Cosmological lore—and some heresies

Cosmology is based on a number of well-founded assumptions, which include Hubble's law and the cosmological principle. Most cosmologists and astronomers also tacitly accept a number of other assumptions and beliefs which constitute a sort of traditional cosmological lore. Among these are the notions that the universe is finite, that if it is not, then there must be an observational horizon which renders it finite for all practical purposes, that it is valid to employ the special relativistic Doppler formula to interpret large cosmological redshifts, and that the expansion of the universe is slowing down toward its ultimate reversal. It is argued that none of these notions is incontrovertible and that some of them involve serious inconsistencies. An alternative approach is proposed which assumes that the universe is expanding uniformly and that it constitutes a fundamental reference frame for light propagation as implied by the Robertson-Walker metric. This approach leads to a model of the universe which is possibly infinite but without a specific observational horizon, and which satisfies the requirements of relativity. It is shown that the proposed model is theoretically consistent and that recent astronomical evidence supports its assumptions and predictions; it therefore presents a serious challenge to commonly held views about the universe.     

Nematics with quenched disorder: violation of self-averaging

We consider the isotropic-to-nematic transition in liquid crystals confined to aerogel hosts, and assume that the aerogel acts as a random field. We generally find that self-averaging is violated. For a bulk transition that is weakly first order, the violation of self-averaging is so severe that even the correlation length becomes non-self-averaging: no phase transition remains in this case. For a bulk transition that is more strongly first order, the violation of self-averaging is milder, and a phase transition is observed.     

Acoustic streaming in a rotating fluid

Acoustic streaming theory is derived that is applicable to a fluid that is slow moving in a reference frame that rotates with a constant angular velocity omega. A simplified streaming equation is obtained for the special case in which the acoustic angular frequency omega is large relative to omega, and the change in fluid density due to rotation alone is negligible. For this special case it is shown that the "driving force" for the acoustic streaming is independent of omega. Thus, if no acoustic streaming is present in a fluid system that is stationary, then no steady-state acoustic streaming is predicted for a similar system that rotates with constant angular velocity. For a system in which acoustic streaming is present, the flow behavior depends on the relative magnitudes of the Coriolis forces and the viscous forces. If the Ekman number is large (that is, the viscous force dominates) then the predicted flow is identical to that which would exist in a stationary system. If, on the other hand, the Ekman number is small then the Coriolis force dominates and the component of flow in the direction of the axis of rotation can be much smaller in the rotating system than in a similar system at rest.     

On the Foundations of Superstring Theory

Superstring theory is an extension of conventional quantum field theory that allows for stringlike and branelike material objects besides pointlike particles. The basic foundations on which the theory is built are amazingly shaky, and, equally amazingly, it seems to be this lack of solid foundations to which the theory owes its strength. We emphasize that such a situation is legitimate only in the development phases of a new doctrine. Eventually, a more solidly founded structure must be sought. Although it is advertised as a “candidate theory of quantum gravity”, we claim that string theory may not be exactly that. Rather, just like quantum field theory itself, it is a general mathematical framework for a class of theories. Its major flaw could be that it still embraces a Copenhagen view on the relation between quantum mechanics and reality, while any “theory of everything”, that is, a theory for the entire cosmos, should do better than that.     

Stratified quantization approach to dissipative quantum systems: Derivation of the Hamiltonian and kinetic equations for reduced density matrices

