Distance Measurement and Wave Dispersion in a Liouville-String Approach to Quantum Gravity

Abstract

Within a Liouville approach to non-critical string theory, we discuss space-time foam effects on the propagation of low-energy particles. We find an induced frequency-dependent dispersion in the propagation of a wave packet, and observe that this would affect the outcome of measurements involving low-energy particles as probes. In particular, the maximum possible order of magnitude of the space-time foam effects would give rise to an error in the measurement of distance comparable to that independently obtained in some recent heuristic quantum-gravity analyses. We also briefly compare these error estimates with the precision of astrophysical measurements.

Testing a (Stringy) Model of Quantum Gravity

“…We note that such modifications of dispersion relations appear as a generic feature of the non-critical string theory approach to quantum gravity, where the time is identified as the Liouville mode [29].…”

“…Together with energy conservation, this requirement leads to the so-called Lindblad parametrization for the non-quantum mechanical evolution [57]. Recently, however, it has been argued [58] that such a special form of linear evolution leads to effects that are significantly more suppressed than (29), by many orders of magnitude, which casts doubt on claims [56] that complete positivity of linear maps can be tested experimentally in the foreseeable future.…”

Probes of Lorentz violation

“…As already mentioned, the idea that the space-time vacuum should be regarded as a non-trivial medium that may have observable effects on particles propagating through it [2] is a very general one, much more general than the heuristic models of space-time foam [3,4] that spawned the suggestion. Nevertheless, we focus here on the motivations provided by such models, while mentioning some other suggestions.…”

“…This possibility was raised specifically in the context of heuristic models of 'spacetime foam', as inspired from string theory [3,4] in particular, according to which quantum-gravitational fluctuations in the vacuum could modify the propagation velocities of photons by amounts that increase with energy.…”

GRBs and Fundamental Physics

“…However, many Quantum Gravity (QG) theories have suggested that quantum fluctuations in the space-time would make it appears discontinuous and chaotic, namely the foamy structure (Amelino-Camelia et al 1997). And the propagation of light through the space-time with the foamy structure would show a non-trivial dispersion relation in vacuum (Amelino-Camelia et al 1998), which could leads to the violation of Lorentz invariance.…”