The preprint version is available on SSRN: A Unified Framework for Quantum Mechanics and Relativity: The Interface Between Quantum States and Spacetime Geometry. https://doi.org/10.2139/ssrn.7088820

A Unified Framework for Quantum Mechanics and Relativity
The Interface Between Quantum States and Spacetime Geometry

Juliet Zhong
Independent Researcher, London, United Kingdom, July 2026
ORCID: 0009-0006-5099-3671 | AI research Tool: Claude, ChatGPT

Abstract

Quantum mechanics and general relativity are the two most successful physical theories of the twentieth century, yet their conceptual frameworks appear deeply incompatible. The standard formulation of this incompatibility holds that quantum superposition of matter states generates an indeterminate energy-momentum tensor, which cannot serve as a unique source for the Einstein field equations, requiring either the quantisation of spacetime geometry or some other fundamental modification of existing theory. This paper argues that the apparent incompatibility arises, at least in part, from a category error: the simultaneous application of two descriptions—quantum and geometric—that properly apply at different levels of physical description. Quantum mechanics describes the probability structure of possible configurations of a physical system; general relativity describes the geometric structure of spacetime associated with definite configurations of matter. These are not competing descriptions of the same physical moment; they are descriptions of different aspects of the same physical situation. On this account, quantum superposition does not entail a corresponding multiplicity of gravitational sources, because the quantum state describes possible configurations of a single physical system rather than multiple simultaneously realised classical matter distributions. The paper develops this conceptual interface, situates it relative to existing approaches to quantum gravity, and argues that the apparent conflict is better understood as a problem of descriptive level-mismatch than of fundamental contradiction. To this end, it proposes a staged mapping, |ψ⟩ → Ci → Tμν(Ci) → Gμν, as the formal interface that any future unified theory must formalise.

Keywords: quantum gravity, general relativity, quantum mechanics, energy-momentum tensor, wave function interpretation, quantum superposition, spacetime geometry, descriptive levels, measurement problem, conceptual unification

Chapter 1: The Nature of the Conflict

1.1 Two Theories, One Problem

Quantum mechanics and general relativity are the two most successful physical theories produced by the twentieth century. Each has been confirmed by experiment to a degree that places them beyond serious empirical challenge within their respective domains. Quantum mechanics accounts for the behaviour of matter at atomic and subatomic scales with a precision that has no parallel in the history of science: the anomalous magnetic moment of the electron, predicted by quantum electrodynamics, agrees with experiment to better than one part in a trillion. General relativity, for its part, describes the large-scale structure of spacetime and the dynamics of gravitational fields with comparable accuracy: from the precession of Mercury's perihelion to the detection of gravitational waves from merging black holes, its predictions have been confirmed wherever they have been tested. No experiment has found either theory to be wrong on its own terms.

Yet the two theories are not compatible with each other. This is not a matter of one contradicting the experimental record of the other. It is a matter of their conceptual structures—the basic objects they define, the questions they are designed to answer, and the mathematical formalisms through which they answer those questions—being mutually inconsistent in ways that become acute precisely where both should apply simultaneously: at the Planck scale, at gravitational singularities, in the early universe, and at the horizon of black holes. In these regimes, both quantum effects and strong gravitational curvature are relevant, and no consistent theoretical description currently exists that incorporates both.

The standard account of this incompatibility identifies several specific sources of tension. General relativity is a classical field theory: it describes spacetime as a smooth, continuous four-dimensional Lorentzian manifold, and the gravitational field as the curvature of that manifold, determined at every point by the distribution of matter and energy through the Einstein field equations. The theory is deterministic in the sense that, given the state of the universe on a spacelike hypersurface, the future evolution of the gravitational field is uniquely determined. There is no place in this picture for probability, superposition, or the kind of fundamental indeterminacy that quantum mechanics assigns to physical systems before measurement.

Quantum mechanics, by contrast, describes physical systems through state vectors in a Hilbert space—mathematical objects that encode not the definite values of physical quantities but the probability distributions over possible values that would result from measurement. The wave function does not necessarily imply that a quantum system possesses a definite position, momentum, energy, or spin as a simultaneously realised classical property prior to measurement. It exists in a superposition of possible states, each with an associated probability amplitude, and only upon interaction with a measuring apparatus does the system acquire a definite value for the measured quantity. This is not merely an expression of ignorance about an underlying classical reality: within the standard textbook formulation of quantum mechanics, the superposition is treated as the complete mathematical description of the system prior to measurement.

The deepest point of conflict between these two pictures concerns the gravitational field and its relationship to the quantum state of matter. In general relativity, the curvature of spacetime—the gravitational field—is determined by the energy-momentum tensor of matter. The Einstein field equations state this relationship explicitly: the geometry of spacetime on the left-hand side of the equations is equated to the energy-momentum content of matter on the right-hand side. The geometry is therefore as definite and classically determinate as the matter distribution that sources it. But if matter can exist in quantum superposition—if its energy and momentum are genuinely indeterminate prior to measurement—then the energy-momentum tensor that sources the gravitational field is itself indeterminate. And if the source of the gravitational field is indeterminate, the question arises immediately and unavoidably: what is the state of the gravitational field?