A technique for describing dissipative quantum systems that utilizes a fundamental Hamiltonian, which is composed of intrinsic operators of the system, is presented. The specific system considered is a capacitor (or free particle) that is coupled to a resistor (or dissipative medium). The microscopic mechanisms that lead to dissipation are represented by the standard Hamiltonian. Now dissipation is really a collective phenomenon of entities that comprise a macroscopic or mesoscopic object. Hence operators that describe the collective features of the dissipative medium are utilized to construct the Hamiltonian that represents the coupled resistor and capacitor. Quantization of the spatial gauge function is introduced. The magnetic energy part of the coupled Hamiltonian is written in terms of that quantized gauge function and the current density of the dissipative medium. A detailed derivation of the kinetic equation that represents the capacitor or free particle is presented. The partial spectral densities and functions related to spectral densities, which enter the kinetic equations as coefficients of commutators, are evaluated. Explicit expressions for the nonMarkoffian contribution in terms of products of spectral densities and related functions are given. The influence of all two-time correlation functions are considered. Also stated is a remainder term that is a product of partial spectral densities and which is due to higher order terms in the correlation density matrix. The Markoffian part of the kinetic equation is compared with the Master equation that is obtained using the standard generator in the axiomatic approach. A detailed derivation of the Master equation that represents the dissipative medium is also presented. The dynamical equation for the resistor depends on the spatial wavevector, and the influence of the free particle on the diagonal elements (in wavevector space) is stated.     

Ghost neutrino fields in flat space-time

The Weyl neutrino equation is integrated in flat space-time assuming that the energy-momentum tensor of the neutrino field vanishes. It is shown that the flux vector of the neutrino field is tangent to a twist-free and shear-free congruence of null geodesics, which is a special Robinson congruence and constitutes a geometrical representation of a null twistor. It is also shown that, conversely, given such a congruence, a ghost neutrino field can be constructed.     

Pulse dispersion in a clad lens-like medium

The effects of a homogeneous cladding on the dispersion of a square-law dielectric guide are investigated using a perturbation technique. Assuming a Gaussian, band-limited input it is shown that for single mode operation the waveguide dispersion is of the order of the material dispersion. For multimode operation the effect of the cladding on the uniformly polarized modes is examined and it is shown that a significant interaction occurs only for the two modes closest to cut-off. Comparison is made between theoretical and experimental results. The perturbation technique is used to analyse the optimum index profile proposed by Okamoto and Okoshi. It is shown that this variation reduces the dispersion to below that of the infinite medium approximation.     

Debye Potentials for Self-Dual Fields

It is shown that in a space-time that admits ageodetic and shear-free null vector field which is aprincipal direction of the conformal curvature(therefore, in any algebraically special solution of the Einstein vacuum field equations), any self-dualelectromagnetic field is locally given by a scalar(Debye) potential which obeys a second-orderdifferential equation and, similarly, that any self-dualYang-Mills field is locally given by a matrix-valuedpotential governed by a nonlinear second-orderdifferential equation. Using the fact that any self-dualelectromagnetic field is the self-dual part of a realsolution of the source-free Maxwell equations, it isshown that in any space-time of this class, the solutionof the source-free Maxwell equations is locally given bya Debye potential.     

Acoustic impedance measurements-correction for probe geometry mismatch

The effect of evanescent mode generation, due to geometrical mismatch, in acoustic impedance measurements is investigated. The particular geometry considered is that of a impedance probe with an annular flow port and a central microphone, but the techniques are applicable to other geometries. It is found that the imaginary part of the measured impedance error is proportional to frequency, and that the sign of the error is positive for measurements made on tubes with diameter much larger than that of the inlet port, but negative for tubes with diameter close to that of the inlet. The result is a distortion of the measured frequencies of the impedance minima of the duct while the maxima are largely unaffected. There is, in addition, a real resistive component to the error that varies approximately as the square root of the frequency. Experiment confirms the results of the analysis and calculations, and a calibration procedure is proposed that allows impedance probes that have been calibrated on a semi-infinite tube of one diameter to be employed for measurements on components with an inlet duct of some very different diameter.     

Logarithmic negativity: a full entanglement monotone that is not convex

It is proven that logarithmic negativity does not increase on average under a general positive partial transpose preserving operation (a set of operations that incorporate local operations and classical communication as a subset) and, in the process, a further proof is provided that the negativity does not increase on average under the same set of operations. Given that the logarithmic negativity is not a convex function this result is surprising, as it is generally considered that convexity describes the local physical process of losing information. The role of convexity and, in particular, its relation (or lack thereof) to physical processes is discussed and importance of continuity in this context is stressed.     

