Triumphalism in the Gospels

While the words ‘triumph', ‘triumphal' and ‘triumphant' are words with a long history, the expression ‘triumphalism' is a modern invention. It seems to have started its career when first Bishop de Smedt of Belgium and later other speakers used it in their speeches in the early sessions of the Second Vatican Council. Through the innumerable articles and books about the Council it became widely known and became a current expression in the terminology of writers on religious themes. The speed and extent of its success showed that it pointed to the existence of an acute problem in the life of the churches. This problem was clearly stated in a contribution to the council's debate on the nature of the Church by Bishop Laszlo of Eisenstad

Quantum Computational Complexity in the Presence of Closed Timelike Curves

Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which represents a valid quantification of resources given the ability to construct compact regions of closed timelike curves. The notion of self-consistent evolution for quantum computers whose components follow closed timelike curves, as pointed out by Deutsch [Phys. Rev. D {\bf 44}, 3197 (1991)], implies that the evolution of the chronology respecting components which interact with the closed timelike curve components is nonlinear. We demonstrate that this nonlinearity can be used to efficiently solve computational problems which are generally thought to be intractable. In particular we demonstrate that a quantum computer which has access to closed timelike curve qubits can solve NP-complete problems with only a polynomial number of quantum gates.Comment: 8 pages, 2 figures. Minor changes and typos fixed. Reference adde

Focusing and the Holographic Hypothesis

The ``screen mapping" introduced by Susskind to implement 't Hooft's holographic hypothesis is studied. For a single screen time, there are an infinite number of images of a black hole event horizon, almost all of which have smaller area on the screen than the horizon area. This is consistent with the focusing equation because of the existence of focal points. However, the {\it boundary} of the past (or future) of the screen obeys the area theorem, and so always gives an expanding map to the screen, as required by the holographic hypothesis. These considerations are illustrated with several axisymmetric static black hole spacetimes.Comment: 8 pages, plain latex, 5 figures included using psfi

Lorentz Violation of Quantum Gravity

A quantum gravity theory which becomes renormalizable at short distances due to a spontaneous symmetry breaking of Lorentz invariance and diffeomorphism invariance is studied. A breaking of Lorentz invariance with the breaking patterns $SO(3,1)\to O(3)$ and $SO(3,1)\to O(2)$, describing 3+1 and 2+1 quantum gravity, respectively, is proposed. A complex time dependent Schr\"odinger equation (generalized Wheeler-DeWitt equation) for the wave function of the universe exists in the spontaneously broken symmetry phase at Planck energy and in the early universe, uniting quantum mechanics and general relativity. An explanation of the second law of thermodynamics and the spontaneous creation of matter in the early universe can be obtained in the symmetry broken phase of gravity.Comment: 10 pages, minor change and reference added. Typos corrected. To be published in Class. Quant. Grav

Stochastically Fluctuating Black-Hole Geometry, Hawking Radiation and the Trans-Planckian Problem

We study the propagation of null rays and massless fields in a black hole fluctuating geometry. The metric fluctuations are induced by a small oscillating incoming flux of energy. The flux also induces black hole mass oscillations around its average value. We assume that the metric fluctuations are described by a statistical ensemble. The stochastic variables are the phases and the amplitudes of Fourier modes of the fluctuations. By averaging over these variables, we obtain an effective propagation for massless fields which is characterized by a critical length defined by the amplitude of the metric fluctuations: Smooth wave packets with respect to this length are not significantly affected when they are propagated forward in time. Concomitantly, we find that the asymptotic properties of Hawking radiation are not severely modified. However, backward propagated wave packets are dissipated by the metric fluctuations once their blue shifted frequency reaches the inverse critical length. All these properties bear many resemblences with those obtained in models for black hole radiation based on a modified dispersion relation. This strongly suggests that the physical origin of these models, which were introduced to confront the trans-Planckian problem, comes from the fluctuations of the black hole geometry.Comment: 32 page

Do black holes radiate?

