The wave is what exists.
The particle is what happens.

What ACT is not

The main accounts keep a particle somewhere, at the detector or on a hidden path, or they keep every outcome, each in a world of its own. ACT does neither.

• Copenhagen brings the particle back at the detector, through a measurement it never defines.
• Bohm keeps it all along, on a path the wave steers.
• The collapse models squeeze the wave down to one place, with a new law and new constants.
• Many Worlds keeps no particle, but it keeps every outcome: a mark at every place the wave could leave one, each in a world of its own. The bath only draws the borders between those worlds.
• Those who say plainly that there are no particles, only fields, part ways with ACT at the detector. Hobson (2013) lets the field collapse there and leaves the cause open. Zeh (1993), who gave up the collapse as well as the particle, was left with every outcome.

ACT keeps no particle, and one outcome. The electron is a wave from start to finish; the particle is the mark the bath makes, and one history of marks is actual. ACT takes the third road: no particle, no collapse, one history, and the bath makes the mark. The event ontologies come nearest to it (Objection 3).

Many Worlds is the opposite, not a relative

Many Worlds shares ACT’s equation, and a real wave that never collapses. The two part at the outcome, and there they are opposites.

• In Many Worlds every outcome happens, each in a world of its own, with a copy of the observer in each. The bath only draws the borders between those worlds; decoherence was brought in later to say where the borders fall.
• In ACT the bath makes the mark, and one history of marks is actual.

No experiment decides between the two. Every detection is one mark, as both predict. ACT takes that mark at face value; Many Worlds counts every other outcome as a world of its own, which no experiment can reach. And where every outcome happens, a “50% chance” needs a new meaning; in ACT one outcome happens, with an ordinary chance.

Occam’s razor: what each account adds

Every account here but the collapse models reproduces the statistics of quantum mechanics exactly; the collapse models depart from them, and survive only where the radiation searches have left their constants open. Where the experiments cannot choose, Occam’s razor decides. Count what each account adds to the physics already measured, the Schrödinger equation and the bath whose decoherence the laboratory has mapped, and what the addition costs.

The razor counts what must be assumed to account for what is observed: one outcome in every run, with Born frequencies. Many Worlds adds nothing to the equation, but to account for the one outcome it holds that every outcome occurs, each in a world of its own with a copy of you, and it has to rebuild what a chance is. ACT adds one postulate, that one history of marks is actual, so the outcome a run shows is the only one that occurs. Both keep the whole wave; they differ over what its other components hold. On ACT, possibilities for events and no events; on Many Worlds, a copy of you who saw another outcome. No run can reach another component to check, and there the razor counts against positing copies of you that no experiment can find. Where Bohm adds a particle with a path at every moment, ACT adds no particle, only the fact of which marks were made. Among the accounts in which an outcome is a fact apart from any agent or system, the count comes down to one comparison: ACT asserts one outcome for each run, the one the run shows; Many Worlds asserts that outcome and every other besides, the others in worlds no run can reach (Objection 11).

The mysteries, with no particle and one history

• Which slit did it go through? The wave went through both. There was never a particle to go through one.
• Does the cat’s fate wait for someone to look? No. In any real box the Geiger counter’s bath makes the mark, whether or not anyone looks. No observer has to turn a wave into a particle.
• Does a later choice reach back in time? There was no particle path for it to decide, and it changes no mark already made.
• Are there copies of you in other worlds? One mark, one history, one of you.

No observer is needed anywhere in this. In the Rock, a slab that nothing reads keeps the record and kills the fringes (Evidence). The comparison in full is in Objections 2 and 3 and the flagship’s §9, with the references: Hobson, “There are no particles, there are only fields,” Am. J. Phys. 81, 211 (2013); Zeh, “There are no quantum jumps, nor are there particles!,” Phys. Lett. A 172, 189 (1993).

One field, composed of modes

The wave/field’s superposition can be described as Fourier modes. That is what superposition and quantum states are.Principle II

There is one real field, with composite internal structure, the way a sound wave contains its harmonics. Its superposition is that structure: its modes. A single photon “in two places” is one excitation of one two-lobed mode:

In the mode basis $\{b,\,b_\perp\}$ it is one photon in one mode. Nothing here is two of anything: superposition is the composition of one wave.

