A Simple Model for Teaching Special Relativity

Mathematical analysis of the Dirac equation indicates that mass is associated with rotation of wave velocity. Hence, we can expect that a wave propagating in a circle would exhibit some properties of elementary particles. Such a stationary wave-like particle can be modeled by drawing lines of constant phase (i.e. wave crests) on a transparency sheet, then rolling up the sheet along an axis parallel to the wave crests to represent waves propagating in circles around a cylinder. Moving particles are then represented by rotating the orientation of each wave crest so that the propagation direction has an axial component, forming helical paths. Comparison of the stationary and moving wave packets offers a good demonstration of special relativity because the wave equation (and any solution) is Lorentz covariant. Time dilation results from assuming that the particle “clock” ticks once each time the wave traverses 360 degrees around the cylinder. Rotation of the wave crests reduces the length of the wave packet along the axis. The relativistic frequency shift results from the fact that rotating the individual wave crests decreases the wavelength. The deBroglie wavelength is simply the spacing between wave crests along the axis of the cylinder.