Spacetime Foam Research Articles

Is a tabletop search for Planck scale signals feasible?

Quantum gravity theory is untested experimentally. Could it be tested with tabletop experiments? While the common feeling is pessimistic, a detailed inquiry shows it possible to sidestep the onerous requirement of localization of a probe on Planck length scale. I suggest a tabletop experiment which, given state of the art ultrahigh vacuum and cryogenic technology, could already be sensitive enough to detect Planck scale signals. The experiment combines a single photon's degree of freedom with one of a macroscopic probe to test Wheeler's conception of "quantum foam", the assertion that on length scales of the order Planck's, spacetime is no longer a smooth manifold. The scheme makes few assumptions beyond energy and momentum conservations, and is not based on a specific quantum gravity scheme.

Disordered locality and Lorentz dispersion relations: An explicit model of quantum foam

Using the framework of Quantum Graphity, we construct an explicit model of a quantum foam, a quantum spacetime with spatial non-local links. The states depend on two parameters: the minimal size of the link and their density with respect to this length. Macroscopic Lorentz invariance requires that the quantum superposition of spacetimes is suppressed by the length of these non-local links. We parametrize this suppression by the distribution of non-local links lengths in the quantum foam. We discuss the general case and then analyze two specific natural distributions. Corrections to the Lorentz dispersion relations are calculated using techniques developed in previous work.

Bounds on Spectral Dispersion from Fermi-Detected Gamma Ray Bursts

Data from four Fermi-detected gamma-ray bursts (GRBs) are used to set limits on spectral dispersion of electromagnetic radiation across the Universe. The analysis focuses on photons recorded above 1 GeV for Fermi-detected GRB 080916C, GRB 090510A, GRB 090902B, and GRB 090926A because these high-energy photons yield the tightest bounds on light dispersion. It is shown that significant photon bunches in GRB 090510A, possibly classic GRB pulses, are remarkably brief, an order of magnitude shorter in duration than any previously claimed temporal feature in this energy range. Although conceivably a>3σ fluctuation, when taken at face value, these pulses lead to an order of magnitude tightening of prior limits on photon dispersion. Bound of Δc/c<6.94×10(-21) is thus obtained. Given generic dispersion relations where the time delay is proportional to the photon energy to the first or second power, the most stringent limits on the dispersion strengths were k1<1.61×10(-5) sec Gpc(-1) GeV(-1) and k2<3.57×10(-7) sec Gpc(-1) GeV(-2), respectively. Such limits constrain dispersive effects created, for example, by the spacetime foam of quantum gravity. In the context of quantum gravity, our bounds set M1c(2) greater than 525 times the Planck mass, suggesting that spacetime is smooth at energies near and slightly above the Planck mass.

Implications of a stochastic microscopic Finsler cosmology

Within the context of supersymmetric space-time (D-particle) foam in string/brane-theory, we discuss a Finsler-induced cosmology and its implications for (thermal) dark matter abundances. This constitutes a truly microscopic model of dynamical space-time, where Finsler geometries arise naturally. The D-particle foam model involves point-like brane defects (D-particles), which provide the topologically non-trivial foamy structures of space-time. The D-particles can capture and emit stringy matter and this leads to a recoil of D-particles. It is indicated how one effect of such a recoil of D-particles is a back-reaction on the space-time metric of Finsler type which is stochastic. We show that such a type of stochastic space-time foam can lead to acceptable cosmologies at late epochs of the Universe, due to the non-trivial properties of the supersymmetric (BPS like) D-particle defects, which are such so as not to affect significantly the Hubble expansion. The restrictions placed on the free parameters of the Finsler type metric are obtained from solving the Boltzmann equation in this background for relic abundances of a Lightest Supersymmetric Particle (LSP) dark matter candidate. It is demonstrated that the D-foam acts as a source for particle production in the Boltzmann equation, thereby leading to enhanced thermal LSP relic abundances relative to those in the Standard ΛCDM cosmology. For D-particle masses of order TeV, such effects may be relevant for dark matter searches at colliders. The latter constraints complement those coming from high-energy gamma-ray astronomy on the induced vacuum refractive index that D-foam models entail. We also comment briefly on the production mechanisms of such TeV-mass stringy defects at colliders, which, in view of the current LHC experimental searches, will impose further constraints on their couplings.

