Does the electron have a structure?

... it ain't likely to have a radius of exactly zero, is the conclusion of H. G. Dehmelt⁽¹⁾ from his Nobel Prize (1989) winning observations on trapped electrons. There are small discrepancies between Dehmelt's observations and the theoretical predictions of quantum electrodynamics (QED), which assumes that the electron is a point particle. Here we present evidence in support of Dehmelt's contention that the electron has a structure. Essentially, we point out that the nonrelativistic limit of QED is at variance with a fundamental principle underlying all of physics, viz. the second law of thermodynamics.     

Does sex induce a phase transition?

We discovered a dynamic phase transition induced by sexual reproduction. The dynamics is a pure Darwinian rule applied to diploid bit-strings with both fundamental ingredients to drive Darwin's evolution: (1) random mutations and crossings which act in the sense of increasing the entropy (or diversity); and (2) selection which acts in the opposite sense by limiting the entropy explosion. Selection wins this competition if mutations performed at birth are few enough, and thus the wild genotype dominates the steady-state population. By slowly increasing the average number m of mutations, however, the population suddenly undergoes a mutational degradation precisely at a transition point m_c. Above this point, the “bad” alleles (represented by 1-bits) spread over the genetic pool of the population, overcoming the selection pressure. Individuals become selectively alike, and evolution stops. Only below this point, m < m_c, evolutionary life is possible. The finite-size-scaling behaviour of this transition is exhibited for large enough “chromosome” lengths L, through lengthy computer simulations. One important and surprising observation is the L-independence of the transition curves, for large L. They are also independent on the population size. Another is that m_c is near unity, i.e. life cannot be stable with much more than one mutation per diploid genome, independent of the chromosome length, in agreement with reality. One possible consequence is that an eventual evolutionary jump towards larger L enabling the storage of more genetic information would demand an improved DNA copying machinery in order to keep the same total number of mutations per offspring.     

Does negative refraction make a perfect lens?

A discussion of a question, studied earlier by Veselago in 1967 and by Pendry in 2000, is given. The question is: can a slab of the material with negative refraction make a perfect lens? Pendry's conclusion was: yes, it can. Our conclusion is: no, in practice it cannot, because of the fluctuations of the refraction coefficient of the slab. Resolution ability of linear isoplanatic optical instruments is discussed.     

How Much Time Does a Measurement Take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.     

Does the glory have a simple explanation?

The explanation for the meteorological glory provided by the complex angular momentum theory is revisited in response to comments that a simpler physical picture would be desirable. New results that confirm the tunneling origin of the glory and the roles of resonances and surface waves in this phenomenon are presented, and expressions for averaged angular distribution and polarization features are given.     

Does a Computer Have an Arrow of Time?

Schulman (Entropy 7(4):221–233, 2005) has argued that Boltzmann’s intuition, that the psychological arrow of time is necessarily aligned with the thermodynamic arrow, is correct. Schulman gives an explicit physical mechanism for this connection, based on the brain being representable as a computer, together with certain thermodynamic properties of computational processes. Hawking (Physical Origins of Time Asymmetry, Cambridge University Press, Cambridge, 1994) presents similar, if briefer, arguments. The purpose of this paper is to critically examine the support for the link between thermodynamics and an arrow of time for computers. The principal arguments put forward by Schulman and Hawking will be shown to fail. It will be shown that any computational process that can take place in an entropy increasing universe, can equally take place in an entropy decreasing universe. This conclusion does not automatically imply a psychological arrow can run counter to the thermodynamic arrow. Some alternative possible explanations for the alignment of the two arrows will be briefly discussed.     

Does the Boltzmann Principle Need a Dynamical Correction?

In an attempt to derive thermodynamics from classical mechanics, an approximate expression for the equilibrium temperature of a finite system has been derived (M. Bianucci, R. Mannella, B. J. West and P. Grigolini, Phys. Rev. E 51: 3002 (1995)) which differs from the one that follows from the Boltzmann principle S = kln(E) via the thermodynamic relation 1/T=S / E by additional terms of dynamical character, which are argued to correct and generalize the Boltzmann principle for small systems (here (E) is the area of the constant-energy surface). In the present work, the underlying definition of temperature in the Fokker–Planck formalism of Bianucci et al., is investigated and shown to coincide with an approximate form of the equipartition temperature. Its exact form, however, is strictly related to the volume entropy S = k ln (E) via the thermodynamic relation above for systems of any number of degrees of freedom ((E) is the phase space volume enclosed by the constant-energy surface). This observation explains and clarifies the numerical results of Bianucci et al., and shows that a dynamical correction for either the temperature or the entropy is unnecessary, at least within the class of systems considered by those authors. Explicit analytical and numerical results for a particle coupled to a small chain (N~10) of quartic oscillators are also provided to further illustrate these facts.     

