Classical theory of mesons

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On the theory of point-particles

It is deduced from the conservation of the energy-momentum tensor that if the flow of energy and momentum into a tube surrounding a time-like world-line, on which the field is singular, become singular as the size of the tube is contracted to zero, then the singular terms are necessarily perfect differentials of quantities on the world-line with respect to the proper time along the world-line. The same can be proved of any other tensor, as, for example, the angular-momentum tensor, which is conserved. It is proved from this that for any point-particle whatever having charge, spin or other properties, which need not be specified, it is always possible to deduce exact equations of motion which are finite. It is proved further that if the energy-momentum tensor is altered by the addition of partial Kμ ν σ/partial xσ, where Kμ ν σ is any tensor antisymmetric in ν and σ , then the equations of motion are unaltered, but it is possible to choose Kμ ν σ in such a way as to make the flow of energy and momentum into a given tube non-singular

Radiation from a Charge Uniformly Accelerated for All Time

A recent paper of Singal [Gen. Rel. Grav. 27 (1995), 953-967] argues that a uniformly accelerated particle does not radiate, in contradiction to the consensus of the research literature over the past 30 years. This note points out some questionable aspects of Singal's argument and shows how similar calculations can lead to the opposite conclusion.Comment: LaTeX, 9 pages, to appear in General Relativity and Gravitatio

Relativistic wave equations for the proton

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Classical theory of electrons

It is shown that when a point charge is present in an electromagnetic field, the conservation of energy and momentum does not in general lead to conservation of angular momentum for the system as a whole. The conservation laws impose stringent restrictions on the possible equations which may describe the motion of the point charge.If it is required that higher derivatives of the velocity than the second should not appear explicitly in these equations, then the choice is unique and the only possible equations are those originally derived by Lorentz. If the third derivative is allowed to appear explicitly in the equations, but no thigher ones, then it is possible to give one other system of equations for describing the behaviour of a point singularity which can be used without entirely artificial initial and final conditions

Classical theory of spinning particles

The exact relativistic classical equations taking radiation reaction into account for the rotation and translation of apoint dipole are given for the case where the dipole is always a pure magnetic dipole in the rest system. These equations are entirely free from any singularities. It is shown that the mass M, angular momentum of the spin I and magnetic moment g2 are three entirely independent constants with no connection between them. The cross-section for the scattering of light by a dipole is given by formula (56). This formula shows that due to radiation reaction the scattering actually decreases as ω-2 for very high frequencies ω, instead of increasing as ω2 when radiation reaction is neglected. The quantum mechanical formula for the scattering of neutral mesons by neutrons is shown to go wrong at energies h ω ≥ 3 μ due to neglect of the effects of radiation damping. The classical formula (56) can still be correctly applied in the range 3μ <h ω < M, where the quantum formula is wrong, M being the neutron mass. Finally reasons are given for thinking that the quantum theory of the electron fails at energies above about √3 × 137m due to neglect of the effect of radiation damping on the spin, and the quantum theory of the meson and its inter-action with the electromagnetic field at √6 × 137µ

On elementary heavy particles with any integral charge

The previous paper having shown that all divergences and large crosssections for neutral mesons being due entirely to neglect of radiation reaction, an attempt is made in this paper to remove those difficulties in the theory of charged mesons which do not occur in the theory of neutral mesons by following up an idea put forward tentatively by the present author some time ago on the ground that it would diminish the excessive scattering of charged mesons. It is assumed that the heavy elementary particles can exist in states of all integral charge, positive, negative or zero, the different states having different rest masses, of which the states with charge 0 ande (neutron and proton) must be assumed to have the lowest rest masses, while the proton states of charge -e and 2e are assumed to have the next lowest. The cross-sections for the creation and annihilation of protons of charge 2e and -e by several processes are calculated. The collision of a fast proton with another stationary proton is the most effective process for creating protons of charge 2e, the cross-section being of the order 10-27 cm.2 The colliding proton must have a kinetic energy of at least 35 M.e-V. Neutrons of the same energy would produce protons of charge -e on colliding with neutrons. The cross-sections for the production of protons of charge 2e and -e by mesons or photons are of the order 10-27 cm.2 The life time for spontaneous decay of these particles is of the order of 1/6 seconds, while the life time in air for reconversion into ordinary protons or neutrons by collision with a nucleus is of the order Z 10-7 secs. for low velocities. These particles have an interaction with the proton or neutron which is the same as the proton-neutron interaction with small additional terms. The energy-range relationship is calculated. The mean ionisation along a tract of a proton of charge 2e is nearly twice that of a proton or half that of an α-particle of the same range. If the theory is correct these particles are expected to occur in the nuclear explosions produced by cosmic rays, though less frequently than ordinary protons. Study of Wilson chamber photographs and photographs of nuclear explosions in the emulsions of photographic plates especially at high altitudes might be expected to reveal or disprove the existence of these particles

The Dirac-Dowker Oscillator

The oscillator-like interaction is introduced in the equation for the particle of arbitrary spin, given by Dirac and re-written to a matrix form by Dowker.Comment: LaTeX file, 4pp. Preprint EFUAZ 94-0

Affinities and Beyond! Developing Ways of Seeing in Online Spaces

This article presents an insider view of an online community of adults involved in sharing digital photography through a host website, Flickr. It describes how reciprocal teaching and learning partnerships in a dynamic multimodal environment are achieved through the creation of a ‘Third Space’ or ‘Affinity Space’, where ‘Funds of Knowledge’ are shared and processed in such a way that new meanings and discourses are generated. It is argued that this process is evidence of valuable learning and of the deepening of global understandings within the local space of Flickr. The new understandings are at least partly identifiable on the Flickr space, through the co-constructed ‘folksonomy’ or ‘online taxonomy’ of ways of looking at the world. Further, the article provides evidence for broadening existing definitions of literacy, at a time when the visual mode increasingly works interactively with verbal cues and explanations