Occupied or Empty: A Working Hypothesis on Matter, Light and the Substrate

Where this comes from

Every electron is identical to every other — same mass, same charge, same spin, to every decimal place measured. Quantum field theory explains that by treating each electron as a ripple in one shared electron field. If particles are patterns in something shared, what is the simplest description of that something — and which tempting versions of the answer fail?

This page records a working hypothesis while it is still open, together with the checks it has already been put through, including the versions that did not survive.

1 · Occupied or empty — states, not places

Layer 1+3 #occupation-number#fermions#phase

In plain terms: physics already counts electrons as “there” or “not there” in each possible state — a particular energy, motion or spin. This page reads matter that way, but only with the quantum phase included (roughly: where each wave is in its cycle), and only for matter, not for light.

Established physics. In quantum field theory, each state of a fermion field — for example one electron state — has an occupation number that is either 0 or 1, never 2. That is the Pauli exclusion principle; in relativistic field theory it follows from the spin–statistics theorem. Photons are different: they are bosons, and any number of them can share one state — a laser beam is exactly that.

The working hypothesis. Matter is read in these terms: each state of a matter field living on the substrate is occupied (1) or empty (0); the phase belongs to the whole configuration of occupied and empty states, not to each state separately (see the third caution below). Here 0 means no matter in that state. It says nothing about light, which is counted separately — any number of photons can share one state — and it does not mean “nothing”: even with every state empty, the quantum vacuum has measurable structure — its electric-field fluctuations have been sampled directly (Riek et al., 2015; see also Bridge 6 in Scientific Bridges).

Three cautions:

• States, not places. Occupation belongs to states, not to regions of space. One region can hold many electrons in different states.
• It depends on how the observer moves. Whether a state counts as occupied depends on the observer’s motion: quantum field theory predicts that an accelerating observer finds particles where an inertial one finds none (the Unruh effect — a firm theoretical result, not yet directly observed). So the 0s and 1s are not labels painted on the substrate itself.
• The phase is shared, not local. The phase belongs to the joint state of many regions at once, which can be entangled. No assignment of a separate phase to each place can reproduce the measured Bell correlations. That is why a substrate of plain classical bits fails without heavy extra assumptions such as superdeterminism, and why the description here is non-local in exactly the way quantum mechanics is. (Strictly, a single electron state is not a qubit either: a superselection rule forbids superposing “one electron” with “no electron”. The phase lives in the relative amplitudes of configurations with the same total charge — the electron here or there.)

A floor, not infinite divisibility. The framework postulates discreteness near the Planck scale (the Planck length is about 1.6 × 10⁻³⁵ m). This is motivated — not derived — by entropy bounds: the Bekenstein bound (for a region of given size and energy) and the holographic bound (set by its boundary area) say a finite region can hold only finite information. Because the holographic bound grows with area rather than volume, it argues for finiteness, not for one independent unit per Planck-sized cell. With the random substrate of section 2, this floor is a fixed amount of spacetime volume per grain, not a minimum length: lengths shrink for moving observers, so a minimum length would single out a frame. None of this proves a discrete substrate.

2 · The substrate: a working choice for a random one

Layer 3 #substrate-choice#lorentz-invariance#causal-set

In plain terms: the smallest scale may be discrete, but the grains are not arranged in a fixed grid. That avoids one serious problem and creates others.

An early version of this idea tied the grid’s cell size to the electron. That does not survive: the electron has no measured size — experiments find no internal structure down to roughly 10⁻¹⁸ m. What remains separates the pattern from what it sits on. The electron is the lightest stable, electrically charged particle. Neutrinos are lighter still but neutral: direct measurements put the effective neutrino mass below about 0.45 eV (KATRIN, 2025), and the lightest may even be massless.

