International Journal of Modern Physics D

The debate between loop quantum gravity and string theory is sometime lively, and it is hard to present an impartial view on the issue. Leaving any attempt to impartiality aside, I report here, instead, a conversation on this issue, overheard in the cafeteria of a Major American University. The personae of the dialog are Professor Simp, a high energy physicist, and a graduate student, Sal. The Professor has heard that Sal has decided to work in loop gravity, and gently tries to talk her out. Here is what was heard.

In this review we critically discuss constraints on minimal supersymmetric models of particle physics as implied by the recent astrophysical observations of WMAP satellite experiment. Although the prospects of detecting supersymmetry increase dramatically, at least within the context of the minimal models, and 90% of the available parameter space can safely be reached by the sensitivity of future colliders, such as Tevatron, LHC and linear colliders, nevertheless we pay particular emphasis on discussing regions of the appropriate phase diagrams, which — if realized in nature — would imply that detection of supersymmetry, at least in the context of minimal models, could be out of colliders reach. We also discuss the importance of a precise determination of the radiative corrections to the muon anomalous magnetic moment, g_μ-2, both theoretically and experimentally, which could lead to elimination of such "out of reach" regions in case of a confirmed discrepancy of g_μ-2 from the standard model value. Finally, we briefly commend upon recent evidence, supported by observations, on a dark energy component of the Universe, of as yet unknown origin, covering 73% of its energy content. To be specific, we discuss how supergravity quintessence (relaxation) models can be made consistent with recent observations, which may lead to phenomenologically correct constrained supersymmetric models, accounting properly for this dark energy component. We also outline their unresolved problems.

The observed ultrahigh energy cosmic rays (UHECR) might require a modification of the basic laws of physics. In low scale gravity models, where the neutrino–nucleon cross section rises to typical hadronic values at energies above 10²⁰ eV, the neutrino becomes a candidate for the primary that initiates these showers. We calculate the neutrino–nucleon cross section at ultrahigh energies by assuming that it is dominated by the production of p-branes. We show, using a generalized Randall–Sundrum model, that the neutrino–nucleon cross-section at neutrino energies of 10²⁰ eV is of the order of 100 mb, which is required for explaining the UHECR events. Similar results also follow in other models such as the Lykken–Randall model.

Considering the physical 3-space t=constant of the space–time metrics as spheroidal and pseudo-spheroidal, cosmological models which are generalizations of Robertson–Walker models are obtained. Specific forms of these general models as solutions of Einstein's field equations are also discussed in the radiation and the matter dominated era of the universe.

The negative values for the squares of both electron and muon neutrino masses obtained in recent experiments are explained as a possible consequence of a change in metric within the weak-interaction volume in the energy–momentum representation. Using a model inspired by a combination of the general theory of relativity and the theory of deformation for continuous media, it is shown that the negative value of the square of the neutrino mass can be obtained without violating allowed physical limits. The consequence is that the negative value is not necessarily unphysical.

An experiment in Low Earth Orbit (LEO) is proposed to measure components of the Riemann curvature tensor using atom interferometry. We show that the difference in the quantum phase Δϕ of an atom that can travel along two intersecting geodesics is given by mR_0i0j/ℏ times the spacetime volume contained within the geodesics. Our expression for Δϕ also holds for gravitational waves in the long wavelength limit.

Over the last few years the study of possible Planck-scale departures from classical Lorentz symmetry has been one of the most active areas of quantum-gravity research. We now have a satisfactory description of the fate of Lorentz symmetry in the most popular noncommutative spacetimes and several studies have been devoted to the fate of Lorentz symmetry in loop quantum gravity. Remarkably there are planned experiments with enough sensitivity to reveal these quantum-spacetime effects, if their magnitude is only linearly suppressed by the Planck length. Unfortunately, in some quantum-gravity scenarios even the strongest quantum-spacetime effects are suppressed by at least two powers of the Planck length, and many authors have argued that it would be impossible to test these quadratically-suppressed effects. I here observe that advanced cosmic-ray observatories and neutrino observatories can provide the first elements of an experimental programme testing the possibility of departures from Lorentz symmetry that are quadratically Planck-length suppressed.

It is by now well known that various condensed matter systems may be used to mimic many of the kinematic aspects of general relativity, and in particular of curved-spacetime quantum field theory. In this essay we will take a look at what would be needed to mimic a cosmological spacetime — to be precise a spatially flat FRW cosmology — in one of these analogue models. In order to do this one needs to build and control suitable time dependent systems. We discuss here two quite different ways to achieve this goal. One might rely on an explosion, physically mimicking the big bang by an outflow of whatever medium is being used to carry the excitations of the analogue model, but this idea appears to encounter dynamical problems in practice. More subtly, one can avoid the need for any actual physical motion (and avoid the dynamical problems) by instead adjusting the propagation speed of the excitations of the analogue model. We shall focus on this more promising route and discuss its practicality.

