Lorentz invariance: an additional fine-tuning problem
Abstract
Trying to combine standard quantum field theories with gravity shows that the usual structure of space and time must break down at around the Planck length, 1.6x10^{-35}m, which leads to the possibility of violations of Lorentz invariance. Calculations [1-7] of preferred-frame effects in quantum gravity have provided an important motivation for high precision searches [8-13] for small violations of Lorentz invariance. Should large efforts be expended on even higher precision searches? Here, we explain that taking account of known elementary particle interactions in the framework of these calculations implies that a Planck-scale preferred frame gives rise to measurable violations of relativity at the percent level, some twenty orders of magnitude higher than the estimates in Refs. [1-7]. This is in violent disagreement with data. Within the framework of the standard model extended to include Lorentz violating terms, this disagreement is only avoided by extreme fine-tuning of the bare parameters of the theory. Therefore the most important task in this area is not improvement of the precision of searches for violations of relativity, but the search for theoretical mechanisms for automatically preserving Lorentz invariance despite the presence of space-time structure at the Planck scale.Keywords
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