Ontology of Quantum Physics: What a Century of "Shut Up and Calculate" Has Been Calculating

The preprint is available on SSRN: Ontology of Quantum Physics: What a Century of "Shut Up and Calculate" Has Been Calculating (September 25, 2026). http://dx.doi.org/10.2139/ssrn.7528765

 

 

Ontology of Quantum Physics:

What a Century of "Shut Up and Calculate" Has Been Calculating

Juliet Zhong

Independent Researcher | London, United Kingdom | September 2026

ORCID: 0009-0006-5099-3671

 

 

Abstract

For a century quantum physics has calculated, with unmatched precision, the probabilities with which matter registers events, from collider cross sections to the electron’s magnetic moment at one part in a trillion. It has not said what it is calculating. “Shut up and calculate”, Mermin’s description of the practice, names the decision to leave the question open. Quantum field theory excludes the two familiar answers: its fields have no values at points, and under their localisation assumptions the theorems of Malament and of Halvorson and Clifton, with the Unruh effect, show that localisable particles cannot be its fundamental objects. This paper proposes that quantum physics describes the radiation domain, the sector of physics without proper duration: quantum fields are the structure of its level S4D, which projects onto the material domain, S3D; particles are registered facts of that structure in S3D; and the quantum state is its description as a laboratory indexes it by a material clock. The identification modifies no equation, yet it resolves six long-standing problems: it accounts for entanglement without any signal through space, for the observer-dependence of the vacuum’s particle content, for the 10^120 vacuum-energy discrepancy, for the absence of a time operator and for the twistor structure of mass, and it unifies the measurement and singularity problems as one boundary. It predicts no collapse beyond registration and no gravitationally mediated entanglement, contrary to quantum-mediator accounts satisfying the assumptions of the proposed protocol.

Keywords: quantum foundations; quantum field theory; ontology of quantum physics; particle localisation; Unruh effect; entanglement; proper time; registration; radiation domain

 

 

1. What Quantum Physics Has Been Calculating

The magnetic moment of the electron is among the most precisely tested predictions in science. Measured on a single electron held in a Penning trap, the ratio g/2 agrees with the value computed from quantum electrodynamics to about one part in a trillion, a calculation that sums Feynman diagrams through the fifth order in the fine-structure constant [Fan et al., 2023; Aoyama, Kinoshita and Nio, 2019]. Every cross section measured at a collider, every line in an atomic spectrum and every rate of radioactive decay is predicted by the same apparatus: a quantum field theory, a set of rules for computing amplitudes, and a rule that converts amplitudes into probabilities. What these computations produce can be stated precisely. In the formulation that underlies every collider prediction, the amplitude is an element of the S-matrix, which connects states of freely propagating particles far from an interaction to states of freely propagating particles far from it on the other side; the reduction formula of Lehmann, Symanzik and Zimmermann extracts these elements from correlation functions of the fields by taking the particles out to the asymptotic region where detectors stand [Lehmann, Symanzik and Zimmermann, 1955]. Heisenberg had proposed in 1943 that the S-matrix, the relation between what goes in and what comes out, might be all that a theory of elementary particles needs to contain [Heisenberg, 1943]. The squared amplitude, integrated over the acceptance of a detector, is a rate of registration. What quantum physics calculates, wherever its calculations meet an experiment, is the probability that matter somewhere will register an event. What it describes, the physical reality whose registrations these are, it has never said. This paper is about that silence and about what fills it.

In the spring of 1926 Erwin Schrödinger believed he knew what his wave was. The function ψ that satisfied his equation for the hydrogen atom was, in his reading, a real vibration of electric charge spread through space, and the discrete energy levels were its standing modes, as the tones of a string are the standing modes of the string [Schrödinger, 1926a]. The reading lasted a few months. Hendrik Lorentz wrote to him in May of that year that a localised wave packet built from these modes would not stay localised, while the electron in a cathode ray plainly did [Przibram, 1967]. The deeper difficulty was one Schrödinger himself stated in his fourth communication: for a system of N particles the wave is not a function on ordinary space but on a space of 3N dimensions, one triple of coordinates for each particle, so that two electrons are described by one function of six variables and not by two waves in the same room [Schrödinger, 1926b]. A charge density lives in three dimensions. The function Schrödinger had found did not. Within weeks Max Born proposed the reading that has governed every laboratory since: the square of the amplitude gives the probability of finding the system in the corresponding configuration, a rule Born added to his paper in a footnote at the proof stage [Born, 1926]. The rule worked at once, and it has never failed. What it replaced, however, was an answer to a question, and it did not supply another answer. Born's rule says what the state predicts. It does not say what the state is a state of.

The century that followed built on the rule and set the question aside. Paul Dirac's Principles of Quantum Mechanics established the state as a vector in an abstract space whose physical meaning is exhausted by the probabilities it yields for the observables one chooses to measure [Dirac, 1930]. Richard Feynman told a lecture audience in 1964 that he could safely say nobody understands quantum mechanics, and advised them not to keep asking how it can be like that, since nobody knows [Feynman, 1965]. In 1989 David Mermin gave the working attitude its name. Asked what the Copenhagen interpretation amounts to, he wrote, he would summarise it as "shut up and calculate" [Mermin, 1989]; he later traced the phrase back to his own column, after it had been attributed for years to Feynman and to Dirac [Mermin, 2004]. The phrase is usually repeated as a joke. It is also an exact description of a decision. The formalism is complete as an instrument of prediction, and the practice of the discipline is to treat the instrument as the whole of the theory. What the instrument refers to is left open, not because the question has been shown to be meaningless but because nothing in the calculation requires it to be answered.

Not everyone accepted the decision. John Bell spent the last years of his life arguing that the word measurement, which the textbooks placed at the foundation of the theory, should be banished from any formulation that claims to be exact, because it divides the world into a system and an apparatus without saying where the division lies or what physical process it names [Bell, 1990]. His positive demand was for what he called beables: the elements of a theory that are supposed to correspond to something physically real, as distinct from observables, which are defined only through the procedures of the laboratory [Bell, 1976]. A theory without beables, in Bell's sense, can predict everything and describe nothing. The demand was not answered. It was absorbed into the interpretation literature as one position among others, and the practice of calculation continued as before, because Bell's demand, like the question behind it, did not change a single prediction. That is precisely the difficulty. A question that changes no prediction can be declined indefinitely by a discipline that measures its progress by predictions, and the longer it is declined, the more the declining comes to look like an answer.

The decision did not remove the question. In June 2025, at the Helgoland conference marking a century since Heisenberg’s first paper, Anton Zeilinger and Alain Aspect disagreed in public about whether there is a quantum world at all: Zeilinger held that the quantum state is information and nothing more, and Aspect replied that quantum states are real and objective. Weeks later, in July 2025, Nature published a survey of more than eleven hundred physicists. The respondents agreed on the formalism and divided on its referent: roughly a third held that the wavefunction represents something real, nearly half that it is only a useful tool, and the remainder spread across a range of other positions [Gibney, 2025]. The disagreement concerns the status of the wavefunction, and the formalism on which both sides agree leaves open what, in physical reality, that object describes. Shut up and calculate is the name of the practice of not naming it.

The question therefore has two faces, and they are one question. The fundamental objects of the theory are quantum fields: the electron field, the photon field, the quark and gluon fields, the Higgs field. Its states are states of those fields, and the wavefunction of ordinary quantum mechanics is recovered, in the nonrelativistic limit, as a description of a fixed-particle-number sector of those states. Its calculations are calculations of the statistics with which excitations of those fields are registered in matter. To ask what quantum physics describes is to ask what physical reality a quantum field is; to ask what it calculates is to ask what reality the registered statistics are statistics of. The answer to the second is the answer to the first. It is not the question of what the theory predicts, which is settled, nor of why one registration occurs rather than another, which the Born rule answers statistically and no theory answers case by case. It is the question of the referent: what, in the physical world, stands to a quantum field as a distribution of charge stands to the classical electromagnetic field. For the classical field the answer is written into the theory. For the quantum field it has been withheld.

Quantum field theory itself excludes the two answers that come first to mind. The first is that a quantum field is a classical field made quantum, a quantity with a value at every point of space that fluctuates. In the axiomatic formulation of Wightman, which fixes what a relativistic quantum field must be for the theory to be consistent, a field is an operator-valued distribution: the symbol φ(x) has no meaning at a point, and only the smeared quantities φ(f) = ∫ φ(x) f(x) d⁴x, taken against smooth test functions spread over a region, are operators at all [Streater and Wightman, 1964]. The restriction is not a technicality. The fluctuations of a free field at a single point are infinite, and the products of fields at coincident points, from which every interaction term is built, must be defined by renormalisation because the naive expressions diverge. A quantum field does not possess a value at a point that a measurement could read. Physicists who take fields to be the fundamental reality say so without equivocation: Wilczek calls the ensemble of fields the Grid, the medium of which everything else is an excitation [Wilczek, 2008], and Weinberg's treatise builds particles out of fields as representations of the symmetries of spacetime [Weinberg, 1995]. Neither says what the Grid is, or where it is, because the formalism does not say. Teller's interpretive study concluded that the field of quantum field theory is best read not as a distribution of values but as a set of determinables whose values are fixed only in the contexts where they are measured [Teller, 1995]. The classical picture of the field has been given up by the theory itself, and nothing physical has been named to replace it.

