Sarah Bell

We have shown in a previous paper that the Dirac bispinor can vary like a four-vector and that Quantum Electrodynamics (QED) can be reproduced with this form of behaviour.(1) In Part I of this paper, we show that QED with the same transformational behaviour also holds in an alternative space we call M-space. We use the four-vector behaviour to model the two-body interaction in M and show that this has similar physical properties to the usual model in L which it predicts. In Part II of this paper we use M-space to show that QED can be reduced to two simple rules for a two-body interaction.

We complete our previous(1, 2) demonstration that there is a family of new solutions to the photon and Dirac equations using spatial and temporal circles and four-vector behaviour of the Dirac bispinor. We analyse one solution for a bound state, which is equivalent to the attractive two-body interaction between a charged point particle and a second, which remains at rest. We show this yields energy and angular momentum eigenvalues that are identical to those found by the usual method of solving of the Dirac equation,(4) including fine structure. We complete our previous derivation(2) of QED from a set of rules for the two-body interaction and generalise these. We show that QED may be decomposed into a two-body interaction at every point in spacetime.

It is usually supposed that the Dirac and radiation equations predict that the phase of a fermion will rotate through half the angle through which the fermion is rotated, which means, via the measured dynamical and geometrical phase factors, that the fermion must have a half-integral spin. We demonstrate that this is not the case and that the identical relativistic quantum mechanics can also be derived with the phase of the fermion rotating through the same angle as does the fermion itself. Under spatial rotation and Lorentz transformation the bispinor transforms as a four-vector like the potential and Dirac current. Previous attempts to provide this form of transformational behavior have foundered because a satisfactory current could not be derived.(14)

The role of parents in the development of anxiety disorders in children is of increasing research and clinical interest. This study investigated interpretation biases of anxious children and their mothers using the ambiguous stimuli task developed by Hadwin, Frost, French, and Richards (1997). Three groups of children (aged 7 to 12 years) and their mothers were recruited; 23 non-clinical controls, 18 children with an anxiety disorder and 15 children with an externalising disorder. Following diagnostic assessments of the children, children and their mothers independently completed the homophone task and self-report measures of anxiety. Mothers of anxious children had significantly higher self-reported anxiety than mothers of non-clinical children. As hypothesised, children in the anxious group had higher threat interpretation scores than the non-clinical group. The hypothesis that mothers of anxious children would make more threat interpretations was not supported. Paired correlations showed no significant association between threat interpretations made by children and their mothers. There was a significant positive correlation between maternal threat interpretation and child anxiety. The results suggest that there is a complex association between mother's anxiety and cognitions and those of their children, which requires further examination in controlled observational and experimental studies, including treatment trials.