The substrate underneath can be imagined in two ways, and they are not two flavours of the same thing:

• A fixed lattice. Grains at regular positions, like atoms in a crystal. This keeps a meaningful grid geometry, but it picks out a preferred frame. Direct astrophysical tests put tight limits on such effects — at first order in energy they must lie beyond the Planck scale, and a first-order dependence on photon helicity is excluded — but a sufficiently symmetric lattice can escape them. The sharper objection is theoretical: tiny Planck-scale violations of relativity tend to leak into low-energy physics through quantum corrections, where they are excluded to high precision, unless something protects them (Collins, Perez, Sudarsky, Urrutia & Vucetich, 2004). No such protection has been shown for this framework.
• A random, statistically uniform substrate. Grains scattered at random through spacetime at a fixed average density — the approach of the causal-set programme (Bombelli, Lee, Meyer & Sorkin, 1987). Because the scattering is random in spacetime, no individual sprinkling picks out a frame (Bombelli, Henson & Sorkin, 2009). This is not the “amorphous lattice” option considered on the Grid Analyses page: a lattice that is irregular in space still has a rest frame; a substrate that is random in spacetime does not.

The working choice (September 2026) is the second. Within the framework it goes by the informal name “flexible cell”: no fixed positions or shapes, but a fixed average density — about one grain per Planck-sized volume of spacetime. It does not mean stretchy: an elastic medium would bring back a preferred frame. In such a substrate every grain exists; there are no empty places. The 0s and 1s of section 1 belong to the matter fields living on it, not to the substrate itself. It also means that spacetime is not a container the substrate sits in: spacetime is built from it.

This choice has costs, and they are real:

• Gravity has to be rethought. A substrate that breaks no Lorentz symmetry cannot use the usual loophole — breaking relativity — that lets an emergent graviton exist despite the Weinberg–Witten theorem (Weinberg & Witten, 1980). Two routes remain. Gravity could be the geometry of the substrate itself — the causal-set route, in which the theorem’s assumptions do not apply at the fundamental level, but which replaces Bridge 2’s picture of an envelope on top of the substrate. Or gravity still emerges as such an envelope, which would require non-locality (Marolf, 2015) — for example holographically — a heavier claim. (That requirement holds for a fixed lattice too; it is not specific to this choice.)
• Matter is harder to place. Describing fermions on a causal set is itself unsolved, and section 1 needs exactly that.
• “Swerves”. In causal-set models, particles are expected to receive tiny random kicks from the discreteness (Dowker, Henson & Sorkin, 2004). Observations already constrain such effects strongly (Kaloper & Mattingly, 2006).
• Older material on this site was written for a fixed lattice — see the list of consequences below.

3 · Transitions between matter and light

Layer 1+3 #annihilation#pair-production#positronium

In plain terms: when matter and antimatter meet, nothing disappears — the energy moves from particles that have rest mass to light that does not. Pair production does the reverse.

Established physics — measured.

• Annihilation. An electron and a positron meet and become photons, usually two gamma rays of 511 keV each. The particles’ rest mass is gone, but the total energy — and even the invariant mass of the system — is unchanged, now carried by massless photons. PET scanners rely on this every day.
• Pair production. A sufficiently energetic photon near an atomic nucleus becomes an electron and a positron. Observed since the 1930s.
• Positronium. Before annihilating, an electron and a positron can briefly orbit each other as a bound “atom” — about 125 picoseconds in one spin configuration, about 142 nanoseconds in the other.

The working hypothesis. In occupation language, annihilation moves occupation from matter to light: the electron and positron states go from occupied to empty (1 → 0), while two photon states go from empty to occupied (0 → 1; for photons the count can also go higher). Nothing becomes “nothing”; energy and momentum carry over in full. Pair production runs the other way. Positronium is not a half-way state — both particles are fully present — but it is the measured, short-lived doorway to the transition. (A different, looser sense of “in-between” already on this site is prediction #45 on the Peer Review page, which treats light stored in an atomic medium as an intermediate phase between a free photon and matter; its mass-scaling claim is explicitly a stipulation, category C.) A separate, older claim about pair production — prediction #17 on the Grid Analyses page — makes a testable statement about resonance peaks; it does not follow from this reading.