On the fluctuation enhanced conductivity of a superconductor: The correct evaluation of the Maki graph

According to Maki, a particular diagram—the Maki graph—gives a contribution to the fluctuation enhanced conductivity of a superconductor which is infinite in the case of a thin film. It is shown that this result is spurious and that it is due to a breakdown of the standard Green function impurity technique. A new method is developed which is strictly based on the Boltzmann equation. It is shown that the temperature dependent contribution of the Maki graph to the conductivity is negligibly small in a dirty metal.     

Fast beating null strip during the reflection of pulsed Gaussian beams incident at the Rayleigh angle

It is well known that harmonic bounded Gaussian beams undergo a transformation into two bounded beams upon reflection on a solid immersed in a liquid. The effect is known as the Schoch effect and can be found at the Rayleigh angle for thick plates and at the different Lamb angles for thin plates. Here, a study is made on the effect of pulsed Gaussian beams reflected on solids. It is found experimentally that the Rayleigh wave phenomenon still generates two reflected bounded beams, whereas Lamb wave phenomena do not generate this effect. This fact may be explained intuitively by realizing that the Rayleigh phenomenon is a coincidental phenomenon that is generated in situ, whereas the Lamb wave phenomenon is a non-coincidental phenomenon that is generated only after incident sound is influenced by both sides of a thin plate. Another explanation is the fact that Rayleigh waves are not dispersive, whereas stimulation and propagation of Lamb waves is frequency dependent. A pulse contains many frequencies and therefore only a fraction of the incident pulse is transformed into a Lamb wave. In this paper, numerical simulations are performed that show that actually the Schoch effect does occur neither for Rayleigh waves, nor for Lamb waves. As a matter of fact, a pulse, incident at the Rayleigh angle, generates two reflected lobes with a null zone of a different kind. The null zone is beating several times during the passage of each pulse. This results in a 'null zone' having a lower mean intensity than any of the two lobes, still less outspoken than for the case of harmonic incident bounded beams. This effect does only occur for Rayleigh wave generation and is much less outspoken for Lamb wave generation.     

Reproduction of a protocell by replication of a minority molecule in a catalytic reaction network

For understanding the origin of life, it is essential to explain the development of a compartmentalized structure, which undergoes growth and division, from a set of chemical reactions. In this study, a hypercycle with two chemicals that mutually catalyze each other is considered in order to show that the reproduction of a protocell with a growth-division process naturally occurs when the replication speed of one chemical is considerably slower than that of the other chemical, and molecules are crowded as a result of replication. It is observed that the protocell divides after a minority molecule is replicated at a slow synthesis rate, and thus, a synchrony between the reproduction of a cell and molecule replication is achieved. The robustness of such protocells against the invasion of parasitic molecules is also demonstrated.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Is a cosmological substratum compatible with relativity?

A cosmological substratum for energy propagation is defined in terms of a hypothesis by McCrea. It has been shown that the assumption of such a substratum for a uniformly expanding universe provides a cosmological interpretation of Special Relativity, and leads further to a theory of gravitation in terms of a universal acceleration field. Following a critical discussion of the bases of General Relativity, it is suggested that the proposed substratum model and its consequences are also compatible with the General Relativistic approach, providing that this is applied in a manner which recognises the centrally directed character of gravitational fields, and hence employs harmonic coordinates as proposed by Fock. It is shown that Fock's procedure leads to results which are consistent with the assumption of a uniformly expanding cosmological substratum. Finally, it is suggested that the cosmological substratum concept is also implied by the formulation of the Robertson-Walker metric.     