This is the precise formulation of the problem that the present paper addresses. It is not the vague intuition that one theory involves probability and the other does not. It is the specific observation that quantum mechanics permits—indeed, requires—that the source term of the Einstein field equations be in a state of superposition, while the field equations themselves have no provision for a superposed or probabilistic spacetime geometry. The two formalisms make mutually inconsistent demands on the same physical quantity: the energy-momentum distribution of matter. This inconsistency cannot be resolved by applying one theory first and then the other; it is a structural incompatibility that arises at the level of their fundamental concepts.

The conventional response to this problem has been to seek a new theory—quantum gravity—that supersedes both general relativity and quantum mechanics in the regime where both are relevant, recovering each as a limiting case. This programme has produced several major research directions: string theory, loop quantum gravity, causal dynamical triangulations, and others. Each attempts, in different ways, to construct a theory in which spacetime itself has quantum properties, so that the inconsistency between a quantum matter source and a classical spacetime geometry is resolved by eliminating the classical spacetime altogether and replacing it with something more fundamental [3]. These approaches are intellectually serious and mathematically sophisticated. None has yet produced a theory that is empirically confirmed, and each faces deep conceptual and technical difficulties that remain unresolved.

The present paper does not propose a new quantum gravity theory. Its aim is different and, in a sense, prior: to examine whether the apparent incompatibility between quantum mechanics and general relativity is as fundamental as it appears, or whether it arises, at least in part, from a conceptual confusion about what each theory is actually describing. The argument to be developed in the following chapters is that the two theories are not, in fact, attempting to describe the same level of physical reality, and that recognising this distinction allows their conceptual frameworks to coexist without contradiction—not by solving quantum gravity, but by reformulating the question that quantum gravity is supposed to answer.

1.2 Two Levels of Description

The claim that quantum mechanics and general relativity are incompatible rests on the assumption that both theories are attempting to describe the same physical object in the same way—that both are, so to speak, answering the same question about the same thing. This assumption is rarely made explicit, and it is worth examining it directly, because it is not obviously correct.

Every physical theory is, among other things, a description of something. It selects certain aspects of the physical world as its object of description, defines the concepts through which that object is characterised, and specifies the relationships between those concepts that constitute its laws. Different theories may describe different aspects of the same underlying reality, or they may describe the same aspect at different levels of resolution, or they may describe the same aspect using different but equivalent conceptual vocabularies. In none of these cases does the existence of two different theories imply that they are in conflict; conflict arises only when two theories purport to give different answers to the same question about the same object.

The question, then, is what question each theory is answering.

General relativity answers a specific set of questions about the structure of spacetime and the relationships between events. Given a distribution of matter and energy, it specifies the curvature of spacetime in which that matter moves. Given the curvature of spacetime, it specifies how matter moves through it. It describes the causal structure of spacetime—which events can influence which other events, and through what paths. It describes the propagation of light, the behaviour of clocks and measuring rods in gravitational fields, and the large-scale dynamics of the universe. The objects that general relativity takes as fundamental are events, spacetime intervals, geodesics, and the metric tensor. Its laws are equations relating these objects. The question it answers, at the deepest level, is: given the matter content of the universe, what is the structure of spacetime, and how do objects move through it?

Quantum mechanics answers a different set of questions. Given a physical system and an initial preparation, it specifies the probabilities of obtaining various outcomes when measurements of physical quantities are performed on that system. It describes how the quantum state of a system evolves in time between measurements, and how it changes upon measurement. It specifies the correlations between the outcomes of measurements performed on different parts of a composite system. the mathematical objects through which quantum mechanics represents physical systems are state vectors, operators representing observables, and probability amplitudes. Its laws are equations governing the evolution of these objects. The question it answers, at the deepest level, is: given the preparation of a physical system, what outcomes will measurement produce, and with what probabilities?

These are not the same question. General relativity asks about the structure of spacetime and the motion of matter through it. Quantum mechanics asks about the outcomes of measurements on physical systems and the probabilities associated with those outcomes. The two questions are related—both are questions about the physical world—but they are not identical. They concern different aspects of physical reality, described through different conceptual frameworks, answering different kinds of inquiry.

This observation does not, by itself, resolve the problem of quantum gravity. It does not explain how to describe a quantum superposition of spacetime geometries, or how to make general relativity compatible with the uncertainty principle. But it does suggest that the incompatibility between the two theories may not be as fundamental as it is often taken to be. If the two theories are not attempting to answer the same question, then the fact that they give different kinds of answers is not, in itself, evidence of contradiction. A contradiction arises when two statements assert incompatible things about the same object. If the two theories are describing different aspects of reality, their apparent incompatibility may reflect a category error in the way the conflict has been framed, rather than a genuine inconsistency in the structure of nature.

