Claim Ledger
How each claim is held
Every substantive claim of Anchored Causality Theory, with its status: established physics, a definition, a result derived or proved in a stated class, a commitment, an interpretive reading, or an open problem. This page is the reference; where any other page disagrees with a row here, the row governs. Last reconciled with the papers on 28 October 2026 (the flagship v3.3, Paper I version 2.5, Paper II v1.8); the four thought experiments added 5 October 2026.
Stated plainly
What ACT Claims, and What It Does Not
ACT claims
- An ontology. The electron is never a particle: one real field with composite structure, from start to finish. A bath, not an observer, makes the mark; the mark is the particle, an anchored record; one history of marks is actual; causal time is made by events.
- A difference at the root. 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. Many Worlds is its opposite, not its relative: every outcome there, one outcome here (What ACT is not).
- An event law in the bath’s own terms. When an event can occur (release, at a rate set by irreversible record production), what can be registered (the alternatives the record architecture supports), and which occurs (Born weights).
- Decoherence as the mechanism. The bath’s decoherence is the process by which a mode enters causal time, not an addition made afterwards.
- A mechanism the laboratory has measured. Four thought experiments, each performed in the laboratory — the Rock, the Valves, the Filter and the Mark — and one hundred experiments that bear on them (the record in numbers). ACT is built from this measured physics and nothing else, and its event boundary is the one the recovery experiments leave standing. Corroborated, not singled out: the experiments test ACT where it stands, because the event rate is read off the same coupling that draws the decoherence curve, with no free constant; in the nondemolition case the two curves are one (Evidence).
ACT does not claim
- An experiment that singles it out. ACT’s core is equivalent to quantum mechanics by construction, so every interpretation that keeps unitary quantum mechanics predicts the same results, and no experiment chooses between them on the statistics. What the experiments do is corroborate ACT’s mechanism and fix its event rule: the decoherence, eraser and echo results confirm each physical ingredient ACT uses, rule out, for event rules of ACT’s kind, each of the three earlier placements that has been tested, and could have refuted release and have not. ACT is as refutable as quantum mechanics: the deviations collapse models predict, and that experiment keeps constraining, would refute it too.
- That decoherence alone decides which alternative occurs. The bath sets when, among which alternatives, and at what rate. Which one occurs is the anchoring.
- That actuality is derived. One actual record history is a primitive, stated openly.
- Locality in Bell’s sense. ACT is nonlocal by outcome dependence only: the outcome at one end depends on the record at the other, with no signal and no time order between them (The Picture).
- That every element is new. The passage from possibility to fact has a long lineage: Heisenberg, Haag, Kastner, Fröhlich. ACT’s contribution is the combination, with the bath as the mechanism.
| Claim | Status | Basis | What would change it |
|---|---|---|---|
| The mechanism | |||
| Decoherence, record formation and conditioned trajectories are real, measured physics | Established | Cavity QED, matter-wave, trajectory and quantum-Darwinism experiments (Evidence) | Nothing: the phenomena are not in doubt. A better microscopic bath model would refine the rates |
| The bath is the photons, phonons and detector modes already present; no new field | Established | Caldeira–Leggett class of spectral densities; Paper I §7 | A named field shown to supply a low-frequency continuum where none was expected would add to the bath, not replace it |
| An anchoring bath needs spectral weight down to low frequencies; a gapped field cannot anchor | Derived | Bounded decoherence functional for a gapped spectral density (Paper I §§7, 10) | A coupling-specific calculation for a named gapped field, not attempted |
| Decoherence is built in: the bath’s decoherence is the phase in which a mode enters causal time | ACT’s framing | A bath decoheres by its nature; the stopped-process identity; the comparison under Objection 3 | A strength of concept, not a prediction: the experiments corroborate the mechanism without distinguishing the framing |
| The decoherence exponent $\Phi_A$ is nonnegative; unbounded in a Markov bath with persistent separation | Derived | Lemma and theorem on the Mathematics page, from the Feynman–Vernon noise kernel | Non-Markovian baths permit bounded growth and partial return; stated as scope |
| The bath sits at the Legendre point: with a bath the passage from structure to states in time is forced and directed | ACT’s framing | Bauer 1931; Caldirola–Kanai; Brittin 1950, Dekker 1981, Senitzky 1960; the influence functional’s retarded and noise kernels | A consistent quantization of damping without a bath would weaken the third support; none is known |
| Records and release | |||