The second answer is that the fundamental objects are particles after all, and that fields are the mathematical device that describes them. Relativistic quantum theory excludes this too, by theorem, under the corresponding localisation assumptions. Malament showed that a relativistic quantum theory with localisable particles, in which the projection operators for finding a particle in bounded regions behave as positions must, together with translation covariance, energy bounded from below, the requirement that no particle be found in two disjoint regions of one spacelike hyperplane at once, and the commutation of localisation operators for spacelike separated regions, admits no particles at all: the localisation operators must vanish [Malament, 1996]. Halvorson and Clifton strengthened the theorem and extended it to unsharp localisation, concluding that there is no place for particles, in the ordinary sense, in relativistic quantum theories [Halvorson and Clifton, 2002]. Fraser showed that in interacting quantum field theories the particle interpretation fails more severely still, since the theory admits no Fock-space representation in which particle number is well defined [Fraser, 2008]. And the Unruh effect shows that whether a region of the field contains particles at all depends on the state of motion of the system that registers them [Unruh, 1976]. Davies stated the lesson in a paper whose title needs no gloss: particles, as fundamental objects, do not exist in quantum field theory [Davies, 1984]. What exists is registration. The operational lesson is exact: a particle is what a particle detector detects [Unruh, 1976; Unruh and Wald, 1984].

The states of quantum fields inherit, on a larger scale, the difficulty Schrödinger met in 1926. In the Schrödinger representation the state of a field is a wavefunctional Ψ[φ] on the space of all classical field configurations over a spatial slice [Weinberg, 1995]. That space is not three-dimensional; it is infinite-dimensional, and the configuration-space problem of two electrons returns with a continuum of degrees of freedom. Wallace and Timpson proposed to read the state as assigning a density operator to every region of spacetime, so that it becomes a physical property of spacetime regions [Wallace and Timpson, 2010]. The proposal locates the state in spacetime by construction, and, as its authors accept, the density operators of separated regions do not determine the state of their union, which is entanglement stated once more in the language of regions. The field-theoretic formalism is among the most precise descriptions of nature ever written. It does not say what its fields are, or what its states are states of, any more than the formalism of 1926 did.

At the level of the state, four results of standard quantum mechanics constrain any answer, and each has been established independently of every interpretation. The first is the one Schrödinger met in 1926. The state of N particles is a function ψ(r₁, r₂, …, r_N) on configuration space ℝ³ᴺ, and for N > 1 it cannot in general be written as N functions on ℝ³. Whatever ψ refers to, it is not a field distributed through the three-dimensional space in which the laboratory stands. The second result is entanglement. Two systems prepared in a common state, such as the spin singlet |Ψ⁻⟩ = (|↑↓⟩ − |↓↑⟩)/√2, possess no individual states of their own: the state of the pair is not the product of a state of the first and a state of the second, and each part taken alone is described by the maximally mixed reduced state ρ = I/2, which carries no trace of the correlation that the pair exhibits [Schrödinger, 1935b]. The third result is the pair of theorems of Kochen and Specker [Kochen and Specker, 1967] and of Bell [Bell, 1964]. The first excludes any assignment of pre-existing values to all observables that is independent of the measurement context; the second, confirmed by experiment in every loophole the tests could close [Aspect et al., 1982; Hensen et al., 2015; Giustina et al., 2015; Shalm et al., 2015], excludes any account in which the outcomes at two separated stations are fixed by local variables carried to each station. The fourth result is the absence of a collapse term. The unitary law of quantum mechanics is linear, and applied to a measuring device it produces a superposition of device readings, not one reading [von Neumann, 1932]. The Born rule supplies the probability distribution over outcomes; unitary evolution alone does not select any one of them, and the single outcome every laboratory records is not generated by the unitary law.

These four results mark the ground on which every answer to the question has been built, and the principal answers can be read by the price each pays on that ground. The operationalist answer, of which Quantum Bayesianism is the most developed modern form, holds that the state is an agent's catalogue of expectations about the outcomes of possible actions, so that the question of what it refers to in the world does not arise [Fuchs, Mermin and Schack, 2014]. Zeilinger's informational reading belongs to the same family: the state represents the information available about a system, and nothing beyond that information is described [Zeilinger, 1999]. These readings are predictively complete, and they are internally consistent. They do not answer the question of the referent; they decline it, and the decline is the whole of their ontological content. Bohmian mechanics takes the opposite course. It retains determinate particle configurations in three-dimensional space and adds a guidance equation through which the wavefunction on configuration space directs them [Bohm, 1952; Dürr, Goldstein and Zanghì, 1992]. The particles are located in ℝ³, but the guidance of each depends at every instant on the positions of all the others, however distant, and the wavefunction that guides them remains an object on ℝ³ᴺ whose own physical nature is the question again, now one level down. Primitive-ontology readings generalise this move, laying down an ontology of localised matter in space and treating the wavefunction as the law that governs it [Allori et al., 2008]. The Everettian reading moves in the other direction and identifies the universal wavefunction with the whole of physical reality [Everett, 1957]; it thereby converts every alternative the state describes into a realised world, and abolishes the distinction between what the state describes and what is registered, which is the distinction the question requires. The distinction between ψ-ontic and ψ-epistemic models [Harrigan and Spekkens, 2010] sharpened the terms of the debate, and the theorem of Pusey, Barrett and Rudolph showed that, under an assumption of preparation independence, a model in which distinct quantum states can describe the same underlying physical state conflicts with the predictions of quantum mechanics [Pusey, Barrett and Rudolph, 2012]. The theorem is strong evidence that the state corresponds to something physical. It is silent on what that something is.

Two conclusions follow, and each is narrower than it first appears. The first is that an answer which places the referent of the field or of its state in three-dimensional space, as localised material structure, can meet these constraints only by adding structure the formalism does not contain: a guidance law, a preferred foliation, an ontology of trajectories that no experiment can distinguish from the predictions of the unadorned theory. The second is that an answer which declines to name a referent leaves the question exactly where Born's footnote left it. Neither conclusion refutes the positions concerned. Both locate the question. What quantum physics describes has no values at points of the laboratory's space, its particles cannot be localised as objects in that space, its states are not distributions in that space, and it becomes a located, dated fact only when matter registers it. The possibility that remains is a physical reality with exactly these properties: not localised in three-dimensional material space, without proper duration of its own, and brought into that space only by interaction. It has not been set out as a candidate in its own right, because no part of established physics has been recognised as supplying a reality with those properties. Established physics does supply one.

This paper proposes that quantum physics describes the radiation domain, and that quantum fields are its structure. The proposal draws on a six-level structural hierarchy developed in previous work, in which the notation SxD (S6D to S1D) marks levels defined by their function and proper-time character rather than by a count of spatial coordinates; the notation distinguishes them from the xD dimensions of conventional physics, which are defined by space and time. The three levels S6D to S4D constitute the radiation domain, which carries no proper duration; the three levels S3D to S1D constitute the material domain, which carries proper duration and in which every registration occurs. S3D is the domain of the laboratory, and it contains the whole four-dimensional spacetime of general relativity; S4D is therefore not four-dimensional spacetime, and nothing in what follows identifies it with any spacetime at all. The claim is that the quantum fields of physics are the structure of S4D, the level of the radiation domain that projects onto S3D; that the quantum state is the description of that structure as the laboratory indexes it; and that registration is the interaction at which it yields one localised fact in S3D. The identification names S4D and not the radiation domain as a whole because only the projecting level projects onto S3D, where registration occurs: what the formalism describes is whatever is projected onto S3D at the boundary where outcomes are produced, and the levels above S4D enter this analysis only through it. Nothing in the argument that follows depends on the structure of those higher levels, and nothing is claimed about them here. The identification is ontological. It modifies no equation of quantum mechanics and does not derive the Born rule; its warrant is that established physics already contains a sector whose description satisfies these constraints without added structure, and that the identification accommodates the two most demanding phenomena of quantum physics, entanglement and the dependence of the vacuum's particle content on the registering system, without any signal passing through space.

2. The Quantum Field as the S4D Radiation Domain

Special relativity, through Wigner's classification of its elementary systems, sorts every physical system into one of two classes, massive and massless, and no continuous change of motion carries a system from one class into the other [Wigner, 1939]. The classification rests on the unitary representations of the Poincaré group, which sort every elementary system by its invariant mass. For m > 0 the little group is the rotation group SO(3), the system possesses a rest frame, and its internal state is labelled by spin. For m = 0 the little group is the Euclidean group of the plane, no rest frame exists, and the internal state is labelled by helicity. The two classes are distinct representations, not two ends of one family. No Lorentz transformation carries a timelike four-momentum into a null one, and the Lorentz factor γ = 1/√(1 − v²/c²), which diverges as v approaches c, is the kinematic statement that the boundary between the classes cannot be reached by acceleration. A massive system, which carries proper duration, can move at any speed below c and change it; a massless system, which carries none, moves at c in every frame and cannot change it. The distinction has a temporal signature that is written into the proper-time relation itself. Along a timelike worldline the proper time dτ = dt √(1 − v²/c²) is strictly positive; along a null worldline ds² = 0 and no proper duration accumulates. Proper duration is therefore the invariant temporal signature of the massive sector and its absence the invariant signature of the massless sector, and the boundary between them is crossed only by interaction, in annihilation and pair production, never by motion [Zhong, 2026a]. That result is not an interpretation. It restates, in a single invariant, what Wigner's classification and the causal structure of Minkowski spacetime already contain.

