  Recently it was shown that classical "relativistic" particle dynamics was
implicit in physics going back to Maxwell. The demonstration utilized a simple
modification of a 1906 thought experiment by which Einstein established the
mass equivalence of energy, independently of the relativity postulates. The
modified thought experiment leads directly to correct expressions for the
momentum and kinetic energy of a particle at high speed. In the present paper,
one additional ingredient is added, namely, the Bohr quantization rule of the
old quantum theory. It is found that a semi-classical model of a hydrogen atom
and a hydrogen molecule ion exhibit, respectively, time dilation and length
contraction.