Black holes in the Brans-Dicke

It is shown that a stationary space containing a black hole is a solution of the Brans-Dicke field equations if and only if it is a solution of the Einstein field equations. This implies that when the star collapses to form a black hole, it loses that fraction (about 7%) of its measured gravitational mass that arises from the scalar interaction. This mass loss is in addition to that caused by emission of scalar or tensor gravitational radiation. Another consequence is that there will not be any scalar gravitational radiation emitted when two black holes collide.     

Validity of linear acoustics for prediction of waveforms caused by sonically moving laser beams

The question is raised as to whether the analysis of the generation of sound by a laser beam moving over a water surface at the sound speed c for an interminable time period requires consideration of nonlinear effects. A principal consideration in this regard is whether the linear acoustics theory predicts a pressure waveform that is bounded in the asymptotic limit when the laser irradiation time is arbitrarily large. It is shown that a bounded asymptotic limit exists when the upper boundary condition corresponds (as is more nearly appropriate) to that of a pressure release surface, but not when it corresponds to that of a rigid surface. The asymptotic solution to the appropriate inhomogeneous wave equation is given exactly for the former case, and it is shown that the highest asymptotic amplitudes, given specified laser power and beam radius a, occur in the limit of a very small light absorption coefficient mu. In this limit, the peak amplitude is independent of mu and occurs at a depth of 0.88/mu. An approximate solution for the pressure waveform at intermediate times establishes that the characteristic time for buildup to the asymptotic limit is of the order of 2.5/(c mu 2a). If this time is substantially shorter than the time that a plane-wave pulse with the asymptotic waveform would take to develop a shock wave, then accumulative nonlinear effects are of minor importance.     

Capillary surfaces in a cone

We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and for which the surface boundary meets the boundary of the cone at a constant angle, is radially graphical if the mean curvature is non-positive with respect to the Gauss map pointing towards the domain bounded by the surface and the boundary of the cone. In the particular case in which the cone is circular, we prove that the surface is a spherical cap or a planar disc. The proofs are based on an extension of the Alexandrov reflection method using inversions about spheres.     

A passive means for cancellation of structurally radiated tones

The concept of cancellation of constant-frequency sound radiated from a vibrating surface by means of an attached mechanical oscillator is discussed. It is observed that the mass of a mechanical oscillator whose spring is attached to the vibrating surface will vibrate at comparatively large amplitudes and out of phase with that surface, provided that the surface vibrates at a frequency that is slightly higher than the oscillator's natural frequency. From this observation it is concluded that an oscillator's mass with a relatively small surface area can produce a volume velocity that is equal and opposite to that of the vibrating surface, resulting in cancellation of the sound radiated from the surface. Practical considerations in the design of such an oscillator are discussed, and the canceling performance from oscillators consisting of edge-supported circular disks is analyzed. An experimental canceling oscillator consisting of an edge-supported disk is described, and measurements made with this disk attached to a piston are shown to be in good agreement with analytical predictions. A tonal noise reduction exceeding 20 dB was demonstrated experimentally.     

Surface pressure in clusters and small particles—is it real?

Using the methods of statistical mechanics and applying the conditions of thermal equilibrium for an ensemble of interacting molecules, it is proved that there is no excess pressure, nor internal and surface stresses, in clusters and small particles that are not subjected to the action of external forces. With this premise taken into account the thermodynamics of spherical and faceted small particles is developed. In a particle-vapour system surrounded by a rigid impervious shell, Kelvin's and Thomson's formulae and Wulff's rule are derived. For a particle-melt system at a constant external pressure it is expected that the melting points of a particle and a bulk solid should be equal. It is noted that, if a particle is not subjected to the action of external fields or bodies, its molecules occupy their natural equilibrium positions, and it is from them that deformations and internal stresses should be counted off. These equilibrium positions differ from those occupied by the same molecules in a bulk solid, which is what usually gives rise to the illusions of the stressed state of a small particle and its deformation caused by the “uncompensated” surface forces.