We construct a world model consisting of a matter field living in 4 dimensional spacetime and a gravitational field living in 11 dimensional spacetime. The seven hidden dimensions are compactified within a radius estimated by reproducing the particle–wave characteristics of diffraction experiments. In the presence of matter fields the gravitational field develops localized modes with elementary excitations called gravonons which are induced by the sources (massive particles). The final world model treated here contains only gravonons and a scalar matter field. The gravonons are localized in the environment of the massive particles which generate them. The solution of the Schrödinger equation for the world model yields matter fields which are localized in the 4 dimensional subspace. The localization has the following properties: (i) There is a chooser mechanism for the selection of the localization site. (ii) The chooser selects one site on the basis of minor energy differences and differences in the gravonon structure between the sites, which at present cannot be controlled experimentally and therefore let the choice appear statistical. (iii) The changes from one localization site to a neighbouring one take place in a telegraph-signal like manner. (iv) The times at which telegraph like jumps occur depend on subtleties of the gravonon structure which at present cannot be controlled experimentally and therefore let the telegraph-like jumps appear statistical. (v) The fact that the dynamical law acts in the configuration space of fields living in 11 dimensional spacetime lets the events observed in 4 dimensional spacetime appear non-local. In this way the phenomenology of CQM is obtained without the need of introducing the process of collapse and a probabilistic interpretation of the wave function. Operators defining observables need not be introduced. All experimental findings are explained in a deterministic way as a consequence of the time development of the wave function in configuration space according to Schrödinger’s equation without the need of introducing a probabilistic interpretation.
We develop a deterministic theory which accounts for the coupling of a high dimensional continuum of environmental excitations (called gravonons) to massive particle in a very localized and very weak fashion. For the model presented Schrödinger's equation can be solved practically exactly in 11 spacetime dimensions and the result demonstrates that as a function of time an incoming matter wave incident on a screen extinguishes, except at a single interaction center on the detection screen. This transition is reminiscent of the wave - particle duality arising from the ''collapse" (also called ''process one") postulated in the Copenhagen-von Neumann interpretation. In our theory it is replaced by a sticking process of the particle from the vacuum to the surface of the detection screen. This situation was verified in experiments by using massive molecules. In our theory this "wave-particle transition" is connected to the different dimensionalities of the space for particle motion and the gravonon dynamics, the latter propagating in the hidden dimensions of 11 dimensional spacetime. The fact that the particle is detected at apparently statistically determined points on the screen is traced back to the weakness and locality of the interaction with the gravonons which allows coupling on the energy shell alone. Although the theory exhibits a completely deterministic "chooser" mechanism for single site sticking, an apparent statistical character results, as it is found in the experiments, due to small heterogeneities in the atomic and gravonon structures.
A particle switching between two sites of a symmetric system in weak interaction with an environmental continuum of high density of states exhibits a telegraph-signal-like time development without the need of the Born-Bohr principle of reduction on eigenstates of the measuring equipment. The origin of the telegraph signal is a very weak local coupling of the particle to the continuum of gravitons which is connected with an enormous slow down of the particle motion. The proposed mechanism envisages entanglement to gravitons in high dimensional spacetime, which, in accord with Gauss law, gives rise to a local and much stronger gravitational law compared to classical gravitation. The physics behind the quantum jumps and the telegraph-signal-like time development is elucidated. The model might be useful for studying environmental decoherence effects on adsorbate localization and quantum diffusion on solid surface.