| Irreversibility is recoverable phase distinguishability over the accessible algebra, $\Phi_{\rm irr}$ | Definition | Paper I, Def. 1; the restriction norm of Paper II | A better measure would replace it; the trace distance is the natural one and cannot be inflated by system-only operations |
| $\Phi_{\rm irr}$ is nondecreasing when the accessible dynamics is CP-divisible | Scope condition | Contractivity of the trace distance (Paper I §9) | Where divisibility fails, phase returns and no hazard is defined; outside the law by statement |
| Release: a record commutes with the system’s accessible future, including return paths | Definition | Paper II §4; stress-tested in the collision model | The covariant form is open (below) |
| For a free output field every record is released as it forms (nondemolition) | Theorem in class | Belavkin; Bouten, van Handel & James; Paper II | Nothing within the class; outside it (returning carriers) release does further work |
| A released record leaves no recoverable phase in any state: $\mathcal D_{\rm acc}\le\lVert\omega_{\rm off}\rVert_1\lVert[R,A]\rVert/\Delta$ | Theorem | Paper II, the bound; converse false; commutator blind to the carrier’s own later history | A version for continuous-valued records (open) |
| Under delayed return, anchoring waits for the exit record; an in-flight “click” can be overturned | Proposition (discrete class) | Atom–mirror collision model, Paper II; Eschner 2001 and Andersson 2019 show the physics | The continuum limit (open) |
| Released records form a commutative algebra whose points are the possible histories; exclusivity is a theorem | Theorem in class | Paper II, Theorem 2; in Paper I a stated commitment | Nothing within the class; beyond fresh carriers, the class itself is the open question |
| The accessible algebra is the detector specification, not a free parameter | Position | Quantum-trajectory theory needs the same input (Wiseman & Gambetta 2012); release is then a property of the dynamics | The apparatus-free case (below) is where this is weakest |
| The event law | |||
| The general event law is the instrument path measure; for counting records $\lambda_r=\mathrm{Tr}[L_r^\dagger L_r\rho_c]$ | Theorem in class | Quantum filtering in the QSDE and collision-model class (Paper II §5) | Beyond the Markov class, when a structured environment supplies a released record (open) |
| Identical particles need nothing added: the records of the event law carry no particle labels | Theorem in class | Paper II, Proposition 5 (the end of §5): record channels built from the electron field — densities, currents, capture into a reservoir — commute with every permutation of the labels or preserve antisymmetry, and inside the electron sector “electron 1 is at $x$” acts as the density at $x$ divided by $N$. A collapse rule written per labelled particle leaves the sector (GRW 1986); its identical-particle versions couple to the density. The worked case finds the exchange hole in two-event statistics (40,000 sampled histories) and, for idealised detectors, the Coulomb hole in helium; independent audit in two rounds, 15 October 2026 | A record channel that cannot be built from field couplings; none is known. The result reproduces standard quantum mechanics: a consistency requirement met, not a test that singles ACT out |
| $h=\dot\Phi_{\rm irr}$ and $S=e^{-\Phi_{\rm irr}}$ in the nondemolition case, with the stopped-process identity | Derived (QND) | Paper I, Prop. 1 and §10; the corollary $L_\pm=\sqrt\Lambda P_\pm$ of the general law | Nothing within the QND case; outside it the general law applies and the scalar hazard does not |
| Born weights are forced by the one-wave law, one history, support certainty, no signalling for every division into here and elsewhere, refinable records and continuity | Forced | Zurek’s envariance argument in Barnum’s no-signalling form; of the six premises, three restate commitments already in the ledger (one wave, one history, support certainty), one extends the ledger’s parameter-independence commitment to every division of the network, one is an assumption about the record architecture (any released record can be refined by a fresh released pointer), and one, continuity, is new; the flagship, §4 and Appendix A; the proof in full, each step tagged with the premise it uses, Paper II, Appendix A (Theorem 9); independent referee audits of the argument and of the proof, 9 October 2026 | A chance law meeting all six premises that is not Born’s; none is known, and each candidate family fails a named premise (|ψ|⁴ renormalized fails no signalling; a basis-dependent rule fails the one law; a never-certain rule fails calibration, which one history and support certainty together give; a rule that treats irrational weights apart fails continuity) |
| The single-history weights and the master equation agree: the conditioned weights form a martingale | Consistency check | Paper I, Prop. 2: outcome-neutral release plus ensemble agreement forces the populations in the nondemolition model, and the martingale carries them to each run; with the weights forced (row above), this is the check that the two laws agree | A nondemolition model in which the forced weights and the ensemble populations disagreed; none is known, and the cut-cone obstruction fixes where sharp projectors stop |
| Record-shaped multilevel events reproduce generic dephasing; sharp projectors cannot | Conditional theorem | Cut-cone obstruction, Paper I Appendix B; the multilevel note | A general uniqueness proof (open) |
