The Hamiltonian of Creation: Operator Foundations of Quantum Gravity and the Modal Genesis of Spacetime

Physics has spent a century attempting to quantize the spatial metric from within the spatial metric, treating spacetime as an irreducible physical container. The consequence of this category error is the Wheeler-DeWitt vanishing identity, where the canonical Hamiltonian constraint evaluates to zero, leaving canonical quantum gravity with a frozen, timeless universe incapable of describing dynamic cosmic genesis.

Furthermore, Einstein’s Equivalence Principle dictates that the gravitational field can always be locally transformed away in a free-falling frame. The short-story is general relativity yields no local conservation law for its own field.

To locate the true conservation principle of gravity, one must step outside the classical container.

Across the death and rebirth of cosmological cycles, the foundational invariant is the Conservation of Probabilia: the strictly unitary preservation of objective quantum potentiality within the pre-geometric Hilbert space of Possibilia. By Stone’s theorem on one-parameter unitary groups, this unbroken unitarity guarantees existence of an exact self-adjoint generator: the Modal Hamiltonian.

Because continuous coordinates and metric tensors dissolve at singular cosmological boundaries, this operator cannot be formulated across spatial coordinates. Instead, it is constructed over an invariant non-spatial conjugate algebra: Informational Volume, which quantifies accessible distinction capacity, and Modular Gravitational Self-Energy Uncertainty, which monitors non-local relational constraint. Through the transitivity of the Gravity-Information-Geometry equivalence class, the quantization of geometry is derived not as an ad hoc postulate, but as an unavoidable deductive consequence of its direct equivalence to discrete, countable information.

Grounding this algebra over the arithmetic scheme of prime knots reveals that the stationary generator operates as an arithmetic resonator whose discrete bound-state spectrum corresponds to the non-trivial Riemann zeros. Dyson level repulsion and Gaussian Unitary Ensemble spectral rigidity exert a trans-Planckian informational degeneracy pressure that permanently stabilizes the pre-collapse vacuum network, preventing collapse into a dead, zero-entropy singular point.

When accumulated modular entanglement saturates the Diósi-Penrose threshold, the system breaches spectral rigidity, triggering the Universal Actualization Event. Non-unitary Lindblad superselection projects out the broken coset directions of an unbroken exceptional master syntax, discharging trapped spectral tension through the Landauer Vacuum Engine. The irreversible erasure of bounded horizon databases converts stored non-local entropy into an explosive outward negative pressure, rupturing event horizons from the inside out and driving the emergence of expanding metric spacetime.

The Hamiltonian of Creation concludes with falsifiable observational commitments in prediction of specific logarithmic harmonic modulations across the stochastic gravitational wave background, accessible to space-based laser interferometers such as LISA, as well as distinct non-linear ringing across the high-multipole acoustic peaks of the Cosmic Microwave Background.

Rigorous, uncompromising, and logically complete, this monograph replaces the container paradigm with a unified, self-sustaining architecture of physical reality.