The two sectors are also the two domains of time in physics. Every clock is a massive system. The analysis of Salecker and Wigner showed that a clock of given accuracy and running time must have a mass bounded below [Salecker and Wigner, 1958], and every clock in use, from a pendulum to an optical lattice, counts the cycles of a material process. The Compton frequency mc²/h of a massive particle is itself a clock rate, and a massless system has none. Physics has therefore always measured time within one of its two sectors only. Taken together with Newton’s distinction between absolute and relative time, this yields the conclusion that the physical world contains a domain governed by relative time, with τ > 0, and a domain in which the proper time of every constituent is identically zero, the two separated by a boundary no Lorentz transformation crosses [Zhong, 2026b]. The partition itself belongs to standard physics: Wigner's m > 0 and m = 0 classes and the timelike and null sectors of Minkowski geometry are textbook results. The names are the present paper's. The first sector is the material domain; the second is identified with the radiation domain of the structural hierarchy introduced above. The division is not a hypothesis added to relativity; it is a partition relativity already enforces and has not been accustomed to name.

The two domains are not sealed from one another. Every particle of the Standard Model is an excitation of a quantum field, and the fields are coupled: an electron and a positron annihilate into photons, and two photons of sufficient energy produce an electron–positron pair, as Breit and Wheeler computed in 1934 [Breit and Wheeler, 1934; Weinberg, 1995]. Matter and radiation are therefore not two independent substances: the material domain receives its content from the radiation domain, and the two are exchanged into one another by interaction. The classificatory habit of calling the electron matter and the photon radiation conceals this. The concealment goes back to the nineteenth-century extension of the word radiation across fluxes of fermions and of gauge bosons alike, and radiation is better understood as a category of transferable field excitation than as the opposite of matter [Zhong, 2026c]. What passes between the two sectors is the capacity to carry proper duration: the photon has none, the electron acquires it at the moment of its production, and loses it at the moment of its annihilation.

Mass, the property that most plainly marks matter off from radiation, is not in quantum field theory an intrinsic possession of a pre-existing particle. The masses of the elementary fermions of the Standard Model arise from their Yukawa couplings to the Higgs field, whose nonzero value throughout space gives each coupled field a mass term; without that coupling the electron field and the quark fields would describe massless excitations, and the discovery of the Higgs boson in 2012 confirmed the mechanism [ATLAS Collaboration, 2012; CMS Collaboration, 2012]. The mass of composite matter has a different origin. About ninety-nine per cent of the mass of the proton and the neutron, and therefore of ordinary matter, comes not from the Higgs couplings of the quarks but from the energy of the quark and gluon fields bound by quantum chromodynamics, as lattice calculations have confirmed by computing the light hadron masses from first principles [Dürr et al., 2008]. The two origins differ, and the difference matters to physics. What they share matters to the present question: in neither case is mass a property that a particle brings with it into existence. Standard physics describes its origin through the interaction of fields, with the Higgs field in one case and between quarks and gluons in the other, and in both cases mass is not carried by the field structure itself: the massive, proper-duration-carrying matter of the laboratory belongs to the material domain, and mass appears only where that structure has entered S3D.

The structure of a massive fermion field shows the same dependence at the level of the field itself. In the Standard Model the electron field is not one field but two chiral fields, a left-handed and a right-handed Weyl field, each of which, taken alone, describes a massless excitation with a definite helicity. The Dirac mass term, m ψ̄ψ = m (ψ̄_L ψ_R + ψ̄_R ψ_L), is a coupling between these two massless components, and in the Standard Model it is itself produced by the Yukawa coupling of the two to the Higgs field. Penrose drew the physical picture that the formula contains: the massive electron is a continual interconversion of two massless constituents, each moving at the speed of light, zig-zagging into one another at a rate fixed by the mass, so that the timelike worldline of the electron is the average of a sequence of null segments [Penrose, 2004]. The picture is a reading of the free Dirac equation in its chiral form, and it modifies nothing in it. What it makes visible is that the proper duration a massive particle carries is not a property of its constituents taken one by one, since each constituent is massless and carries none; it arises from the coupling between them. The same holds at the scale of the universe. In the electroweak theory the Higgs expectation value falls toward zero across a smooth crossover near a temperature of 160 GeV, and well above that temperature the masses that the Higgs coupling gives the gauge bosons and the elementary fermions are suppressed [Weinberg, 1967; Kajantie et al., 1996; D'Onofrio and Rummukainen, 2016]. The elementary fields of matter, in the regime in which the Higgs coupling gives them no appreciable mass, are fields of the massless sector. The massive, registrable matter of the present universe is that massless structure as it appears in the material domain, and the elementary matter and gauge fields are fields whose excitations carry no mass of their own; mass is the form they take in S3D.

The registration of radiation displays the same exchange in every laboratory. Glauber's theory of photodetection, on which quantum optics rests, describes the registration of a photon as its absorption: the counting rate of an ideal detector is proportional to the expectation value of the normally ordered product of the negative- and positive-frequency parts of the field, and the positive-frequency part is an annihilation operator [Glauber, 1963]. A photon is not registered and then allowed to continue. It is registered by ceasing to exist as a photon and becoming an excitation of matter: a photoelectron, a bound electron promoted to a higher level, a chemical change in an emulsion. The registration of the massless sector is therefore always its conversion into the massive sector, and the point at which the photon is found is the point at which that conversion occurs. The general form of the relation was stated by Wheeler in the language of the delayed-choice experiments: no elementary phenomenon is a phenomenon until it is a registered phenomenon, brought to a close by an irreversible act of amplification [Wheeler, 1978; Wheeler and Zurek, 1983]. Wheeler's sentence is usually read as a statement about knowledge. Read with the partition of the sectors in view, it states a physical fact about registration: every registered phenomenon is closed in matter, because only matter carries the proper duration in which an irreversible record persists.

The massless sector has a further property that bears directly on the question of location. In 1949 Newton and Wigner asked which states of an elementary relativistic system can be called localised at a point, and constructed a position operator from the requirements that localised states be carried into localised states by translations and rotations and be orthogonal when localised at different points [Newton and Wigner, 1949]. For every massive system the construction succeeds. For massless systems with helicity of magnitude one or more, which includes the photon, it fails: no position operator of this kind exists, and the photon has no localised states in the Newton–Wigner sense. Wightman confirmed the result in the language of systems of imprimitivity [Wightman, 1962]. The photon is registered at a point, by an absorbing atom or a detector pixel, but it possesses no position observable of the Newton–Wigner kind that a massive particle possesses; the point at which it is found is fixed by the registering interaction, not by a localised state the photon occupied beforehand. Hegerfeldt added a result of wider scope. In relativistic quantum theory a state localised at one instant in a bounded region acquires, at any later instant, a nonzero probability of being found arbitrarily far away, so that strict localisation and relativistic causality cannot both hold for the state as an object in space [Hegerfeldt, 1974; Hegerfeldt, 1998]. The localisation of a relativistic quantum system in three-dimensional space is therefore not a property the formalism can attribute to the unregistered state without strain. It is a property of registration.

Proper duration attaches to trajectories. It is defined along a timelike worldline as the integral of dτ between two events on it, and a massive particle in a definite state of motion carries one. A quantum field is not a trajectory. It is defined over the whole of spacetime at once, as the net of operator algebras assigned to its regions [Haag, 1996], and nothing in that definition picks out a worldline along which a proper duration could accumulate. The massive excitations of a field acquire tracks, and with them proper durations, to the extent that they are registered along a path, as in a cloud chamber, a silicon tracker or an ion trap, where successive registrations in matter mark the path out; the massless excitations acquire none even then. This is not a theorem that fields lack proper time, since the concept was never defined for fields. It is the observation that the quantity by which physics has always individuated material objects, a duration counted along a path, is a quantity of registered excitations and not of the field that is excited.

