REVIEW
Lorentz invariance and quantum gravity: an additional fine-tuning problem?
General Relativity and Quantum Cosmology · Submitted 12 Mar 2004 · 30 references
Pith's verdict: A clean naturalness argument that reframes the Lorentz-violation search program; the conditional is stated up front, though the body's 'ruled out' language runs a bit hotter than the hedge.
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Referee report
The paper
The paper claims
The paper argues that a Planck-scale preferred frame generically produces percent-level Lorentz violation at low energies through ordinary particle loops, about twenty orders of magnitude above earlier estimates, unless the theory's bare参数s
The reading
What carries the argument
The argument turns on ultraviolet power counting for self-energy diagrams, illustrated by the one-loop scalar self-energy with a fermion loop. A preferred-frame cutoff function $f(|k|/Lambda)$ replaces the Lorentz-invariant cutoff; the would-be logarithmic divergence becomes a finite, cutoff-independent Lorentz-violating contribution $xi = frac{g^2}{6pi^2}[1+2int_0^infty dx, x f'(x)^2]$. The integral is order unity for smooth $f$, so the effect is controlled by $g^2$ rather than by $E/E_P$. The same counting applies to all fields, and the differing couplings prevent a universal redefinition of the metric from removing the violation.
Extended reading notes
Core claim
The central claim is that Planck-scale Lorentz violation is not automatically screened at low energies. In a theory with a preferred frame, the same power counting that controls ultraviolet divergences makes dimension-four Lorentz-violating operators natural, with order-one coefficients. Evaluating a one-loop self-energy with a smooth preferred-frame cutoff gives a Lorentz-violating coefficient $xi$ of order $g^2$, independent of the cutoff scale $Lambda$; this modifies the speed of light in the dispersion relation by a factor $1+xi/4+O(xi^2)$. Because different Standard Model fields have different couplings, no single metric rescaling can absorb the effect, and the resulting fractional differences in $c$ are around $0.1%$ to $10%$, in conflict with bounds below $10^{-20}$.
Load-bearing premise
The load-bearing premise is that a Planck-scale preferred frame generates dimension-four Lorentz-violating operators with order-one coefficients, with no symmetry or dynamical mechanism suppressing them.
Editorial extensions
If this is right
- Planck-scale preferred-frame scenarios of the kind considered in string theory and loop quantum gravity are ruled out unless a new symmetry or dynamical mechanism protects Lorentz invariance at low energies.
- Searches motivated by tiny $E/E_P$-suppressed Lorentz violation lose their main target, because existing bounds on species-dependent $c$ already probe the natural percent-level effect.
- Lorentz invariance joins the cosmological constant, the Higgs bare mass, and mass hierarchies on the list of fine-tuning problems in fundamental physics.
- Any proposal with modified dispersion relations must show that low-energy Lorentz invariance survives loop corrections involving known particle interactions.
- Noncommutative field theories face an even stronger version of the constraint, since their loop corrections violate Lorentz invariance and require a cutoff far below the noncommutativity scale.
Reading between the lines
- The argument is a naturalness argument, not a no-go theorem: an ultraviolet completion could make all dimension-four Lorentz-violating coefficients naturally zero or tiny through a custodial symmetry or a Lorentz-invariant regulator, which would evade the percent-level estimate.
- If the reasoning is right, the interesting experimental target shifts from tiny energy-dependent dispersion to species-dependent constants and dimension-four coefficients, where null results at the $10^{-20}$ level already constrain the natural parameter space.
- The same loop-matching logic could apply to any high-scale background field that breaks a spacetime symmetry, making it a template for testing whether Planck-scale discreteness can be phenomenologically invisible.
- The paper's call for automatic Lorentz invariance plays a role analogous to custodial symmetry in electroweak physics: finding such a structure for spacetime may be a structural requirement on quantum gravity rather than an optional refinement.
Original 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.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.06 | 0.03 | hedged possibility 0.58 |
| s1 | Calculations of preferred-frame effects in quantum gravity have further motivated high precision searches for Lorentz violation. | background 1.00 | 0.07 | 0.03 | asserted 0.90 |
| s2 | 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. | result 0.96 | 0.84 | 0.81 | asserted 0.99 |
| s3 | 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. | future work 0.95 | 0.10 | 0.73 | asserted 0.96 |
What was examined, and what was not
- arXiv listing abstract v4
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Figures
Figures reproduced from arXiv:gr-qc/0403053 by the authors.
References
How the literature uses it
72 arXiv papers cite this in 98 sentences
Papers citing it · 75 sentences without a confident label
Builds on it 1 paper
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[ref] , making explicit various steps as well as considering the percolation of LIV on the fermion field.
Lorentz violation naturalness revisited · Summary and discussion · 1.00
Compares with it 1 paper
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[ref] of unsuppressed LIV percolation.
Lorentz violation naturalness revisited · Smooth LI cutoff · 0.90
Cites it as support 9 papers
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On the other hand the result in [ref] together with constraints from the validity of Lorentz symmetry strongly suggest that any kind of Planckian granularity must be of a relational nature, i.e. only apparent when the spacetime geometry is curved and is probed with the suitable degrees of freedom, and thus its phenomenological manifestation is severely restricetd ( see for instance [ref] ).
Black holes, Planckian granularity, and the changing cosmological `constant' · The present tension and our approach · 0.99
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In fact, it is generic that, even starting with an EFT with only mass dimension 5 or 6 LV operators for free particles, radiative corrections due to particle interactions will generate lower dimension LV terms without introducing any further suppression [ref] .
GZK photon constraints on Planck scale Lorentz violation in QED · Introduction · 0.99
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This argument has been made, e.g., in [ref] .
Lorentz invariance violations in the interplay of quantum gravity with matter · Introduction · 0.99
Cites it as background 7 papers
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(For a detailed review about IR effects of Lorentz invariance violation introduced at extremely large energy scales and, in particular, with reference to quantum gravity models, see [ref] ).
Ultraviolet properties of Lifshitz-type scalar field theories · Lifshitz scaling · 0.96
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These models were often embedded within more fundamental theories, such as String Theory and Quantum Gravity [ref] , from which the violation of Lorentz symmetry at low energies emerged as an effective feature.
Very Special Relativity in Accelerated Frames: Non-relativistic Effects in Gravitational Spectroscopy of Ultracold Neutrons · Introduction · 0.98
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Therefore, various applications have been considered so far to theories that are otherwise non-renormalizable, such as the case of the field theoretical formulation of gravity [ref] .
Higher-derivative four-dimensional sine-Gordon model · introduction · 0.85
Discussion
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