The prediction that black holes radiate due to quantum effects is often considered one of the most secure in quantum field theory in curved space-time. Yet this prediction rests on two dubious assumptions: that ordinary physics may be applied to vacuum fluctuations at energy scales increasing exponentially without bound; and that quantum-gravitational effects may be neglected. Various suggestions have been put forward to address these issues: that they might be explained away by lessons from sonic black hole models; that the prediction is indeed successfully reproduced by quantum gravity; that the success of the link provided by the prediction between black holes and thermodynamics justifies the prediction. This paper explains the nature of the difficulties, and reviews the proposals that have been put forward to deal with them. None of the proposals put forward can so far be considered to be really successful, and simple dimensional arguments show that quantum-gravitational effects might well alter the evaporation process outlined by Hawking. Thus a definitive theoretical treatment will require an understanding of quantum gravity in at least some regimes. Until then, no compelling theoretical case for or against radiation by black holes is likely to be made. The possibility that non-radiating "mini" black holes exist should be taken seriously; such holes could be part of the dark matter in the Universe. Attempts to place observational limits on the number of "mini" black holes (independent of the assumption that they radiate) would be most welcome.Comment: review article, 80 pp., 3 included eps figures, IOP macros (included

Fermionic microstates within Painlev\'e-Gullstrand black hole

We consider the quantum vacuum of fermionic field in the presence of a black-hole background as a possible candidate for the stabilized black hole. The stable vacuum state (as well as thermal equilibrium states with arbitrary temperature) can exist if we use the Painlev\'e-Gullstrand description of the black hole, and the superluminal dispersion of the particle spectrum at high energy, which is introduced in the free-falling frame. Such choice is inspired by the analogy between the quantum vacuum and the ground state of quantum liquid, in which the event horizon for the low-energy fermionic quasiparticles also can arise. The quantum vacuum is characterized by the Fermi surface, which appears behind the event horizon. We do not consider the back reaction, and thus there is no guarantee that the stable black hole exists. But if it does exist, the Fermi surface behind the horizon would be the necessary attribute of its vacuum state. We also consider exact discrete spectrum of fermions inside the horizon which allows us to discuss the problem of fermion zero modes.Comment: LaTeX, 20 pages, 2 figure

Cosmological Dark Energy: Prospects for a Dynamical Theory

We present an approach to the problem of vacuum energy in cosmology, based on dynamical screening of Lambda on the horizon scale. We review first the physical basis of vacuum energy as a phenomenon connected with macroscopic boundary conditions, and the origin of the idea of its screening by particle creation and vacuum polarization effects. We discuss next the relevance of the quantum trace anomaly to this issue. The trace anomaly implies additional terms in the low energy effective theory of gravity, which amounts to a non-trivial modification of the classical Einstein theory, fully consistent with the Equivalence Principle. We show that the new dynamical degrees of freedom the anomaly contains provide a natural mechanism for relaxing Lambda to zero on cosmological scales. We consider possible signatures of the restoration of conformal invariance predicted by the fluctuations of these new scalar degrees of freedom on the spectrum and statistics of the CMB, in light of the latest bounds from WMAP. Finally we assess the prospects for a new cosmological model in which the dark energy adjusts itself dynamically to the cosmological horizon boundary, and therefore remains naturally of order H^2 at all times without fine tuning.Comment: 50 pages, Invited Contribution to New Journal of Physics Focus Issue on Dark Energ

Comparison of relativity theories with observer-independent scales of both velocity and length/mass

We consider the two most studied proposals of relativity theories with observer-independent scales of both velocity and length/mass: the one discussed by Amelino-Camelia as illustrative example for the original proposal (gr-qc/0012051) of theories with two relativistic invariants, and an alternative more recently proposed by Magueijo and Smolin (hep-th/0112090). We show that these two relativistic theories are much more closely connected than it would appear on the basis of a naive analysis of their original formulations. In particular, in spite of adopting a rather different formal description of the deformed boost generators, they end up assigning the same dependence of momentum on rapidity, which can be described as the core feature of these relativistic theories. We show that this observation can be used to clarify the concepts of particle mass, particle velocity, and energy-momentum-conservation rules in these theories with two relativistic invariants.Comment: 21 pages, LaTex. v2: Andrea Procaccini (contributing some results from hia Laurea thesis) is added to the list of authors and the paper provides further elements of comparison between DSR1 and DSR2, including the observation that both lead to the same formula for the dependence of momentum on rapidit