Causality and the renormalization group

We suppose that for the invariant coupling constant (ICC) the spectral representation of the Källen-Lehmann type is valid. By combining this conjecture with the general solution of the functional renormalization group (RG) equation it is possible to analyze the type of singularity in the coupling constant at g=0. For logarithmic models it is of the form exp (-1/g).     

Causality and the speed of sound

A usual causal requirement on a viable theory of matter is that the speed of sound be at most the speed of light. In view of various recent papers querying this limit, the question is revisited here. We point to various issues confronting theories that violate the usual constraint.     

Equal autophonic level curves under different room acoustics conditions

The indirect auditory feedback from one's own voice arises from sound reflections at the room boundaries or from sound reinforcement systems. The relative variations of indirect auditory feedback are quantified through room acoustic parameters such as the room gain and the voice support, rather than the reverberation time. Fourteen subjects matched the loudness level of their own voice (the autophonic level) to that of a constant and external reference sound, under different synthesized room acoustics conditions. The matching voice levels are used to build a set of equal autophonic level curves. These curves give an indication of the amount of variation in voice level induced by the acoustic environment as a consequence of the sidetone compensation or Lombard effect. In the range of typical rooms for speech, the variations in overall voice level that result in a constant autophonic level are on the order of 2 dB, and more than 3 dB in the 4 kHz octave band. By comparison of these curves with previous studies, it is shown that talkers use acoustic cues other than loudness to adjust their voices when speaking in different rooms.     

Causality and the effective range expansion

We derive the generalization of Wigner’s causality bounds and Bethe’s integral formula for the effective range parameter to arbitrary dimension and arbitrary angular momentum. We also discuss the impact of these constraints on the separation of low- and high-momentum scales and universality in low-energy scattering. Some of our results were summarized earlier in a letter publication. In this work, we present full derivations and several detailed examples.     

Causality of the brane universe

Causal structure of the brane universe with respect to null geodesics in the bulk spacetime is studied. It is pointed out that apparent causality violation is possible for the brane universe which contains matter energy. It is also shown that there is no "horizon problem" in the Friedmann-Robertson-Walker brane universe.     

Causality and quantum mechanics

Statistical causality is recommended as the name of the generalized causality needed in quantum mechanics, instead of statistical correspondence used by Pauli.     

Causality and Cauchy horizons

LetS be a partial Cauchy surface for (M, go) which remains a partial Cauchy surface under small metric perturbations. In general, the Cauchy horizon H⁺(go, S) may be unstable to small changes in the metric. Points of the horizon may move by large amounts and even the topological type of the horizon may change under arbitrarily small changes in the metric tensor. In this paper, we investigate sufficient conditions for existential, locational, and topological stability of Cauchy horizons under metric changes which perturb the light cones by small amounts.     

Composite Structure and Causality

We study the question of whether a composite structure of elementary particles, with a length scale 1/Λ, can leave observable effects of non-locality and causality violation at higher energies (but ≲Λ). We formulate a model-independent approach based on Bogoliubov-Shirkov formulation of causality. We analyze the relation between the fundamental theory (of finer constituents) and the derived theory (of composite particles). We assume that the fundamental theory is causal and formulate a condition which must be fulfilled for the derived theory to be causal. We analyze the condition and exhibit possibilities which fulfil and which violate the condition. We make comments on how causality violating amplitudes can arise.     

Causality violations and singularities

We announce and justify two theorems (proofs will appear in Refs. 1 and 2): i) A generalization of the singularity theorem of Hawking and Penrose [3] to space-times with chronology violations. Although it is impossible to remove the chronology condition completely the announced theorem is in a well defined sense optimal: the chronology condition is replaced by a strictly weaker condition that cannot be removed because of counter examples, ii) If the chronology violating setV has compact closure and the strong energy and generic conditions hold, thenV is generated by incomplete null geodesics. It follows that if the region of causality violation does not extend to infinity thenV contains singularities.This essay received an honourable mention from the Gravity Research Foundation, 1989     

Relativistic Simultaneity and Causality

We analyzed two types of relativistic simultaneity associated to an observer: the spacelike simultaneity, given by Landau submanifolds, and the lightlike simultaneity given by past-pointing horismos submanifolds. We study some geometrical conditions to ensure that Landau submanifolds are spacelike and we prove that horismos submanifolds are always lightlike. Finally, we establish some conditions to guarantee the existence of foliations in the space-time whose leaves are these submanifolds of simultaneity generated by an observer. These foliation structure allows us to incorporate the simultaneity submanifolds for studying some dynamical systems, for instance free elementary massless particles.     

Laminar and unstable burning velocities and Markstein lengths of hydrogen–air mixtures at engine-like conditions

Hydrogen offers an attractive alternative to conventional fuels for use in spark ignition engines. It can be burned over a very wide range of equivalence ratios and with considerable exhaust gas recirculation. These help to minimise pumping losses through throttleless operation and oxides of nitrogen (NO_x) production through reduced temperature. Full understanding of hydrogen-fuelled engine operation requires data on the laminar burning rate of hydrogen–air residuals under a wide range of conditions. However, such data are sparse. The present work addresses this need for experimental data. Spherically expanding H₂–air flames were measured at a range of temperatures, pressures, and equivalence ratios and with varying concentrations of residuals of combustion. Unstretched burning velocities, u_l, and Markstein lengths, L_b, were determined from stable flames. At the higher pressures, hydrodynamic and diffusional-thermal instabilities caused the flames to be cellular from inception and prohibited the derivation of values of u_l and L_b. The effect of pressure on the burning rate was demonstrated to have opposing trends when comparing stoichiometric and lean mixtures. The present measurements were compared with those available in the literature, and discrepancies were attributed to neglect, in some works, the effects of stretch and instabilities. From the present measurements, the effects of pressure, temperature, and residual gas concentration on burning velocity are quantified for use in a first step towards a general correlation.     

Faster-than-Light Signals and Causality

The problems of causality are analyzed in terms of space-time models which admit the propagation of signals with superrelativistic velocities. It is shown that there is no violation in causality if the propagation of faster-than-light signals is described by general-covariant equations and occurs along invariant curves, as it is in some well-known models.     

Causality and the threshold anomaly of the nucleus-nucleus potential

According to the causality principle, a scattered wave cannot be emitted before the arrival of the incident wave. This principle implies the existence of a dispersion relation between the real and the imaginary parts of the optical potential. We discuss the difference between the dispersion relations which hold for nucleus-nucleus scattering on the one hand and for nucleon-nucleus scattering on the other hand. In the case of nucleus-nucleus scattering, the dispersion relation predicts that the modulus of the real part of the optical potential has a bell-shaped maximum, as a function of energy, when the imaginary part approaches zero, i.e. for energies near the top of the Coulomb barrier. The shape of this apparent anomaly is investigated in the framework of several models. It is shown that there exists an algebraic model which is at the same time simple and sufficiently accurate in the sense that the difference between its outcome and that of more realistic models is smaller than the uncertainties introduced by the assumptions which have to be made. Various systems are discussed, in particular ¹⁶O + ²⁸⁰Pb and α + ⁴⁰Ca. Several implications of the anomaly are pointed out, including its effect on the sub-barrier fusion of two heavy ions.