An analogy may be helpful here, though it should not be pressed too far. Consider the relationship between thermodynamics and statistical mechanics. Thermodynamics describes the macroscopic behaviour of physical systems in terms of temperature, pressure, entropy, and the laws governing their relationships. Statistical mechanics describes the microscopic behaviour of the same systems in terms of the positions, momenta, and interactions of their constituent particles, and derives the macroscopic properties of thermodynamics from the statistical behaviour of large numbers of microscopic constituents. The two theories describe the same physical systems, but at different levels of resolution. They are not in conflict; they are complementary descriptions of different aspects of the same reality. The entropy that appears in thermodynamics as a macroscopic state function is related to, but not identical with, the microstate distribution that appears in statistical mechanics. Understanding the relationship between the two requires understanding what each theory is describing and at what level of description it operates.

The relationship between quantum mechanics and general relativity is not identical to the relationship between thermodynamics and statistical mechanics—the analogy should not be over-extended. But the structural point is the same: before concluding that two theories are in fundamental conflict, it is necessary to establish that they are attempting to describe the same object at the same level of description. The argument of this paper is that, in the case of quantum mechanics and general relativity, this has not been adequately established, and that examining it more carefully opens the possibility of a different understanding of their relationship.

The distinction between levels of description is not merely a philosophical nicety. It has direct implications for how the incompatibility between the two theories should be characterised and for what kind of resolution should be sought. If the two theories are not describing the same aspect of physical reality at the same descriptive level, then the task is not necessarily to find a single theory that replaces both, but to understand how their descriptions articulate with each other—what the interface between their respective domains of description looks like, and what constraints consistency places on that interface. This is a different problem from finding a quantum theory of gravity in the sense of quantising the gravitational field, and it may be a more tractable one.

1.3 A Different Question

The dominant framing of the relationship between quantum mechanics and general relativity treats their incompatibility as evidence that one or both theories are incomplete, and that a more fundamental theory is required to supersede them. This is a natural response to the situation, and it has motivated some of the most ambitious theoretical projects in modern physics. But it is not the only possible response, and it is worth pausing to ask whether the incompatibility, properly understood, requires this response, or whether it admits of a different kind of resolution.

The conventional framing assumes that the conflict between quantum mechanics and general relativity is a conflict between two theories that are both attempting to describe the fundamental structure of physical reality, and that the conflict arises because their descriptions are mutually inconsistent at that fundamental level. On this assumption, the resolution must be a new, more fundamental theory that describes reality correctly where the existing theories fail. The project of quantum gravity is the attempt to construct such a theory.

But there is another possibility. The conflict between quantum mechanics and general relativity may arise not from an inconsistency in the structure of nature, but from an inconsistency in the conceptual framework through which the two theories have been interpreted and brought into contact. That is: the two theories may each be giving a correct and complete description of the aspect of physical reality they are designed to describe, and the appearance of conflict may arise from a failure to recognise that they are describing different aspects, or from imposing on one theory demands that properly belong to the other.

This is not a deflationary claim. It does not assert that quantum gravity is a pseudo-problem, or that the difficulties at the Planck scale are illusory. Gravitational singularities are real. The breakdown of classical general relativity at extreme curvatures is real. The difficulties of defining quantum field theory in curved spacetime are real. These are genuine physical problems that require genuine solutions. What the present paper questions is not the existence of these problems but the diagnosis of their source—specifically, the assumption that they arise from a fundamental incompatibility between two correct theories, rather than from a conceptual confusion about what those theories are describing and how their descriptions relate.

The different question that this paper proposes to ask is this: rather than asking how to construct a new theory that supersedes both quantum mechanics and general relativity, ask whether the apparent incompatibility between them is an artefact of the way their relationship has been conceptualised. Is the conflict intrinsic to the theories themselves, or is it introduced by the way those theories have been interpreted, combined, and brought into contact? If the latter, then resolving the conflict may not require a new theory at all—it may require a clearer understanding of what the existing theories are saying.

This reframing has a specific target. The sharpest version of the incompatibility between quantum mechanics and general relativity is the problem of the quantum state of the gravitational field when matter is in superposition. If a particle is in a superposition of two different position states—say, located at point A with amplitude α and at point B with amplitude β—then its energy-momentum distribution is, correspondingly, in a superposition of two different configurations. The Einstein field equations require that the spacetime geometry be determined by the energy-momentum distribution. But a superposed energy-momentum distribution cannot, within the classical framework of general relativity, determine a unique spacetime geometry. The two descriptions—quantum state of matter, classical geometry of spacetime—are mutually inconsistent.

The standard response is to conclude that spacetime geometry must itself be quantised. The present paper proposes a different response: to examine whether the inconsistency arises from the physics of the situation or from a conceptual error in the way the two descriptions have been juxtaposed. Specifically, it proposes to examine whether the demand that a superposed quantum state of matter immediately and directly determine a classical spacetime geometry is a demand that follows from the physics, or a demand that follows from an unexamined assumption about how the two frameworks are supposed to relate. If the latter, then the apparent inconsistency may be resolved not by quantising gravity but by clarifying the relationship between quantum descriptions of matter and classical descriptions of spacetime—understanding them as descriptions that apply at different stages or levels of the physical situation, rather than as simultaneous and competing descriptions of the same thing.

