Six approaches to the measurement problem, what each one sacrifices,
and what decoherence settled and left open
Part I: The Problem
The measurement problem has haunted physics for a century. Brilliant minds have proposed radically different solutions. Each one works — and each one costs something fundamental.
"Don't ask"
"Everything happens"
"Hidden guides"
"Spontaneous collapse"
"Probability as agent's belief"
"The environment matters"
One thread runs through the first five: each keeps a particle somewhere — at the detector, on a hidden path, in a squeezed wave — or keeps every outcome, each in a world of its own, or, like QBism, makes the mark the agent’s experience. Decoherence alone leaves the mark unexplained. ACT does none of these: the particle is the mark the bath makes, and one history of marks is actual.
Bohr, Heisenberg, 1920s
Measurement is a fundamental, irreducible process. The quantum state describes probabilities, not reality. When you measure, the wave function "collapses" — but don't ask what physically happens.
Practically effective. Generations of physicists have used it to make correct predictions without needing to resolve the deeper question.
No mechanism. Measurement is declared fundamental but never explained. It draws an arbitrary line between "quantum" and "classical" that nature doesn't seem to respect.
A theory that forbids asking how is not a complete theory. Its postulates were fixed in 1927; decoherence theory was brought in decades later to explain why the cut can be moved.
Everett, 1957
There is no collapse. Every possible outcome actually happens, each in its own world. In one world the cat is alive; in another, dead. Both are equally real. Crucially, you are copied too — there is a version of the observer in every world.
No collapse is needed: the wave is real and evolves unitarily. ACT agrees on exactly this, and on nothing after it.
Every outcome happens, so the worlds are an infinity no experiment can reach — not by accident but by construction: decoherence is what keeps the branches from ever meeting. That is the first cost. The second is probability: if every outcome occurs with certainty, what does "70% probability" mean, and why does our one history show Born frequencies? Measures over worlds, self-locating uncertainty, decision theory — decades of machinery, no consensus. The third is what Everett must say about the record in front of you: that it is one world's fact among equally real others.
The math is clean. The bill is an unobservable infinity and a probability it cannot yet define. Its postulates were fixed in 1957; decoherence was brought in later to answer which of the worlds are the worlds. Same equation as ACT, and the same real wave; the opposite answer at the outcome: there every outcome happens and the bath only draws the borders between the worlds; in ACT the bath makes the mark, and one history of marks is actual.
Bohm, 1952 (building on de Broglie, 1927)
Particles are real and always have definite positions. But they're guided by a "pilot wave" — the quantum wave function — which tells each particle where to go. The wave goes through both slits; the particle goes through one.
Realist. Particles have definite positions at all times. Reproduces all standard QM predictions. Single outcomes emerge naturally.
Fundamentally nonlocal — the pilot wave connects distant particles instantaneously. Bell-type Bohmian quantum field theories do exist (with particle creation and annihilation), but they pay in nonlocal beables (hidden positions acted on at a distance) and difficult relativistic structure. Adds hidden structure that can never be measured directly.
Decoherence is not needed for outcomes here, since positions are always definite; it explains why the empty parts of the wave stop mattering, as Bohm himself argued in 1952. And a caveat the course will keep: ACT is nonlocal too, in the milder form every one-history theory must have — outcome dependence only, no signalling (Lecture 7). Where Bohm keeps a particle all along, ACT keeps no particle: the particle is the mark.
Ghirardi, Rimini, Weber (1986) • Pearle (1989)
Modify the Schrödinger equation: add a random, spontaneous collapse mechanism. Each particle has a tiny probability of spontaneously localizing at any moment. For 10²³ particles in a cat, at least one collapses almost instantly — dragging the whole system with it.
A real dynamical modification — not just interpretation. Provides an actual mechanism for collapse. Testable in principle.
Standard CSL predicts anomalous energy gain — collapse noise with no compensating dissipation. Dissipative CSL was built to fix exactly this, at the price of additional phenomenological dynamics and parameters. In every variant, the noise field is postulated rather than identified with known physics.
On one axis GRW/CSL is ACT's closest predecessor: discrete events at a physical rate. But it invents its noise field and modifies the dynamics, and its collapse noise was postulated without the damping every real bath brings — the damping was added later. ACT will use the bath that's already there, and modify nothing.
Caves, Fuchs, Schack, 2002; Mermin later
The wave function isn't a real physical thing — it's a tool for an agent to organize their beliefs about future experiences. Measurement isn't a physical process that needs explanation; it's simply the moment an agent updates their expectations.
Philosophically rigorous. Avoids many conceptual puzzles by refusing to treat the wave function as real. Internally consistent.
Abandons realism entirely. If the wave function isn't real, what is? Physics becomes about experiences rather than the world.
QBism treats the quantum state as an agent's information rather than an objective field — a coherent stance ACT declines in favor of objective records.
Coherence — the ability of a wave's components to interfere — is lost at a rate the environment sets. The numbers shocked physicists when they first calculated them.
~10⁻¹² s
Extrapolated to air from the collision rate measured at 10⁻⁷–10⁻⁶ mbar (Hornberger et al. 2003)
~10⁻¹⁵ s
About a femtosecond, for a 10 µm grain separated by its own size (Joos & Zeh 1985)
10⁴⁰ ×
Decoherence runs 10⁴⁰ times faster than the damping that comes with it (Zurek 1991) — a ratio, not a time
Decoherence is so fast for macroscopic objects that quantum behavior is effectively impossible to observe.
An analogy that captures the gap.
One wave reaches a Geiger counter. Decoherence spreads its components into the counter’s surroundings, so they can no longer interfere.
It sorts the possibilities. It makes none of them happen.
What we actually see is one mark: the counter clicks, or it does not. Not both. Not a blend.
Decoherence alone can’t make the click. In ACT the bath’s released record is the click, and one history of such marks is actual — there was never a second cat.
Decoherence explains the blur. It doesn’t explain the mark.
Before decoherence:
diagonal terms = probabilities | off-diagonal terms = interference
After decoherence, the off-diagonal terms are suppressed:
The catch: this is a reduced density matrix — obtained by tracing over the environment (averaging over everything the environment could be doing). The full system+environment state is still pure and still contains both components. The off-diagonal terms didn't vanish; they moved into system-environment correlations.
Three questions people put to decoherence. Two have answers. One is the gap.
This is usually not missing: microscopic decoherence theory routinely identifies the relevant fields and interactions in detail for a given system. ACT adopts those models rather than replacing them.
Standard open-system theory specifies the coupling per system: the photons, phonons and detector modes already present in the world — the quantum Brownian bath. ACT adds no coupling of its own — mass enters only as the field's clock.
This is the gap, and it has two halves. Decoherence alone yields an improper mixture: it says nothing about when, in a run, a record becomes a fact, and nothing about which one. ACT answers the first with physics — the bath's own rate, at release — and the second with a stated postulate.
ACT's distinctive addition is one primitive — one record history is actual — placed at release, when the bath has carried the record beyond recovery. Anchoring does not reduce the wave; it adds a determination.
Decoherence isn't wrong — it's incomplete. ACT doesn't replace it; ACT completes it.
The event law in three sentences. When: an event can occur only at release, at the rate the bath sets. What: the alternatives are the ones the coupling can hold stable. Which: one of them, with Born weights — and that one such history is actual is the postulate.
It explains the blur, and it does not explain the mark.
The next two lectures assemble what does: one wave with its clock, and the bath that is already there.
Next: Lecture 3 — Fields Are Fundamental