| Fragment records support only classical post-processings of the localization instrument | Conditional theorem | Paper I §12 and Appendix A, in the fast-record, position-diagonal regime; the dilation note | Model-independent uniqueness and the general POVM case (open); outside the fast-record regime the conclusion inverts |
| The rate is physical: it depends on the detector’s size, couplings and environment | ACT’s framing | Original Picture, sentence 4; the event intensity is built from the actual couplings | Nothing: a consequence of the mechanism |
| The four thought experiments (Evidence) | |||
| The Rock: a passive dissipative body that nothing reads keeps a which-path record, in proportion to its loss, so the source of the decoherence is a bath, not an observer; interaction without a record does not | Established | Sonnentag & Hasselbach 2007; Kerker 2020 with its gold control; Chapman 1995; Hornberger 2003; the no-record control of Perreault & Cronin 2005; 19 experiments (Evidence). Corroborates principle III: the record, not the observer, is what counts | Nothing now. It could have failed if interaction without a record had killed fringes, or a lossy body with no readout had left them intact; it did not. It does not establish that an event occurred in any one run |
| The Valves: the rate of record formation is a measured number, continuous in every channel, set by coupling, separation and temperature, and the laboratory can dial it; classical dephasing, which records nothing, is not record formation | Established | Brune 1996; Myatt and Turchette 2000 (laser cooling); Hornberger 2003; Deléglise 2008; Buks 1998; the Zeno pair; Gustafsson 2014; Andersson 2019; Yin 2013; the ion experiments’ random-field reservoirs, the fake valve, and the Hahn echo as control; 15 experiments (Evidence). Corroborates sentence 4 of the Picture | Nothing now. It could have failed if decoherence had been all-or-nothing, a universal constant, or independent of the coupling; it did not. It does not establish anything beyond decoherence theory |
| The Filter: an apparatus picks components out of one wave and never the outcome; the coupling sets which components a record can register; picking them out is unitary and reversible; the event can first be at release, and event rules of ACT’s kind placed earlier are ruled out | Established | Stern–Gerlach from 1922 to Margalit’s full loop 2021; Goy 1983 and Hulet 1985, emission sped and suppressed by the modes on offer; Turchette’s reservoir-chosen pointer bases; the quantum-Darwinism redundancy results; the eraser, echo and delayed-choice boundary experiments; 30 experiments (Evidence). Corroborates principle II and the event law’s what and which | Nothing now. It could have failed if the apparatus had fixed the outcome, if the split had been irreversible, if emission had ignored the modes on offer, or if coherence had failed to return while a record could; it did not. It does not establish which alternative wins |
| The Mark: every detection is one mark, and the marks build a wave’s fringes when no record of the path was kept and a particle pattern when one was; events are discrete, one mark per event and never two, with the hazard restarting after each and Born-distributed frequencies; the conditioned history is an observable object | Established | Grangier, Roger & Aspect 1986; Merli 1976 and Tonomura 1989; the 1986 quantum jumps; Kimble 1977 and Diedrich 1987 antibunching; Murch 2013; Guerlin 2007; 12 experiments (Evidence). Corroborates the last link of the chain and principle I | Nothing now. It could have failed if one event had ever left two marks, if the marks had built fringes after a record of the path was released, or if the frequencies had failed Born; it did not. It does not establish that the marks’ history is the one actual history: that is the postulate, below |
| What is added | |||
| One record history is actual | Postulate | The one primitive commitment. Attached at release, as ACT attaches it, the commitment changes no prediction. It is not a hidden variable of Bohm’s kind: Bohm adds a particle with a definite position at all times; ACT adds no particle, only the fact of which marks were made. | An empirical distinction from ensemble interpretations, which ACT does not claim |
| Global unitary dynamics are never modified (Option B) | Commitment | ACT is not a collapse model; the event law adds a determination, not a dynamics | Nothing: a defining choice |
| No new field, constant, threshold or noise | Stated | The rate is the bath’s; the instrument is selected by the record architecture; damping and noise are paired by fluctuation–dissipation | Nothing |
| Corroborated by experiment, not singled out: the mechanism is measured, the boundary mapped, the placement never refuted. The decoherence record tests what ACT’s event law predicts, since the event rate is read off the same coupling that draws the decoherence curve (in the nondemolition case the two curves are one), where Copenhagen, Everett and Bohm added decoherence after their postulates were fixed and are tested in what they accommodate; no experiment chooses between ACT and other unitary interpretations on the statistics | Stated | Equivalence to quantum mechanics by construction; the 100 experiments on the Evidence page — 76 corroborate the four thought experiments (19 the Rock, 15 the Valves, 30 the Filter, of which 15 map the boundary, 12 the Mark), 2 are the no-record controls, 11 the constraints, 11 the collapse searches; 0 discriminate | A recovery failure at release, or the excess radiation collapse models predict, would refute ACT; a discriminating prediction would change its standing, and none is claimed |