Turbulence: Does Energy Cascade Exist?

To answer the question whether a cascade of energy exists or not in turbulence, we propose a set of correlation functions able to test if there is an irreversible transfert of energy, step by step, from large to small structures. These tests are applied to real Eulerian data of a turbulent velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype model equation for wave turbulence. First we demonstrate the irreversible character of the flow by using multi-time correlation function at a given point of space. Moreover the unexpected behavior of the test function leads us to connect irreversibility and finite time singularities (intermittency). Secondly we show that turbulent cascade exists, and is a dynamical process, by using a test function depending on time and frequency. The cascade shows up only in the inertial domain where the kinetic energy is transferred more rapidly (on average) from the wavenumber \(k_{1}\) to \(k_{2}\) than from \(k_{1}\) to \(k'_{2}\) larger than \(k_{2}\).     

Does a randall-sundrum scenario create the illusion of a torsion-free universe?

We consider spacetime with torsion in a Randall-Sundrum scenario where torsion, identified with the rank-2 Kalb-Ramond field, exists in the bulk together with gravity. While the interactions of both graviton and torsion in the bulk are controlled by the Planck mass, an additional exponential suppression comes for the torsion zero-mode on the visible brane. This may serve as a natural explanation of why the effect of torsion is so much weaker than that of curvature on the brane. The massive torsion modes, on the other hand, are correlated with the corresponding gravitonic modes and may be detectable in TeV-scale experiments.     

Does a Heisenberg Hamiltonian describe magnetic interactions in a MnSi film properly?

We report theoretical studies of magnetic excitations in an ultra-thin MnSi film on Si(0 0 1) substrate. Both transversal and longitudinal fluctuations of the magnetic moments are discussed. We show that the values of the Heisenberg exchange parameters depend on the assumed distance of the short range magnetic order and on the values of the atomic moments. The limitations of the mapping of the system on a Heisenberg model are studied.     

Does a neutron know that the earth is rotating?

In 1979 we observed the quantum mechanical phase shift of neutron deBroglie waves due to the Earth’s rotation. After the result was published, a number of very nice theoretical papers on the experiment appeared. I have two favorites: The one by M. Dresden and C. N. Yang in which they view the effect as due to the Doppler shift created by reflection from moving mirrors; and the other one by J. J. Sakurai in which he views the origin of the effect as being due to a flux of rotation threading the neutron interferometer loop, in much the same way that magnetic flux threads the electron interferometer loop to create the topological Aharonov-Bohm effect. Here, I would like to place their explanations of the physics of this experiment in juxtaposition with my own understanding of it. This paper is part of the 60th birthday Festschrift for Prof. Bahram Mashhoon.     

Does molecular environment cause a substructure underlying the expected eigenstates of a molecule?

The paper reports on Hanle effect experiments in NO₂ which indicate that the environment of the molecule may add a substructure to the expected eigenstates of NO₂. It is concluded that isolation of the molecule is presumably not possible.     

Does the entropy of the Universe tend to a maximum?

Ordinary, macroscopic systems, naturally tend to a state of maximum entropy compatible with their constraints. However, this might not hold for gravity-dominated systems since their entropy may increase without bound unless this is precluded by the formation of a black hole. In this short note we suggest, based on the Hubble expansion history, that our Universe likely behaves as an ordinary system, i.e., that its entropy seems to tend to some maximum value.     

Does a varying speed of light solve the cosmological problems?

We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised Einstein equations for Friedmann universes and show that arbitrary time-variations of c and G never lead to a solution to the flatness, horizon or Λ problems for a theory satisfying the strong energy condition. In order to do so, one needs to construct a theory which does not reduce to the standard one for any choice of time, length and energy units. This can be achieved by breaking a number of invariance principles such as covariance and Lorentz invariance.