Abstract
We propose that the gravitational effects attributed to dark matter are produced by the classical electromagnetic zero-point field of stochastic electrodynamics (SED), formally characterized as an indivisible stochastic process in the sense of Barandes. Boyer has shown that this field is real, classical, Lorentz-invariant, and that its energy density scale is set by Planck's constant. We argue that this field must contribute to the stress-energy tensor, that its energy density acquires spatial structure near matter through the conformal mechanism Boyer derives, and that this structured energy density is the phenomenon currently attributed to dark matter. The key open question is quantitative: does the predicted distribution match observed galactic rotation curves and gravitational lensing profiles?
I. The Zero-Point Field is Real and Gravitates
Stochastic electrodynamics is classical electrodynamics with one modification: the homogeneous solution to Maxwell's equations is not zero but is instead a Lorentz-invariant spectrum of random classical radiation, the zero-point field. The presence of this field is not a theoretical postulate — it is inferred directly from experimental measurements of Casimir forces between conducting plates at low temperatures, which do not vanish as temperature approaches absolute zero as traditional classical physics predicts they should.
Boyer has shown that this zero-point field has a specific energy spectrum per normal mode set precisely by Planck's constant, and that this scale factor is the same constant that appears throughout quantum theory. Planck's constant, on this account, is not a mysterious quantum of action imposed on nature from outside. It is the scale factor of the classical electromagnetic zero-point field — a property of the field's coupling to the geometry of relativistic spacetime.
Boyer's 2012 derivation establishes something stronger. The Planck spectrum of blackbody radiation — the foundational result that launched quantum theory — follows entirely from zero-point radiation and the structure of relativistic spacetime, without quantum postulates. The derivation proceeds through conformal transformations connecting the zero-point spectrum in inertial and non-inertial frames. The zero-point field's two-point correlation function in an inertial frame depends only on the spacetime interval between the two points — it encodes the geodesic structure of spacetime and nothing else. As Boyer states explicitly: at zero temperature, the random radiation gives no more information than is contained in the structure of spacetime itself.
This field has energy density. Energy density curves spacetime. The Einstein field equations have no exception for fields that are inconvenient for the standard model. If Boyer is right, the zero-point field must appear in the stress-energy tensor and must produce gravitational effects. The only question is what those effects are and whether they match observations.
II. The Quantum-Classical Boundary: Division Events
The standard account of quantum mechanics treats quantization as a fundamental feature of nature — discrete energy levels, wave function collapse, entanglement as irreducible nonlocality. SED has long suggested these features emerge from the interaction of matter with the zero-point field rather than being fundamental. But SED has lacked a formal characterization of precisely where and how the discrete outcomes arise from the continuous field.
Barandes provides this characterization. Working from an attempt to construct a pedagogical analogy between stochastic processes and quantum mechanics, Barandes discovered that the analogy dissolved — the two frameworks became identical once the Markov assumption was dropped. The Markov assumption, standard in classical probability theory, holds that the present state of a system contains all information relevant to its future evolution. Barandes found that dropping this assumption — allowing the history of a system to influence its future in ways not fully captured by its present state — produces quantum mechanical behavior exactly.
The resulting framework describes quantum systems as indivisible stochastic processes: classical probability processes whose transition probabilities cannot be decomposed into finer substeps without changing their character. The indivisibility is not a quirk of the mathematics — it is the formal signature of what happens at measurement, at interaction, at the boundary between the continuous stochastic terrain and the discrete outcomes we observe.
This formal characterization dissolves several quantum puzzles. Entanglement, in Barandes' framework, is not a mysterious nonlocal connection between distant systems — it is a feature of the joint probability structure of an indivisible process, requiring no faster-than-light influence and no exotic ontology. Wave-particle duality similarly dissolves: there are no particles in the fundamental ontology, only a continuous field producing discrete outcomes at interaction events. The discreteness is not where you thought it was.
II.5 The Physical Carrier of Non-Markovian Memory
Barandes establishes that quantum systems are intrinsically non-Markovian — that the history of a system influences its future in ways not captured by its present state alone. He frames this non-Markovianity as a form of non-locality in time consistent with the light-cone structure of special relativity, and identifies it as a fundamental feature of closed quantum systems rather than a phenomenological approximation. What Barandes does not specify is the physical substrate that carries this memory.
We propose that the physical carrier of non-Markovian memory is the classical electromagnetic zero-point field of stochastic electrodynamics.
