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Unification: The Quasi-Classical World is Quantum-Gravity Reality

Andrew Soltau

Published Sep 14, 2026• 1 citation
Publisher

Abstract

Quantum mechanics is the physics of a superposed class of relativistic worlds. The direct evidence is the formalism itself: it is class arithmetic throughout. All worlds that share the same correlation record are indistinguishable, and by that principle constitute one world. The result is a 'class-of-worlds-as-a-world': literally a metaworld. This is the ontology of the quasi-classical world, and the explanation of the physics. The term quantum gravity becomes an ontological description of the quasi-classical world. This is quantum-gravity reality: the quantum superposition of gravitational spacetime worlds. As quantum mechanics is the superposition of the relativistic operation of all the worlds, the science is unified. The cycle of the standard von Neumann formulation is thus the operation of one causal principle, effective alternately at the two levels of logical type. In addition to Process 1, collapse, and Process 2, linear evolution, this framework identifies Process 0: the determinate relativistic dynamics of each world in the class. Process 2 is then the class-level superposition of Process 0; Process 1 is its class-level consequence when it causes the correlation record to change. Thus the formalisms are fully unified, together forming a single causal order. No new equations or dynamics are required. The same physical unification is exposed geometrically in the Compton-Schwarzschild crossing. In the standard resolving experiment, the same physical process operates at the two levels of logical type: the class-level Compton localisation scale contracts as the energy rises, while the element-level Schwarzschild radius expands, the two becoming equal at Planck order. At the crossing, the higher-logical-type quantum description loses its physical referent and the physically instantiated resolving scale becomes Schwarzschild geometry. The crossing is not a merger of the two formalisms at the Planck scale, but the transition for the enclosed region to element-level reality alone. The higher-logical-type class-of-worlds-as-a-world ceases to be constituted there, while relativistic physics continues. In reverse, the same transition is the genesis of the quantum universe in the Big Bang.