Anisotropic structures and wormholes with loop quantum gravity holonomy corrections

Anisotropic spherically symmetric systems are studied in the connection and densitized triad variables used in loop quantum gravity. The material source is an anisotropic fluid, which is arguably the most commonly used source term in anisotropic studies within general relativity. The gravitational+anisotropic fluid constraints are derived and analyzed and then quantum gravity inspired holonomy replacements are performed. The quantum properties of the fluid are dictated by the modified constraint equations. Particular attention is paid to wormhole throats, as they provide a simplistic model of the structures thought to be ubiquitous in the quantum gravity space-time foam at high energy scales. In comparison to the purely classical theory, the quantum corrections act to increase the energy density of the fluid, which indicates that they may lessen the energy condition violation present in the classical theory. Related to this, in principle it would be possible to have scenarios where the classical solution yields everywhere negative (with a zero at the throat) fluid energy density but the corresponding quantum corrected theory possesses only small regions of negative energy density or even everywhere non-negative energy density.

Using observations of distant quasars to constrain quantum gravity

Aims. The small-scale nature of spacetime can be tested with observations of distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533, 71) which claims that Hubble Space Telescope observations of the most distant quasars place severe constraints on models of foamy spacetime. Methods. If space is foamy on the Planck scale, photons emitted from distant objects will accumulate uncertainties in distance and propagation directions thus affecting the expected angular size of a compact object as a function of redshift. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We also address the mechanics of carrying out such a test. We draw upon our previously published work on this subject (Christiansen et al. 2011), which carried out similar tests as Tamburini et al. and also went considerably beyond their work in several respects. Results. When calculating the path taken by photons as they travel from a distant source to Earth, one must use the comoving distance rather than the luminosity distance. This then also becomes the appropriate distance to use when calculating the angular broadening expected in a distant source. The use of the wrong distance measure causes Tamburini et al. to overstate the constraints that can be placed on models of spacetime foam. In addition, we consider the impact of different ways of parametrizing and measuring the effects of spacetime foam. Given the variation of the shape of the point-spread function (PSF) on the chip, as well as observation-specific factors, it is important to select carefully -- and document -- the comparison stars used as well as the methods used to compute the Strehl ratio.

Quantum Gravity phenomenology: achievements and challenges

Motivated by scenarios of quantum gravity, Planck-suppressed deviations from Lorentz invariance are expected at observable energies. Ultra-High-Energy Cosmic Rays, the most energetic particles ever observed in nature, yielded in the last two years strong constraints on deviations suppressed by O(E2/M2Pl) and also, for the first time, on space-time foam, stringy inspired models of quantum gravity. We review the most important achievements and discuss future outlooks.

No quantum gravity signature from the farthest quasars

Context: Strings and other alternative theories describing the quantum properties of space-time suggest that space-time could present a foamy structure and also that, in certain cases, quantum gravity (QG) may manifest at energies much below the Planck scale. One of the observable effects could be the degradation of the diffraction images of distant sources. Aims: We searched for this degradation effect, caused by QG fluctuations, in the light of the farthest quasars (QSOs) observed by the Hubble Space Telescope with the aim of setting new limits on the fluctuations of the space-time foam and QG models. Methods: We developed a software that estimates and compares the phase variation in the interference patterns of the high-redshift QSOs, taken from the snapshot survey of HST-SDSS, with those of stars that are expected to not be affected by QG effects. We used a two-parameter function to determine, for each test star and QSO, the maximum of the diffraction pattern and to calculate the Strehl ratio. Results: Our results go far beyond those already present in the literature. By adopting the most conservative approach where the correction terms, that describe the possibility for space-time fluctuations cumulating across long distances and partially compensate for the effects of the phase variations, are taken into account. We exclude the random walk model and most of the holographic models of the space-time foam. Without considering these correction terms, all the main QG scenarios are excluded. Finally, our results show the absence of any directional dependence of QG effects and the validity of the cosmological principle with an independent method; that is, viewed on a large scale, the properties of the Universe are the same for all observers, including the effects of space-time fluctuations.

D-foam-induced flavor condensates and breaking of supersymmetry in free Wess-Zumino fluids

Recently we argued that a particular model of string-inspired quantum space-time foam (D-foam) may induce oscillations and mixing among flavoured particles. As a result, rather than the mass-eigenstate vacuum, the correct ground state to describe the underlying dynamics is the flavour vacuum, proposed some time ago by Blasone and Vitiello as a description of quantum field theories with mixing. At the microscopic level, the breaking of target-space supersymmetry is induced in our space-time foam model by the relative transverse motion of brane defects. Motivated by these results, we show that the flavour vacuum, introduced through an inequivalent representation of the canonical (anti-) commutation relations, provides a vehicle for the breaking of supersymmetry (SUSY) at a low-energy effective field theory level; on considering the flavour-vacuum expectation value of the energy-momentum tensor and comparing with the form of a perfect relativistic fluid, it is found that the bosonic sector contributes as dark energy while the fermion contribution is like dust. This indicates a strong and novel breaking of SUSY, of a non-perturbative nature, which may characterize the low energy field theory of certain quantum gravity models.

