The measurement problem

Quantum mechanics has two rules that contradict each other, and no rule for which to apply. A hundred years on this is not settled, and the lesson that says otherwise is lying to you.

1926 – today20 min

By the end you should be able to

State the two rules precisely and say why they cannot both be fundamental
Explain what decoherence does explain and what it does not
Compare the main interpretations on what each one gives up

Two rules that have nothing in common

Quantum mechanics contains two prescriptions for how a state changes, and they could hardly be more different. Rule 1 — Schrödinger evolution. Smooth. Continuous. Deterministic. Reversible. Linear. Give it the state now and it hands you the state at any later time, with no probabilities anywhere in it. Rule 2 — measurement. Abrupt. Random. Irreversible. Non-linear. One outcome occurs, the others vanish, and probability appears from nowhere. Von Neumann set this out precisely in 1932 and named them process 2 and process 1. And here is the trouble: nothing in the theory says when to apply which. There is no equation that detects a measurement. There is no definition of "measurement" in the formalism at all — it is a word taken from ordinary language and given a starring role in a mathematical theory that otherwise defines everything it uses.

The 1927 Solvay Conference group photograph: twenty-nine physicists in three rows. — Solvay, October 1927. Seventeen of the twenty-nine people in this photograph won a Nobel Prize. They could not agree on what their own theory meant — and a century later, neither can anyone else. That is the honest state of this lesson’s subject, not a rhetorical flourish.

Slide the cut up and down the chain. Watch the prediction while you do it.

Loading the magnets…

Every link is made of atoms, and quantum mechanics describes atoms — so the equation says each one becomes correlated with the one before it, and joins the superposition. Somewhere you must declare that an outcome has occurred. Von Neumann proved you can place that line anywhere and every prediction is identical.

Follow the chain and the problem is unavoidable. An atom in a superposition of up and down enters the magnet. The magnet is made of atoms, so the equation describes it too — and what the equation says is that the magnet becomes correlated with the atom. It is now in a superposition of having deflected the atom up and having deflected it down. So is the detector. So is the pointer. So are the photons leaving the display, the rhodopsin in your retina, and the firing pattern in your brain. At no point does the equation produce a single outcome. It is linear: feed it a sum of possibilities and it returns a sum of possibilities, forever. So somewhere you have to stop and say an outcome has occurred. That dividing line is the cut — sometimes the Heisenberg cut — and it is not in the mathematics. You put it there.

You might think

Schrödinger’s cat is an illustration of how strange quantum superposition is.

Actually

Schrödinger constructed it in 1935 as a reductio ad absurdum — an argument that the prevailing interpretation leads to nonsense and must therefore be incomplete. His paper calls the resulting situation burlesque. The point was: if you take the standard account seriously and apply it consistently, since the detector and the flask and the cat are all made of atoms, you are committed to a cat in superposition — and that is absurd, so the account is wrong somewhere. He was arguing against the position his cat is now routinely used to illustrate. Einstein, who had prompted the exchange with a similar example about unstable gunpowder, agreed entirely. Using the cat as a colourful demonstration of quantum weirdness inverts its purpose.

What decoherence explains

Correlation with an environment you do not track destroys interference. The part of the mathematics that makes a superposition observably different from an ordinary list of possibilities — the interference terms — decays away as the system entangles with its surroundings. And given the collision rates above, it does so essentially instantaneously for anything larger than a molecule. This is real, calculable physics, and it is a genuine achievement. It explains: Why you never see a cat in superposition. Not because cats are special, but because a cat is correlated with its surroundings faster than any conceivable measurement could catch. Why the classical world looks classical, and why certain quantities (position, mostly) are the ones that appear definite, while others are not — the environment monitors position, so position is what gets defined. Why the cut can be placed anywhere sensible with no practical consequence. Once decoherence has occurred, it makes no difference to any prediction whether you declare the outcome at the detector or at the retina.

You might think

Decoherence solves the measurement problem.

Actually

It does not, and this is where popular accounts most often overreach. Decoherence turns a superposition into something indistinguishable from a list of possibilities with probabilities attached. It does not tell you why one of them happens. The mathematics still contains every branch — what has changed is that they no longer interfere, so you cannot detect the others. You have gone from a state that says up and down to a state that says up and down, in a form that cannot be told apart from up or down. That is enormously useful. It is not the same thing. The "and" has not become an "or". Decoherence explains the appearance of classicality; the question of why a single outcome occurs is untouched by it, and the physicists who developed decoherence said so themselves.

So there are interpretations. It is worth stating what each one gives up, because none of them is free. Copenhagen, roughly. The cut goes wherever is convenient; quantum mechanics describes measurement outcomes rather than an underlying reality; asking what is happening in between is a misuse of the theory. Coherent, widely held, and it gives up any account of what is going on. Its defenders regard that as a virtue rather than a cost. Many worlds (Everett, 1957). Delete Rule 2 entirely. There is only Schrödinger evolution, nothing ever collapses, and every branch continues — including branches containing a version of you who saw the other result. Extremely economical in axioms, extremely extravagant in what exists. Its main technical difficulty is probability: if everything happens, it is genuinely hard to say what the numbers in the Born rule are numbers of. Pilot wave (de Broglie 1927, Bohm 1952). Particles have definite positions at all times, guided by a real physical wave. Reproduces every prediction exactly, restores determinism, and has no measurement problem at all. The price is that it is explicitly and unavoidably non-local — and after Act 7 you may find that price lower than it sounds. Objective collapse (GRW 1986, and successors). Modify the equation so that collapse is a real physical process: each particle spontaneously localises very rarely, but a macroscopic object contains so many particles that one of them localises almost immediately, dragging the rest with it. No cut, no observer, no ambiguity.