The chapters that follow develop this argument in detail. Chapter 2 examines the nature of quantum states, probability, and physical reality, arguing that the quantum description of matter does not have the ontological implications that are standardly assumed—in particular, that quantum superposition does not entail the simultaneous existence of multiple classical realities. Chapter 3 examines the specific point of contact between the quantum description of matter and the general relativistic description of spacetime, and proposes a way of understanding that contact that dissolves the apparent inconsistency without requiring the quantisation of the gravitational field. Chapter 4 draws out the implications of this reconceptualisation, compares it with existing approaches to quantum gravity, and identifies the questions it leaves open.

The aim throughout is not to dismiss the problem of quantum gravity but to ask whether the right conceptual tools are being brought to bear on it. A problem correctly formulated is already half solved. If the apparent incompatibility between quantum mechanics and general relativity is partly a product of how the problem has been framed, then reformulating the problem—asking a different question—may open paths that the standard framing forecloses.

Chapter 2: Quantum States, Probability, and Physical Reality

2.1 What the Wave Function Describes

The wave function is the central mathematical object of quantum mechanics. It encodes everything that quantum mechanics permits us to say about the state of a physical system, and its evolution according to the Schrödinger equation constitutes the complete dynamical law of the theory. Yet what the wave function describes—what it refers to in the physical world—remains one of the most contested questions in the foundations of physics. The answer given to this question has direct consequences for how the relationship between quantum mechanics and general relativity is understood, and for whether the apparent incompatibility between them is as deep as it is standardly taken to be.

The most common popular account of the wave function presents it as describing a physical system that simultaneously exists in multiple states at once. On this account, a particle in a superposition of two position states is literally in both positions at the same time; the wave function is a catalogue of all the realities that the particle simultaneously inhabits. This account has the advantage of being vivid and easily communicated, and it underlies the intuition that quantum mechanics is deeply paradoxical—that it describes a world radically unlike the one we perceive. But it is not the only account available, and there are strong reasons to question whether it is the most accurate one.

The alternative account, which this paper adopts and defends, is that the wave function describes not the simultaneous existence of multiple classical realities but the probability structure of a single physical system—the full set of possible outcomes that could result from measuring the system under specified conditions, together with the probabilities associated with each outcome. On this account, a particle in a superposition of two position states does not exist simultaneously at two locations; rather, the system has a definite physical character—a quantum state—that is such that, were its position to be measured, either location could be the result, with probabilities determined by the amplitudes of the respective components of the superposition. The superposition is not a description of multiple coexisting realities; it is a description of the probability structure of a single reality prior to the determination of a specific measurement outcome.

This distinction is not merely semantic. It has substantive implications for what quantum mechanics is claiming about the physical world, and for how its claims relate to those of general relativity. If superposition means simultaneous existence in multiple classical states, then a superposed quantum system is, in a well-defined sense, in multiple places at once, with multiple momenta, multiple energies—and, by implication, with multiple energy-momentum distributions, each of which would, through the Einstein field equations, determine a different spacetime geometry. The problem of quantum gravity then appears as the problem of what to do with these multiple, simultaneously existing, mutually inconsistent spacetime geometries. This is a genuine and very hard problem.

But if superposition means not multiple simultaneous realities but a probability distribution over possible outcomes—if the quantum state describes what could result from measurement rather than what simultaneously exists—then the situation is different. A superposed matter system does not, on this account, have multiple simultaneously existing energy-momentum distributions. It has a quantum state that encodes the probabilities of various energy-momentum outcomes being realised under measurement. The question of what spacetime geometry corresponds to this quantum state is then not the question of how to superpose multiple geometries, but the question of how the probabilistic description of matter at the quantum level relates to the geometric description of spacetime at the classical level. This is still a hard question, but it is a different question—and, as Chapter 3 will argue, a more tractable one.

To make this account precise, it is necessary to be clear about what probability means in quantum mechanics. Quantum probabilities are not expressions of ignorance about an underlying classical reality. It is not that the particle really is at a definite location, and we simply do not know which one; quantum mechanics, as understood through Bell's theorem and its experimental confirmations, rules out this interpretation for most observables. Bell-type experiments rule out local hidden-variable explanations for quantum correlations, establishing that quantum probabilities are not reducible to classical probabilities over pre-existing definite values. But irreducible probability is not the same as simultaneous multiple existence. A die, before it is thrown, does not simultaneously occupy six different faces; it has a probability distribution over possible outcomes. The analogy is imperfect—quantum probabilities are not classical probabilities, and the physical situation is not classical—but the logical point holds: probability, even irreducible probability, describes the structure of possible outcomes, not the simultaneous realisation of all of them.

A conceptual model may be useful here. Consider a leaf falling from a tree. Before it lands, its final resting position is undetermined—not merely unknown, but, in the relevant sense, not yet fixed. The leaf is a single object with a single physical trajectory, subject to forces—gravity, air resistance, turbulence—that are in principle deterministic but in practice sensitive to initial conditions in ways that make the outcome unpredictable. We can, however, assign a probability distribution over possible landing positions, based on the known conditions of the fall. This probability distribution is not a description of many leaves falling simultaneously to many different positions; it is a description of the range of possible outcomes for a single leaf. When the leaf lands, one outcome is realised, and the probability distribution is replaced by a definite fact.