D-FOAM PHENOMENOLOGY: DARK ENERGY, THE VELOCITY OF LIGHT AND A POSSIBLE D-VOID

In a D-brane model of cosmology and space–time foam, there are contributions to the dark energy that depend on the D-brane 10-velocities and on the density of D-particle defects in the ten-dimensional bulk. The latter may also reduce the speeds of energetic photons, establishing a phenomenological connection with astrophysical probes of the universality of the velocity of light. Specifically, the cosmological dark energy density measured at the present epoch may be linked to the apparent retardation of energetic photons propagating from nearby AGN's. However, this nascent field of "D-foam phenomenology" may be complicated by variations in the D-particle density encountered at different cosmological epochs. A reduced density of D-particles encountered at redshifts z ~ 1 — a "D-void" — would increase the dark energy while suppressing the vacuum refractive index, and thereby might reconcile the AGN measurements with the relatively small retardation seen for the energetic photons propagating from GRB 090510, as measured by the Fermi satellite.

Limits on spacetime foam

Plausibly spacetime is "foamy" on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and AGNs. This is a null test in the sense that the continued presence of unresolved "point" sources at the milli-arc second level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as GRBs have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble Ultra-Deep Field (UDF) provide the most stringent test of spacetime foam theories. While random walk models ($\alpha = 1/2$) have already been ruled out, the holographic ($\alpha=2/3$) model remains viable. Here $\alpha \sim 1$ parametrizes the different spacetime foam models according to which the fluctuation of a distance $l$ is given by $\sim l^{1 - \alpha} l_P^{\alpha}$ with $l_P$ being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the UDF images selected for this study. Using existing data in the {\it Hubble Space Telescope (HST)} archive we find it is impossible to rule out the $\alpha=2/3$ model, but exclude all models with $\alpha<0.65$. By comparison, current GRB time lag observations only exclude models with $\alpha<0.3$.

Stringy Space-Time Foam and High-Energy Cosmic Photons

In this review, I discuss briefly stringent tests of Lorentz-violating quantum space-time foam models inspired from String/Brane theories, provided by studies of high energy Photons from intense celestial sources, such as Active Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict modifications to the radiation dispersion relations, which are quadratically suppressed by the string mass scale, and time delays in the arrival times of photons (assumed to be emitted more or less simultaneously from the source), which are proportional to the photon energy, so that the more energetic photons arrive later. Although the astrophysics at the source of these energetic photons is still not understood, and such non simultaneous arrivals, that have been observed recently, might well be due to non simultaneous emission as a result of conventional physics effects, nevertheless, rather surprisingly, the observed time delays can also fit excellently the stringy space-time foam scenarios, provided the space-time defect foam is inhomogeneous. The key features of the model, that allow it to evade a plethora of astrophysical constraints on Lorentz violation, in sharp contrast to other field-theoretic Lorentz-violating models of quantum gravity, are: (i) transparency of the foam to electrons and in general charged matter, (ii) absence of birefringence effects and (iii) a breakdown of the local effective lagrangian formalism.

Quantum-gravity induced Lorentz violation and dynamical mass generation

In Ref. [1] (by J. Alexandre) a minimal extension of (3+1)-dimensional Quantum Electrodynamics has been proposed, which includes Lorentz-Violation (LV) in the form of higher-(spatial)-derivative isotropic terms in the gauge sector, suppressed by a mass scale $M$. The model can lead to dynamical mass generation for charged fermions. In this article I elaborate further on this idea and I attempt to connect it to specific quantum-gravity models, inspired from string/brane theory. Specifically, in the first part of the article, I comment briefly on the gauge dependence of the dynamical mass generation in the approximations of [1], and I propose a possible avenue for obtaining the true gauge-parameter-independent value of the mass by means of Pinch Technique argumentations. In the second part of the work I embed the LV QED model into multibrane world scenarios with a view to provide a geometrical way of enhancing the dynamical mass to phenomenologically realistic values by means of bulk warp metric factors, in an (inverse) Randall-Sundrum hierarchy. Finally in the third part of this note, I demonstrate that such Lorentz Violating QED models may represent parts of a low-energy effective action (of Finsler-Born-Infeld type) of open strings propagating in quantum D0-particle stochastic space-time foam backgrounds, which are viewed as consistent quantum gravity configurations.

