Topos for Foundations of Quantum Gravity and Spectral Sequences induced by Non-Discrete Systems

The theory of temporal topos (or t-topos) gives a new definition for treating particlewave duality as one entity, i.e., as a presheaf over a Grothendieck site (generalized time category). The theory t-topos also gives a new definition of an entanglemet of particles providing a natural explanation of the EPR-type non-locality which is much simpler than the well established definition of entanglement given in terms of the Hilbert space decompositions and Hilbert space associated with the global quantum system (See, e.g., [AMS] for the definition.). The notion of generalized time is also discussed in [R.S]. For quantum gravity the theory called the t.g. relativistic principles of t-topos will be announced in [Topos'O4] based on the current project, [E.P.T.T] and [P.M.S.T].