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Logic of ER III - Physics Underdetermination: Constructive Toy Models for a Dynamic Ontology in Spacetime and Hilbert Space

Tenzin Trepp

Published Apr 4, 2026• 0 citations
Publisher

Abstract

We challenge the common view that relativity and quantum formalisms compel a static block-universe ontology. Instead, we show that Existential Realism (ER) – can be formulated as an ontological extension of the specific physical models studied here, leaving empirical predictions unchanged so long as the added ER structure remains empirically idle. First, we clarify that the mathematical formalism of physics is neutral: one can impose a preferred foliation or an existence predicate without changing the equations. Second, we explicitly construct ER-compatible models for Minkowski spacetime (special relativity) and a finite-dimensional quantum system. In these Minkowski-spacetime and finite-dimensional quantum toy models, we show that the standard relativistic dynamical laws, Born-rule calculations, and unitary evolution between measurements are preserved, while the ER additions remain extra ontological structure. More precisely, we have constructed models that are empirically equivalent and dynamically identical while differing in their ontological assignments, thereby demonstrating underdetermination in a model-theoretic sense. We conclude that relativity and quantum theory, in the model presented here, do not logically force eternalism, leaving ER as a viable alternative ontology.

DOI
10.5281/zenodo.20020404

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We challenge the common view that relativity and quantum formalisms compel a static block-universe ontology. Instead, we show that Existential Realism (ER) – can be formulated as an ontological extension of the specific physical models studied here, leaving empirical predictions unchanged so long as the added ER structure remains empirically idle. First, we clarify that the mathematical formalism of physics is neutral: one can impose a preferred foliation or an existence predicate without changing the equations. Second, we explicitly construct ER-compatible models for Minkowski spacetime (special relativity) and a finite-dimensional quantum system. In these Minkowski-spacetime and finite-dimensional quantum toy models, we show that the standard relativistic dynamical laws, Born-rule calculations, and unitary evolution between measurements are preserved, while the ER additions remain extra ontological structure. More precisely, we have constructed models that are empirically equivalent and dynamically identical while differing in their ontological assignments, thereby demonstrating underdetermination in a model-theoretic sense. We conclude that relativity and quantum theory, in the model presented here, do not logically force eternalism, leaving ER as a viable alternative ontology.
Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, and complement. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by many factors, such as static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Cause and effect are not considered primitive assumptions in ER, but as derived features of lawful transition when one distinction directionally conditions another relative to a selected ordering basis. Derivation and recovery constraints for the major models of physics are presented in this paper. Classical Hamiltonian mechanics is recovered through symplectic, interaction-conditioned transitions. Born-rule probability is motivated through normalization, additivity over exclusive distinctions, and context-consistency in Hilbert-space event structures. Schrödinger evolution follows from reversible transitions preserving quantum distinguishability, while entanglement corresponds to nonfactorizable joint transition. Quantum field theory is incorporated by treating fields as context-indexed operator structures and particles as excitation distinctions. Lorentzian signature, general relativity, gauge connections, the Standard Model gauge group, and conservation laws are treated as context-specific recoveries. The paper proposes empirical programs to test whether context-boundary residuals associated with ER can improve existing physical explanations.
Quantum physics has dramatically reshaped our understanding of time and reality, revealing that the present moment occupies a uniquely privileged position within physical processes. In the first paper ("Quantum Physics Prefers the Present: A Temporal Ontology Grounded in Measurement"), we saw how quantum phenomena such as wavefunction collapse and measurement highlight the “now” as the only time when possibilities become actual. However, simply embracing presentism – the doctrine that only the present exists – is not enough. Presentism’s traditional metaphysical stance, which conflates existence with reality by declaring all non-present things unreal, runs into serious conceptual roadblocks when confronted with quantum experiments and the demands of causality and truth over time. This second paper advocates Existential Realism (ER) as a more nuanced and robust ontological framework that builds on those quantum insights while overcoming presentism’s limitations. By rigorously distinguishing existence from reality, ER provides a richer account of quantum phenomena – one that honors the special role of the present without erasing the past or negating the future. We will argue that ER better captures the ontology implied by quantum mechanics, from delayed-choice experiments and collapse theories to decoherence, and that it empowers a view of time where “becoming” and temporal agency are coherent and defensible. In short, Existential Realism preserves the empirical centrality of the present while acknowledging the tangible reality of past causes and future possibilities — making it a more comprehensive fit for quantum reality.
