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John E. Carroll
local time: 2024-11-22 05:01 (+00:00 )
John E. Carroll (Abstracts)
Titles Abstracts Details
  • Light Cone Representations and Geometric Algebra in Electromagnetic Material Moving at Relativistic Speeds (2010) [Updated 8 years ago]

  • Photon-Like Solutions of Maxwell's Equations (2009) [Updated 1 decade ago]

    Novel photon-like solutions of Maxwell's equations in free-space are constructed where transverse fields, propagating at frequency ? with phase (group) velocities vp (vg), possess local helical rotations at a frequency ? over the whole crosssection. These are referred to as distributed spin rotations. The frequencies ?  and ? are independent with the helical modulation propagating at vg, unlike single frequency classical solutions with helical phase fronts. These novel solutions are accessible only with vector formalisms although the axial fields satisfy the standard scalar wave-equation. The theory is outlined using the compact Riemann Silberstein formulation of Maxwell's equations with a field vector F = E + icB. Light-cone coordinates facilitate a manifestly Lorentz invariant theory. Appropriately chosen distributed spin rotations provide a wide variety of Lorentz invariant packets that envelope the classical fields and contain energy that is proportional to the total helical rotation over the length of the packet. The requirement that both transverse and axial fields are enveloped together leads to quantisation of the rotational energy in integer units, N. Solutions with different N are orthogonal. Operators can be formed, which increase (decrease) the rate of helical rotation and hence increase (decrease) the energy, and behave as promotion and demotion operators of standard quantum theory supporting a view that these new solutions form a photon-analogue. The paper concludes with a review of single-photon experiments that are in keeping with this model. Appendices contain detailed mathematics, speculative material and theorise on quantum-like features of the photon-analogue with regard to interference, polarisation and entanglement.


  • Correlations Leading to Space-time Structure in an Ether (2008) [Updated 8 years ago]

    It is proposed that the ether behaves like a coordinate invariant system. By using the general theory of signals in systems, the paper describes a formalism similar to quantum theory, provides a rationale for Lagrangian methods and also discovers how geometric structures naturally form. From the concepts of convolution and correlation used in linear systems it is shown that the multi-vectors of the ?Hestenes' geometric algebra correspond with generalised correlation matrices that link an observer's view of even and odd properties of incoming signals in the ether system. The analysis shows why three spatial dimensions is the lowest dimensionality to give a homogeneous space. Any fourth dimension, even if it were not time, has to behave differently from the other three spatial dimensions and cannot create a homogeneous space. A more speculative approach suggests that 3+1 space-time is embedded in a 3+3 space-time ether. Elsewhere it has been shown that Maxwell's equations could be construed as a necessary consequence of this embedding process, while here a Dirac equation with vector potentials emerges from similar assumptions. Mass is created by correlations in a temporal plane that is transverse to the temporal axis. Future prospects for this generalised theory are discussed.


  • A Relativistic Wave-Particle Based on Maxwell's Equations: Part II (2008) [Updated 8 years ago]
    by John E. Carroll   read the paper:

    At PIRT 2006, a speculative concept of a photon-like solution to Maxwell's classical equations was presented in which helically rotating solutions appeared to have properties that are typically associated with photons. Since that time, our understanding of these solutions has increased and the previous work has to be modified. This paper will present a digest of the latest results that enables us to clarify past work and review new experimental evidence for the theory.


  • Measuring a One Way Light Speed (2008) [Updated 8 years ago]
    by John E. Carroll   read the paper:

    A novel method of measuring measuring a one way light speed (OWLS) is proposed using standard equipment of frequency generators, laser pulse generators and oscilloscopes with periodic pulses going from A to B and also from B to A. The method can then inform B how long it has taken light pulses to reach B?s laboratory from A and similarly A can establish how long the pulses have taken to come from B. The method is based on experimental work that actually used a very similar method to measure the relative speeds of photons and classical pulses. It is expected that with classical optical pulses, the method could measure the one way velocity to an accuracy better than 1 part in 106.


  • A Relativistic Wave-Particle Based on Maxwell?s Equations: A Model for a Classical Photon (2006) [Updated 8 years ago]
    by John E. Carroll   read the paper:

    This quasi-classical theory is the first to contain such a large number of the features required to model a photon. The model uses Maxwell?s equations that not only embody relativity but contain elements of quantum theory. Conventional localised wave-packets cannot explain quantisation or the non-local behaviour of a photon. Standard methods for quantising Maxwellian modes using the harmonic oscillator formalism at angular frequency w, have the unsatisfactory feature that the Schr?dinger frequencies (M+?)w (integer M) have no clear physical significance and do not explain why, in a dispersive wave-guide, experiments indicate no difference between the velocity of single photons (M=1) and classical groups (M >>1). With this motivation, novel solutions to Maxwell?s classical equations in a dispersive system such as a circular guide are considered in a relativistic format. A helical twist with an arbitrary angular frequency W can modulate an arbitrary classical mode (angular frequency w, group velocity vg) provided that the helical velocity vh equals vg. Pairs of waves with modal and helical frequencies (w, W) and (w, -W) can trap one temporal period, (2p/w), of the underlying mode given that W = (M+?)w : the ?Schr?dinger? frequencies. The value of M is found to have no effect on group velocity or polarisation. A relativistic format shows how to create stable resonant wave-packets where conventional retarded waves overlap unconventional advanced waves. Energy is postulated to be carried only in the region of overlap and follows a ?Planck?s law? where the energy is proportional to the helical modulation frequency. Causality is never violated. Standard concepts of promotion and demotion have the clear physical meaning of increasing or decreasing the helical frequency. Advanced waves enable phase and polarisation to be predicted along all possible future paths and may help to explain the outcomes of experiments on delayed-choice interference and entanglement.