Which decomposition matters physically is not a human choice; the dynamics decide. For a free, translation-invariant field they select its Fourier modes. For a field meeting an apparatus they select the alternatives the interaction can hold stable; spin is the reminder that not every relevant decomposition is literally Fourier. Once a mode is coupled to a detector and its environment, the state becomes

Entanglement between separate systems cannot be undone by re-choosing modes, so these terms are no longer modes in the strict sense. They are still terms in the decomposition of one state. Anchoring makes one record-supported alternative of the composite state actual; it destroys none of the other components and does not alter the global wave. The Mathematics page sets out the mode expansion.

Structure before events

The quantum wave/field is atemporal until it is subjected to a quantum Brownian bath.Principle I

Before the bath, a mode has structure but no temporal causal history. Its evolution can be run either way, and nothing in it marks a before from an after. The laboratory shows this directly. An atom in a cavity gives its excitation to one mode and takes it back (Brune et al. 1996). Which-path information held by a single photon can be erased, and the conditioned fringes return in the sorted subsets (Chapman et al. 1995; Kim et al. 2000; Walborn et al. 2002). Nothing has happened yet.

Once the bath has taken the record irreversibly, something has happened, and it has a place in causal order. The Schrödinger parameter $t$ orders the global state throughout, unanchored components included, but what it orders there is a trajectory of structure, not a sequence of events. Before anchoring, the quantum state does not yet constitute a determinate temporal history of localized events.

This is ACT’s interpretive layer, and no proof depends on it. The physics it points to is the difference between evolution that can be undone and evolution that cannot. Where a mode crosses from one to the other is set out on the Mechanism page; where the crossing sits in the mathematics, at the Legendre point, on the Mathematics page.

The world is the history of anchored records

When a mode couples to a quantum Brownian bath, the bath decoheres it. While that decoherence can still be undone, nothing has happened. When the bath has carried the record off for good, an event is anchored: one record, one fact, now in causal time. The accumulating history of anchored records is the definite, temporal, causal world.

Nothing collapses. The field’s structure persists, and its global evolution is never modified.

Two senses of “real” are in play here, and ACT keeps them apart. The components of the wave are real in the first sense: they are the structure of the one wave, which is what exists. They carry amplitude; while no record is released they can still interfere; and an observable a record leaves unrecorded can still anchor later. An alternative is real in the second sense when it is the case: when a released record has made it actual. After an event, the alternatives the record did not select keep the first kind of reality and never acquire the second. They are not destroyed, and they are not things; they are structure of one wave in which no event has occurred. “Anchoring picks out one alternative” means exactly that: picks out, never removes.

Anchoring is like a phase change — not of the field, which stays a wave, but of the world. A mode that was reversible structure becomes an irreversible fact, the way a droplet condenses out of a supersaturated vapor: nothing happens until a nucleus is past the size from which it can dissolve back, and then it grows and stays. A cloud chamber shows the whole picture at once — one spherical wave, a straight line of droplets, each droplet an anchored event (Mott 1929). In ACT the critical size is release, the nucleation rate is the bath’s, and the fraction of runs not yet anchored is the coherence that remains. There is no wave–particle duality in this: the wave is what exists, and a particle is what happens.

Anchoring does not reduce the wave. It adds a determination. What was indeterminate — which record obtains — becomes determinate, and stays so.Kelly Sonderegger, August 7, 2026

Anchoring selects a definite causal event from a real quantum wave structure; it does not retroactively erase the coherent structure from which that event arose.Kelly Sonderegger, August 13, 2026

Probability is ordinary: one outcome occurs, with a Born-weighted chance. The weights are not a further postulate. They are forced by what the picture already says — one wave with one law of chance, one history, no record where the wave has no component, records that can be refined — together with two requirements the theory states: a record’s chance here does not change when a record is made elsewhere, and it changes continuously with the wave (Objection 4; the flagship, Appendix A; the proof in full in Paper II, Appendix A). The martingale descent of the conditioned weights is the check that the single-history law and the master equation agree. What remains is why there is chance at all.

Beyond standard quantum mechanics, ACT adds one commitment: one history of marks is actual. That no event leaves two marks is a theorem for the systems the companion papers treat, and a further commitment beyond them. For those systems, continuously monitored ones, the released records form a commutative algebra whose points are the possible histories (Paper II).