Modern physics has increasingly highlighted the special role of the present moment in the unfolding of reality.Quantum experiments suggest that reality is not a static fourdimensional block but is actively determined in the present moment, 1 as measurements seem to bring about definite outcomes only at the instant they are performed.This resonates with presentist intuitions (the view that only the present exists), yet strict presentism faces serious metaphysical problems.How can only the present be real, if past causes clearly leave effects and future events are anticipated?This paper advocates Existential Realism (ER) as a superior ontological framework that preserves the primacy of the present while accounting for the reality of past causes and future possibilities.Building on our earlier introduction of ER and critique of presentism's limits, we will show that ER provides a richer ontology for quantum phenomena -one that distinguishes between existence and reality, and accommodates genuine becoming and temporal agency in ways that purely present-based theories 1 Wheeler, J.
Modern quantum mechanics, despite its relativistic extensions, provides intriguing support for a present-centered view of time. This paper argues that quantum phenomena – indeterminacy, wavefunction collapse, the Born rule, and temporal asymmetries in measurement – challenge the static block universe of eternalism and instead elevate the present moment to ontological prominence. Remaining largely interpretation-neutral, we draw on a range of perspectives (from Einstein’s relativity to collapse models, and thinkers like Heisenberg, Rovelli, Maudlin and others) to show that quantum theory operationally distinguishes past, present, and future in a way classical physics did not. We examine how the measurement problem and the randomness of quantum outcomes resist a fully eternalist description, highlight how quantum mechanics introduces an arrow of time at a fundamental level, and consider proposals (e.g. GRW theory, delayed-choice experiments) that make a global present – or something akin to it – conceptually necessary. Classical philosophers and physicists from Einstein to Schrödinger are discussed alongside contemporary voices. While stopping short of endorsing any single ontology outright, we contend that the empirical success of quantum theory re-opens the case for presentism or related “A-theoretic” models of time. In closing, we introduce Existential Realism as a novel metaphysical framework aligning with these insights – one which preserves the special status of the present while accommodating the reality of past and future in a more dynamic ontology. The result is a rigorous yet accessible interdisciplinary inquiry: quantum physics, we conclude, prefers the present, suggesting time’s passage and the now are more than mere illusions.
This paper develops an extension of Existential Realism, a philosophical framework that distinguishes existence (what concretely is in the present moment) from reality (the broader causal–structural domain that includes past events, causal relations, informational traces, and structured future possibilities that are real but not presently existent). We synthesize core ideas from the original Existential Realism framework—ontological emergence, entanglement, temporal asymmetry, dimensional collapse, and the notion of a “dimensionless source”—and push them into new conceptual terrain. Time is placed at the heart of ontology: the present moment is the locus of existence, continually generating new actuality from prior reality. Past and future are real (with causal efficacy and structure) yet lack present existence. We explore how this two-tiered temporal ontology can accommodate key features of modern physics and metaphysics. In particular, we argue that ontological emergence at each moment provides a genuine arrow of time and a solution to the puzzle of how determinate events arise from an indeterminate backdrop. Quantum entanglement and nonlocal correlations, far from undermining a temporally oriented realism, instead hint at a deeper layer of unity “beneath” spacetime—a layer we articulate as a dimensionless source of reality. The dimensionless source is defined as a non-spatiotemporal relational structure encoding the informational constraints under which spatiotemporal events emerge through sequential actualization. It contains the informational constraints and lawful relations governing the generation of successive present states of the universe. We propose that spacetime and its separations emerge from this atemporal, aspatial ground, such that phenomena like entanglement and wavefunction collapse reveal the traces of a more fundamental order where spatial distance and temporal succession are secondary. Throughout, we connect these ideas to contemporary debates in quantum foundations (e.g. the measurement problem and objective collapse theories), philosophy of time (presentism, eternalism, and the reality of becoming), and speculative metaphysics (structural realism and process ontology). The result is a comprehensive, present-centered realist ontology that aims to reconcile the lived reality of time’s flow with the insights of modern physics, suggesting new avenues for understanding causality, identity, and agency in a dynamic universe.
Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, complement, admissible transformation class, and boundary structure. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Derivation, recovery, and reinterpretation constraints for the major models of physics are presented. Classical Hamiltonian mechanics and quantum field theory are recovered as special context structures. Born-rule probability, continuous Schrödinger evolution, Lorentzian signature, and gauge connection result from conditional derivations under stated auxiliary assumptions. General relativity is developed in greater depth through the Proposition of Metric-Stress-Energy Co-Admissibility, in which diffeomorphism covariance, shared variational closure, boundary consistency, covariant balance, and local second-order metric dynamics constrain the admissible coupling between a metric-ruler context and a matter context to the Einstein form within the declared regime. The paper also specifies admissibility conditions for contexts and transitions and proposes micro-to-macro emergence as the primary empirical application.