  150 years after the discovery of quaternions, Hamilton's conjecture that
quaternions are a fundamental language for physics is reevaluated and shown to
be essentially correct, provided one admits complex numbers in both classical
and quantum physics, and accepts carrying along the intricacies of the
relativistic formalism. Examples are shown in classical dynamics,
electrodynamics, and quantum theory. Lanczos's, Einstein's, and Petiau's
generalizations of Dirac's equation are shown to be very naturally formulated
with biquaternions. The discussion of spin, isospin, and mass quantization is
greatly facilitated. Compared with other formalisms, biquaternions have the
advantage of giving compact but at the same time explicit formulas which are
directly usable for algebraic or numerical calculations.