Between division events, the zero-point field evolves continuously according to Maxwell's equations, carrying forward the correlation structure established by every previous atom-field interaction. Boyer's two-point correlation functions make this explicit: the field's correlation between any two spacetime points depends on the geodesic interval between them, encoding the full history of matter-field interactions in the local field configuration. When an atom undergoes a new division event, it interacts not with a memoryless field but with a field whose correlation structure has been shaped by its own prior interactions and those of neighboring matter.
This identification resolves a longstanding puzzle in the history of stochastic reformulations of quantum mechanics. Barandes notes that all previous attempts — Nelson's stochastic mechanics, Bopp, Fenyes, and others — assumed Markovian dynamical laws, which limited their ability to capture the full behavior of quantum systems. The reason those approaches failed is now clear: they attempted to model the memory of the process without identifying its physical carrier. The zero-point field is what Nelson's guiding wave was always physically pointing at, but without SED there was no classical field to fill that role. SED provides the physical substrate that Nelsonian stochastic mechanics required but could not supply.
III. The Atom as Division Event Site
We propose that the division events in the sense of Barandes occur specifically at atom-field interactions. The atom is the site where the continuous zero-point field produces discrete outcomes — where the analog becomes digital, where the classical stochastic terrain produces the discrete energy exchanges that quantum theory describes as photon emission and absorption.
This claim has support from Boyer's SED program. The discrete spectral lines of atomic emission, which historically demanded quantum explanation through Bohr's postulates, emerge in SED from parametric resonance at atom-field interaction sites — the classical continuous field interacting with the atom's internal structure produces sharp resonances at discrete frequencies without any quantum postulate. The discreteness is a property of the interaction, not of the field or the atom separately.
The photon, on this account, is not a third ontological primitive alongside the field and matter. It is a name for the discrete energy exchange that occurs at a division event — the discrete outcome of an indivisible stochastic process at an atom-field interaction site. Between division events, the field evolves continuously, locally, and causally according to Maxwell's equations. The appearance of particle-like behavior is an artifact of sampling the continuous field at interaction events, not a feature of the field itself. Boyer showed that Einstein's original evidence for photons — the particle-like fluctuations in blackbody radiation — dissolves into interference between thermal and zero-point radiation once the zero-point field is properly included.
Planck's constant, the scale factor of the zero-point field, is therefore a property of the atom-field interaction — specifically of the energy scale at which atomic resonances occur in a universe bathed in zero-point radiation. It is not a free-floating constant of nature imposed from outside but a consequence of atomic structure interacting with the geometric minimum of the zero-point field.
III.5 Division Events and the Configuration Space
Barandes' framework makes a precise distinction between the kinematical and dynamical content of a physical theory. The configuration space — the space of possible states a system can occupy — provides the ontological content, what exists. The transition probabilities — the first-order conditional probabilities governing how states evolve between division events — provide the nomological content, the laws.
In the SED-Barandes synthesis, this distinction maps cleanly onto the physics. The configuration space is the continuous zero-point field, the ontological terrain. The transition probabilities are the atom-field interaction rules, the nomological maps from one field configuration to another. The division events are the atom-field interactions themselves — the moments at which the continuous stochastic terrain produces discrete outcomes and the transition probabilities become defined.
This mapping has a further consequence. Barandes shows that the Hilbert space formalism of standard quantum mechanics — wave functions, density matrices, unitarity — emerges as a mathematical convenience from the underlying indivisible stochastic structure. In the SED-Barandes picture, this emergence has a physical interpretation: the Hilbert space is the most compact description of the atom-field interaction statistics, derived from the zero-point field's correlation structure at division events. Wave functions are not ontological. They are efficient encodings of the field's memory at the last division event.
IV. Classical Emergence and the Frame Rate of Physics
Barandes' framework explains not only the quantum regime but the classical regime. Division events at atom-field interactions occur at a rate determined by Planck's constant and the local zero-point field density. At human scales, these events occur so frequently and densely that the discrete structure averages out and the terrain appears continuous. Classical physics is the high-frequency limit of the same indivisible stochastic process that produces quantum behavior at the atomic scale.
The Markov assumption, which underlies all of classical probability theory and much of classical physics, works at human scales precisely because the division events are frequent enough that the non-Markovian memory of the process is washed out statistically before it accumulates to observable effect. Classical physics is not the foundation from which quantum physics departs — it is the other end of the same process, approached from the opposite direction. Both are limiting cases of the indivisible stochastic terrain.
