Stefano Liberati

TeV astrophysics constraints on Planck scale Lorentz violation

Cerenkov radiation, photon decay and photo-production of electron-positron pairs. We show that the parameter plane for cubic momentum terms in the dispersion relations is constrained to an order unity region in Planck units. We find that the threshold configuration can occur with an asymmetric distribution of momentum for pair creation, and with a hard photon for vacuum y Cerenkov radiation. There are several reasons to suspect that Lorentz in- variance may be only a low energy symmetry. This possi- bility is suggested by the ultraviolet divergences of local quantum field theory, as well as by tentative results in various approaches to quantum gravity and string the- ory (1, 2, 3, 4, 5). Moreover, Lorentz symmetry can only ever be verified up to some finite observationally accessi- ble velocity, which leaves untested an infinite volume of the supposed symmetry group. The possibility of Lorentz violation can be studied, without a particular fundamental theory in hand, by con- sidering its manifestation in dispersion relations for par- ticles. If rotational invariance is preserved, it is natural to assume that deviations from the Lorentz invariant dis- persion relation E 2 (p) = m 2 + p 2 can be characterized at low energies by an expansion with integral powers of momentum, E 2 = m 2 + p 2 + P ∞=1 anp n , where the an are coefficients with mass dimension 2− n which might be positive or negative. (Throughout this letter p de- notes the absolute value of the 3-momentum vector p, and we use units with the low energy speed of light in vacuum equal to unity.) Different approaches to quantum gravity suggest different leading order Lorentz violating terms. The terms with n ≤ 4 have mostly been consid- ered so far. Observations limit the coefficientsa1,2 to be extremely small (see e.g. (6, 7, 8) and references therein). In this letter we shall assume they are precisely zero. The cubic and higher order coefficients have negative mass dimension, so if the Lorentz violation descends from the Planck scale MP = (¯ hc 5 /G) 1/2 ≃ 1.22 � 10 19 GeV, an would be expected to be of order M 2−n P. In this case the Lorentz violation is naturally suppressed, and the lowest order term would dominate all the higher ones as long as the momentum is less than MP, hence we shall restrict to a single Lorentz violating term. We thus consider the constraints that high energy observations impose on dispersion relations of the form E 2

A strong astrophysical constraint on the violation of special relativity by quantum gravity

The structure of spacetime at the Planck scale may lead to a breakdown of Lorentz invariance at high energies in the form of non-linear dispersion relations for fundamental particles. We show that observations of synchrotron emission from the Crab nebula constrain the energy scale EQG of subluminal Lorentz violation in the electron dispersion relation at order O(E/EQG) to EQG > 4.5×10 27 GeV. This is eight orders of magnitude larger than the Planck mass, and is an improvement of nine orders of magnitude over the best previous bounds. jacobson@physics.umd.edu liberati@physics.umd.edu davemm@physics.umd.eduSpecial relativity asserts that physical phenomena appear the same to all unaccelerated observers. This is called Lorentz symmetry and relates long wavelengths to short ones: if the symmetry is exact it implies that space-time must look the same at all length scales. Several approaches to quantum gravity, however, suggest that there may be a microscopic structure of space-time that leads to a violation of Lorentz symmetry. This might arise because of the discreteness or non-commutivity of space-time, or through the action of extra dimensions. Here we determine a very strong constraint on a type of Lorentz violation that produces a maximum electron speed less than the speed of light. We use the observation of 100-MeV synchrotron radiation from the Crab nebula to improve the previous limit by a factor of 40 million, ruling out this type of Lorentz violation, and thereby providing an important constraint on theories of quantum gravity.

Threshold effects and Planck scale Lorentz violation: Combined constraints from high-energy astrophysics

Recent work has shown that dispersion relations with Planck scale Lorentz violation can produce observable effects at energies many orders of magnitude below the Planck energy M. This opens a window on physics that may reveal quantum gravity phenomena. It has already constrained the possibility of Planck scale Lorentz violation, which is suggested by some approaches to quantum gravity. In this work we carry out a systematic analysis of reaction thresholds, allowing unequal deformation parameters for different particle dispersion relations. The thresholds are found to have some unusual properties compared with standard ones, such as asymmetric momenta for pair creation and upper thresholds. The results are used together with high energy observational data to determine combined constraints. We focus on the case of photons and electrons, using vacuum Cerenkov, photon decay, and photon annihilation processes to determine order unity constraints on the parameters controlling O(E/M) Lorentz violation. Interesting constraints for protons (with photons or pions) are obtained even at O((E/M)^2), using the absence of vacuum Cerenkov and the observed GZK cutoff for ultra high energy cosmic rays. A strong Cerenkov limit using atmospheric PeV neutrinos is possible for O(E/M) deformations provided the rate is high enough. If detected, ultra high energy cosmological neutrinos might yield limits at or even beyond O((E/M)^2).