The remaining possibility asks for a reality with three properties, and established physics contains one that has them. The first property is the absence of a location in three-dimensional space: quantum fields have no values at points, their states are defined on configuration spaces of unbounded dimension, and neither massless states in the Newton–Wigner sense nor relativistic particles in the sense of Malament and of Halvorson and Clifton can be localised as objects in space. The second is the absence of a proper duration: proper duration belongs to trajectories and, by Wigner's classification and the proper-time relation, to the massive sector; the field is not a trajectory, and its massless sector carries none. The third is that it becomes a located, dated fact only by interaction: every registration of a field excitation is an interaction with matter, and the registration of radiation is, by Glauber's theory, its absorption. The sector of established physics in which the three properties are native is the massless sector, which has no rest frame and no localisation within itself, accumulates no proper duration, and meets the massive sector only through interaction; and the origin of mass shows that the massive sector is not presupposed by the fields but is the form their structure takes in the material domain. The present paper identifies the quantum fields of physics, as physical reality, with the radiation domain, and specifically with S4D, the level at which it projects onto S3D. The S4D structure carries no mass; mass and proper duration belong to the material domain S3D. The radiation present within S3D, light and every other electromagnetic flux, is radiation from S4D propagating in the material domain, and the massive particles that registration produces are the form that S4D radiation takes once it has entered S3D. The two forms are distinguishable within S3D itself. Radiation that has taken material form carries rest mass and proper duration, and moves at speeds below c that can change (m > 0, dτ > 0, v < c): it is matter. Radiation that has entered S3D without taking material form carries no rest mass and no proper duration, and moves at c in every frame (m = 0, dτ = 0, v = c): it is S4D radiation propagating unchanged in the material domain. The fields that the Standard Model writes with mass terms describe the S4D structure as it appears in S3D, not a mass that the structure possesses at S4D. Particles are the registered facts of that structure in S3D, and the quantum state is its description as the laboratory writes it.

The identification is supported by these relations; it is not deduced from them. What the relations establish is that the reality quantum physics requires is not an invention, since physics already contains a sector with exactly the properties required. The identification is then tested by what it explains, and the explanations that follow rest on it rather than supporting it.

The identification must be read with its scope fixed. It does not assert that the electron is a photon, or that a massive particle in flight is a massless particle in disguise. The electron registered at a screen is a material fact in S3D, with mass and charge, and the registered fact, a located and dated event in the material domain, begins at the registration. What the identification concerns is the electron field, and the state ψ that the formalism assigns to it while no registration has occurred, which evolves unitarily and yields, at the screen, one spot. That state is not the electron as registered, and the four constraints show that it cannot be a localised material electron travelling unseen. The mass parameter m appears in the Hamiltonian that governs ψ, as it must, since the state is a state of possible material registrations and the registrations will be massive. The proposal is that the reality of which ψ is the description is not itself a material object, but the radiation-domain state from which material registrations are drawn.

Each of the other possibilities answers part of the question, and the parts they leave unanswered are the parts the radiation domain supplies. Configuration-space realism [Albert, 1996; Ney, 2021] correctly records that the state is not a distribution in ℝ³, but it converts a fact about where the mathematics is represented into a claim about where physical reality is, and it must supply a further account of why a world whose fundamental arena has 3N dimensions presents itself in three. The informational and relational readings [Zeilinger, 1999; Rovelli, 1996] correctly record that the state is specified relative to registrations and to the systems that make them, but a specification requires something that is specified, and these readings are silent on what bears the state between one registration and the next. The nonlocal material readings correctly retain a physical bearer, but they place it in the material domain and must then explain how a bearer with proper duration and a location in ℝ³ carries correlations that no location in ℝ³ supports. The radiation-domain identification keeps what each of these readings gets right and adds what none of them supplies: a bearer that is physical, that is not in ℝ³, that carries no proper duration, and whose contact with ℝ³ is the interaction that every measurement already is. It does not require a new space, since the massless sector is part of the physics of the one space there is; it does not require a new law, since the unitary law and the Born rule are retained unchanged; and it does not require the bearer to be hidden, since its excitations are registered in every laboratory, always at the point where they are absorbed.

3. The Registration Boundary

The temporal words in which quantum physics is stated belong to the laboratory. The formalism speaks of the state before measurement and of collapse at measurement, and these are words of the laboratory. The ordering they express is the ordering of the laboratory's clock, which is a material clock in S3D. The radiation domain carries no proper duration, and nothing in it is before or after anything else. When the state is said to be unregistered, the phrase describes the state from the side of the material domain: it is the state as the laboratory must write it at clock readings at which no outcome has yet been recorded. The unitary evolution of ψ in the parameter t is correspondingly the law by which the laboratory's description of the radiation-domain state is indexed by the laboratory's clock. It is not a history the radiation domain undergoes.

Standard physics has already shown that time can enter a quantum description in exactly this way. In the canonical quantisation of general relativity the Wheeler–DeWitt equation, Ĥ|Ψ⟩ = 0, contains no time parameter at all: the state of the universe does not evolve [DeWitt, 1967]. Page and Wootters showed how evolution is nevertheless recovered: if the global state is stationary but correlates a clock subsystem with the rest, then the state of the rest, conditioned on the clock's reading, evolves according to the Schrödinger equation in that reading [Page and Wootters, 1983]. Time, in this construction, is not a parameter the global state carries. It is a relation between the rest of the system and a material clock inside it. Moreva and co-workers realised the construction with entangled photons, one of which served as the clock, and observed the conditional evolution appear for an observer who read the clock while the global state, examined by an observer outside it, remained static [Moreva et al., 2014]. The laboratory's ψ(t) is read here in the same relational way. The parameter t is the reading of a material clock, the evolution in t is the correlation between that reading and the registrations the state can yield, and nothing in the construction requires the referent of the state to carry a time of its own.

The registration boundary can now be stated in three parts that are not three states and not three stages of one process in time. There is the radiation-domain state, which the laboratory describes by ψ and indexes by its clock. There is the registering interaction, the coupling between that state and a material arrangement at a place in S3D. And there is the registered fact, a located and dated event in the material domain, carrying proper duration from that event onward in whatever material record it is written into. The first is described by the unitary law, the probabilities of the second are given by the Born rule, and the third is described by classical and relativistic physics. The word before, applied to the first in relation to the third, is the laboratory's word for the reading of its clock at which no record has yet been written; it does not assert that the radiation-domain state exists earlier than the fact in some time of its own. The formalism has always carried these three parts in its three distinct rules. The third part is the one without which no physical theory has a subject: a physical fact exists only as registered by a material system, and the registering system is the precondition of every quantity a theory can state, not a later addition to a description already complete without it [Zhong, 2026d]. What the formalism has not said is that the first belongs to a domain without proper duration and the third to the domain where proper duration is counted.

The boundary so stated meets its sharpest test in the case of nested observers. Wigner imagined a friend inside a sealed laboratory who measures a system and obtains a definite result, while Wigner, outside, describes the laboratory and the friend together by a unitarily evolving state in which no result has been obtained [Wigner, 1961]. Frauchiger and Renner showed that when agents apply quantum mechanics to systems that contain other agents and reason about one another's conclusions, the conclusions contradict one another [Frauchiger and Renner, 2018], and an experiment on a simplified photonic version of the scenario has reported violation of a related inequality for local observer independence [Proietti et al., 2019]. The contradiction arises from treating the friend's registration and Wigner's description as two descriptions of one state at one level. On the registration boundary they belong to two levels. The friend's registration is a fact of the material domain, written into the friend's apparatus and records and carrying proper duration from that event onward. Wigner's description is the description of the radiation-domain structure as his own clock indexes it, and it describes what his own registration, when it occurs, can yield. For Wigner to observe interference between the friend's alternatives, he must reverse the friend's registration entirely and erase every material record of it. The scenario therefore does not present two contradictory facts. It presents a registered fact on one side and, on the other, a description that remains a description until it is itself registered: a registration is a fact in S3D, and a state is a description of S4D.

Proper duration connects the partition directly to the state of the field. A superposition of two paths is coherent only so long as nothing in the world distinguishes them, and one of the things that can distinguish them is proper time itself. Zych, Costa, Pikovski and Brukner showed that if a particle carrying an internal clock is sent through an interferometer whose arms differ in gravitational potential, the proper times accumulated along the two arms differ, the clock records which arm was taken, and the visibility of the interference falls in exact proportion to the distinguishability of the two clock readings [Zych et al., 2011]. Margalit and co-workers realised the effect with a self-interfering clock in the laboratory, erasing the interference by making the clock's time differ between the arms [Margalit et al., 2015]. The result is standard quantum mechanics applied to a clock, and it states something about the relation between superposition and proper duration that the ordinary textbook presentation does not make visible. A superposition persists to the extent that no record of proper duration separates its components; when such a record is written, the superposition is lost to every measurement that could reveal it. In these experiments proper duration is not merely compatible with registration. A difference in proper duration, written into the internal state of the clock, functions as a which-path record.

The same structure appears in the theory of decoherence, where it is usually described without reference to time. A system in superposition interacts with its environment: a stray photon scatters from it, a molecule of air collides with it, a phonon is exchanged with its support. Each interaction writes into the environment a record that distinguishes the components of the superposition, and the interference between those components becomes inaccessible in proportion to the distinguishability of the records [Zurek, 2003; Joos and Zeh, 1985]. Every one of these records is material. It is written into scattered particles and displaced atoms that carry proper duration, and it persists because the material carriers persist. The clock of Zych and Brukner is the limiting case in which the record is written into the proper time of the system itself rather than into its surroundings, and it shows that the record need not be a separate object at all: the elapsed proper duration of a massive system along one alternative, as opposed to another, is enough.