We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally observable quantum phase shifts in the wavefunction of an extended object due to the coupling of its multipole moments with the gravitational field are obtained. Also, since the theory may be quantized using the action, the present approach is useful in the interface between general relativity and quantum mechanics.

In the standard approach to defining a Planck scale where gravity is brought into the quantum domain, the Schwarzschild gravitational radius is set equal to the Compton wavelength. However, ignored thereby are the charge and spin, the fundamental quantized aspects of matter. The gravitational and null-surface radii of the Kerr–Newman metric are used to introduce spin and charge into a new extended Planck scale. The fine structure constant appears in the extended Planck mass and the recent discovery of the α variation with the evolution of the universe adds further significance. An extended Planck charge and Planck spin are derived. There is an intriguing suggestion of a connection with the α value governing high-energy radiation in Z-boson production and decay.

The size of Hilbert space for quantum gravity is examined in the light of the holographic principle. The fluctuation of lengths results in a bound on the amount of quantum information that may exist in a volume of space, and prevent divergences at the Planck energy.

It is generally accepted that the entropy of an asymptotically de Sitter universe is bounded by the area, in Planck units, of the de Sitter horizon. Based on an analysis of the entropy associated to the vacuum quantum fluctuations, we suggest that the existence of such a holographic bound constitutes a possible explanation for the observed value of the cosmological constant, theoretically justifying a relation proposed 35 years ago by Zel'dovich.

Black holes are always irradiated by the cosmic background radiation. This captured radiation field determines the physical and geometrical nature of the singularity inside the black hole. We find that non-compact radiation fields (similar to the cosmic background radiation) affect dramatically the singularity, and may determine the fate of a falling astronaut. In particular, the dark energy which accelerates the expansion of the universe determines whether the "tunnel" inside the black hole is blocked, or whether the possibility of using the black hole as a portal for hyperspace travel cannot be ruled out as yet.

Quantization of gravity suggests that a finite region of space has a finite number of degrees of freedom or 'bits'. What happens to these bits when spacetime expands, as in cosmological evolution? Using gravity/field theory duality we argue that bits 'fuse together' when space expands.

In this essay it will be shown that the introduction of a modification to Heisenberg algebra (here this feature means the existence of a minimal observable length), as a fundamental part of the quantization process of the electrodynamical field, renders states in which the uncertainties in the two quadrature components violate the usual Heisenberg uncertainty relation. Hence in this context it may be asserted that any physically realistic generalization of the uncertainty principle must include, not only a minimal observable length, but also a minimal observable momentum.

We consider, within a string theoretic context, the accessibility of events inside a black hole horizon. We present a gedankenexperiment which uses the nonlocal nature of precursors in the AdS/CFT correspondence, as well as the global nature of event horizons, to argue that the dual field theory does contain information about physics inside black holes. This alleviates the causal obstacles to accessing behind-the-horizon physics, thereby rendering more tractable certain long-standing questions of quantum gravity, such as the information paradox and possibly even singularity resolution.

Production of high-energy gravitational objects is a common feature of gravitational theories. The primordial universe is a natural setting for the creation of black holes and other nonperturbative gravitational entities. Cosmic black holes can be used to probe physical properties of the very early universe which would usually require the knowledge of the theory of quantum gravity. They may be the only tool to explore thermalization of the early universe. Whereas the creation of cosmic black holes was active in the past, it seems to be negligible at the present epoch.

Spacetimes of general relativity containing closed timelike curves (CTC) are usually dismissed as non-physical. However, it is now known that CTC may appear in spacetimes modelling simple laboratory experiments, and two such experiments are described in this essay. We therefore need a realistic interpretation of CTC. I suggest that a region containing CTC may represent a new type of singularity, called a torsion singularity.

The principle of equivalence is shown to extend to situations involving radiation reaction. For example, the Lorentz force law governs the motion of an isolated charge undergoing radiation reaction. In the case of an isolated uncharged particle of small mass, it is the geodesic equation which governs the motion, even when radiation reaction is included. For a local observer to understand such motion he must subtract the singular field of the particle from the actual electromagnetic and gravitational fields he measures. The remaining source-free fields are then used in computing the motion of the particle. With only local measurements, the observer has no knowledge of the existence of radiation and sees no effect which he would be compelled to describe as radiation reaction.

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius r_g. The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at r_g leads to the question of correspondence between classical and quantum theories, which in turn can be unambiguously resolved by considering the issue of general covariance. The O(ℏ⁰) loop contributions turn out to violate the principle of general covariance, thus revealing their essentially quantum nature. The violation is O(1/N), where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence principle.