This reframes the quantum-classical boundary question that Boyer identifies as central but leaves open in his 2019 overview. The boundary is not defined by the appearance of Planck's constant, or by energy scales alone, or by the size of the system. It is defined by the rate of division events relative to the timescale of observation. Where division events are sparse relative to the observation timescale, quantum behavior is visible. Where they are dense, classical behavior emerges. The atom-field interaction rate, set by Planck's constant and the local zero-point field density, is the frame rate of physics.
V. The Gravitational Prediction
The between-event zero-point field energy is real, continuous, and present throughout spacetime. In an inertial frame with no matter, it is uniform and isotropic — its correlation function depends only on the spacetime interval between points, encoding the geodesic structure and nothing else. It contributes to the stress-energy tensor uniformly and produces no observable spatial structure in gravitational effects.
Near matter, this changes. Boyer's conformal mechanism shows that the zero-point field acquires spatial structure in non-inertial frames and near gravitating matter. The field's correlation function near matter is no longer purely geodesic — it is modified by the local time-dilation associated with the gravitational field, through the equivalence principle connecting acceleration to gravity. The between-event field energy is denser where atom-field interactions are densest, which is where matter is.
This spatially structured field energy contributes to the stress-energy tensor non-uniformly. It produces spacetime curvature beyond what the visible matter alone would produce. This additional curvature is the phenomenon currently attributed to dark matter.
The vacuum catastrophe does not arise in this picture. The standard quantum field theory calculation sums over all field modes as persistent particle excitations, producing an energy density 120 orders of magnitude larger than observed. SED does not sum over persistent particle modes — there are no persistent photons in the fundamental ontology, only a continuous classical field whose energy density is set by the Casimir-calibrated scale factor. The infinity that plagues QFT does not appear because the ontology that generates it does not exist.
V.5 Bell's Theorem and the Light Cone
A natural concern for any classical field theory is Bell's theorem, which appears to rule out local hidden variable accounts of quantum correlations. Barandes addresses this directly, arguing that locality in space is preserved in indivisible quantum theory at the cost of non-Markovianity — a form of non-locality in time rather than space, consistent with the light-cone structure of special relativity. He commits to addressing Bell's theorem in detail in future work.
In the SED-Barandes picture, the physical implementation of this temporal non-locality is again the zero-point field. The field's correlation functions, as Boyer derives them, depend on the spacetime interval between points along geodesics. These correlations are not instantaneous spatial connections — they are structured by the light-cone geometry of relativistic spacetime. The apparent nonlocality of entangled quantum systems, in this picture, is the signature of a field whose correlations are non-Markovian in time but strictly local in space, propagating at the speed of light through the zero-point radiation background.
This is consistent with Boyer's result that zero-point radiation is the unique spectrum that is time-stationary in both inertial and all Rindler frames simultaneously. A field with this property is precisely what you would require as the physical carrier of correlations that are relativistically local but temporally non-Markovian. The zero-point field is not just consistent with Bell's theorem under Barandes' treatment — it is the natural physical realization of the mechanism Barandes requires.
VI. The Key Technical Question and Research Program
The hypothesis makes a specific and testable prediction: the zero-point field, characterized as an indivisible stochastic process and coupled to spacetime geometry through Boyer's conformal mechanism, produces a spatial distribution of energy density near matter that matches the observed signatures of dark matter — galactic rotation curves, gravitational lensing profiles, and large-scale structure.
The key technical question is whether the stress-energy tensor of SED's zero-point field, properly formulated in the Einstein-Maxwell framework, produces this distribution quantitatively. Boyer's 2012 paper has partially assembled the mathematical home for this calculation — the zero-point field's correlation functions are already written in terms of spacetime geodesics and proper time, and the stress-energy tensor appears explicitly in the derivation. The gap between Boyer's existing results and the gravitational prediction may be smaller than it appears.
The research program has three steps. First, formalize SED's zero-point field as an indivisible stochastic process in Barandes' mathematical language, establishing the precise connection between the two frameworks. Second, characterize the between-event field energy via the stochastic stress-energy tensor in the Einstein-Maxwell equations. Third, derive the predicted spatial distribution of that energy near matter and compare with dark matter observations.
If the predicted distribution matches observations, the implications are significant in both directions. Dark matter would be explained without new particles, new forces, or modifications to gravity. And SED would acquire the distinct empirical prediction it has lacked — a prediction that standard quantum field theory not only fails to make but cannot make, given that QFT's treatment of the vacuum energy produces the wrong answer by 120 orders of magnitude.