The experiment that shows this most directly used the radiation a massive system emits. Hackermüller and co-workers sent C70 fullerene molecules through a Talbot–Lau interferometer after heating them with lasers to internal temperatures between roughly one thousand and three thousand kelvin [Hackermüller et al., 2004]. At the lower temperatures the interference fringes were fully visible. As the temperature rose, the molecules began to emit thermal photons during their flight, and once the emitted photons had wavelengths short enough to resolve the separation between the interferometer paths, the fringes faded and vanished. The photons carried away from the molecule only energy, momentum and the record of where they left it; the loss of interference was quantitatively accounted for by the which-path information those photons carried. The molecule is a massive system of seventy carbon atoms, and its coherent state survived as long as nothing it emitted could be absorbed as a which-path record by the material surroundings. What destroyed the superposition was not the mass of the molecule but the writing of a record in matter by radiation it released.

What decoherence describes as the leaking of which-path information into the environment is, in these terms, the writing of material records, and a superposition survives only in the absence of them. The quantum state is coherent to exactly the extent that the material domain holds no record distinguishing its components. This is what the identification leads one to expect: if the field state belongs to a domain without proper duration, any record of proper duration that distinguishes its alternatives is a registration in the material domain, and the coherence of the alternatives is lost when such a record is written.

Quantum Darwinism, developed by Zurek, extends the account of decoherence to the question of why independent observers agree. When a system decoheres, information about its pointer states is copied redundantly into many fragments of the environment, so that many observers, each intercepting a different fragment of scattered light or of the surrounding gas, can read the same outcome without disturbing the system or one another [Zurek, 2009]. The redundancy has been observed in engineered systems, where a small fraction of the environment was found to carry nearly all the available information about the system [Unden et al., 2019]. On the registration boundary this is the structure that material records must have. A registration is not a single mark but a fact written into matter, and matter copies it: each photon scattered from a registered pointer and absorbed elsewhere writes the fact again. The objectivity of the classical world, its sameness for every observer, is the multiplication of material records of one registration across the material domain. It requires no agreement between observers beyond what the records already carry, because every observer reads a copy of the same fact.

The same boundary identifies what quantum physics calculates. A scattering amplitude is computed between asymptotic states, and asymptotic states are defined by where registration occurs: particles far from the interaction region, freely propagating, registered by matter. The Lehmann–Symanzik–Zimmermann reduction removes the interaction region from the final description and keeps only the relation between registrations at the two ends. Inside the calculation the Feynman expansion introduces internal lines, the virtual particles, which carry momenta off the mass shell and are never registered: they are terms in the expansion of the field's amplitude, not objects that pass through the laboratory [Feynman, 1949]. What the calculation delivers at the end is a number that becomes a probability of registration when squared. The quantities quantum physics computes and matches to experiment, from the anomalous magnetic moment of the electron to the cross sections of the Large Hadron Collider and the levels of the hydrogen atom read off its spectral lines, have this form: the statistics with which the field's structure is registered in matter where detectors stand. The century of calculation has been a century of computing, with extraordinary exactness, the registrations of the radiation domain in the material domain. The calculations never needed to say what was being registered, because the quantities they compute are the registrations themselves.

Read in these terms, the features of quantum mechanics that the practice of calculation has left without a referent acquire one, and each is an interpretation of an established structure rather than a new derivation. Superposition is the state structure of a domain in which no registration has distinguished the alternatives; it is not a blurred material object, and the Zych–Brukner result shows directly that it ceases precisely where a material record begins. The configuration space on which ψ lives is the space of possible material registrations of a state that is not itself located in the space where those registrations occur; the 3N dimensions are the coordinates of the registrations the state can yield, not the extension of the state. The contextuality established by Kochen and Specker receives the same reading. Their theorem shows that the value a measurement yields cannot in general be regarded as a pre-existing property of the system that the measurement merely reveals, since no assignment of such values to all observables at once is consistent with the functional relations among them; the value depends on which compatible observables are measured together. On the present account a value is not a property the radiation-domain state possesses in the material domain's terms at all. It is the outcome of a registration, and a registration is an interaction between the state and a particular material arrangement. That the outcome depends on the arrangement is then not a paradox about hidden properties but the ordinary consequence of the fact that the value comes into existence in the registration that the arrangement performs. The Born probabilities are the statistics of registration at the boundary between the domains. The paper does not derive the square |ψ|² from this reading, and the rule enters here exactly as it enters the formalism, as the law of the boundary; what the reading supplies is the location of the rule, which is the interface between the two domains and not a process inside either. The absence of a collapse term from the unitary law follows the same location. The unitary law governs the description of the radiation-domain state; registration is an event of the material domain produced by interaction at the boundary; a law of the one does not contain the event of the other. A previous analysis identified collapse as the boundary between the domain of possibility and the domain of realised fact [Zhong, 2026e], and the present identification supplies the physical character of the two sides: one side carries no proper duration, and the other side is where proper duration is counted.

The identification also places, without altering it, the mathematically real object of a two-level distinction drawn in previous studies: the Zeilinger–Aspect disagreement cannot be settled within a single ontological level, and it dissolves once the level of the wavefunction, mathematically real and objectively defined, is separated from the level of measurement outcomes, which is the level of physical actuality [Zhong, 2026f, 2026g]. This separation says where the wavefunction belongs in the order of description; it does not say what the mathematically real object describes. At the level of description available in S3D, ψ is mathematical reality: an objective and exactly defined structure that no laboratory instrument registers as such, since every instrument registers an outcome. The referent of that structure, the physical reality it is a description of, is the radiation-domain state. The two statements belong to two levels and do not compete. The first says what ψ is for any description written in the material domain; the second says what that description describes. The same placement gives a physical content to a problem that has been treated as purely logical. Krause has developed the view that the quanta of physics are non-individuals, entities to which the classical theory of identity does not apply, and has built a quasi-set theory in which such entities can be counted without being labelled [Krause, 2023]. His programme specifies the identity conditions of the entities the state represents; the present proposal addresses the same referential question at a different level, by specifying the physical domain to which the unregistered state belongs. On the present account non-individuality receives a physical interpretation: identity in the classical sense is re-identification across a registered history, and the radiation-domain state carries no proper duration in which such a history could be written, so that no fact of which one is which can arise there.

4. Entanglement, the Vacuum and the Open Problems

Einstein, Podolsky and Rosen framed their challenge of 1935 as a question about completeness, and the question they asked was the question of the referent in its sharpest form [Einstein, Podolsky and Rosen, 1935]. Two particles interact and separate. A measurement of position on the first allows the position of the second to be predicted with certainty; a measurement of momentum on the first allows the momentum of the second to be predicted with certainty; since no disturbance travels from the first particle to the second, the second must possess both quantities as elements of reality, and the quantum state, which assigns it neither, cannot be a complete description. Schrödinger replied within months with the word that has named the phenomenon ever since. The state of two systems that have interacted, he wrote, is not in general a product of states of the parts, and he called this entanglement, Verschränkung, "not one but rather the characteristic trait of quantum mechanics" [Schrödinger, 1935a; Schrödinger, 1935b]. Einstein's own phrase for what the formalism implied was spukhafte Fernwirkung, spooky action at a distance, in a letter to Born of 1947 [Born, 1971]. Both men saw that entanglement is where the question of what the state describes cannot be deferred, because the state describes two separated systems at once and the separated systems do not have states of their own.

Bell turned the question into an inequality [Bell, 1964]. If the outcome at each station is fixed by the local setting and by variables the two particles carried from their common source, then the correlations between the stations satisfy a bound; in the form given by Clauser, Horne, Shimony and Holt, the combination S of four correlation functions satisfies |S| ≤ 2 [Clauser et al., 1969]. Quantum mechanics predicts, for the singlet and suitably chosen settings, |S| = 2√2. Aspect and his collaborators confirmed the violation with settings changed during the flight of the photons [Aspect et al., 1982], and in 2015 three groups closed the locality and detection loopholes simultaneously, one with electron spins in diamond separated by 1.3 kilometres and two with entangled photons [Hensen et al., 2015; Giustina et al., 2015; Shalm et al., 2015]. The experimental verdict is not in doubt. No account in which each outcome is determined by what was locally present at its own station reproduces the observed correlations.

The same formalism that predicts the violation also forbids its use. The no-signalling theorem shows that the probability of any outcome at one station, summed over the outcomes at the other, is independent of the setting chosen at the other: P(a | x, y) = P(a | x) for every pair of settings x, y [Eberhard, 1978; Ghirardi, Rimini and Weber, 1980]. In the singlet the reduced state at each station is I/2 whatever is done at the other, and the local outcomes are individually random. The correlation appears only when the records of the two stations are brought together and compared, and bringing them together requires an ordinary channel limited by c. Experiments have also sought a finite speed at which the correlation might be established, treating it as if it were carried by an influence travelling in some preferred frame; they have found none, and the lower bounds on such a speed exceed c by factors of ten thousand and more [Salart et al., 2008; Yin et al., 2013].

