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3.5.11 Particle Structure

In this present work, mass is treated as a highly concentrated form of energy, a region of the continuum where energy density is extremely high. For reasons of symmetry, such regions are spherical, and high energy density is maintained by high values of curvature. These regions of high energy content constitute particles in which energy content is measured in terms of mass rather than Joules. This is similar to the way that water locked up in ice bergs is measured in tons rather than liters.

Logically, a stationary particle would have the shape of a perfect sphere, and a moving particle would necessarily take up a non- symmetrical shape biased in the direction of its movement. The simplest possibility is that it would become a 'prolate' sphere, that is, shaped like a rugby ball.

The volume of a perfect sphere is \(4/3 \pi r^3\), and for a prolate sphere volume is given as \(4/3 \pi r^3 (1+\Delta r/r)\), where \(r\) is the mid-section radius, and \((r+\Delta r)\) is the radius of the long axis. This constitutes an increase in volume of a moving particle and hence an increase in its energy content assuming that energy density, \(\rho_p\), remains constant. This increase in energy is kinetic energy, and may be calculated as follows.
\begin{align} 'rest'\ energy\ of\ particle =&\ E_o = \frac{4 \pi}{3} r^3 \times \rho_p \nonumber \\
energy\ of\ moving\ particle\ E_m\ =&\ \frac{4 \pi}{3} r^3 (1+\Delta r/r) \times \rho_p =E_o (1+\Delta r/r) \nonumber \\ Kinetic\ energy\ E_k =&\ E_m - E_o = E_o \ \Delta r/r \nonumber \end{align}

This somewhat superficial analysis of particle structure and the consideration of energy content rather than mass, demonstrates the power of structural models over purely mathematical ones. A more detailed analysis of kinetic energy is given in the following section.

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