Using 5D membrane/induced-matter theory as a basis, we derive the equations of motion for a novel gauge. The latter admits both particle and wave behaviour, as well as super-communication (wherein there is causal contact in the higher-dimensional manifold among points which are disjoint in spacetime). Possible ways to test this model are suggested, notably using particle mass.

Recent attempts to resolve the ambiguity in the loop quantum gravity description of the quantization of area has led to the idea that j=1 edges of spin-networks dominate in their contribution to black hole areas as opposed to j=1/2 which would naively be expected. This suggests that the true gauge group involved might be SO(3) rather than SU(2) with attendant difficulties. We argue that the assumption that a version of the Pauli principle is present in loop quantum gravity allows one to maintain SU(2) as the gauge group while still naturally achieving the desired suppression of spin-1/2 punctures. Areas come from j=1 punctures rather than j=1/2 punctures for much the same reason that photons lead to macroscopic classically observable fields while electrons do not.

The nature of dark energy, which presently dominates the universal energy budget, remains a complete mystery. Models in which it is currently evolving tend to be overly sensitive to initial conditions, and necessarily involve a very light degree of freedom which is very difficult to obtain from realistic microscopic physics. This essay describes recent progress in understanding how the dark energy can arise as a residue of extra-dimensional gravitation, leading to new insights into how dark-energy cosmology might work. This picture produces dark energy dynamics within which couplings slowly run (or: 'walk') over cosmological times. It also has several unusual experimental predictions, including measurable modifications to Newton's Law on sub-millimeter scales and dramatic implications at next-generation collider experiments.

Astronomical observations strongly suggest that our universe is now accelerating and contains a substantial admixture of dark vacuum energy. Using numerical simulations to study this newly consolidated cosmological model (with a constant density of dark energy), we show that astronomical structures freeze out in the near future and that the density profiles of dark matter halos approach the same general form. Every dark matter halo grows asymptotically isolated and thereby becomes the center of its own island universe. Each of these isolated regions of space-time approaches a universal geometry and we calculate the corresponding form of the space-time metric.

Are universal fundamental constants really constant over cosmological times? Recent observations of the fine structure of spectral lines in the early universe have been interpreted as due to a variation of the fine structure constant e²/4πε₀ℏc. From the assumed validity of Maxwell equations in general relativity and well known experimental facts, it is proved that e and ℏ are absolute constants. On the other hand, the speed of light need not be constant.

A recently proposed model which accounts for the observed time dependence of the fine structure constant is summarized. The model is based on the combined effect of the fourth Heisenberg relation and the gravitation of all the expanding universe on the quantum vacuum. As is shown here, it predicts that the light must have now an acceleration close to H₀c≃6.9×10^-10 m/s². This suggests an explanation of the anomalous acceleration a_P≃8.5×10^-10 m/s² found in the Pioneer 10 spacecraft, because an acceleration of light has the same radio observational signature as an acceleration of the ship.

The search for a quantum theory of gravity has followed two parallel but different paths. One aims at arriving at the final theory starting from a priori assumptions as to its form and building it from the ground up. The other tries to infer as much as possible about the unknown theory from the existing ones and use our current knowledge to constrain the possibilities for the quantum theory of gravity. Probably the biggest success of the second path has been the results of black hole thermodynamics. The subject of this essay is a new, highly promising such result, the application of quasinormal modes in quantum gravity.

A sketch of the affine quantum gravity program illustrates a different perspective on several difficult issues of principle: metric positivity; quantum anomalies; and nonrenormalizability.

Smolin has put forward the proposal that the universe fine tunes the values of its physical constants through a Darwinian selection process. Every time a black hole forms, a new universe is developed inside it that has different values for its physical constants from the ones in its progenitor. The most likely universe is the one which maximizes the number of black holes. Here we present a concrete quantum gravity calculation based on a recently proposed consistent discretization of the Einstein equations that shows that fundamental physical constants change in a random fashion when tunneling through a singularity.

The scenario of an expanding universe envisioned in the early part of the 20th century has been replaced by one where we live in a chaotic, eternally bubbling universe. Every bubble has the potential for developing into a new habitable universe. In this essay I describe how large-scale quantum effects could be driving the chaotic bubbling universe.

Electroweak gauge bosons have masses of the order of 10²GeV [/c²], while masses of additional bosons involved in gravito-electroweak unification are expected to be still higher. These are at least eleven orders of magnitude higher than sub-eV range indications for neutrino masses. Under these circumstances we suspect that the sub-eV particles are created in a spacetime where gravitational effects of massive gauge bosons may become important. The question that we thus ask is: What is the spacetime group around a gravito-electroweak vertex? Modeling it as de-Sitter we find that sub-eV particles may carry a negative mass square of the order of . Neutrino oscillation data then hints at 30–75 TeV scale for M_unif., where M_unif. characterizes gravito-electroweak unification scale.