This Volume III develops a complete geometric formulation of quantum mechanics, demonstrating that quantum phenomena emerge from the very structure of spacetime. We demonstrate that Einstein's field equations—when interpreted in the spectral domain and taking phase coherence into account—already contain the entire structure of quantization. Quantum mechanics appears not as an axiom, but as a geometric consequence. Based on the experimental and mathematical results consolidated in Volumes~0, I, and II, the present work shows that quantization need not be postulated: it arises inevitably from three fundamental geometric elements—proper frequency, parallel transport, and phase coherence. The action appears as the phase accumulated along the worldline, and its discretization into coherence windows, derived without external hypotheses, naturally leads to the condition
Sn=nh and to all associated quantum phenomenology. We derive the Schrödinger equation as the limit of short windows, obtain the commutator
[x,p]=iℏ from the incompatibility between spatiotemporal synchronizations, and reinterpret interference, propagators, and decoherence as spectral properties of parallel transport. The Hilbert space arises as the spectral space of the metric, observables correspond to generators of isometric deformations, while the collapse is understood as the geometric selection of coherent subspaces. The formalism extends to relativistic particles, spin, quantum statistics, the Dirac equation, harmonic oscillators, and field quantization, where spectral modes of the metric assume the role of particles: photons as harmonic 1-forms, weak modes as connections of 2-forms, gluons as 3-forms, and the Higgs as the fundamental scalar curvature mode. The reinterpretation of the Standard Model thus becomes a direct consequence of spectral geometry. The Volume culminates in the Central Theorem —Geometry = Quantization— showing that the entire quantum structure is a manifestation of the spectral granularity of spacetime. We conclude with experimental predictions and falsification criteria, as well as the conceptual framework necessary for Volume~IV, dedicated to the complete quantization of the metric within the same paradigm.
Quantum systems are viewed as emergent systems from the fundamental degrees of freedom. The laws and rules of quantum mechanics are understood as an effective description, valid for the emergent systems and specially useful to handle probabilistic predictions of observables. After introducing the geometric theory of Hamilton-Randers spaces and reformulating it using Hilbert space theory, a Hilbert space structure is constructed from the Hilbert space formulation of the underlying Hamilton-Randers model and associated with the space of wave functions of quantum mechanical systems. We can prove the emergence of the Born rule from ergodic considerations. A geometric mechanism for a natural spontaneous collapse of the quantum states based on the concentration of measure phenomena as it appears in metric geometry is discussed.We show the existence of stable vacua states for the quantized matter Hamiltonian. Another consequence of the concentration of measure is the emergence of a weak equivalence principle for one of the dynamics of the fundamental degrees of freedom. We suggest that the reduction of the quantum state is driven by a gravitational type interaction. Such interaction appears only in the dynamical domain when localization of quantum observables happens, it must be a classical interaction. We discuss the double slit experiment in the context of the framework proposed, the interference phenomena associated with a quantum system in an external gravitational potential, a mechanism explaining non-quantum locality and also provide an argument in favour of an emergent interpretation of every macroscopic time parameter. Entanglement is partially described in the context of Hamilton-Randers theory and how naturally Bell's inequalities should be violated.
Subtitle: Temporal Field Realism: A Deterministic Foundation for Quantum Phase and Wavefunction Dynamics (Quantum mechanics as temporal resonance, the Born rule as statistical phase averaging, and measurement as phase synchronization.) Theory of Time is a fundamental four-volume corpus that presents time as a physical condensate — the Temporal Condensate. Together, the four volumes establish a self-consistent physical framework, spanning the deterministic ontology of quantum fields, the structure of elementary particles, the cosmological evolution of the Universe, and the dynamical nature of gravitation. Theory of Time I: The Core This volume introduces Temporal Field Realism, establishing time as a fundamental dynamical field rather than a passive coordinate. The quantum wavefunction ψ is derived as a resonant excitation mode of the temporal field τ. The Born rule emerges as a statistical consequence of phase averaging, while quantum measurement is reinterpreted as a process of dynamical phase synchronization between physical systems and the temporal medium. Theory of Time II: The Evidence This volume demonstrates that the spectrum of elementary particles arises from topological vortices of temporal flow. Leptonic and quark masses are derived as harmonic modes of hypertime, reducing the empirical parameters of the Standard Model to geometric constants of the temporal manifold. The work provides a structural interpretation of particle generations, mixing matrices, and mass hierarchies. Theory of Time III: The Scale This volume develops the cosmological implications of temporal field dynamics. The inflationary paradigm is replaced by the dynamics of a non-commutative time operator T̂(x). The horizon and flatness problems are resolved through algebraic connectivity of the five-dimensional temporal manifold. The model predicts observational signatures in primordial gravitational wave spectra and potential anomalies in the Cosmic Microwave Background. Theory of Time IV: The Gravity This volume reformulates gravitation as transport and conductivity within the temporal condensate. Dark matter and dark energy are interpreted as emergent effects of temporal susceptibility χτ and internal temporal pressure. Gravitational waves are described as longitudinal acoustic modes propagating through the temporal medium, providing a unified dynamical description of inertial, gravitational, and cosmological phenomena.