Matter and light under gravity. Gravity acts on both: it bends light and shifts its frequency, and it can hold matter in stable bound patterns — orbits, planets, stars. Light, having no rest mass, can be deflected and even trapped behind a black hole’s horizon, but around black holes and ordinary stars it cannot be held in a stable orbit — it can only circle on an unstable “photon sphere”. (Stable light orbits would need exotic horizonless ultracompact objects, none of which has been observed; Cunha, Berti & Herdeiro, 2017.)

Versions of this idea that did not survive

While developing the hypothesis, several stronger versions were checked against published measurements. They are listed because a framework should show its failures as clearly as its proposals.

• “Light does not feel gravity.” Rejected. Starlight bends around the Sun (first measured at the 1919 solar eclipse; Dyson, Eddington & Davidson, 1920), light climbing out of a gravitational field shifts in frequency (Pound & Rebka, 1960), and — as general relativity predicts and black-hole imaging is consistent with — light cannot escape a black hole. The correct statement is narrower: around black holes and known stars, gravity cannot hold light in a stable orbit.
• “What we measure as antimatter is really a transition state.” Rejected. Antihydrogen is held in magnetic traps for many minutes, and its 1S–2S spectral line matches hydrogen’s to a few parts in 10¹² (ALPHA collaboration, 2018). Antimatter is a stable pattern, not a transition.
• “Antimatter gravitates differently and drives cosmic expansion.” Rejected for the repulsive version. A cosmology built on antimatter with repulsive gravity exists in the literature (the Dirac–Milne universe; Benoit-Lévy & Chardin, 2012), but the ALPHA-g experiment (2023) saw antihydrogen fall down, with an acceleration consistent with ordinary gravity within its uncertainty, and its data strongly disfavour repulsion.
• “A large part of the universe is antimatter, hidden in separate regions.” Rejected. Where regions of matter and antimatter meet, annihilation would produce a diffuse gamma-ray glow that is not observed; analyses of this (Cohen, De Rújula & Glashow, 1998) exclude large antimatter domains within the observable universe.
• “Dense or highly ordered patterns are pulled more strongly by gravity.” Rejected. The MICROSCOPE satellite compared the free fall of titanium and platinum — very different nuclei, electron structure and crystal patterns — and found no difference, to a few parts in 10¹⁵ (2022). Pattern does contribute to mass, but only through its energy: graphite and diamond are made of the same carbon atoms in different patterns, and their weights differ only by the tiny binding-energy difference (Δm/m ≈ 2 × 10⁻¹², from E = mc²). Claims of anomalous gravity near superconductors, where electrons pair up, were not reproduced.

4 · Expansion that need not be uniform

Layer 2+3 #inhomogeneous-cosmology#dark-energy#expansion

In plain terms: the universe is lumpy, and a lumpy universe need not expand at the same rate everywhere. Whether that matters for what we call dark energy is an open, disputed question — and it is other people’s research, not this framework’s.

The universe is not uniform: matter collapses into galaxies, stars and black holes, while the voids between them empty out and expand faster. General relativity already says that expansion then runs at different rates in different places — that much is not in dispute. The working hypothesis is that this averaging is not a negligible correction: that treating the universe as smooth measurably distorts the inferred expansion history, as the backreaction and timescape programmes propose. Whether the difference matters for the global picture is the open question.

This does not follow from the substrate choice in section 2. A causal-set-like substrate is statistically uniform by construction; the non-uniformity comes from matter, not from the substrate.