This model is not a physical model of quantum systems. Quantum mechanics is not classical mechanics with hidden variables, and a leaf falling in air is a classical system subject to deterministic laws, not a quantum system subject to irreducible indeterminacy. The leaf model is a conceptual model—a device for distinguishing between two ways of interpreting a probability distribution. The first interpretation takes the probability distribution as a description of multiple simultaneous realities: many leaves, many positions, all equally real. The second interpretation takes the probability distribution as a description of the range of possible outcomes for a single system: one leaf, one future position, not yet determined. The leaf model illustrates the second interpretation, not because quantum systems are like falling leaves, but because the logical structure of the second interpretation—probability as the description of possible outcomes for a single system, not as a catalogue of simultaneously existing realities—is the same in both cases.

The argument of this paper is that the second interpretation is the correct one for quantum mechanics as well. The wave function describes the probability structure of a single physical system—the range of possible outcomes for that system under specified measurement conditions—not the simultaneous existence of multiple classical realities. This interpretation is consistent with the mathematical formalism of quantum mechanics, consistent with the experimental record, and, as the following sections argue, consistent with the most defensible accounts of quantum measurement and physical reality.

2.2 The Observer as Physical Interaction

The role of the observer in quantum mechanics has been the source of more philosophical confusion than almost any other aspect of the theory. The standard formulation of quantum mechanics assigns a special role to measurement: the wave function of a system evolves continuously and deterministically according to the Schrödinger equation until a measurement is performed, at which point it undergoes a discontinuous, probabilistic change—the collapse of the wave function—to an eigenstate of the measured observable. This measurement postulate is essential to the predictive success of quantum mechanics, but it raises an immediate question: what counts as a measurement, and what is special about it?

The history of quantum mechanics includes a range of answers to this question, some of which have introduced unnecessary complexity and confusion by treating the observer—the entity that performs the measurement—as something distinct from the physical systems that quantum mechanics describes. On the most extreme versions of this view, the observer is identified with a conscious mind, and the collapse of the wave function is taken to require the intervention of consciousness. This view is not widely held among physicists today, but traces of the associated confusion persist in the way quantum measurement is often discussed, and in the intuition that quantum mechanics is somehow about the role of the observer as a perceiving subject.

The position defended here is different and more straightforward: the observer, in quantum mechanics, is not a conscious mind, a subject of experience, or anything that stands outside the physical description. The observer is a physical system—any physical system—that interacts with the quantum system under study. A measurement is a physical interaction between the quantum system and the measuring apparatus; the measuring apparatus is itself a physical system, subject to the same physical laws as the system being measured. The outcome of the measurement—the result registered by the apparatus—is the result of this physical interaction, and it is determined by the physical conditions of the interaction, not by the presence of a conscious observer.

This account of the observer as physical interaction has several important consequences. First, it removes the appearance of subjectivity from quantum mechanics. The outcomes of measurements are not created by consciousness; they are produced by physical processes. The role of the observer is not to collapse the wave function by looking at it but to interact with the quantum system in a way that produces a definite outcome. The definiteness of the outcome is a consequence of the physical interaction, not of the observer's awareness of it.

Second, it connects the account of measurement to the theory of decoherence. Decoherence is the process by which a quantum system loses its quantum coherence—the ability to exhibit interference effects—through interaction with its environment. When a quantum system interacts with a large number of environmental degrees of freedom, the different components of its superposition become entangled with different states of the environment, and the interference terms between them become unmeasurable in practice, even if they remain present in the full quantum state of the system-plus-environment. The result is that the quantum system behaves, for all practical purposes, as if it were in a definite classical state, even though the full quantum state of the combined system remains a superposition. Decoherence does not solve the measurement problem—it does not explain why a particular outcome occurs rather than another—but it does explain why quantum superpositions are not directly observable at macroscopic scales, and why the classical world of definite objects and definite properties emerges from the quantum world of superpositions and probabilities.

The account of the observer as physical interaction fits naturally with the decoherence picture. The measuring apparatus is a macroscopic physical system with enormously many degrees of freedom. When it interacts with the quantum system being measured, it decoheres the quantum system very rapidly—on timescales many orders of magnitude shorter than any that are experimentally accessible. The result is that the quantum system, from the perspective of any subsequent interaction with the environment or with a human observer, behaves as if it were in a definite eigenstate of the measured observable. The apparent collapse of the wave function is, on this account, not a fundamental physical process distinct from the Schrödinger evolution; it is the practical consequence of rapid decoherence caused by the physical interaction between the quantum system and the measuring apparatus.

Third, and most importantly for the argument of this paper, the account of the observer as physical interaction clarifies the relationship between quantum descriptions and classical descriptions. The quantum state of a system is a description of its probability structure—the range of possible outcomes for interactions with other physical systems. When a physical interaction occurs, one outcome from that range is realised. The interaction is itself a physical process, described by physical laws. The outcome of the interaction—the definite result—is then the object that enters the classical description: the definite position, the definite momentum, the definite energy. The transition from quantum description to classical description is not a transition from one world to another; it is a transition from a description of possible outcomes to a description of an actual outcome, mediated by a physical interaction.