| Nonlocal in Bell’s sense: outcome dependence only, no signalling, no time order between distant records | Stated | Loophole-free Bell tests; conditional state and no-signalling sum (Mathematics); adopted 3 October 2026 | Nothing: a consequence of one history with Born weights, without superdeterminism or retrocausality |
| No events in a laboratory that stays coherently reversible (extended Wigner’s friend) | Stated | Release: no record is released inside such a laboratory | Nothing: a consequence of release |
| The interpretive layer | |||
| The pre-anchored field is not yet in time: structure without a temporal causal history | Interpretive | Principle I; the physics it points to is the difference between reversible and irreversible evolution | No proof depends on it; a sharper operational consequence, if one can be derived, would change its status |
| Superposition is the composition of one wave; the dynamics select the decomposition | Interpretive | Principle II; the mode expansion; dynamical selection of alternatives by the coupling | The general map from modes to alternatives (open) |
| Mass gives the field a clock; anchoring gives the clock its readings | Interpretive | de Broglie 1924; Lan et al. 2013; matter-wave interference to 172 kDa; the Higgs condensate is why particles have clocks, not the bath | Nothing: a reading of established physics |
| A particle is an anchored event; anchoring is analogous to nucleation — a phase change in the record, not in the field | ACT’s framing | Mott 1929 (α-ray tracks: one spherical wave, a straight line of droplets); detector physics (droplets, bubbles, grains, hotspots); the stopped-process identity read as the survival law of a nucleation process | Nothing: a reading, no prediction rides on it |
| Open | |||
| Covariant release | Open | Fewster–Verch instruments give a partially ordered record history; “central relative to the accessible future” is not yet stated covariantly | A covariant statement; Kent 2014 shows a one-history unitary ontology can be Lorentz covariant |
| Selection without an apparatus | Open | What fixes the accessible algebra for a dust grain in the microwave background; the sharpest open item | A selection principle from the environment’s own fragment structure |
| Delayed return in the continuum limit; non-Markovian release | Open | The delayed quantum stochastic equation is not of Hudson–Parthasarathy form | A continuum version of the deferred-anchoring proposition |
| The energy ledger of a single event | Open | Ensemble energy is exchanged with a physical bath; the per-event account needs a bath-conditioned event map | An explicit energy-conserving dilation |
| Alignment of record-selected alternatives with dynamically robust structure | Conjecture | Exact in the QND class; coherent-state pointers in quantum Brownian motion are the candidate answer | A regime with small QND-breaking and large misalignment would refute it |
One postulate, one scope, stated openly
The electron is never a particle: it is one wave from start to finish, and the particle is the mark a bath makes. What ACT adds to quantum mechanics is one primitive: one record history is actual. Exclusivity is a theorem in the record-algebra class, and a further commitment beyond it; the event rate is the bath’s; the alternatives are selected by the record architecture; the Born weights are forced, by two stated requirements on the chance law. Everything else is standard open-system physics, arranged.
The ontology is proposed generally. The derivations are established in Markovian, CP-divisible record-forming regimes, principally approximately nondemolition and linear–Gaussian ones. That asymmetry, a regional derivation of a law proposed universally, is stated in Paper I and repeated here.
The statuses
- Established
- Physics ACT adopts unchanged and shares with every interpretation that keeps unitary quantum mechanics.
- Definition
- A quantity ACT defines; it can be replaced by a better one, not refuted.
- Derived · Theorem · Forced
- Proved within a stated model or class; “forced” means proved from premises the row lists, of which two are stated requirements rather than commitments about what exists. “In class” names the class: the quantum stochastic and collision-model setting of Paper II, or the nondemolition model of Paper I.
- Framing · Stated · Consistency check
- How ACT reads established results, or what it says of itself; no new prediction rides on these.
- Postulate · Commitment
- What ACT adds. Not derived, and not claimed to be.
- Interpretive
- The reading of the physics that no proof depends on.
- Position
- A choice ACT makes about how a quantity is fixed, defended by argument rather than proved.
- Scope condition
- A stated restriction on where the derivations hold.
- Conjecture
- A stated expectation with a named refuter, not yet proved.
- Open
- Named, unsolved, and listed with what would solve it.