The experiment

Looking for collapse that is not there

Multiple groups: LISA Pathfinder, underground germanium and X-ray searches, matter-wave interferometry · 2010s – present · Gran Sasso, orbit, and molecular-beam laboratories

The question: Objective collapse models are the only interpretations that make different predictions. If collapse is a real physical process, it must deposit a tiny amount of energy in everything, and it must destroy interference in large objects even under perfect isolation. Does it?
The apparatus: Three lines of attack. Spontaneous collapse would heat matter continuously, so ultra-low-noise systems become detectors: LISA Pathfinder’s free-falling test masses, and cryogenic detectors deep underground where cosmic rays are screened out. Collapse also predicts spontaneous X-ray emission from accelerated charges, searched for in germanium detectors at Gran Sasso. And it predicts a mass threshold beyond which interference cannot survive, probed directly by interfering ever-larger molecules.

Theory predicted

Standard quantum mechanics predicts no anomalous heating, no spontaneous radiation, and interference at any mass given sufficient isolation. Collapse models predict all three, with rates set by two free parameters — a collapse rate and a localisation length.

They measured

No anomalous heating, no spontaneous emission, and interference surviving to molecules above 25,000 amu. Large regions of the parameter space are excluded, including the original values Ghirardi, Rimini and Weber proposed in 1986.

How sure could they be? Sufficient to rule out the original GRW parameters, and pressing hard on the wider family. Not sufficient to exclude collapse models entirely — the parameters can be pushed to make the effect weaker, at the cost of making the model less motivated.

Why it mattered

This is the part of the measurement debate that is genuinely empirical, and it deserves emphasis on a site about evidence. Copenhagen, many worlds and pilot wave agree on every number and cannot be distinguished by any experiment. Collapse models can, and are being squeezed. If one were confirmed, the measurement problem would be solved by physics rather than by argument.

This is genuinely unresolved

It is worth being plain about the state of play, because a great deal of writing on this topic is not. Every interpretation agrees on every number. There is no experiment that distinguishes Copenhagen from many worlds from pilot wave. They are different accounts of the same predictions, and the predictions have never failed. Except objective collapse, which does differ, and is being tested, and is losing ground. And it is not settled. This is not a case where professionals quietly agree and popular accounts lag behind. Surveys of physicists at foundations conferences return divided results, with no position commanding a majority. Serious people hold incompatible views today, and have for a century. Anyone who tells you the answer is obvious is telling you their opinion. That includes the ones who say it is obviously Copenhagen, and the ones who say it is obviously many worlds. What is settled is that the theory works, to more decimal places than any theory in history, and that nobody can say what it is describing.

Bell on the word "measurement"

John Bell — who appears properly in the next act — wrote a short paper in 1990 called "Against 'Measurement'", arguing that the word should be banished from the foundations of the subject. His objection was that it is hopelessly vague at exactly the point where precision is required: it suggests something is being ascertained about a pre-existing value, and it smuggles in an undefined division between apparatus and system. He proposed that a fundamental theory should be formulated entirely without reference to observers, measurements or information, in terms of what he called "beables" — things that simply are, rather than things that get observed. The paper is unusually blunt for a physics journal and worth reading; it is also a useful corrective to the idea that discomfort with the standard account is the mark of an amateur.

1926Born’s rule introduces probability; the two-rule structure appears immediately.
1932Von Neumann formalises it, and shows the cut can be placed anywhere.
1935Schrödinger’s cat, as a reductio. Also the EPR paper — the subject of Act 7.
1952Bohm revives the pilot-wave theory, showing a deterministic account is possible.
1957Everett proposes dropping Rule 2 altogether.
1970s–80sZeh, Zurek and others develop decoherence.
1986Ghirardi, Rimini and Weber propose physical collapse — a testable alternative.
2020sOriginal GRW parameters excluded experimentally. The debate continues.

Where this act leaves us

Act 6 built a theory that works: one equation, a rule for reading probabilities off it, and a century of experiments it has never failed. It also opened a hole at the centre that has not been closed. But the hole so far is interpretive. Every position agrees on every measurable number, so a hard-headed physicist can decline to care, and many do. That is about to stop being an option. In 1935 — the same year as the cat — Einstein, Podolsky and Rosen published an argument that quantum mechanics must be incomplete: that particles must carry definite properties the theory fails to describe, because the alternative is a kind of instantaneous influence between distant places that Einstein called spooky. For thirty years that was regarded as philosophy, and mostly ignored. Then in 1964 a physicist at CERN, working on it in his spare time and expecting to vindicate Einstein, proved that the question has an experimental answer — that the two positions predict different numbers, and you can go and measure which is right. Somebody did.