  Extra dimensions are introduced: 3 in Classical Mechanics and 6 in
Relativistic Mechanics, which represent orientations, resulting from rotations,
of a particle, described by quaternions, and leading to a 7-dimensional,
respectively 10-dimensional, world. The concept of spin is thus defined in both
cases, which results to be different from angular momentum. It leads to the
known concept of Quantum Mechanical spin in both cases. In particular,
application of these new ideas to (Relativistic) Quantum Mechanics, leads to
quantization of energy levels in free electrons, which could be in principle
detectable via their spectrum, confirming the theory.