Analogue gravity from Bose-Einstein condensates

We analyse prospects for the use of Bose–Einstein condensates as condensedmatter systems suitable for generating a generic ‘effective metric’, and for mimicking kinematic aspects of general relativity. We extend the analysis due to Garay et al (2000 Phys. Rev. Lett. 85 4643, 2001 Phys. Rev. A 63 023611). Taking a long-term view, we ask what the ultimate limits of such a system might be. To this end, we consider a very general version of the nonlinear Schr¨ odinger equation (with a 3-tensor position-dependent mass and arbitrary nonlinearity). Such equations can be used, for example, in discussing Bose–Einstein condensates in heterogeneous and highly nonlinear systems. We demonstrate that at low momenta linearized excitations of the phase of the condensate wavefunction obey a ( 3+1 )-dimensional d’Alembertian equation coupling to a ( 3+1 )-dimensional Lorentzian-signature ‘effective metric’ that is generic, and depends algebraically on the background field. Thus at low momenta this system serves as an analogue for the curved spacetime of general relativity. In contrast, at high momenta we demonstrate how one can use the eikonal approximation to extract a well controlled Bogoliubovlike dispersion relation, and (perhaps unexpectedly) recover non-relativistic Newtonian physics at high momenta. Bose–Einstein condensates appear to be an extremely promising analogue system for probing kinematic aspects of general relativity.

New Limits on Planck Scale Lorentz Violation in QED

Constraints on possible Lorentz symmetry violation (LV) of order E/M(Planck) for electrons and photons in the framework of effective field theory (EFT) are discussed. Using (i) the report of polarized MeV emission from GRB021206 and (ii) the absence of vacuum Cerenkov radiation from synchrotron electrons in the Crab Nebula, we improve previous bounds by 10(-10) and 10(-2), respectively. We also show that the LV parameters for positrons and electrons are different, discuss electron helicity decay, and investigate how prior constraints are modified by the relations between LV parameters implied by EFT.

Faster-than-c Signals, Special Relativity, and Causality

Motivated by the recent attention on superluminal phenomena, we investigate the compatibility between faster-than-c propagation and the fundamental principles of relativity and causality. We first argue that special relativity can easily accommodate—indeed, does not exclude—faster-than-c signaling at the kinematical level. As far as causality is concerned, it is impossible to make statements of general validity, without specifying at least some features of the tachyonic propagation. We thus focus on the Scharnhorst effect (faster-than-c photon propagation in the Casimir vacuum), which is perhaps the most plausible candidate for a physically sound realization of these phenomena. We demonstrate that in this case the faster-than-c aspects are “benign” and constrained in such a manner as to not automatically lead to causality violations.

Analogue gravity from field theory normal modes

We demonstrate that the emergence of a curved spacetime `effective Lorentzian geometry is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of `analogue models of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (that is, a field-theoretic `normal-mode analysis) results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime `effective metric. In the simple situation considered in this paper (a single classical scalar field), this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Upon quantizing the linearized fluctuations around this background geometry, the one-loop effective action is guaranteed to contain a term proportional to the Einstein-Hilbert action of general relativity, suggesting that while classical physics is responsible for generating an `effective geometry, quantum physics can be argued to induce an `effective dynamics. The situation is strongly reminiscent of, though not identical to, Sakharovs `induced-gravity scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cut-off implicit in molecular dynamics.)

Probing semiclassical analog gravity in Bose-Einstein condensates with widely tunable interactions

Bose-Einstein condensates BEC’s have recently been the subject of considerable study as possible analog models of general relativity. In particular it was shown that the propagation of phase perturbations in a BEC can, under certain conditions, closely mimic the dynamics of scalar quantum fields in curved space times. In two previous papers Int. J. Mod. Phys. A 18, 3735 2003; Int. J. Mod. Phys. D to be published, e-print gr-qc/0305061 we noted that a varying scattering length in the BEC corresponds to a varying speed of light in the ‘‘effective metric.’’ Recent experiments have indeed achieved a controlled tuning of the scattering length in 85 Rb. In this paper we shall discuss the prospects for the use of this particular experimental effect to test some of the predictions of semiclassical quantum gravity, for instance, particle production in an expanding universe. We stress that these effects are generally much larger than the Hawking radiation expected from causal horizons, and so there are much better chances for their detection in the near future.

Analogue Models of and for Gravity

Condensed matter systems, such as acoustics in flowing fluids, light in moving dielectrics, or quasiparticles in a moving superfluid, can be used to mimic aspects of general relativity. More precisely these systems (and others) provide experimentally accessible models of curved-space quantum field theory. As such they mimic kinematic aspects of general relativity, though typically they do not mimic the dynamics. Although these analogue models are thereby limited in their ability to duplicate all the effects of Einstein gravity they nevertheless are extremely important—they provide black hole analogues (some of which have already been seen experimentally) and lead to tests of basic principles of curved-space quantum field theory. Currently these tests are still in the realm of gedanken-experiments, but there are plausible candidate models that should lead to laboratory experiments in the not too distant future.

Towards the Observation of Hawking Radiation in Bose–Einstein Condensates

Acoustic analogues of black holes (dumb holes) are generated when a supersonic fluid flow entrains sound waves and forms a trapped region from which sound cannot escape. The surface of no return, the acoustic horizon, is qualitatively very similar to the event horizon of a general relativity black hole. In particular Hawking radiation (a thermal bath of phonons with temperature proportional to the surface gravity) is expected to occur. In this note we consider quasi-one-dimensional supersonic flow of a Bose–Einstein condensate (BEC) in a Laval nozzle (converging-diverging nozzle), with a view to finding which experimental settings could magnify this effect and provide an observable signal. We discuss constraints and problems for our model and identify the issues that should be addressed in the near future in order to set up an experiment. In particular we identify an experimentally plausible configuration with a Hawking temperature of order 70 n K; to be contrasted with a condensation temperature of the order of 90 n K.