What these results establish must be kept apart from what they do not. For the singlet, the joint state does not factorise, ρ_AB ≠ ρ_A ⊗ ρ_B, while each reduced state is ρ_A = Tr_B ρ_AB = I/2 and ρ_B = Tr_A ρ_AB = I/2. The pair is therefore not reducible to two independent local states, and each registered marginal is locally random. Bell's theorem establishes, under its assumptions of locality and measurement independence, that no local hidden-variable account reproduces the joint statistics. The no-signalling theorem establishes that the correlations cannot be used to send a controllable message. The speed-bound experiments establish that any influence carried in a preferred frame would have to exceed c by at least four orders of magnitude. None of these results identifies the physical bearer of the joint state, and none of them singles out the radiation-domain identification over other readings. What they supply is a demanding set of conditions that any proposed bearer must meet at once: it must carry correlations no local account reproduces, it must leave every marginal independent of the distant setting, and it must do so without requiring an influence of any finite speed. The test of the present proposal is whether it meets all three without added structure.

The standing problem that these results leave is often stated as the problem of what carries the correlation from one station to the other. That statement presupposes an answer, since it assumes that the correlation is something that must be carried, and Bell's theorem does not establish that anything is carried. It establishes only that the outcomes are not fixed by local variables. The precise problem is different, and it is the problem of the referent once more: what kind of physical state the formalism describes when two outcomes, registered at stations whose separation is spacelike, stand in a correlation that neither station's local state contains. Maudlin's analysis showed how sharply this problem sits against relativity [Maudlin, 2011]. If the state is taken to be a physical object in spacetime that changes when an outcome is registered, the change must occur along some hypersurface, and the choice of hypersurface is a choice of frame: in one frame the first station registers first and the state of the second particle changes as a consequence, and in another frame the order is reversed. Aharonov and Albert showed that no covariant account of this kind assigns the state a frame-independent history along the worldlines of the particles [Aharonov and Albert, 1981]. The correlation is Lorentz invariant; the story of its production, told as a change of an object in spacetime, is not.

The identification of the unregistered state as a radiation-domain state removes the presupposition on which that story depends. The entangled pair is not two material objects carrying a shared state through space, and it is not one material object extended across the laboratory. It is one radiation-domain state, and the two registrations at the separated stations are two localised facts drawn from it in S3D by interaction at two places. The spatial separation of the stations is a quantity of the material domain: it is measured by rods and clocks, which are material, and it exists between the two registration events, both of which are events of S3D. It is not a separation within the radiation-domain state, which has no location in three-dimensional space to be separated across. The correlation between the two outcomes is therefore not a relation that must be transmitted from one place to another, because the two outcomes are not two independent facts whose agreement requires a messenger. They are two registrations of one state. Nothing crosses the space between the stations, because what correlates them is not in that space.

For photons propagating in free space, as in the tests of Aspect and of Yin and co-workers [Aspect et al., 1982; Yin et al., 2013], established relativity already exhibits the relation on which this reading rests. For each detected photon of an entangled pair, the emission event at the source and the detection event are connected by a null interval: the invariant interval between them is zero. Photons guided in optical fibre propagate below c, and the kinematic statement applies to them only as the vacuum limit of their propagation. The two detection events are spacelike separated from one another, and each is at zero interval from the common source. Proper duration relates neither detection to the emission, and the only nonzero invariant separation in the configuration is the spacelike separation between the two detections, which is the separation of two registered events in the material domain. The radiation-domain reading interprets in ontological terms what the null geometry states kinematically: on the side of the configuration that carries no proper duration, source and registrations are not held apart by any interval, and the separation that the laboratory measures belongs entirely to the side where registration has occurred. The electron spins of the Delft test do not travel on null worldlines, and the reading there does not rest on this kinematic fact. It is worth recording that their entanglement was established by the interference and joint detection of photons emitted by the two spins [Hensen et al., 2015], so that the correlated state of two massive systems a kilometre apart was created through the massless sector; the reading requires no more than this, and claims no more.

The case with three particles removes the last appeal to statistics. Greenberger, Horne and Zeilinger showed that for three spin-½ particles in the state (|↑↑↑⟩ − |↓↓↓⟩)/√2 the product of the outcomes of certain spin measurements is fixed with certainty for each run: for three of the four combinations of settings the product is +1, and for the fourth, which any assignment of local values would force to be +1 as well, quantum mechanics predicts −1 [Greenberger et al., 1990]. The contradiction with local values arises in a single run, not in the accumulation of correlations over many, and it was confirmed with three entangled photons [Pan et al., 2000]. The GHZ case leaves no room for the thought that the correlation is a statistical pattern that some hidden local mechanism might approximate. In every run, three registrations at three separated stations yield outcomes whose product is fixed, while each outcome alone is random. On the radiation-domain reading this is what three registrations of one state show: the constraint on the product belongs to the state, the randomness of each factor belongs to the local registration, and nothing passes among the three stations because the three outcomes are not three independent facts that must be brought into agreement.

The strongest version of the case was produced by experiments in which the temporal order of registration is not merely frame-dependent but inverted. In entanglement swapping, two independent entangled pairs are prepared, one photon from each pair is brought to a joint measurement, and the two remaining photons, which never interacted, are thereby projected into an entangled state [Żukowski et al., 1993]. Ma and co-workers performed the joint measurement after the two remaining photons had already been registered, with the choice of whether to perform an entangling or a separable measurement made by a quantum random number generator at that later time; the registered photons displayed entanglement or separability according to a choice made after their own registration [Ma et al., 2012]. Megidish and co-workers went further and entangled two photons that never coexisted: the first was registered before the second was emitted, and the correlation between them was established nonetheless [Megidish et al., 2013]. No account in which the correlation is a physical influence propagating forward in the laboratory's time can describe these results without an influence travelling backwards. Standard quantum mechanics predicts them without difficulty, because the formalism makes the joint statistics independent of the order in which the measurements are performed. What the formalism does not say is what kind of state admits correlations indifferent to temporal order. The radiation-domain reading answers that it is a state that carries no temporal order: since the radiation domain has no proper duration, nothing in it is earlier or later, and the order of the registrations drawn from it is a fact only of the material clocks that record them. The delayed-choice results are naturally accommodated by such a state, whereas a state located in material space and time can accommodate them only by influences running against the laboratory's own order of time or by a preferred foliation that the formalism does not contain.

The frame-dependence that troubled the account of collapse as a change of an object in spacetime does not arise on this reading, because the reading assigns no such change. Each registration is a local event in S3D, with a definite place and a definite reading of the local clock. The question of which registration occurred first has, for spacelike separated stations, no frame-independent answer, and on the present account it needs none: the radiation-domain state carries no proper duration and no temporal order, so that there is no fact within it about which registration it yielded first. The order in which a given frame lists the two events is a fact about the material domain's description of two material events, and the correlation between them does not depend on it. The Lorentz invariance of the correlation is thus matched by an account of its origin that contains nothing frame-dependent, since the only temporal and spatial relations the account contains are those between registered events, which relativity already treats covariantly.

No-signalling follows on the same reading without additional assumption. Each registration is a local event drawn from the radiation-domain state by interaction at its own station, and what the local registration can yield is fixed by the local interaction and the state, not by what is done at the other station. The marginal distribution at each station is the local statistics of registration, and the formalism fixes it as the reduced state I/2, independent of the distant setting. The correlation is present in the joint distribution of the two records, and it becomes a fact available to anyone only when the two records, each a material object, are brought together through the material domain at speeds no greater than c. The reading does not allow the correlation to be used for signalling, for the same reason that it does not require the correlation to be transmitted: the correlation is a feature of the state from which the two registrations are drawn, not a message sent between them. The failure of experiments to find a finite speed for the establishment of the correlation is consistent with the reading, which posits no influence travelling between the stations and therefore no speed to be found.

The reading does not derive the value 2√2. Popescu and Rohrlich showed that correlations stronger than the quantum ones, reaching |S| = 4, are consistent with no-signalling [Popescu and Rohrlich, 1994], and the quantum maximum is fixed by Tsirelson's bound, which follows from the Hilbert-space structure of the formalism [Cirel'son, 1980]. The radiation-domain reading takes that structure as the correct description of the state and does not reconstruct it. Its claim in the case of entanglement is exactly this: that Bell violation, no-signalling, the absence of any finite speed of establishment and the frame-independence of the correlation are accommodated together by one ontology in which the correlated outcomes are two registrations of one state that is not located in the space between them. That ontology adds no guidance law, no preferred foliation and no hidden variables, and it removes the one element on which every picture of spooky action depends, the assumption that the referent of the entangled state is something in the space the stations share.

