We propose a formalism in which gravity arises not as a fundamental force but as the macroscopic geometric manifestation of quantum state collapse. In this framework, the probabilistic quantum domain (governed by quantum mechanics) and the deterministic spacetime domain (governed by general relativity) represent distinct ontological states connected by a collapse mapping \(C: \mathcal{H} \rightarrow \mathcal{M}\). Spacetime curvature emerges as a record of collapse events (\(R = -8\pi G \rho_C\)), and time arises procedurally from collapse progression (\(d\tau = k \, dC\)). The model resolves long-standing paradoxes including the cosmological constant problem, the arrow of time, and quantum non-locality by treating spacetime as the emergent geometry of realized quantum interactions rather than a fundamental background.
The model posits two fundamentally distinct ontological domains:
The connection between these domains is formalized through a collapse mapping:
This mapping transforms probabilistic quantum states into deterministic spacetime configurations, with the local collapse density defined as:
Theorem 1 (Collapse-Curvature Correspondence)
The Ricci scalar curvature is proportional to the local collapse density:
where the divergence term vanishes under complete collapse, recovering Einstein's field equations.
Theorem 2 (Time-Collapse Equivalence)
Proper time emerges from collapse progression:
Time advances if and only if collapse occurs, making temporal flow a procedural aspect of quantum realization.
Quantum mechanics describes not objects in spacetime, but the fundamental relational logic from which spacetime and objects co-emerge. The quantum state encodes a network of possible interactions and correlations - a "pre-geometric" domain where "where" and "when" are not yet defined.
Key Insight: Quantum phenomena like entanglement and superposition represent intrinsic, non-spatial relatedness. Indeterminacy reflects the simultaneous presence of multiple coherent relational patterns awaiting realization.
The critical transition between domains occurs at the inflection manifold \(\Sigma\), defined by:
This null hypersurface acts as the operational horizon where:
Light propagates along this interface, serving as the messenger of realization.
Spacetime geometry is not a pre-existing stage but the causal and geometric structure dynamically formed by networks of realized quantum interactions. Each measurement or observation constitutes a "realization event" that contributes to spacetime fabric.
The perceived geometry is perspectival: each observer's trajectory is defined by their unique sequence of realization events. Geometry represents the internal view of a system realizing itself through interactive processes.
In this framework, General Relativity represents the large-scale thermodynamics of the quantum realization process:
Curvature reflects not mass-energy directly, but the local density and flow of realization events. High matter density corresponds to persistent, rapid actualization of quantum potential.
The vacuum energy catastrophe (10¹²² discrepancy) dissolves because:
Temporal asymmetry emerges naturally from the one-way mapping \(C: \mathcal{H} \rightarrow \mathcal{M}\). The future - present direction of collapse provides a dynamical origin for time's arrow without special initial conditions.
Entanglement correlations appear "spooky" only when viewed through emergent spacetime:
No violation of relativistic causality occurs.
Wavefunction collapse is not mysterious but constitutes the physical process that generates classical reality. Measurement represents a complex form of the same interaction dynamics that build spacetime.
The first law of thermodynamics - energy cannot be created or destroyed - finds a natural interpretation in this framework:
Energy exists in two forms:
The collapse mapping \(C: \mathcal{H} \rightarrow \mathcal{M}\) transforms energy from probabilistic to deterministic form without creation or destruction. Each collapse event converts quantum potential \(\Delta E_{\text{quantum}}\) into geometric imprint \(\Delta T_{\mu\nu}\), with the Bianchi identity ensuring conservation through the emergent spacetime geometry.
This framework naturally resolves the vacuum energy catastrophe:
Key Insight: Energy conservation acts as the fundamental accounting rule governing the transition between quantum potential and classical reality. The "bookkeeper" role of gravity ensures the energy ledger remains balanced across the ontological divide.
The collapse mapping \(C: \mathcal{H} \rightarrow \mathcal{M}\) operates with a fundamental conversion rate given by Einstein's equation:
This reformulation reveals that \(E = mc^2\) is not merely an energy-mass equivalence, but the exchange rate of the collapse process itself. The constant \(c^2\) quantifies how much geometric mass emerges from each unit of quantum energy realized through collapse.
In this view, the speed of light squared (\(c^2\)) becomes the fundamental conversion constant between the probabilistic and deterministic domains - the "exchange rate" at the quantum-geometric interface.
Key Reformulation: The collapse mapping \(C\) operates with the fundamental conversion rate \(c^2\), making Einstein's equation the bridge between quantum potential and spacetime geometry. Mass emerges as the geometric signature of realized quantum energy, with \(c^2\) as the precise conversion factor.
The Planck interface may be summarized as a single projection relation:
Legend. K: dimensionless pre-state of the wave function; \(\Psi(K)\): probabilistic field; \(\Sigma\): inflection (Planck-scale slit) through which the pre-state redirects into the dimensional observables of mass \(m\), vacuum energy density \(\rho_{\mathrm{vac}}\), spacetime metric \(g_{\mu\nu}\), and procedural time \(t\).
The model makes a decisive prediction:
Falsification: Observation of gravitational entanglement before collapse would refute the framework.
Each quantum collapse should produce a transient, classical-like fluctuation in local gravitational potential, detectable as correlated signals in:
Manipulating which-path information should statistically shift collapse timing distributions, observable in coincidence analyses.
The abstract collapse map C finds mechanistic implementation through RTI's offer-confirmation handshakes:
Transactional entropy generation links to Verlinde's entropic gravity:
Yielding MOND-like corrections and cosmological constant terms naturally.
