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Without a Path: Why Quantum Mechanics and Relativity Imply Each Other Without Mediation

Timothy Speed

Published Jan 26, 2026• 1 citation
Publisher

Abstract

The persistent incompatibility between quantum mechanics (QM) and general relativity (GR) is commonly treated in physics as a technical or mathematical problem. Either a deeper dynamics is sought that connects both theories, or a formal meta-theory that unifies their concepts.This paper proposes a different reading. It claims neither a unification nor a correction of the existing theories. Instead, it shows that the contradiction between QM and GR is not a deficit of the theories themselves, but the consequence of an unspoken ontological omission: the lack of a determination of the transition from possibility to facticity.At the center stands the thesis that quantum mechanics and relativity mutually imply one another without being connected by a process, a path, or a shared dynamics. The transition between openness and stability is not a physical event within the world, but a shift in the conditions under which a world can occur at all.Using the terms indimergence and shift of being (Seinsverschiebung), this transition is specified as a boundary structure: indimergence designates the non-dynamical coercion toward objectivity, while shift of being denotes the irreversible change of the conditions of further world-formation. From this perspective, it becomes intelligible why the conflict between QM and GR cannot be “solved” — and why precisely therein lies its ontological significance.

DOI
10.5281/zenodo.18375588

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The persistent incompatibility between quantum mechanics (QM) and general relativity (GR) is commonly treated in physics as a technical or mathematical problem. Either a deeper dynamics is sought that connects both theories, or a formal meta-theory that unifies their concepts.This paper proposes a different reading. It claims neither a unification nor a correction of the existing theories. Instead, it shows that the contradiction between QM and GR is not a deficit of the theories themselves, but the consequence of an unspoken ontological omission: the lack of a determination of the transition from possibility to facticity.At the center stands the thesis that quantum mechanics and relativity mutually imply one another without being connected by a process, a path, or a shared dynamics. The transition between openness and stability is not a physical event within the world, but a shift in the conditions under which a world can occur at all.Using the terms indimergence and shift of being (Seinsverschiebung), this transition is specified as a boundary structure: indimergence designates the non-dynamical coercion toward objectivity, while shift of being denotes the irreversible change of the conditions of further world-formation. From this perspective, it becomes intelligible why the conflict between QM and GR cannot be “solved” — and why precisely therein lies its ontological significance.
What defines an emergent quantum mechanics (EmQM)? Can new insight be advanced into the nature of quantum nonlocality by seeking new links between quantum and emergent phenomena as described by self-organization, complexity, or emergence theory? Could the development of a future EmQM lead to a unified, relational image of the cosmos? One key motivation for adopting the concept of emergence in relation to quantum theory concerns the persistent failure in standard physics to unify the two pillars in the foundations of physics: quantum theory and general relativity theory (GRT). The total contradiction in the foundational, metaphysical assumptions that define orthodox quantum theory versus GRT might render inter -theoretic unification impossible. On the one hand, indeterminism and non -causality define orthodox quantum mechanics, and, on the other hand, GRT is governed by causality and determinism . How could these two metaphysically-contradictory theories ever be reconciled? The present work argues that metaphysical contradiction necessarily implies physical contradiction. The contradictions are essentially responsible also for the measurement problem in quantum mechanics. A common foundation may be needed for overcoming the contradictions between the two foundational theories. The concept of emergence, and the development of an EmQM, might help advance a common foundation - physical and metaphysical - as required for successfull inter-theory unification .
We discuss the problems of quantum theory (QT) complicating its merging with general relativity (GR). QT is treated as a general theory of micro-phenomena—a bunch of models. Quantum mechanics (QM) and quantum field theory (QFT) are the most widely known (but, e.g., Bohmian mechanics is also a part of QT). The basic problems of QM and QFT are considered in interrelation. For QM, we stress its nonrelativistic character and the presence of spooky action at a distance. For QFT, we highlight the old problem of infinities. And this is the main point of the paper: it is meaningless to try to unify QFT so heavily suffering of infinities with GR. We also highlight difficulties of the QFT-treatment of entanglement. We compare the QFT and QM based measurement theories by presenting both theoretical and experimental viewpoints. Then we discuss two basic mathematical constraints of both QM and QFT, namely, the use of real (and, hence, complex) numbers and the Hilbert state space. We briefly present non-archimedean and non-hilbertian approaches to QT and their consequences. Finally, we claim that, in spite of the Bell theorem, it is still possible to treat quantum phenomena on the basis of a classical-like causal theory. We present a random field model generating the QM and QFT formalisms. This emergence viewpoint can serve as the basis for unification of novel QT (may be totally different from presently powerful QM and QFT) and GR. (It may happen that the latter would also be revolutionary modified.)
The persistent tension between Quantum Mechanics and General Relativity is commonly framed as the need for a deeper theory capable of unifying both within a single ontological structure. In this work, a different strategy is adopted. Rather than pursuing direct unification, we propose a triadic conceptual framework that emphasizes organization prior to unification, treating Quantum Mechanics and General Relativity as complementary descriptions of a single physical system operating under distinct epistemic commitments. Within this framework, each theory is assigned a specific functional role, and a third element—a principle of coherence—is introduced to clarify how these roles may be consistently related without reduction. Approaches grounded in information theory and quantum information are highlighted as natural candidates for articulating this coherence interface, given their ability to mediate between operational descriptions and structural constraints. It is argued that several well-known conflicts between the quantum and relativistic frameworks can be reinterpreted as tensions arising from mismatched levels of description rather than fundamental physical inconsistencies. The proposed approach is structural and organizational in nature, aiming to provide a conceptual map for existing and future work in the foundations of physics.