The vacuum is the second test, and for a theory of fields the more direct one. In the Minkowski vacuum an inertial detector registers nothing. Unruh showed that a detector undergoing uniform acceleration a in the same vacuum registers a thermal distribution of particles at the temperature T = ħa/(2πck_B) [Unruh, 1976; Crispino, Higuchi and Matsas, 2008]. Nothing about the field state differs between the two cases; only the state of motion of the registering matter differs. Unruh and Wald analysed the case in detail and showed that the two descriptions agree on every registration: what the inertial observer describes as the detector's emission of a Minkowski particle upon its excitation, the accelerated observer describes as the detector's absorption of a Rindler particle from a thermal bath [Unruh and Wald, 1984]. The effect is the clearest statement quantum field theory makes about its own particles. The particle content of a field state is not a property of the field state alone. It is a relation between the field state and the material system that registers it, fixed in the Unruh case by the registering system's trajectory. On the radiation-domain identification this is what one expects: the field is not a population of objects located in space, and what it yields in the material domain depends on the material arrangement in which it is registered, as the outcome of a measurement depends on its context. The Unruh temperature for accelerations attainable in a laboratory is minute, and the effect has been studied through analogue systems rather than directly; the theoretical result, which follows from the axioms of quantum field theory alone, is not in dispute.

The Reeh–Schlieder theorem states the same relation at the level of the field's algebra [Reeh and Schlieder, 1961]. Operators localised in any bounded region of spacetime, however small, acting on the vacuum, generate a dense set of states of the entire field: by operations confined to a laboratory one can in principle approximate any state of the field, including states that differ from the vacuum in regions spacelike separated from the laboratory. The theorem does not permit signalling, since the operations involved cannot be realised as measurements with chosen outcomes, and it does not say that the vacuum is full of objects. What it shows is that the vacuum is entangled across every spatial division: the state of the field in one region is not independent of its state in any other, and the vacuum itself violates Bell's inequality between spacelike separated regions [Summers and Werner, 1985]. A population of objects in space would allow space to be divided into independent parts. The field does not. On the present identification the vacuum is the radiation-domain structure in its unexcited form, and its entanglement across all regions of space is the same fact as the entanglement of an EPR pair, stated for the ground state: the structure is not located in the space whose regions are being divided.

The Casimir effect is often cited as direct evidence of the vacuum's energy. Two uncharged conducting plates separated by a distance d attract each other with a pressure P = π²ħc/(240d⁴), and the force has been measured to within a few per cent [Casimir, 1948; Lamoreaux, 1997]. Jaffe pointed out that the force can be computed without reference to zero-point energy, as a relativistic van der Waals force between the charges in the plates, and that it vanishes as the fine-structure constant goes to zero [Jaffe, 2005]. The measured force therefore does not establish that empty space contains energy in the way a box of gas does. What it establishes is narrower and sufficient: the unexcited field has a structure with measurable consequences, and those consequences appear as forces on material plates, which is to say as registrations in matter. The vacuum registers only through matter, as every excitation of the field does. The empirical vacuum, a region in which nothing is detected, and the vacuum state of a Hamiltonian are two criteria sharing one name, and neither establishes absence [Zhong, 2026h]. The present identification states what the unexcited structure is: the radiation domain, registered in matter only through interaction with matter.

The discrepancy between the vacuum energy density computed in quantum field theory and the cosmological constant inferred from cosmic acceleration, some 120 orders of magnitude, has been called the worst prediction in physics [Weinberg, 1989]. On the present identification the calculation computes a quantity of the radiation-domain structure, while the observation measures a quantity registered in the material domain, and the two numbers stand at two different addresses. Their ratio is the compound transmission ratio across the levels that separate the radiation domain from S3D, and the differentials of those levels form a ladder whose exponents ascend in equal steps of twenty, fixed by two empirical anchors, the 10^120 vacuum discrepancy and the 10^80 baryon count of the observable universe [Zhong, 2026i]. The ladder yields, as an output and not as an input, the 10^40 that Weyl, Eddington and Dirac found unexplained [Dirac, 1937], realised as the ratio of the Hubble radius to the classical electron radius. The cosmological constant problem is thereby dissolved rather than solved: the vacuum energy requires no cancellation, because it was never a quantity of the level at which the cosmological constant is measured.

The identification extends to other problems that the formalism has left open. The origin of mass, which the Standard Model describes through the Higgs and strong interactions without saying what it is that acquires mass, receives a kinematic statement on the same identification. In Penrose’s twistor geometry a single twistor carries a null momentum and a helicity, the data of the massless little group [Penrose, 1967]; a massive momentum cannot be carried by one twistor and requires two, together with an internal SU(2) index, the data of the massive little group. The mass of the composite is the infinity-twistor contraction of the pair, m² = |I_αβ Z₁^α Z₂^β|², and the same invariant fixes the threshold at which two photons produce an electron–positron pair [Zhong, 2026j]. The Dirac mass term, which couples two massless chiral components (Section 2), and the Breit–Wheeler threshold are one structure read twice: a massive state is the composite of two elements of the massless sector, neither of which carries proper duration. Mass is not a property that a third ingredient adds to radiation. It is the form radiation takes when two of its elements enter S3D as one composite.

The same reading explains a formal fact that standard quantum mechanics records without explaining. Pauli showed that no self-adjoint time operator conjugate to a Hamiltonian bounded from below can exist, so that t in quantum mechanics is a parameter and not an observable [Pauli, 1958]. The time–energy relation accordingly differs in kind from the position–momentum relation, and every attempt to define times of arrival or tunnelling times has had to replace self-adjoint operators with positive-operator-valued measures [Busch, 2008]. Within the formalism the theorem is a constraint imposed by the spectrum. On the present identification it is a physical consequence: the referent of the state carries no proper duration, so no observable of that referent can be a time, and the only time in the description is the reading of the material clock that indexes it (Section 3). The asymmetry Pauli found between time and the other variables is the asymmetry between the material domain, where time is counted, and the radiation domain, where it is not.

A parallel asymmetry concerns position, and it has divided the realist interpretations. Bohmian mechanics assigns every particle a trajectory in ℝ³, but for the photon the Newton–Wigner result denies the position observable from which a trajectory would be built, and Bohm and Hiley, extending the theory to the electromagnetic field, assigned its beables to field configurations rather than to photon trajectories [Bohm, Hiley and Kaloyerou, 1987]. That theory accommodates the asymmetry without explaining it: matter receives trajectories, light does not. On the present identification the asymmetry is a consequence of where the massless sector belongs. A photon is radiation propagating in S3D without taking material form; it carries no proper duration and no rest frame, and it acquires a position in ℝ³ only at absorption. No trajectory is missing, because nothing in the unregistered photon is of the kind a trajectory describes.

Beyond quantum mechanics, the identification also applies to the counterpart of the measurement problem in general relativity, which has been treated as a separate difficulty. The singularity theorems show that geodesics terminate where the quantities of the theory diverge [Hawking and Penrose, 1970], and the unitary law fails to produce the single outcome that every laboratory records. The two failures have been traced to one source: the quantum formalism reads the passage from possibility to realised fact prospectively and general relativity reads it retrospectively, each fails where its reading leaves its own level, and the measurement problem and the singularity problem are two faces of one boundary [Zhong, 2026k]. The present identification names the two sides of that boundary. The quantum formalism describes the S4D structure and does not contain the registered fact; general relativity describes registered matter in S3D and fails where it is extrapolated towards the source of what is registered. The two failures are one failure, located at the registration boundary of Section 3.

5. Predictions, Limits and the Condition of Failure

The identification places several problems that have been treated separately along one line: a radiation-domain structure, an interaction with matter, and a registered fact. Quantum fields are not a medium of values filling space; they are the structure of the radiation domain at S4D. Particles are not the fundamental objects; they are registrations of that structure in S3D, which is why they cannot be localised as objects and why their number depends on the registering system. What is calculated is not the behaviour of objects in space but the statistics of registration. Superposition is not a material object occupying several places in three-dimensional space; it is the state structure of the radiation-domain state, whose alternatives no material record distinguishes. Measurement is not the creation of a fact from nothing, nor a process the unitary law has failed to describe; it is the interaction at the boundary between the two domains, where the state yields one located, dated fact. The configuration space on which ψ is written is the space of the material registrations the state can yield, not a space in which the state resides. Contextuality is the dependence of an outcome on the registering arrangement, since values come into existence in registration. Entanglement is not a connection between two objects that were independently located; it is one radiation-domain state yielding registrations at separated places. No-signalling is the independence of each local registration from what is done elsewhere, together with the fact that the correlation becomes available only when material records are compared in the material domain. Non-individuality is the absence of a registered history across which identity could be established. The indifference of entangled correlations to the temporal order of registration is the absence of temporal order in a domain without proper duration. The formalism has always carried these features. The identification gives them one referent.

The limits of the identification are as definite as its content. It does not derive the Born rule; it takes the rule as the law of the boundary and locates it there. The identification taken alone does not derive the couplings or mixing angles of the Standard Model, the Tsirelson bound or the correlation function of the singlet; it takes the Hilbert-space structure that fixes the last two as the correct description of the radiation-domain state. It does not supply a detector model or specify the physical conditions under which registration occurs in a given apparatus, which remains the open question of the measurement process in its narrowest and most exact form. It modifies neither the unitary law nor any prediction drawn from it. What it supplies is an answer to the question the practice of calculation has declined to answer, predictions that separate it from its rivals, and the conditions under which it fails.