DOI
10.5281/zenodo.22757161

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Quantum mechanics is the physics of a superposed class of relativistic worlds. The direct evidence is the formalism itself: it is class arithmetic throughout. All worlds that share the same correlation record are indistinguishable, and by that principle constitute one world. The result is a 'class-of-worlds-as-a-world': literally a metaworld. This is the ontology of the quasi-classical world, and the explanation of the physics. The term quantum gravity becomes an ontological description of the quasi-classical world. This is quantum-gravity reality: the quantum superposition of gravitational spacetime worlds. As quantum mechanics is the superposition of the relativistic operation of all the worlds, the science is unified. The cycle of the standard von Neumann formulation is thus the operation of one causal principle, effective alternately at the two levels of logical type. In addition to Process 1, collapse, and Process 2, linear evolution, this framework identifies Process 0: the determinate relativistic dynamics of each world in the class. Process 2 is then the class-level superposition of Process 0; Process 1 is its class-level consequence when it causes the correlation record to change. Thus the formalisms are fully unified, together forming a single causal order. No new equations or dynamics are required. The same physical unification is exposed geometrically in the Compton-Schwarzschild crossing. In the standard resolving experiment, the same physical process operates at the two levels of logical type: the class-level Compton localisation scale contracts as the energy rises, while the element-level Schwarzschild radius expands, the two becoming equal at Planck order. At the crossing, the higher-logical-type quantum description loses its physical referent and the physically instantiated resolving scale becomes Schwarzschild geometry. The crossing is not a merger of the two formalisms at the Planck scale, but the transition for the enclosed region to element-level reality alone. The higher-logical-type class-of-worlds-as-a-world ceases to be constituted there, while relativistic physics continues. In reverse, the same transition is the genesis of the quantum universe in the Big Bang.
The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. No new physics is required. The complex formalism that seems deeply counterintuitive is class arithmetic. Superposition and interference: properties of classes of worlds. Measurement: set-selection of a subclass compatible with the observed outcome. The uncertainty principle: incompatible set-selections. Fourier transforms: switching set-selection. Operators: enactment of set-selection. Decoherence: loss of coherence between worlds. Normalisation is required because all worlds are equally real, thus the probability of an outcome is essentially the proportion of worlds that instantiate it. True probability arises through phase, which is the degree to which the rest of each world aligns internally with this outcome. This is the second-logical-type phenomenon of interference: the degree to which worlds cohere in the classical actions that give rise to the outcome.This transforms the familiar structures of the formalism from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world: this is the quantum realm. The classical world, quantum mechanics and relativistic physics are unified in logical types.
The quasi-classical world of modern physics is a class of classical worlds superposed, literally a 'metaworld'. The measurement problem is itself evidence for the two different types of world, at the different levels of logical type. The enactment of linear dynamics in the classical worlds alters the class invariant, and thus induces physical collapse of the metaworld to a subclass. The complex formalism that seems deeply counterintuitive is class arithmetic. Measurement: set-selection of a subclass compatible with the observed outcome. Observable operators: partition of the class. Projection operators: set-selection of a subclass. Fourier transforms: switching set-selection. The uncertainty principle: incompatible set-selections. All the familiar structures of the formalism are transformed from postulates to inherent attributes of the class structure. The Born rule, unitary evolution, the complex structure of amplitudes, the probabilistic character of prediction, and the wave-mechanical form of the theory emerge as outputs of the ontology rather than independent axioms. The wavefunction is real. It is the ontological architecture of the metaworld and the reality of the quasi-classical world. The classical world, quantum mechanics and relativistic physics are unified in logical types.
At present, there are two possible, and equally plausible, explanations for the physics of quantum measurement. The first explanation, known as the many-worlds interpretation, does not require any modification of quantum mechanics, and asserts that at the time of measurement the Universe splits into many branches, one branch for every possible alternative. The various branches do not interfere with each other because of decoherence, thus providing a picture broadly consistent with the observed Universe. The second explanation, which requires quantum mechanics to be modified from its presently known form, is that at the time of measurement the wavefunction collapses into one of the possible alternatives. The two explanations are mutually exclusive, and up until now, no theoretical reasoning has been put forward to choose one explanation over the other. In this article, we provide an argument which implies that the collapse interpretation is favored over the many-worlds interpretation. Our starting point is the assertion (which we justify) that there ought to exist a reformulation of quantum mechanics which does not refer to a classical spacetime manifold. The need for such a reformulation implies that quantum theory becomes nonlinear on the Planck mass/energy scale. Standard linear quantum mechanics is an approximation to this nonlinear theory, valid at energy scales much smaller than the Planck scale. Using ideas based on noncommutative differential geometry, we develop such a reformulation and derive a nonlinear Schrödinger equation, which can explain collapse of the wavefunction. We also obtain an expression for the lifetime of a quantum superposition. We suggest ideas for an experimental test of this model.
I will propose that the reality to which the quantum formalism implicitly refers is a kind of generalized history, the word history having here the same meaning as in the phrase sum-over-histories. This proposal confers a certain independence on the concept of event, and it modifies the rules of inference concerning events in order to resolve a contradiction between the idea of reality as a single history and the principle that events of zero measure cannot happen (the Kochen-Specker paradox being a classic expression of this contradiction). The so-called measurement problem is then solved if macroscopic events satisfy classical rules of inference, and this can in principle be decided by a calculation. The resulting conception of reality involves neither multiple worlds nor external observers. It is therefore suitable for quantum gravity in general and causal sets in particular. Quantum gravity and quantal reality Why, in our attempts to unify our theories of gravity and the quantum, has progress been so slow? One reason, no doubt, is that it's simply a very hard problem. Another is that we lack clear guidance from experiments or astronomical observations. But I believe that a third thing holding us back is that we haven't learned how to think clearly about the quantum world in itself, without reference to “observers” and other external agents. Because of this we don't really know how to think about the Planckian regime where quantum gravity is expected to be most relevant. We don’t know how to think about the vacuum on small scales, or about the inside of a black hole, or about the early universe. Nor do we have a way to pose questions about relativistic causality in such situations.
According to the Everett interpretation of quantum mechanics, the apparent paradoxes of quantum theory require no change either in our philosophical attitude toward scientific theories or in the formalism of quantum mechanics itself. Rather, the unaltered theory can be understood as a literal description of physical reality. But the physical reality thus described is one of many noninteracting, approximately classical worlds. These worlds enter the theory not at the fundamental level—they are nowhere to be found in the basic formalism—but at a higher, emergent level; in this sense they are (ontologically speaking) on a par with the ontology of the special sciences.