Where this meets current research (independent of Coherence):

• Inhomogeneous cosmology. The backreaction programme (Buchert, 2000) and the timescape model (Wiltshire, 2007) propose that treating a lumpy universe as if it were smooth distorts what we infer about expansion. Backreaction work generally asks how much of the apparent acceleration averaging could account for; timescape — the name refers to clock rates that differ between dense regions and voids — attributes all of it to averaging and has no dark energy at all. A 2025 supernova analysis by the timescape group (Seifert et al., MNRAS Letters) reports very strong statistical evidence for timescape over the standard model; the result depends on how supernova data are standardised and on which nearby supernovae are included, it is not settled, and timescape remains a minority position.
• Evolving dark energy. DESI’s baryon-acoustic-oscillation data, combined with the cosmic microwave background and supernova samples, prefer dark energy that changes over time: 2.8–4.2σ in the 2025 analysis depending on the supernova sample, and about 3σ in DESI’s latest analysis (July 2026). The conventional discovery threshold is 5σ.
• The Hubble tension. Local and early-universe measurements of the expansion rate disagree; how strongly depends on the local method used, and the cause is debated. This framework’s own earlier attempt at a Hubble-tension formula (prediction #34 on the Peer Review page) had its functional form rejected.
• Two routes from discreteness to dark energy — neither of them ours. Before accelerating expansion was discovered in 1998, Rafael Sorkin combined causal-set discreteness with unimodular gravity to argue that the cosmological constant should fluctuate around zero with a magnitude of the order later observed — a heuristic estimate that did not predict the sign (Sorkin, 1991; 1997). The “everpresent Λ” model develops this (Ahmed, Dodelson, Greene & Sorkin, 2004). Its simplest form is strongly constrained by the uniformity of the cosmic microwave background (Barrow, 2007), and tests against data are mixed: one study found fits comparable to the standard model (Zwane, Afshordi & Sorkin, 2018), a later one found that current versions fit the cosmic microwave background much worse (Das, Nasiri & Yazdi, 2024). A second route lets matter lose energy to Planck-scale discreteness, with that energy acting as dark energy (Josset, Perez & Sudarsky, 2017; Perez & Sudarsky, 2019). These are other researchers’ results, not Coherence results; they are mentioned because they are the worked-out links between discreteness and dark energy.

The Coherence reading in this section was formed after — and prompted by — the 2025 DESI and timescape results and the Hubble tension. Agreement with them is built in, so it carries no evidential weight: at most ≈ Convergent (post-diction, retrospective), never a prediction.

What choosing a random substrate would change elsewhere

The working choice in section 2 has consequences for material written earlier for a fixed lattice. None of these is settled, and not every affected page reflects the working choice yet. They are listed here so that the tension is visible rather than hidden.

• Prediction #15 (Planck-scale effects in gamma-ray-burst timing, on the Grid Analyses page) was written for a lattice geometry. Under a random substrate there is no preferred direction, so #15 has no content under this working choice — it does not simply change its numbers. What that means for its status is not yet decided.
• Prediction #39 (a finite faster-than-light carrier for entanglement, on the Originals page) needs a preferred frame in which that finite speed is defined, so it too belongs to the fixed-lattice branch.
• Prediction #1 (resolution-dependent deviations at LHC energies, on the Peer Review page) would lose its derivation: the lattice supplied the parameter behind it. Whether a random substrate — which has a minimum volume but no minimum length — produces any such deviation is open. Since September 2026 its tile carries a “derivation under review” note, and its test and falsification condition are suspended; its category is unchanged pending a decision.
• Prediction #16 (decoherence as energy dissipated into the substrate) is affected, but not automatically helped. Random-substrate models do let matter exchange energy with the discreteness (Dowker, Henson & Sorkin, 2004; Perez & Sudarsky, 2019), but the best-studied effect — swerves — makes massive particles gain energy rather than lose it, and it is already tightly bounded (Kaloper & Mattingly, 2006); for photons, which #16’s proposed test uses, the sign of any energy drift is not fixed and is bounded by the spectrum of the cosmic microwave background (Philpott, Dowker & Sorkin, 2009). A fixed lattice with vibrations of its own could also absorb energy under ordinary quantum mechanics, as a crystal does. Under either choice, #16 still needs a stated coupling and a sign.
• Chapter 3 (“Resolution: The Pixels of Reality”) and the homepage (“Reality is Pixelated”) were written reading the Planck length as the universe’s pixel size. Since September 2026 both describe it as an average grain density under the working choice, and chapter 3 marks its correction to the uncertainty principle — derived for a lattice, and once called its testable content — as under review; that correction would need re-deriving.
• Bridge 2 (gravity as an emergent envelope) would need one of the two routes in section 2, and Bridge 3 (resolution as a Planck-scale grain) presents its uncertainty-principle correction for a fixed lattice — material that belongs to the other branch. Both are in Scientific Bridges.