This account of measurement and observation has direct relevance to the problem of quantum gravity. If measurement is a physical interaction, and if the classical properties of matter—its definite position, momentum, and energy-momentum distribution—are the outcomes of such interactions, then the relationship between the quantum description of matter and the classical description of spacetime can be understood in terms of the relationship between possible outcomes and actual outcomes. The quantum state of matter describes the probability structure of possible energy-momentum configurations. The relationship between quantum descriptions of matter and classical descriptions of spacetime may therefore be understood through the relationship between possible outcomes and physically realised configurations—a point developed in Chapter 3. The two descriptions do not compete; they apply at different stages of the physical situation.

2.3 Quantum Reality Beyond Ontological Assumptions

The question of what quantum mechanics tells us about physical reality—about what really exists, and in what form—is one that the theory does not answer unambiguously. The mathematical formalism of quantum mechanics is well-defined and predictively successful; the interpretation of that formalism—what it says about the nature of physical reality—is not. This interpretational underdetermination has generated a large philosophical literature and several competing interpretations of quantum mechanics, each of which takes a different position on the ontological status of the wave function, the nature of quantum probability, and the relationship between the quantum description of the world and the classical world of experience.

The present paper does not adjudicate between these interpretations. Its argument does not depend on any particular interpretation being correct, and the conceptual bridge it proposes between quantum mechanics and general relativity is intended to be compatible with the range of interpretations that take quantum probability seriously as a feature of physical reality. What this section does is examine the ontological assumptions that are most commonly brought to the interpretation of quantum mechanics—specifically, the assumption that quantum superposition requires the simultaneous existence of multiple classical realities—and argue that this assumption is not forced by the formalism of quantum mechanics, and that rejecting it opens a more coherent account of the relationship between quantum and classical descriptions.

The most prominent interpretation that does embrace the ontology of multiple simultaneous realities is the Everett, or many-worlds, interpretation. Everett proposed that the wave function is the complete description of physical reality, that it never collapses, and that all components of a superposition are equally real. On this account, when a quantum measurement is performed, the universe branches: every possible outcome of the measurement is realised, in a separate branch of the universal wave function. There is no collapse, no selection of a single outcome; all outcomes occur, in different branches, and the branches evolve independently thereafter. The apparent definiteness of measurement outcomes in our experience is explained by the fact that observers are themselves part of the wave function and therefore branch along with the system they are measuring; each branch-observer experiences a definite outcome, because within that branch, only one outcome has occurred.

The many-worlds interpretation is internally consistent, and it has the significant virtue of taking the Schrödinger equation seriously as a complete and universal law, without introducing any additional collapse postulate. But it comes at a significant ontological cost: the postulation of an enormously large—indeed, continuously proliferating—number of equally real but mutually inaccessible branches of the universe. This ontological extravagance is not forced by the mathematics; it is a choice made in the interpretation of the mathematics. The wave function formalism, in itself, does not require that all components of a superposition correspond to simultaneously existing classical realities. It requires only that the probabilities of measurement outcomes be given by the squared amplitudes of the wave function. The many-worlds interpretation is one way of accounting for those probabilities; it is not the only way.

Niels Bohr's Copenhagen interpretation, by contrast, declines to assign any ontological status to the wave function beyond its role as a predictive tool. On the Copenhagen view, the wave function is not a description of physical reality; it is a representation of the knowledge available to an observer, and its collapse upon measurement is not a physical process but an update of that knowledge in response to new information. The quantum world, on this view, does not have definite properties independently of measurement; physical reality, as quantum mechanics describes it, is defined only relative to a measurement context. What exists between measurements is not a question that quantum mechanics, or indeed physics, can or should answer.

Bohr's position has been criticised for introducing a problematic distinction between the quantum system and the classical measuring apparatus, and for its apparent dependence on a classical description of the measurement context that is not itself grounded in quantum mechanics. Werner Heisenberg offered a related but somewhat different account: the wave function describes objective tendencies or potentialities—what Heisenberg called the potentia of Aristotelian philosophy—that are real features of the physical world, not merely of our knowledge, but that are not actualities until they are realised through interaction. On Heisenberg's account, quantum reality is a realm of potentiality, distinct from the classical realm of actuality, and measurement is the process through which potentiality is converted into actuality.

The account developed in this paper is closest to Heisenberg's, though it does not endorse any specific metaphysical framework. The wave function describes the probability structure of a physical system—the range of possible outcomes for interactions with other systems, and the probabilities associated with each outcome. This probability structure is a real feature of the physical world: it is not merely a representation of our ignorance, as a classical hidden-variable account would have it, but a genuine property of the system, one that determines the statistical pattern of outcomes over many measurements. At the same time, it is not a description of multiple simultaneously existing classical realities: the probabilities describe possible outcomes, not simultaneous actualities.