This paper proposes a conceptual hypothesis reconciling free will and destiny by integrating insights from Quantum Mechanics and General Relativity within a layered ontological framework. Rather than treating freedom and determinism as competing explanations within a single domain, the model distinguishes between two coexisting realities: a quantum realm characterized by ontological openness and a relativistic spacetime realm characterized by structural fixity. Free will is located at the threshold between impulse and action, where constrained agency operates as selection among possibilities. Destiny is identified not as an external force but as the completed and coherent structure of spacetime, which records events irreversibly without negating agency. The paper introduces the “read-only spacetime” postulate to clarify irreversibility, moral accountability, and temporal consistency, while allowing for local experiential branching that converges globally to preserve coherence. A formal mathematical representation is presented using a direct sum of ontological domains, alongside conceptual diagrams to aid non-technical understanding. The hypothesis does not claim physical unification of quantum mechanics and general relativity, but offers a philosophically disciplined framework in which both remain valid within their respective descriptive planes. The work aims to restore moral responsibility, meaning, and purpose without invoking randomness, fatalism, or metaphysical contradiction, and is intended as a foundation for further interdisciplinary inquiry rather than a final resolution.
As the two pillars of modern physics, relativity and quantum mechanics have both achieved overwhelming experimental success in their respective domains, yet they have never realized self-consistent unification at the underlying logical level. Most existing studies focus on the mathematical technical difficulties of quantum gravity, while generally neglecting the structural divergence of the core concepts of "observer" and "time" between the two theories. Through conceptual analysis and logical tracing, this paper points out that the observer in relativity is essentially a massless geometric coordinate marker with no intrinsic clock, which only undertakes the functions of event marking and reference frame mutual translation. It belongs to the object level concept within the classical world, and can be summarized as the translator of the ready-made world. The observer required by quantum mechanics is a physical entity that can trigger wave function collapse and carry the time metric benchmark. It is the logical premise for the generation of the observable classical world, belonging to the meta-level concept, and can be summarized as the legislator of the real world. The divergence between the two is not an isolated terminological difference. Its deep root lies in the completely heterogeneous presuppositions of the two theories on "time": time in quantum mechanics is a transcendental, uniform global background parameter "before the birth of clocks", that is, a "logical concept before measurement"; time in relativity is a local, operable relative metric result "after the birth of clocks", that is, a "logical concept of the classical deterministic motion world". As physical theories both belonging to the principle theory paradigm, both actively skip the construction of the physical ontology of time and directly presuppose the functional role of time, which eventually leads to the double logical dislocation of observer and time concepts. Relativity lacks the "first chapter" of deriving observers from the vacuum substrate, and quantum mechanics lacks the physical carrier definition of observers, which are essentially two manifestations of the same ontological gap. Metretics Dynamics (MD; formerly Time Field Theory, TFT) takes the scalar time field as the only physical ontology, defines mass as the local condensed state of the time field, and deduces the ontological proposition that "mass is the observer". It eliminates the absolute division between meta-level and object level from the ontological level, and reduces "global background time" and "local relative time" to the apparent forms of the same physical field under different condensation degrees. The continuous unitary evolution of the wave function corresponds to the uniform rhythmic flow of the time field in its diffuse state, while wave function collapse is essentially a local state mutation of the time field when coupled with a macroscopic mass condensate. Both processes are unified under the intrinsic dynamical laws of the time field. Within a unified framework, it simultaneously accommodates the metric anchor of quantum measurement and the coordinate mutual translation mechanism of relativity, providing a constructive ontological path for the conceptual compatibility of the two major theories.
The persistent challenge of unifying quantum mechanics with general relativity is often traced to a series of apparent structural tensions: complex versus real ontology, probabilistic versus deterministic dynamics, linear versus nonlinear evolution, and spectral discreteness versus geometric continuity. We argue that these tensions do not signal a fundamental incompatibility between the theories, but rather originate from surplus structure in the conventional formulation of quantum mechanics. The term unification is used in a structural sense, referring to compatibility of quantum dynamics with classical field theory rather than a modification of general relativity. Beginning from the physically indispensable requirement of matter stability, we prove that the Hamiltonian spectrum can always be shifted to become non-negative. The consequent positivity of energy enforces one-sided temporal frequency support for all physical unitary orbits. Equivalently, all scalar temporal components of physical states arise as boundary values of functions analytic in the lower half of the complex time plane, selecting the Hardy space—or, more generally, analytic tempered distributions—as the admissible solution space. In these spaces, the real and imaginary parts of the wave function are not independent; they are linked uniquely via the temporal Hilbert transform. Hence, the complex structure of quantum mechanics emerges as a representational artifact of an underlying real operator algebra. Building on our earlier work on Unified Quantum Mechanics and the Unified Real Wave Equation, we establish a rigorous proof of exact equivalence between the real-field evolution and the Schr\"odinger equation on the physical subspace. Probabilistic quantities arise naturally as quadratic invariants of analytic signals, rather than as independent postulates. We further show that quantum spectral discreteness arises from operator-theoretic confinement and boundary conditions on a smooth spacetime manifold, and does not imply any fundamental discreteness of spacetime. The resulting framework provides a real-field formulation of quantum mechanics and gravitation, with stability and causality implemented as foundational principles, and demonstrates that the Einstein field equations are compatible with a unified field-theoretic description of spacetime and matter. Extending the same analyticity principle to spacetime geometry, we propose an analytic formulation of the Einstein field equations, from which classical general relativity is recovered exactly as the real projection.