Particle motion

This is what motion is for a particle.  It's a first order (first derivative) Gaussian wave.  (All images as stolen from the internet.)

Motion is left to right.  The particle is both the center (zero point) of the wave, and the entire wave.

Here it is in 3D.

The important part about a field is the gradient (relative change at any point).  This is what does work.  Work is change.  Gravity and motion are the same thing, so they must share a cause.  Spacetime is the field that describes motion.  Lorentzian gamma shift is caused by the particle's internal gradient, combined with the gradient of the spacetime path.  Two particles with identical velocity (speed and direction) in a level field will have blue and red shifts that exactly cancel out between them.  Notice that there is no blue/red shift at 90 degrees to the direction of motion.

Always remember the zeroth law of physics - everything except energy adds up to nothing.

For some deeper insight into energy, see Hans G. Schantz's paper on standing waves.