Until one branch is formally dropped, the two disagree about the measurement behind #15: the fixed-lattice branch reads systematic energy-dependent photon speeds as a signature (however small), the random branch forbids them. A gamma-ray-burst result, either way, therefore cannot count as support for the framework as a whole.

What this page does not claim

• It does not claim that reality is made of bits — the strong reading of Wheeler’s “it from bit” (1990). The occupation language is a description with a phase — a lens that must earn its place, like the frequency language elsewhere on this site.
• It does not claim that light is “nothing”, or that light is unaffected by gravity.
• It does not claim that antimatter behaves differently from matter under gravity.
• It does not claim that pattern density, rather than energy, produces gravity.
• It does not claim to explain dark energy or dark matter.
• It does not claim priority: the ingredients — occupation numbers, causal sets, inhomogeneous cosmology, everpresent Λ, emergent fermions — come from other people’s work, listed under Sources.

What would move this forward — or retire it

In summary: two parts are established physics in new words, one is a provisional design choice, and one is a reading of other people’s open research. None of it is a result yet.

Sources

• Wheeler, J. A. (1990). “Information, physics, quantum: the search for links.” In W. H. Zurek (ed.), Complexity, Entropy and the Physics of Information. Addison-Wesley.
• Finkelstein, D. & Rubinstein, J. (1968). “Connection between spin, statistics, and kinks.” J. Math. Phys. 9, 1762.
• Levin, M. & Wen, X.-G. (2005). “Colloquium: Photons and electrons as emergent phenomena.” Rev. Mod. Phys. 77, 871.
• Unruh, W. G. (1976). “Notes on black-hole evaporation.” Phys. Rev. D 14, 870.
• Riek, C. et al. (2015). “Direct sampling of electric-field vacuum fluctuations.” Science 350, 420.
• Surya, S. (2019). “The causal set approach to quantum gravity.” Living Rev. Relativ. 22, 5.
• Bombelli, L., Lee, J., Meyer, D. & Sorkin, R. D. (1987). “Space-time as a causal set.” Phys. Rev. Lett. 59, 521.
• Bombelli, L., Henson, J. & Sorkin, R. D. (2009). “Discreteness without symmetry breaking: a theorem.” Mod. Phys. Lett. A 24, 2579.
• Collins, J., Perez, A., Sudarsky, D., Urrutia, L. & Vucetich, H. (2004). “Lorentz invariance and quantum gravity: an additional fine-tuning problem?” Phys. Rev. Lett. 93, 191301.
• Weinberg, S. & Witten, E. (1980). “Limits on massless particles.” Phys. Lett. B 96, 59.
• Marolf, D. (2015). “Emergent gravity requires kinematic nonlocality.” Phys. Rev. Lett. 114, 031104.
• Dowker, F., Henson, J. & Sorkin, R. D. (2004). “Quantum gravity phenomenology, Lorentz invariance and discreteness.” Mod. Phys. Lett. A 19, 1829.
• Kaloper, N. & Mattingly, D. (2006). “Low energy bounds on Poincaré violation in causal set theory.” Phys. Rev. D 74, 106001.
• Philpott, L., Dowker, F. & Sorkin, R. D. (2009). “Energy-momentum diffusion from spacetime discreteness.” Phys. Rev. D 79, 124047.
