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3.3.3 Moving Objects

As already noted, in this new theory, mass is assumed to be a concentration of energy in the form of spherical particles which are also the origin of gravity. These 'gravitational particles' are part of the energy continuum in the sense that there is no hard boundary between the energy in the particle and the energy in the surrounding continuum. When a particle moves through the energy continuum, the actual 'thing' that moves is simply a region of high energy density.

In dealing with the motion of a material object within the continuum, it is convenient to view it as an aggregation of gravitational particles. This means that massive objects may be analyzed as a single particle on the basis that a theory of movement of one particle will be the same for a whole aggregate. This is similar to the way that Newton reduced objects to their centers of gravity, and represented them as geometrical points. However, in single particle reduction, atomic theory remains valid because a gravitational particle is a structure of finite extent consisting of energy - it is not a geometrical point.

In analyzing the behavior of particles in motion, mathematical relationships between local variables may be established via local coordinate systems conveniently located and of appropriate dimensionality. Straight line motion of a gravitational particle within the continuum is easily analyzed using only two axes. Since expansion of the continuum and motion within it consists of two straight trajectories, a coordinate system which represents them can be established on an imaginary flat surface common to both. One axis is required to represent location of the continuum in the fourth dimension (f-axis) into which it is moving. The other axis (x-axis), represents the location of a particle within the continuum.

On the scale of individual particles, the curvature of the continuum is negligibly small, so that in the following analysis the continuum is assumed to be three dimensional and flat (Euclidean). Hence, whatever the direction of straight line motion of a particle within the continuum, it is always at right angles to the direction of expansion. Therefore, without loss of generality, we can specify that a moving particle does so along the x-axis, and this x-axis represents the continuum which, itself, is moving into the fourth dimension with expansion velocity \(v_x=c_0\), where \(c_0\) is the expansion velocity of the stationary continuum.

The trajectory in four dimensions of a stationary particle, \(v=0\), can be represented in two dimensions, as a straight line parallel to the f-axis (direction of expansion). For a particle moving within the continuum, with velocity, v, its total velocity in four dimensions, \(c_v\), is given by the vector addition, \(c_v^2 = c_0^2 + v^2\). Its trajectory is now at the tilt angle \(\theta\) to the f-axis, where $\theta$ is given by, \(\tan(\theta) = v/c_0\), or equivalently by \(\cos(\theta) =c_0/c_v\).

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