We formalize the notion of isolated objects, and we build a consistent theory to describe their evolution and interaction. We further introduce a notion of indistinguishability of distinct spacetime paths of a unit, for which the evolution of the state variables of the unit is the same, and a generalization of the equivalence principle based on indistinguishability. Under a time reversal condition on the whole set of indistinguishable paths of a unit, we show that the quantization of motion of spinless (...) elementary particles in a general potential field can be derived in this framework, in the limiting case of weak fields and low velocities. Extrapolating this approach to include weak relativistic effects, we explore possible experimental consequences. We conclude by suggesting a primitive ontology for the theory of isolated objects. (shrink)

This article is a summary of an expanded version of my previous publication Ref. [ 1 ]. In particular, in Ref. [1] using a new axiomatic matrix approach – which has been formulated on the basis of ring theory and Clifford algebra – by first quantization (followed by a basic procedure of minimal coupling to the space-time geometry) of a special relativistic algebraic matrix equation, a certain massive form of gravitational field equations – with new matrix formalism and also a (...) definite form of torsion which generates the gravitational field's invariant mass – is derived uniquely. It is shown that the massless case of these derived equations is equivalent to the Einstein field equations (including a cosmological constant). Moreover, it has been shown that the matrix formalism of derived gravitational field equations, is compatible with matrix representations of certain Clifford algebras. (shrink)