• KATRIN Collaboration (2025). “Direct neutrino-mass measurement based on 259 days of KATRIN data.” Science 388, 180.
• ALPHA Collaboration (2018). “Characterization of the 1S–2S transition in antihydrogen.” Nature 557, 71.
• Anderson, E. K. et al. (ALPHA-g, 2023). “Observation of the effect of gravity on the motion of antimatter.” Nature 621, 716.
• Benoit-Lévy, A. & Chardin, G. (2012). “Introducing the Dirac–Milne universe.” Astron. Astrophys. 537, A78.
• Cohen, A. G., De Rújula, A. & Glashow, S. L. (1998). “A matter–antimatter universe?” Astrophys. J. 495, 539.
• Touboul, P. et al. (MICROSCOPE, 2022). “MICROSCOPE mission: final results of the test of the equivalence principle.” Phys. Rev. Lett. 129, 121102.
• Dyson, F. W., Eddington, A. S. & Davidson, C. (1920). “A determination of the deflection of light by the Sun’s gravitational field, from observations made at the total eclipse of May 29, 1919.” Phil. Trans. R. Soc. A 220, 291.
• Pound, R. V. & Rebka, G. A. (1960). “Apparent weight of photons.” Phys. Rev. Lett. 4, 337.
• Cunha, P. V. P., Berti, E. & Herdeiro, C. A. R. (2017). “Light-ring stability for ultracompact objects.” Phys. Rev. Lett. 119, 251102.
• Buchert, T. (2000). “On average properties of inhomogeneous fluids in general relativity: dust cosmologies.” Gen. Rel. Grav. 32, 105.
• Wiltshire, D. L. (2007). “Cosmic clocks, cosmic variance and cosmic averages.” New J. Phys. 9, 377.
• Green, S. R. & Wald, R. M. (2011). “A new framework for analyzing the effects of small scale inhomogeneities in cosmology.” Phys. Rev. D 83, 084020.
• Seifert, A., Lane, Z. G., Galoppo, M., Ridden-Harper, R. & Wiltshire, D. L. (2025). “Supernovae evidence for foundational change to cosmological models.” MNRAS Letters 537, L55.
• DESI Collaboration (2025). “DESI DR2 results II: measurements of baryon acoustic oscillations and cosmological constraints.” Phys. Rev. D 112, 083515 (arXiv:2503.14738).
• DESI Collaboration (2026). “DESI DR2 results IV: Alcock–Paczyński measurements from the Lyman alpha forest and cosmological constraints.” arXiv:2607.27410.
• Sorkin, R. D. (1991). “Spacetime and causal sets.” In J. C. D’Olivo et al. (eds.), Relativity and Gravitation: Classical and Quantum, 150–173. World Scientific.
• Sorkin, R. D. (1997). “Forks in the road, on the way to quantum gravity.” Int. J. Theor. Phys. 36, 2759.
• Ahmed, M., Dodelson, S., Greene, P. B. & Sorkin, R. D. (2004). “Everpresent Λ.” Phys. Rev. D 69, 103523.
• Barrow, J. D. (2007). “A strong constraint on ever-present Lambda.” Phys. Rev. D 75, 067301.
• Zwane, N., Afshordi, N. & Sorkin, R. D. (2018). “Cosmological tests of Everpresent Λ.” Class. Quantum Grav. 35, 194002 (arXiv:1703.06265).
• Das, S., Nasiri, A. & Yazdi, Y. K. (2024). “Aspects of Everpresent Λ. Part II. Cosmological tests of current models.” J. Cosmol. Astropart. Phys. 10 (2024) 076.
• Josset, T., Perez, A. & Sudarsky, D. (2017). “Dark energy from violation of energy conservation.” Phys. Rev. Lett. 118, 021102.
• Perez, A. & Sudarsky, D. (2019). “Dark energy from quantum gravity discreteness.” Phys. Rev. Lett. 122, 221302.

Last updated: September 27, 2026