Wojciech Zurek's programme of quantum Darwinism offers a further perspective on how classical reality emerges from quantum reality. Zurek argues that the classical properties of objects—the properties that are robust, reproducible, and accessible to many observers—are those that are preferentially recorded in the environment through decoherence. The environment acts as a witness to the quantum system, copying information about certain of its properties into many environmental degrees of freedom. The properties that are thus multiply recorded are the ones that acquire an objective, classical character; they are the ones that multiple observers can agree on, and that therefore constitute the shared classical world. Quantum Darwinism does not resolve the measurement problem in the sense of explaining why a particular outcome occurs, but it does explain how certain quantum properties acquire the robustness and objectivity that characterise classical reality.

The common thread in these accounts—Heisenberg's potentia, decoherence, quantum Darwinism—is that the transition from quantum description to classical description is not a transition between two ontologically separate realms, but a transition between two levels of description of the same physical reality: the level of possible outcomes and the level of actual, classically robust outcomes. The quantum state describes the former; the classical state describes the latter. Neither description is more fundamental in an absolute sense; each is appropriate to its domain of application.

A principle that cuts across these interpretational differences can be stated as follows: the multiplicity of possible outcomes encoded in a quantum state does not imply a corresponding multiplicity of physical sources. A quantum state may assign non-zero probability amplitude to two different energy-momentum configurations, but the physical system it describes remains one system—not two systems, not a superposition of independently existing matter distributions. The probability space expands; the number of physical entities does not. This principle—that quantum state multiplicity does not entail physical source multiplicity—provides the conceptual basis for the argument developed in Chapter 3, where the relationship between quantum descriptions of matter and gravitational descriptions of spacetime is examined directly.

For the purposes of this paper, the critical point is that this understanding of the relationship between quantum and classical descriptions does not require the many-worlds ontology of simultaneously existing branches. The probability structure described by the wave function is real; the multiple simultaneous classical realities are not required. A physical system in a superposition of two energy-momentum states has a real quantum state—a real probability structure over possible energy-momentum outcomes—but it does not necessarily require two simultaneously existing classical energy-momentum distributions as its physical correlate. It has one quantum state, from which one classical energy-momentum distribution will emerge through physical interaction. The relationship between the quantum description of matter and the classical description of spacetime is therefore not, on this account, a relationship between multiple simultaneous matter configurations and multiple simultaneous spacetime geometries. It is a relationship between a quantum probability structure and the classical geometry that corresponds to the actual matter configuration that is realised through physical interaction. This is the conceptual basis for the argument developed in Chapter 3.

Chapter 3: Gravity and the Quantum State

3.1 Where the Descriptions Diverge

The precise point at which quantum mechanics and general relativity come into conceptual conflict can be identified with some care. It is not, as is sometimes suggested, simply the fact that one theory is probabilistic and the other is deterministic. Deterministic theories can be approximations to probabilistic ones, or probabilistic theories can emerge from deterministic ones, without either being in fundamental conflict with the other. The conflict is more specific, and it concerns the relationship between the quantum state of matter and the spacetime geometry that general relativity associates with that matter.

In general relativity, the gravitational field—the curvature of spacetime—is determined by the energy-momentum tensor of matter. This relationship is encoded in the Einstein field equations, which equate the Einstein tensor, a measure of spacetime curvature, to the energy-momentum tensor of matter, scaled by appropriate constants. The energy-momentum tensor is a classical object: it assigns to each point in spacetime a definite value, encoding the density and flux of energy and momentum at that point. Given a definite matter distribution—a definite energy-momentum tensor—the Einstein field equations determine a definite spacetime geometry. The relationship is local, deterministic, and unique: one matter distribution, one geometry.

Quantum mechanics, as argued in the preceding chapter, describes matter through a wave function that encodes not a definite energy-momentum distribution but a probability structure over possible energy-momentum outcomes. A quantum particle does not, in general, have a definite position or momentum prior to measurement; correspondingly, it does not have a definite contribution to the energy-momentum tensor. If the particle is in a superposition of two different position states, its contribution to the energy-momentum tensor is, in the quantum description, correspondingly indeterminate—not a definite value but a probability distribution over possible values.

The conflict, stated precisely, is this: quantum mechanics assigns to matter a state from which no definite energy-momentum tensor can be extracted, while general relativity requires a definite energy-momentum tensor in order to determine the spacetime geometry. The two frameworks make inconsistent demands on the same physical quantity. This inconsistency is what drives the project of quantum gravity: the attempt to construct a theory in which the spacetime geometry itself acquires quantum properties, so that a superposed matter state corresponds not to a definite geometry but to a superposition of geometries.

But the standard framing of this inconsistency contains an assumption that is worth examining. It assumes that the quantum state of matter—the superposition—must be directly and simultaneously translated into a gravitational description. It treats the quantum description and the gravitational description as if they must be applied at the same moment, to the same physical situation, and reconciled with each other in that moment. This assumption is what generates the appearance of a hard contradiction: if you demand that a superposed quantum state immediately determine a classical spacetime geometry, you will find that it cannot, because the quantum state does not provide the definite energy-momentum tensor that the Einstein field equations require.

