  The paper investigates the physical content of a recently proposed
mathematical framework that unifies the standard formalisms of classical
mechanics, relativity and quantum theory. In the framework states of a
classical particle are identified with Dirac delta functions. The classical
space is "made" of these functions and becomes a submanifold in a Hilbert space
of states of the particle. The resulting embedding of the classical space into
the space of states is highly non-trivial and accounts for numerous deep
relations between classical and quantum physics and relativity. One of the most
striking results is the proof that the normal probability distribution of
position of a macroscopic particle (equivalently, position of the corresponding
delta state within the classical space submanifold) yields the Born rule for
transitions between arbitrary quantum states.
