How a mode enters causal time

The bath that is already there

The bath is not a new field. It is the photons, phonons and detector modes already present in the world: a continuum of modes coupled to the system. What lets it anchor is its spectrum. An anchoring bath needs spectral weight down to low frequencies, so that records can spread without coming back; a field with a mass gap has no low-frequency continuum and cannot carry records away (Paper I, §7). The simplest bath is a rock: a slab beside one path of a two-slit experiment, read by nothing, kills the fringes in proportion to how lossy it is (Evidence: the Rock).

Coupled to a bath, a mode undergoes one process with three faces:

1. It decoheres. The relative phase of the mode’s alternatives passes into the bath.
2. Its dynamics gains a direction. A closed evolution is reversible: it can be run either way, and nothing in it marks a before from an after. A mode coupled to a bath evolves, in the Markov regime, by a semigroup, which runs forward only and has no physical inverse. Before and after become physically distinct.
3. It keeps what it takes. What passes into a continuum does not come back. A large finite bath returns it only after an astronomically long time.

Decoherence is built in

Decoherence is foundational to the bath’s anchoring: it is the phase in which a mode of the field enters causal time. ACT’s bath presumes it, because that is how a bath works.

A theory whose mechanism is a bath does not need to add decoherence; it cannot avoid it. Whatever the coupling — dissipative, as in Brownian motion, or pure dephasing — a bath acquires information about the variable it couples to, and superpositions of that variable lose coherence.

When the bath also damps, the decoherence is fixed by the damping. In the Caldeira–Leggett model of quantum Brownian motion both descend from a single quantity in the bath’s spectral density, and their ratio has no freedom:

Here $\gamma$ is the rate at which the bath damps the motion and $\Delta x$ is the separation of the two alternatives. One cannot dial the decoherence rate without dialling the damping. For a 1 g object displaced by 1 cm at room temperature, the decoherence is about $4\times10^{40}$ times faster than the damping.

The laboratory has watched this happen. A superposition of two cavity fields lost its coherence progressively, faster for larger separations (Brune et al. 1996), and the fading was later reconstructed snapshot by snapshot (Deléglise et al. 2008). In trapped ions, classical noise standing in for a hot bath gave the same growth with the square of the separation (Myatt et al. 2000; Turchette et al. 2000). Pressure, heating, detector current, a cavity’s leak, the gap between paths: every valve that opens a record channel moves the contrast by the same rule (Evidence: the Valves).

ACT is the interpretation whose mechanism is the bath. Decoherence is therefore presumed, not added: the bath’s decoherence is itself the process by which a mode enters causal time and an event occurs.

The decoherence data are the same for every interpretation that keeps unitary quantum mechanics, so this is a strength of foundation, not a new prediction. The experiments test ACT where it stands, since the curve is its event law’s own prediction (Evidence). When each of the other interpretations met decoherence, and what it does in each, is set out under Objection 3. In Many Worlds, for one, decoherence only draws the borders between worlds, and every outcome still happens; here the bath’s released record is the one mark, and one history of marks is actual (What ACT is not).

Where a mode enters causal time

“Phase” is the right word for the entry: it has a beginning that can still be undone. The experiments show where it ends.

• Decoherence of the system’s own state is not yet the event. One scattered photon decoheres an atom’s path, yet selecting photons whose direction leaves the path undetermined restores the fringes (Chapman et al. 1995). Quantum erasers restore them in coincidence counts (Kim et al. 2000; Walborn et al. 2002).
• An excitation given to a single mode, or to a field that can return, comes back. An atom in a cavity trades its excitation back and forth with one mode (Brune et al. 1996). Emission returned by a mirror (Eschner et al. 2001) or along an acoustic delay (Andersson et al. 2019) alters the source’s own emission.

In each case what took the phase was one mode, one photon, or a field that could return. A bath does not give back. The same atom shows the whole difference: in a cavity its emission is not an event, because the excitation comes back; in open space it emits into the continuum, and the event law applies. The entry into causal time begins with decoherence and is complete, as an anchored event, when the bath has made it irreversible. That completion is called release: the record is beyond coherent recovery by the system’s accessible future, that is, by anything the system and what it is still coupled to could do from here on. The experiments that map this boundary, and the event rules they rule out, are set out on the Evidence page (Evidence: where the event can sit).

The detector/observer effect is the bath’s effect

A detector is a device built to couple a signal into a continuum, with amplification. Detectors and observers anchor events because they are coupled to the bath, not because they are observers. Which record is written is fixed by what is physically coupled — the detector actually present — not by anyone’s choice. The Rock is the whole point in one picture: remove the observer, and the record remains (Evidence).

The event law

The law says three things: 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 alternative occurs (Born weights). The Filter is the what in one picture: an apparatus picks components out of one wave, as a radio picks a station out of the air, and never picks the outcome; a Stern–Gerlach magnet’s split beams recombine (Evidence: the Filter). The which is one mark per event, never two, with Born weights: one photon at a beam splitter fires one detector, never both (Evidence: the Mark).

In the simplest case

For a record that does not disturb the recorded variable (the quantum-nondemolition case), Paper I sets the probability that no event has yet occurred equal to the fraction of the alternatives’ relative phase that can still be recovered:

Here $S$ is the survival probability and $h$ the hazard: the event rate, the chance per unit time that the event happens now given that it has not happened yet. With that law, the ensemble’s decoherence is reproduced exactly as a mixture of runs not yet anchored, which are still coherent, and runs already anchored:

No additional dephasing term is imposed by the event ontology, and nothing is double-counted. In ACT, decoherence is anchoring seen in the ensemble. The Mark shows it on a screen: the band is the anchored fraction, the fringes the surviving one, and a rock that records weakly lays the one over the other in the proportion $S$ (Evidence: the Mark). The simulation below shows it run by run.

In general

For counting records, the event intensity is built from the bath’s own jump operators $L_r$, the same operators that generate the decoherence:

For an excited atom emitting into open space, $L=\sqrt{\gamma}\,\sigma_-$ and the click rate is $\gamma\langle e|\rho_c|e\rangle$, with $\gamma$ the rate at which the continuum damps the atom. The simplest case above is the special case $L_\pm=\sqrt{\Lambda}\,P_\pm$, for which the total intensity is $\Lambda=\dot\Phi_{\rm irr}$.

Probability, and what is postulated

Probability is ordinary: one outcome occurs, with a Born-weighted chance, and the weights are forced rather than postulated, by two stated requirements on the chance of a record: no signalling, for every division of the world into here and elsewhere, and continuity in the wave (the flagship, §4 and Appendix A; the proof in full in Paper II, Appendix A). 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. The Picture states the commitment and what follows from it.

The rate is physical

Because anchoring is done by real couplings, its rate depends on the detector’s architecture: its size, its couplings, its environment. The laboratory has measured the boundary this requires — decoherence controlled by distinguishability, coherence recoverable until the record spreads, pointer records redundantly imprinted across the environment. The Evidence page sets this out as four thought experiments, each performed in the laboratory: the Rock, the Valves, the Filter and the Mark. One hundred experiments are counted there, each with what it corroborates and what it does not establish.