The framework suggests:
The Planck scale represents not a limit of smallness, but an ontological boundary where dimensional concepts undergo fundamental transformation:
This mathematical singularity marks the transition from dimensional spacetime to non-dimensional potentiality, where:
The divergences that appear in quantum field theory below Planck scale are not mathematical pathologies but ontological boundary markers:
Below the Planck boundary lies a domain characterized by:
The fundamental equation becomes:
Where Planck units serve as conversion factors between dimensional and non-dimensional domains.
This framework reveals that the quest to "quantize gravity" is misguided. Instead, we discover that:
Fundamental Reversal: We are not quantizing spacetime, but discovering that spacetime is already the classical approximation of a more fundamental non-dimensional computational domain. The infinities at Planck scale are the mathematical signature of this ontological transition.
This ontological transition at the Planck scale finds deeper expression through a reconsideration of the Heisenberg uncertainty principle, revealing it as a signature of the dimensional boundary itself:
The Heisenberg relation, $$\Delta x\,\Delta p \ge \frac{\hbar}{2},$$ is commonly read as a limit on simultaneous knowledge of position and momentum. Within the GaC interpretation this bound is not a defect of measurement but the signature of a deeper geometry: the quantum state is fundamentally non-dimensional. Before realization the state \( \Psi(K) \) exists as a singular, atemporal unity outside the coordinates of space and time. When it is projected through the Planck-scale inflection \( \Sigma \) into dimensional variables \((x,p)\), a single relation becomes two complementary observables. Their mutual indeterminacy marks the interface where a dimensionless origin meets the dimensional manifold.
At this interface a momentary parity arises - an equilibrium between potential and realized states, between the future and the present. The Planck inflection therefore functions as a parity surface: $$\Psi(K)\ \overset{\text{parity}}{\underset{\Sigma}{\leftrightarrow}}\ \Phi(x).$$ Such perfect balance cannot persist, for a static parity would freeze realization and halt time. Collapse must therefore occur as the resolution of parity, selecting one aspect of the symmetry for realization while preserving its conjugate as uncollapsed potential. In each collapse event the quantum domain yields a localized spacetime asymmetry - mass, curvature, and causal direction - yet retains global equilibrium through the persistence of its remaining amplitudes.
The process maintains overall unitarity: $$\int |\Psi(K)|^2\,dK = 1.$$ Probability is the bookkeeping that guarantees the conservation of global symmetry as local asymmetries emerge. Collapse does not destroy the quantum state; it redistributes symmetry - pairing every realized outcome in spacetime with an unmanifested complement in the quantum domain. Spacetime, with its apparent direction and entropy, is thus the cumulative record of these asymmetric resolutions, while the quantum substrate remains a perfectly symmetrical whole.
In summary, the uncertainty principle exposes the dimensional boundary of a non-dimensional quantum state; parity defines the equilibrium between potential and realization; collapse resolves that equilibrium, ensuring dynamical continuity; and symmetry is globally preserved even as spacetime arises through local asymmetry. Collapse is therefore not the breaking of symmetry but its continual preservation through transformation—the mechanism by which a timeless quantum unity manifests as an evolving universe. In this view, the realized universe is one coherent sequence of such resolutions—a singular timeline drawn from an infinite field of simultaneous potential timelines. Each collapse defines one path through the non-dimensional symmetry, while the uncollapsed potentials preserve the totality of all possible histories. Our measurable reality is thus a single projection within an atemporal ensemble that remains perfectly symmetrical in the quantum domain.
Spacetime geometry emerges through ontological inversion where quantum potential transforms into geometric reality. This inversion represents a fundamental dimensional transformation - potentially a time inversion, energy inversion, topological inversion, or convective process - that bridges the quantum and classical domains:
This framework proposes:
The inversion is formalized as a projective transformation:
where \(\mathcal{H}_0\) represents zero-dimensional quantum potential, \(\mathcal{M}\) the emergent spacetime manifold, \(\rho_0\) primordial potential density, and \(\rho_C(x)\) local collapse density.
Key Resolutions:
Every spacetime point maintains connection to the zero-point via collapse mapping \(C\), making the universe a holographic projection from fundamental potential.
The Converged Transaction-Collapse Model represents a fundamental inversion of the quantum gravity problem. Rather than quantizing spacetime geometry, it geometrizes quantum collapse. This inversion arises from a profound ontological insight: because we cannot observe the quantum domain directly, we are bound to the post-collapse present - the deterministic realm where classical physics prevails.
The Planck scale reveals itself as the ultimate frontier, where dimensional physics undergoes ontological transformation into non-dimensional computation. The mathematical singularities that appear are not problems to be solved but boundary markers indicating where our familiar concepts of space, time, and matter dissolve into pure potentiality.
The frontier between probabilistic future and deterministic present manifests as a geometric ledger, where the act of realization imprints itself as the fundamental phenomena we experience: mass (compacted realization), light (propagating realization), vacuum (unrealized potential), and gravity (the curvature of realization itself), all unfolding under the single currency of time.
In this framework, any deterministic system can serve as an "observer" - from conscious beings to measuring devices to elementary particles. What defines an observer is not consciousness but participation in the deterministic domain through interaction. Every collision, every entanglement, every measurement that resolves quantum ambiguity contributes to the geometric ledger of spacetime.
Thus, gravity emerges not as a force to be quantized, but as the macroscopic trace of the quantum-to-classical transition itself. The model provides a unified resolution to multiple paradoxes through a single coherent principle: spacetime is the historical geometry of quantum realization. This framework is empirically testable, mathematically formalizable, and ontologically coherent, offering a promising path toward unifying quantum theory and general relativity.