"Quantum-Spacetime Phenomenology"
Giovanni Amelino-Camelia 
1 Introduction and Preliminaries
1.1 The “Quantum-Gravity problem” as seen by a phenomenologist
1.2 Quantum spacetime vs quantum black hole and graviton exchange
1.3 20th century quantum-gravity phenomenology
1.4 Genuine Planck-scale sensitivity and the dawn of quantum-spacetime phenomenology
1.5 A simple example of genuine Planck-scale sensitivity
1.6 Focusing on a neighborhood of the Planck scale
1.7 Characteristics of the experiments
1.8 Paradigm change and test theories of not everything
1.9 Sensitivities rather than limits
1.10 Other limitations on the scope of this review
1.11 Schematic outline of this review
2 Quantum-Gravity Theories, Quantum Spacetime, and Candidate Effects
2.1 Quantum-Gravity Theories and Quantum Spacetime
2.2 Candidate effects
3 Quantum-Spacetime Phenomenology of UV Corrections to Lorentz Symmetry
3.1 Some relevant concepts
3.2 Preliminaries on test theories with modified dispersion relation
3.3 Photon stability
3.4 Pair-production threshold anomalies and gamma-ray observations
3.5 Photopion production threshold anomalies and the cosmic-ray spectrum
3.6 Pion non-decay threshold and cosmic-ray showers
3.7 Vacuum Cerenkov and other anomalous processes
3.8 In-vacuo dispersion for photons
3.9 Quadratic anomalous in-vacuo dispersion for neutrinos
3.10 Implications for neutrino oscillations
3.11 Synchrotron radiation and the Crab Nebula
3.12 Birefringence and observations of polarized radio galaxies
3.13 Testing modified dispersion relations in the lab
3.14 On test theories without energy-dependent modifications of dispersion relations
4 Other Areas of UV Quantum-Spacetime Phenomenology
4.1 Preliminary remarks on fuzziness
4.2 Spacetime foam, distance fuzziness and interferometric noise
4.3 Fuzziness for waves propagating over cosmological distances
4.4 Planck-scale modifications of CPT symmetry and neutral-meson studies
4.5 Decoherence studies with kaons and atoms
4.6 Decoherence and neutrino oscillations
4.7 Planck-scale violations of the Pauli Exclusion Principle
4.8 Phenomenology inspired by causal sets
4.9 Tests of the equivalence principle
5 Infrared Quantum-Spacetime Phenomenology
5.1 IR quantum-spacetime effects and UV/IR mixing
5.2 A simple model with soft UV/IR mixing and precision Lamb-shift measurements
5.3 Soft UV/IR mixing and atom-recoil experiments
5.4 Opportunities for Bose–Einstein condensates
5.5 Soft UV/IR mixing and the end point of tritium beta decay
5.6 Non-Keplerian rotation curves from quantum-gravity effects
5.7 An aside on gravitational quantum wells
6 Quantum-Spacetime Cosmology
6.1 Probing the trans-Planckian problem with modified dispersion relations
6.2 Randomly-fluctuating metrics and the cosmic microwave background
6.3 Loop quantum cosmology
6.4 Cosmology with running spectral dimensions
6.5 Some other quantum-gravity-cosmology proposals
7 Quantum-Spacetime Phenomenology Beyond the Standard Setup
7.1 A totally different setup with large extra dimensions
7.2 The example of hard UV/IR mixing
7.3 The possible challenge of not-so-subleading higher-order terms
8 Closing Remarks

8 Closing Remarks

Clearly, the most significant development of these first few years of quantum-spacetime phenomenology has been our ability to uncover some experimental/observational contexts in which, through appropriate data analyses, we could gain access to effects introduced genuinely at the Planck scale. The compellingness of such instances of genuine Planck-scale sensitivity, which are most simply and clearly illustrated in Section 1.5, should be contrasted to the more frequent case of “dimensional-analysis Planck-scale sensitivities”, which typically involve a description of a plausible quantum-spacetime effect in terms of a dimensionless parameter, estimated arbitrarily as a ratio of the Planck length and some characteristic length scale of the problem.

Looking at the results summarized in this review, different readers, depending on how stringent their criteria for genuine Planck-scale sensitivity, will only recognize one or two examples. Not much, but much better than expected even just 15 years ago. And, as stressed, we do have, at this point, a rather encouraging list of contexts in which, while the availability of genuine Planck-scale sensitivity has still not been fully established, it appears that sensitivity to effects introduced genuinely at the Planck scale could be achieved in a not-so-distant future.

The fact that the development of this phenomenology is proving beneficial for the study of the idea of spacetime quantization is perhaps best testified by the fact that it is already managing to truly affect the directions taken by more formal work on spacetime quantization, especially in the areas of LQG and spacetime noncommutativity. Theorists in these areas follow the developments on the phenomenology side and do their best (the technical challenges they are facing are very severe) to derive results that can be exploited for the opportunities in phenomenology that are being established. In turn the phenomenology takes notice of the developments on the theory side, finding in them new input for enlarging the list of candidate quantum-spacetime effects that one could attempt to investigate experimentally.

The goal of testing/falsifying rigorous theories of spacetime quantization appears to still be beyond our present reach. But while most of the work in quantum-spacetime phenomenology so far has relied on simple-minded test theories describing candidate quantum-spacetime effects, I see first indications of a phase of further maturation of this phenomenology, in which we will actually test/falsify at least the most virulent rigorous formalizations of quantum spacetime. Planck-scale theories formulated in noncommutative versions of Minkowski spacetime are the example where we are presently closer to this goal.

The (however limited) information presently available to us appears to provide a clear invitation to continue to focus most of our efforts in the search for effects describable in terms of a (low-energy) expansion in powers of the Planck length, though other opportunities clearly should not be overlooked. Concerning the type of data on which quantum-spacetime phenomenology can rely, I have attempted to maintain throughout this review some visible separations between different proposals on the basis of whether they concern astrophysics, cosmology or controlled laboratory experiments. It is very clear that astrophysics has so far provided the most fruitful arena, but cosmology has the greatest potential reach (although for the most part this potential has not yet materialized). The role played so far in quantum-spacetime phenomenology by controlled laboratory experiments is rather marginal, but it would be important for the future development of quantum-spacetime phenomenology to find more opportunities for controlled laboratory experiments.

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