Study on Real Hilbert Spaces Theory of Measurements

Herein we present an alternative version of non-relativistic Newtonian mechanics within the
mathematical framework of a real Hilbert space. It has been demonstrated that the physics of this
scheme correspond to the standard formulation. Heisenberg-Schrödinger non-relativistic quantum
mechanics is considered to be adequate and complete. The present paper is devoted mainly to
problems related to measurement theory. Within the classical world we are working in a Heisenberg
representation. The Hilbert space appears to be uniquely defined and rigid and plays the role of a
passive arena for events associated with the dynamics of the physical system. The space-time
continuum plays a similar role in the standard formulation of Newtonian mechanics. Since the
suggested theory is dispersion free, the linear superposition principle, while not violated cannot affect
measurement results due to the spectral decomposition theorem for self-adjoint operators (the
collapse of the wave function).