Entangled records, and Bell

ACT is nonlocal in Bell’s sense, in the mildest form a one-history theory can take. An entangled pair is one structure. When one end’s record is anchored, the other end anchors from what is left of that structure consistent with the record, so its outcome depends on the first, while nothing of the first detector’s setting reaches it. Records far apart have no time order, and it makes no difference which end is taken first.

Why the nonlocality is forced

Loophole-free Bell tests rule out every theory in which each outcome depends only on its own detector and on something both particles share, with the detector settings independent of whatever fixes the outcomes (Hensen et al. 2015; Giustina et al. 2015; Shalm et al. 2015; Storz et al. 2023). ACT has one actual record history with Born weights. It does not make the settings conspire with the source, and it sends no influence backward in time. So it is nonlocal in Bell’s sense, as every theory with one outcome per run must be on those terms.

Which kind

Bell’s locality condition splits in two (Jarrett 1984). ACT violates outcome independence: the outcome at one end depends on the outcome recorded at the other. It keeps parameter independence: no outcome depends on how the distant detector was set, which is why the correlation can carry no signal. Shimony called this “passion at a distance,” as against action at a distance. Quantum mechanics with definite outcomes and the collapse models share it. Bohmian mechanics, in which an outcome depends on the distant setting, has the stronger kind.

What is left over

In ACT’s event law the second record’s Born weights come from the state conditioned on the first record. Nothing is removed from the field: what is left over is what is still available to the actual history. The Mathematics page gives the conditional state, the no-signalling sum and the order symmetry.

The same resolution as delayed choice

In a delayed-choice quantum eraser, the later record on the idler side never changes the earlier detection of its partner. It decides which subset that detection belongs to. Interference reappears only after the signal detections are sorted by the corresponding idler outcomes; the unsorted signal distribution contains no interference and therefore permits no signalling (Kim et al. 2000). A Bell test has the same structure laid out in space: two records of one structure, a correlation that appears only when the records are compared, and no influence passing between them.

What atemporality does here

It removes the question of time order. There is no preferred frame, and nothing reaches back. It is not offered as a way around Bell nonlocality. A covariant statement of release, the remaining piece of the relativistic account, is open (Mathematics).

Mass gives the field a clock; anchoring gives the clock its readings

A massive excitation’s phase turns at its rest-energy rate, $mc^2/\hbar$ — de Broglie’s “internal periodic phenomenon” (1924). A working clock has been built from that rate (Lan et al. 2013). The rate is structure. Elapsed, recorded time exists only as anchored events.

• Mass is present before anchoring. Matter-wave fringes are spaced by $\lambda=h/mv$ out to 172 kDa (Pedalino et al. 2026), and neutrons in an interferometer feel gravity on their mass while still in superposition (Colella, Overhauser & Werner 1975).
• A scale, then a frequency. In the Lagrangian, $m$ is a scale. Past the Legendre point it is rest energy: a frequency.
• The photon. A photon has no mass and no proper time; its only temporal facts are its emission and its absorption. When a detector absorbs it, its energy becomes rest mass of the absorber, $\Delta m=h\nu/c^2$ — the case from which Einstein first derived $E=mc^2$ (1905), with emitted light. At a photodetection anchoring, mass and time really are introduced for that energy.
• The neutrino. A neutrino travels as three mass components with different clock rates; oscillation is the beat between them. A definite mass appears only if something records which mass is involved (Kayser 1981).
• Where the clocks come from. The Higgs condensate is why elementary particles have clocks at all. The bath is a different thing: anchoring needs a low-frequency continuum, which a field with a mass gap cannot supply (Paper I, §7). Most of an atom’s mass is QCD binding energy, and the clock depends on rest energy, whatever its origin.

This is the mature form of the Original Picture’s second sentence: mass is the enabler, not the gateway.

Three words, kept apart

The full working vocabulary is in the Glossary.

1. K. Sonderegger, From Matter Waves to Anchored Events (Paper I, 2026), §§5, 7, 9–10; Released records (Paper II, 2026).
2. N. F. Mott, The wave mechanics of α-ray tracks, Proc. R. Soc. Lond. A 126, 79 (1929).
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