The identification might be read as a change of names, in which the word radiation is attached to what physics has always called the quantum field. It is not a change of names, because it asserts something the formalism leaves open and experiment can contradict. It asserts that the fields are not located in three-dimensional material space, that proper duration and temporal order belong to their registrations and not to them, and that everything registered of them is registered through matter. A reading that places the fields in space as a medium with local values must add what the Wightman axioms exclude; a reading that takes particles as fundamental must set aside what Malament, Halvorson and Clifton, and Unruh established; a reading that declines to name what the fields are adds nothing that could be contradicted. The identification proposed here says what the fields are, in terms that established physics already uses for one of its two sectors, and it therefore has consequences that a change of names would not have. It predicts that no coherence survives a proper-duration record distinguishing the alternatives, that no observer-independent particle content will be found to serve as the fundamental ontology of field states in general, and that no entangled correlation will be found to depend on the temporal order of its registrations. The first is the subject of active experiment; the second is already contained in the dependence of particle content on the registering system that the Unruh effect establishes; the third has been tested in the delayed-choice experiments and has held.

The identification makes two predictions on which it parts company with its rivals. The first concerns gravitation. If quantum fields are the structure of the radiation domain, and the radiation domain carries no mass and no proper duration, then gravitation, which couples to mass-energy and is measured through the proper durations of material clocks, is not a field of that domain. A previous analysis argued that the quantum state does not source spacetime curvature directly, and expressed the relation as a staged mapping |ψ⟩ → Cᵢ → Tμν(Cᵢ) → Gμν, in which the Einstein tensor is defined only at the level of realised configurations Cᵢ [Zhong, 2026l]. The present identification supplies the physical reason for that staging: Cᵢ is a registered configuration in S3D, and gravity belongs to the domain in which registration has occurred. There is no gravitational field in the radiation domain to be quantised, and no graviton. Bose and co-workers and Marletto and Vedral proposed that two masses, each placed in a spatial superposition and coupled only through gravity, can become entangled only if the gravitational interaction carries quantum coherence, so that observing such entanglement would establish that gravity is not classical [Bose et al., 2017; Marletto and Vedral, 2017].

Their argument rests on a theorem of quantum information: under the assumptions of the proposed protocol, which include initially separable masses and no shared quantum resource other than the mediator, a mediator that acts only through local operations and classical communication cannot create entanglement between the two masses. Any quantum-mediator account satisfying these assumptions predicts gravitationally mediated entanglement under the specified conditions. The present identification predicts otherwise, and the classical-mediator condition follows from it. Gravity is sourced only by registered configurations in S3D, and a registered configuration is a definite material fact, not a superposition of alternatives (Section 3). A coupling sourced only by definite facts transmits only the values of those facts, which is classical information, and it carries no coherence between the alternatives of either mass. Its action on each mass is therefore a local operation conditioned on classical information, which is the condition of the theorem. The entanglement witness must remain within the separable-state bound under the specified experimental conditions.

The second prediction concerns collapse. The identification excludes, in every parameter range, the spontaneous-collapse models of the GRW and CSL type, which add a stochastic term to the unitary law [Ghirardi, Rimini and Weber, 1986; Bassi et al., 2013]. On the present account coherence is lost only through a material record, a material state that distinguishes the alternatives in the sense of Section 3, so any confirmed loss of coherence in the absence of such a record, at a rate exceeding that accounted for by decoherence, contradicts it.

Two further predictions belong to previous work and lie outside the scope of the present argument, which neither derives nor depends on them; they are recorded here because they concern the fermion content of the quantum fields themselves. One analysis derived the sixteen states of a fermion generation from recursive dichotomy of two conjugate kinds and read the three generations as three registrations in S3D of one content, concluding that no fourth generation exists and that neutrino masses follow normal ordering [Zhong, 2026m]. A second identified the Koide value Q = 2/3 of the charged leptons [Koide, 1983] as the structural constant of free registration and derived m_τ = 1776.97 MeV from the electron and muon masses and, under normal ordering with current oscillation data, a neutrino mass sum Σm_ν ≈ 0.059 eV [Zhong, 2026n]. Each value is exposed to measurement now under way.

The two predictions of the present identification fix its position against its rivals in terms experiment can decide: massive superpositions undergo no collapse beyond registration, and they acquire no entanglement through gravity alone. Observation of gravitationally mediated entanglement or of a spontaneous-collapse rate refutes the identification. Beyond these two predictions, the identification stands or falls on a single condition concerning the bearer of the unregistered state. It asserts that the reality described by quantum fields and their states is not an object located in three-dimensional material space, and that localisation in that space, with its accompanying proper duration, belongs only to registration. It would fail if an experimental result, or a theoretical result consistent with all existing data and accepted on that basis, showed that the unregistered state requires an independent bearer localised in three-dimensional space, carrying its own proper duration, which no radiation-domain description can accommodate. The condition is directly exposed to the programmes now under way. The clock-interferometry experiments that follow Zych, Brukner and Margalit test whether coherence survives when proper-duration records distinguish the alternatives; the reading requires that it never does, in any regime of mass, separation or gravitational potential. The macromolecular interference experiments that push superposition to ever larger masses test whether a localised material bearer becomes necessary above some scale; the reading requires that coherence be lost only through the formation of a record in the material domain, including a record written by proper duration, and never through the emergence of such a bearer. A demonstration that a superposition persists while a proper-duration record distinguishes its components, or that a localised bearer with its own worldline underlies an interfering state, would refute the identification. No such result exists. Interference has been observed with molecules of more than twenty-five thousand atomic mass units, delocalised over distances large compared with their own size [Fein et al., 2019], and in these experiments interference persisted wherever no which-path record was available.

A related programme approaches the same boundary from the side of gravitation. Penrose proposed that a superposition of two mass distributions sufficiently different to correspond to distinct spacetime geometries is unstable, and that it decays into one of its components on a timescale of order ħ/E_G, where E_G is the gravitational self-energy of the difference between the two distributions [Penrose, 1996; Diósi, 1987]. The proposal has the same structure as the reading developed here in one respect: it places the loss of superposition where the alternatives would carry distinguishable material geometry and therefore distinguishable proper time. It differs in treating the loss as a spontaneous physical process with its own rate, where the reading treats it as registration. The distinction is testable. In its simplest parameter-free form the Diósi–Penrose model predicts a faint spontaneous radiation from ordinary matter, and an underground experiment at the Gran Sasso laboratory found none at the predicted level [Donadi et al., 2021]. The reading developed here predicts no loss of coherence beyond what registration, including registration by gravitational time dilation, accounts for; the collapse-model programmes and the clock-interferometry programmes are therefore probing, from opposite directions, the one boundary on which the identification depends.

6. Conclusion

For a hundred years quantum physics has calculated with a precision no other science has matched, and for a hundred years it has not said what it was calculating. Schrödinger's charge cloud was abandoned because the wave lived in a space of 3N dimensions; Born's rule replaced the answer with a prediction; the practice Mermin named shut up and calculate made the replacement permanent; and quantum field theory, among the most precise descriptions of nature ever written, removed the remaining candidates without supplying another, since its fields have no values at points and its particles cannot be localised as objects in space. What survives these exclusions is a reality that is not located in three-dimensional material space, carries no proper duration of its own, and becomes a located and dated fact only when matter registers it. Established physics contains such a reality: the massless sector, which has no rest frame, accumulates no proper duration and meets the massive sector only through interaction, while the massive sector is the form that this structure takes once it enters the material domain. This paper concludes that quantum physics describes the radiation domain. Its quantum fields are the structure of the radiation domain at the level S4D, which projects onto S3D; its particles are the registrations of that structure in the material domain S3D; its states are the description of that structure as a laboratory indexes it by a material clock. What it calculates is the statistics with which that structure is registered in matter. The structure itself is never registered as such: what instruments in S3D register are its excitations, and calculation is the only access the material domain has to the structure that yields them. Superposition ends where a proper-duration record begins. Entanglement is one field state registered at separated places, and its correlations cross no space because what correlates them is not in space. The particle content of the vacuum depends on the matter that registers it, because particles are registrations. Gravity, sourced only by registered matter, mediates no entanglement, and no superposition is lost except by registration. Shut up and calculate was the discipline's agreement to go on computing the registrations of something it had not named. The equations are unchanged. What they have been calculating for a century is the radiation domain as matter registers it.

 

 

 

 

 

Declarations

Funding: This research received no external funding.

Conflicts of interest: The author declares no conflicts of interest.

Data availability: No new data were generated in this study.

Author contributions: Juliet Zhong: conceptualisation, methodology, formal analysis, writing.

Ethics and Consent to Participate declarations: not applicable.

Consent to Publish declaration: not applicable.

Preprint: This manuscript is available as a preprint on SSRN, doi:10.2139/ssrn.7528765.

 

Acknowledgement:

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process: During the preparation of this work, the author used Claude (Anthropic) and ChatGPT (OpenAI) for assistance with drafting text, checking calculations, locating references, and language editing. The author reviewed and edited the output as needed and takes full responsibility for the content of the published article.

 

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