of magnitude higher than earlier estimates, unless the bare parameters of the theory are unnaturally strongly fine-tuned. Therefore an important task is not just the improvement of the precision of searches for violations of Lorentz invariance, but also the search for theoretical mechanisms for automatically preserving Lorentz invariance.

Figures (1)

• Figure 1: Lowest order self-energy graph. Interactions of quantum fields require an unrestricted integral over the momenta of the virtual particles up to the highest momenta allowed in the theory.