Quantum Wave Mechanics as the Magnetic Interaction of Dirac Particles

It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic force between two classical point charges, each undergoing relativistic circulatory motion of small radius compared to the separation between their centers of circulation, and assuming a time-symmetric electromagnetic interaction, is modulated by a factor that behaves similarly to the Schr\"odinger wavefunction. The magnetic force between relativistically-circulating charges has been shown previously to have a radially-directed inverse-square part of similar strength to the Coulomb force, and sinusoidally modulated by the phase difference of the charges' circulatory motions. The magnetic force modulation in the case of relatively moving centers of charge circulation solves an equation formally identical to the time-dependent free-particle Schr\"odinger equation, apart from a factor of two on the partial time derivative term. Considering motion in a time-independent potential obtains that the modulation also satisfies an equation formally similar to the time-independent Schro\"dinger equation. Using a formula for relativistic rest energy advanced by Osiak, the time-independent Schr\"odinger equation is solved exactly by the resulting modulation function. The significance of the quantum mechanical wavefunction follows straightforwardly from these observations. After considering the modification of Wheeler-Feynman absorber theory required by the adoption of Minkowski-Osiak relativity, the model is extended to obtain the full complex Schr\"odinger wavefunction.Comment: 17 pages, no figures. Added two new subsections to section V, new sections VI, VII, and VII

Modeling of Stress, Distortion, and Hot Tearing

International audienceComputational modeling of mechanical behavior during solidification is becoming more important. Thermal and microstructural simulations alone are insufficient to predict the quality of the final product that is desired by the casting industry. Accurate calculation of displacements, strains, and stresses during the casting process is needed to predict residual stress and distortion and defects such as the formation of cracks such as hot tears. It also helps predict porosity and segregation. As computing power and software tools for computational mechanics advance, it is becoming increasingly possible to perform useful mechanical analysis of castings and these important related behaviors

What can inactivity (in its various forms) reveal about affective states in non-human animals? A review

Captive/domestic animals are often described as inactive, with the implicit or explicit implication that this high level of inactivity is a welfare problem. Conversely, not being inactive enough may also indicate or cause poor welfare. In humans, too much inactivity can certainly be associated with either negative or positive affective states. In non-human animals, however, the affective states associated with elevated or suppressed levels of inactivity are still not well understood. Part of the complexity is due to the fact that there are many different forms of inactivity, each likely associated with very different affective states. This paper has two aims. One is to identify specific forms of inactivity that can be used as indicators of specific affective states in animals. The other is to identify issues that need to be resolved before we could validly use the remaining, not yet validated forms of inactivity as indicators of affective state. We briefly discuss how inactivity is defined and assessed in the literature, and then how inactivity in its various forms relates to affective (either negative or positive) states in animals, basing our reasoning on linguistic reports of affective states collected from humans displaying inactivity phenotypically similar to that displayed by animals in similar situations, and, when possible, on pharmacological validation. Specific forms of inactivity expressed in response to perceived threats (freezing, tonic immobility, and hiding) appear to be, to date, the best-validated indicators of specific affective states in animals. We also identify a number of specific forms of inactivity likely to reflect either negative (associated with ill-heath, boredom-like, and depression-like conditions), or positive states (e.g. ‘sun-basking’, post-consummatory inactivity), although further research is warranted before we could use those forms as indicators of the affective states. We further discuss the relationship between increased inactivity and affective states by presenting misleading situations likely to yield wrong conclusions. We conclude that more attention should be paid to inactivity in animal welfare studies: specific forms of inactivity identified in this paper are, or have the potential to be, useful indicators of affective (welfare) states in animals