Limits on spacetime foam

Limits on spacetime foam

Stringy space–time foam, Finsler-like metrics and dark matter relics

We discuss modifications of the thermal dark matter (DM) relic abundances in stringy cosmologies with D-particle space–time foamy backgrounds. As a result of back-reaction of massive DM on the background space–time, owing to its interaction with D-particle defects in the foam, quantum fluctuations are induced in the space–time metric. We demonstrate that these lead to the presence of extra source terms in the Boltzmann equation used to determine the thermal dark matter relic abundances. The source terms are determined by the specific form of the induced metric deformations; the latter depend on the momentum transfer of the DM particle during its interactions with the D-particle defects and so are akin to Finsler metrics. In the case of low string scales, arising from large extra dimensions, our results may have phenomenological implications for the search of viable supersymmetric models.

STRING QUANTUM GRAVITY, LORENTZ-INVARIANCE VIOLATION AND GAMMA RAY ASTRONOMY

In the first part of the review, I discuss ways of obtaining Lorentz-Invariance Violating (LIV) space–time foam in the modern context of string theory, involving brane world scenarios. The foamy structures are provided by lower-dimensional background brane defects in a D3-brane universe, whose density is a free parameter to be constrained phenomenologically. Such constraining can be provided by high energy gamma ray photon tests, including ultra-high energy/infrared photon–photon scattering. In the second part, I analyze the currently available data from MAGIC and FERMI telescopes on delayed cosmic photon arrivals in this context. It is understood of course that conventional astrophysics source effects, which currently are far from being understood, might be the dominant reason for the observed delayed arrivals. I also discuss how the stringent constraints from studies of synchrotron-radiation from distant Nebulae, absence of cosmic birefringence and nonobservation of ultra-high energy cosmic photons can be accommodated within the aforementioned stringy space–time foam model. I argue that, at least within the currently available sets of astrophysical data, the stringy foam model can avoid all theses constraints in a natural range of the string coupling and mass scale. The key features are: (i) transparency of the foam to electrons and charged probes in general, (ii) absence of birefringence effects and (iii) a breakdown of the local effective Lagrangian formalism. However, in order to accommodate, in this theoretical framework, the data of the FERMI satellite on the delayed arrival of photons from the short intense Gamma Ray Burst GRB 090510, in a way consistent with the findings of the MAGIC telescope, a nonuniform density of brane foam defects must be invoked.

SPIN-SURFING THE SPACE–TIME FOAM

We present the quantum spin as a novel test tool for probing directly the Planck scale space–time foam of quantum gravity. Quantum fluctuations of spatial support for the electric vector associated with the spin-one photon affect its polarization sufficiently to allow us to gain deep insights and unprecedented constraints on the most important and fundamental aspect of quantum gravity — the fluctuating structure of space–time with a Planck scale three-dimensional web. We show that the survival of strong polarization of X-rays and gamma rays from the Crab Nebula rejects the conventional space–time foam at Planck length scale and constrains the microscopic scale of quantum gravitational fluctuations to below 2 × 10-8l P .

QUANTUM GRAVITY AND TURBULENCE

We apply recent advances in quantum gravity to the problem of turbulence. Adopting the AdS/CFT approach we propose a string theory of turbulence that explains the Kolmogorov scaling in 3 + 1 dimensions and the Kraichnan and Kolmogorov scalings in 2 + 1 dimensions. In the gravitational context, turbulence is intimately related to the properties of space–time or quantum foam.

A NOTE ON THE ANALOGY BETWEEN KOLMOGOROV TURBULENCE AND QUANTUM GRAVITY

Based on a formal analogy between space-time quantum fluctuations and classical Kolmogorov fluid turbulence, we suggest that the dynamic growth of the Universe from Planckian to macroscopic scales should be characterized by the presence of a fluctuating volume-flux (FVF) invariant. The existence of such an invariant could be tested in numerical simulations of quantum gravity, and may also stimulate the development of a new class of hierarchical models of quantum foam, similar to those currently employed in modern phenomenological research on fluid turbulence. The use of such models shows that the simple analogy with Kolmogorov turbulence is not compatible with a fine-scale fractal structure of quantum space-time. Hence, should such theories prove correct, they would imply that the scaling properties of quantum fluctuations of space-time are subtler than those described by the simple Kolmogorov analogy.

Comments on ultra-high-energy photons and D-foam models

We revisit the constraints that the non-observation of ultra-high-energy photons due to the GZK cutoff can impose on models of Lorentz violation in photon propagation, following recent work by Maccione, Liberati and Sigl (2010) [arXiv:1003.5468] that carries further an earlier analysis by the present authors [J. Ellis et al., Phys. Rev. D 63 (2001) 12402, hep-th/0012216]. We argue that the GZK cutoff constraint is naturally evaded in the D-brane model of space–time foam presented recently by the present authors [J. Ellis et al., Phys. Lett. B 665 (2008) 412, arXiv:0804.3566], in which Lorentz-violating effects on photon propagation are independent of possible effects during interactions. We also note a novel absorption mechanism that could provide a GZK-like cutoff for photons in low-scale string models.