VII. A Note on Existing Gaps in SED
SED remains an incomplete research program. It has not yet fully reproduced all of quantum mechanics — the hydrogen atom calculation is unresolved, particle diffraction has only a qualitative account, and excited atomic states require further development. These are real gaps, not minor details.
However, Barandes' framework addresses the most challenging case directly. Entanglement, widely considered SED's hardest problem, is deflated by Barandes at the formal level — it is a feature of the joint probability structure of indivisible processes rather than a mysterious nonlocal phenomenon requiring physical explanation. SED does not need to reproduce entanglement as a physical effect because entanglement, properly understood, is not a physical effect but a formal feature of the probability calculus.
The remaining gaps are computational rather than foundational. They reflect the smallness of the research community Boyer notes in his 2019 overview — a tiny group of scientists against thousands working on quantum theory — rather than defects in the framework's foundations. The synthesis proposed here may provide additional motivation and formal tools for closing those gaps.
VIII. Conclusion
Boyer has shown that the classical electromagnetic zero-point field is real, that its energy scale is set by Planck's constant, and that the Planck spectrum follows from this field and the structure of relativistic spacetime alone. Barandes has shown that quantum mechanics is the theory of indivisible stochastic processes, dissolving quantum oddities including entanglement without remainder. We propose that these two frameworks are describing the same terrain from different directions, that the atom-field interaction is the division event site connecting them, and that the gravitational effects of the between-event zero-point field energy are the phenomenon currently attributed to dark matter.
If this hypothesis is correct, dark matter is not a new particle or a modification of gravity. It is the geometric imprint of the zero-point field — the gravitational shadow of the continuous classical field that Boyer has spent a career characterizing and that Barandes has given a precise mathematical home. The question is no longer whether the zero-point field gravitates. It must. The question is whether the calculation matches the observations. That calculation is the next step.
VIII.5 Barandes' Open Question and the Gravitational Prediction
In his July 2025 paper, Barandes explicitly identifies as future work "new ways of thinking about generalizing quantum theory to accommodate gravity." This paper is a direct response to that invitation.
The gravitational generalization follows from taking the SED-Barandes synthesis seriously. The zero-point field contributes to the stress-energy tensor — this is not optional, it is required by general relativity for any field with energy density. Boyer's 2012 derivation has already partially assembled the mathematical home for this contribution: the zero-point field's correlation functions are written explicitly in terms of spacetime geodesics and proper time, the stress-energy tensor appears in the derivation, and the field's behavior in non-inertial frames is characterized through conformal transformations that couple directly to the local spacetime geometry.
The gravitational prediction — that the spatially structured between-event zero-point field energy produces the effects attributed to dark matter — is the first concrete consequence of generalizing indivisible quantum theory to accommodate gravity. It is testable, it distinguishes SED from standard quantum field theory, and it resolves simultaneously the vacuum catastrophe and the dark matter problem through the same mechanism.
The calculation Barandes identifies as future work and the gravitational prediction identified here are the same project approached from opposite directions. Barandes is approaching from the quantum foundations side; Boyer has been approaching from the classical electrodynamics side for fifty years. The present synthesis identifies where those approaches meet.
References
Boyer, T. H. "The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics." Foundations of Physics, 42, 595–614, 2012. arXiv:1107.3446.
Boyer, T. H. "Stochastic Electrodynamics: The Closest Classical Approximation to Quantum Theory." Physics, 2019. arXiv:1903.00996.
Barandes, J. A. "The Stochastic-Quantum Correspondence." Philosophy of Physics, 3(1):8, June 2025. arXiv:2302.10778.
Barandes, J. A. "Quantum Systems as Indivisible Stochastic Processes." July 2025. arXiv:2507.21192.
Casimir, H. B. G. "On the Attraction Between Two Perfectly Conducting Plates." Proceedings of the Royal Netherlands Academy of Arts and Sciences, 51, 793–795, 1948.
Glick, J. R. and Adami, C. "Markovian and Non-Markovian Quantum Measurements." Foundations of Physics, July 2020. arXiv:1701.05636.
Milz, S. and Modi, K. "Quantum Stochastic Processes and Quantum Non-Markovian Phenomena." PRX Quantum, 2:030201, May 2021. arXiv:2012.01894.
Generated from a conversation with Claude: