Such an EFT framework for CPT violation-known as the Standard-ModelExtension (SME)-is indeed available. In particular,an EFT model can include the usual Standard Model and general relativity,so that essentially all presently feasible CPT tests can be studied. Moreover, EFT can implement CPT violation at themost fundamental level in established physics, which can guarantee internaltheoretical consistency at all levels of presently known physics. Note in partic-ular that the latter area involves discrete backgrounds and non-relativisticdynamical aspects, features that may have to be modeled also in quantum-gravity phenomenology. We proceed here at the level of EFT for the following reasons.EFT is a tremendously successful tool in various areas of physics includingelementary-particle, nuclear, and condensed-matter physics. Various levels ofCPT test models ranging from ad hoc assumptions of mass differences be-tween particle and antiparticle to effective field theory (EFT) can in principlebe considered. To test CPT invariance, it is desirable to employ a framework that allowsfor departures from this symmetry: such a framework places the identificationand analysis of suitable CPT tests on a more solid footing. In what follows, we will review the field-theory description of CPT violationat low energies and discuss its predictions for (anti)hydrogen spectroscopy aswell as antihydrogen free-fall measurements. For example, in the con-text of axiomatic field theory with conventional quantum mechanics and localinteractions, CPT violation goes hand in hand with Lorentz breaking. The discrete spacetime symmetry is CPT invariance.Note that these symmetries are closely intertwined. The ten continuous ones are four translations, three rotations, andthree Lorentz boosts. Spacetime symmetries therefore represent anexcellent area for research in this context.Spacetime symmetries fall into two classes: continuous and discrete sym-metries. Thethird desirable feature is that at least some theoretical approaches to quantumgravity should allow for departures from the established physics in questions,so as to provide motivation for research efforts along these lines.Spacetime symmetries satisfy the above three requirements: they can bestudied experimentally with ultra-high precision, they hold exactly in knownphysics, and various theoretical ideas in the field of quantum gravity can ac-commodate their breakdown. A further condition on such a re-lation or principle is that it should hold exactly in established physics, so thateven the smallest observed deviations would definitely imply new physics. It involves the identification of physical relations or physics principlestestable with present-day or near-future technology at sensitivity levels thatcan be interpreted as having Planck reach. Examples are large extra dimensions or novel particles.Another path towards quantum-gravity phenomenology is a bottom-up ap-proach. Acommon avenue to tackle this issue is to look for model predictions that are not Ralf LehnertIndiana University Center for Spacetime Symmetries, Bloomington, IN 47405, USATel.: +1-81Fax: +1-81E-mail: Ralf Lehnert primarily by the expected Planck suppression of quantum-gravity effects. While there are a number of the-oretical approaches in this context, phenomenological progress is hampered, For example, certain situations, such as the descrip-tion of the birth of our universe, are characterized by conditions that call forthe simultaneous application of both quantum theory and general relativity.For this reason, significant efforts are presently directed towards a morefundamental description of nature that contains both quantum theory andclassical general relativity as limiting cases. Although the description of the physical worldby these two theories is tremendously successful phenomenologically, the ap-parent necessity for two distinct frameworks is somewhat unsatisfactory froma theoretical perspective. Present-day established physics is well described by two different, mutuallyincompatible frameworks: quantum theory, which governs nature at the mi-croscopic level, and classical general relativity, which dominates physical phe-nomena at large distance scales.We discuss this reasoning in more detail,comment on the connection between CPT and Lorentz invariance, and reviewhow CPT breaking would affect the (anti)hydrogen spectrum. Since CPT symmetry can be measuredwith ultrahigh precision, CPT tests offer an interesting phenomenological av-enue to search for underlying physics. Various approaches to physics beyond the Standard Model can leadto small violations of CPT invariance.
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