  We construct an idealized universe for didactic purposes. This universe is
assumed to consist of absolute Euclidean space and to be filled with a
classical medium which allows for sound waves. A known solution to the wave
equation describing the dynamics of the medium is a standing spherical wave.
Although this is a problem of classical mechanics, we demonstrate that the
Lorentz transformation is required to generate a moving solution from the
stationary one. Both solutions are here collectively referred to as "spherons".
These spherons exhibit properties which have analogues in the physical
description of matter with rest mass, among them de Broglie like phase waves
and at the same time "relativistic" effects such as contraction and a speed
limit. This leads to a theory of special relativity by assuming the point of
view of an observer made of such spheronic "matter". The argument made here may
thus be useful as a visualisation or didactic approach to the real universe, in
which matter has wave-like properties and obeys the laws of special relativity.