Consider the following example, which makes the logical structure of the difficulty vivid. Schrödinger's cat is a physical system—a cat in a sealed box—that is placed, by the setup of the experiment, into a quantum superposition of two states: alive and dead. Before the box is opened and the cat's state is observed, quantum mechanics assigns to the cat a superposition of these two outcomes, each with some probability amplitude. The question that the standard framing of the quantum gravity problem would then ask is: what is the gravitational field of this cat? If the cat is in a superposition of alive and dead, and if these two states correspond to different energy-momentum configurations—a living cat has a different metabolic activity, different internal energy distribution, than a dead one—then what spacetime geometry does the Einstein field equations assign to the cat?

The standard framing treats this as a genuine and hard problem: the cat is in a superposition, its energy-momentum tensor is therefore indeterminate, and the spacetime geometry is therefore undefined. But notice what this framing obscures. Whatever the quantum state of the cat—alive, dead, or in superposition—there is exactly one cat in the box. Not two cats, not a probability-weighted average of cats, not an infinite ensemble of cats corresponding to every possible quantum outcome simultaneously: one cat. The gravitational field outside the box is the gravitational field of one cat, of a specific mass, occupying a specific volume. The quantum superposition does not double the cat, or split it into multiple simultaneously existing versions of itself. It describes the probability structure of the cat's internal state—whether, upon observation, it will be found alive or dead—without in any way multiplying the number of cats or the total mass-energy that generates the gravitational field.

This observation cuts directly against the standard framing of the quantum gravity problem. The problem, as standardly posed, implicitly assumes that the quantum superposition of the cat's internal state requires a corresponding superposition of spacetime geometries—that because the cat's energy-momentum tensor is, in the quantum description, indeterminate, the spacetime geometry must be correspondingly indeterminate or superposed. But this assumption conflates two distinct things: the quantum indeterminacy of the cat's internal state, and the gravitational field generated by the cat as a whole. At the coarse-grained level relevant to the gravitational field, not all quantum degrees of freedom necessarily correspond to independent degrees of freedom in the spacetime geometry. The relevant gravitational source may depend only on conserved or coarse-grained properties of the system—properties that are not necessarily placed in superposition by the quantum state under discussion. There is one cat, with one mass, generating one gravitational field, regardless of whether its internal quantum state is alive, dead, or in superposition.

This is not to say that there is no quantum gravitational effect at all, or that the quantum state of matter never has implications for the gravitational field. At sufficiently fine-grained scales—at the Planck scale, where quantum effects and gravitational effects are both relevant—the quantum state of matter does have implications for the structure of spacetime, and a complete theory must account for these implications. But the standard framing of the quantum gravity problem at the conceptual level—the claim that quantum superposition immediately and necessarily generates an inconsistency with the classical spacetime geometry—rests on an assumption that the quantum description and the gravitational description must be applied simultaneously and at the same level of resolution. The Schrödinger's cat example illustrates why this assumption is questionable: the quantum indeterminacy of the cat's internal state does not render the gravitational field of the cat indeterminate, because the gravitational field is determined by the cat's total mass-energy, which is not in superposition.

The more general point is this. Quantum superposition is a feature of the quantum description of a physical system—a description of the probability structure of possible measurement outcomes. It is not a feature of the system's total mass-energy, or of any other conserved quantity that is the same across all branches of the superposition. When a physical system is in a superposition of two states, quantum superposition does not necessarily imply a corresponding multiplicity of gravitational sources, because the quantum state describes possible configurations of a single physical system rather than multiple simultaneously realised classical energy-momentum distributions. The apparent conflict between quantum mechanics and general relativity is sharpest when it is assumed that every quantum degree of freedom directly and independently determines a corresponding gravitational degree of freedom—that the quantum state must be translated, point by point and moment by moment, into a classical gravitational field. But this assumption is not forced by either theory. It is a choice about how to relate the two descriptions, and it is a choice that, as the cat example illustrates, is not obviously correct.

3.2 A Conceptual Realignment

The argument of the preceding section establishes that the standard framing of the quantum gravity problem rests on a contestable assumption: that the quantum description of matter and the gravitational description of spacetime must be applied simultaneously, at the same level of description, and reconciled with each other in that moment. This section proposes a different way of understanding the relationship between the two descriptions—one that does not require this assumption, and that dissolves the apparent inconsistency without either quantising gravity or abandoning the quantum description of matter.

—— End of the Selected Chapter ——

Acknowledgements

The author used generative AI tools as linguistic, mathematical, and structural assistance in the drafting of this manuscript. All theoretical frameworks, regime classifications, mechanism analyses, and final conclusions were developed and verified by the author, who assumes full responsibility for the integrity of the work.

Declarations

Competing interests: The author declares no competing interests.

Data availability: No experimental data are reported in this theoretical paper. All numerical estimates are derived from the parameter ranges specified in the text and are reproducible from the expressions given.

Funding: This work received no external funding.

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Juliet Zhong

A Unified Framework for Quantum Mechanics and Relativity: The Interface Between Quantum States and Spacetime Geometry