Quantum mechanics · 1935 · decoherence · what opening the box can tell

The Cat Was an Objection

Schrödinger's cat is usually told as physics saying a cat can be alive and dead at once. Schrödinger built it in 1935 to say something else: that the quantum description cannot simply be read as a blurred picture of how things really are. Here are two sealed boxes. One holds the cat the way the equations describe it, both ways at once; in the other the matter was settled when the box was closed. Open them as often as you like and you will not find out which is which. Only an interference test can, and one stray molecule that carries away a record of the outcome is enough to erase it.

What Schrödinger wrote

The cat is one paragraph in a long three-part essay, “Die gegenwärtige Situation in der Quantenmechanik” (The present situation in quantum mechanics), printed in Die Naturwissenschaften in November and December 1935. Earlier that year Einstein, Podolsky and Rosen had published “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, and Schrödinger says in a footnote that it prompted his essay. In John D. Trimmer's 1980 English translation the paragraph reads:

“One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The ψ-function of the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.”

E. Schrödinger, 1935, section 5, “Are the Variables Really Blurred?”, tr. J. D. Trimmer (1980), p. 328

The next paragraph says what the case is for:

“It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a ‘blurred model’ for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.”

the same, p. 328

Read in its place, the cat is the end of an argument. The section asks whether the quantities of quantum mechanics are really blurred, the way the ψ-function, the wavefunction, seems to say. Inside the nucleus, he says, “blurring doesn't bother us”. The cat carries the same smearing up to something you can see, and when you look, you never see a smeared cat. So the ψ-function cannot be read naively as a fuzzy photograph of a fuzzy world. The section after it puts it in one line: “In Sect. 5. we saw that the indeterminacy is not even an actual blurring, for there are always cases where an easily executed observation provides the missing knowledge.” Where the translation says “quite ridiculous cases”, the German, as German Wikipedia quotes it, says “ganz burleske Fälle”.

The cat had a parent. On 8 August 1935 Einstein had written to Schrödinger about a charge of gunpowder that could go off by itself, with an average life of a year, and said the ψ-function would then describe “a sort of blend of not-yet and already-exploded systems”, adding: “Through no art of interpretation can this psi-function be turned into an adequate description of a real state of affairs; in reality there is no intermediary between exploded and not-exploded.” Schrödinger answered with the cat. Einstein replied: “Your cat shows that we are in complete agreement.” Fifteen years later, writing to Schrödinger again, Einstein described the box as holding a “charge of gun powder” and the cat, his own 1935 example folded into Schrödinger's.

So the famous image was built by two people who agreed, in Einstein's words in that reply, that “A ψ-function that contains the living as well as the dead cat just cannot be taken as a description of the real state of affairs.” It was never a claim that cats are ever half dead. What the page does next is take the description at its word and ask a sharper question: if the box really were in the state the ψ-function gives it, could anyone tell?

Two sealed boxes

Model the box the way Schrödinger built it: an atom and a chain of parts that copy its fate, a counter, a hammer, a flask and the cat. Each part has two states, “nothing happened” and “it happened”. Then fill boxes in two ways, with the same odds.

A both box holds what the ψ-function says: one state in which every part is “nothing happened” and every part is “it happened”, superposed, with amplitudes whose squares are the two chances. A decided box was settled when it was sealed: a coin weighted by those same chances was tossed, and the box holds one outcome or the other, though you don't know which. Every real experiment of this kind has to be repeated on many freshly prepared copies, and so does this one: each time you open a box, it is a new box filled the same way.

Below, one box of each kind has been sealed and labelled L and R at random. Your job is to say which one is the “both” box.

Why opening can't tell

Open as many as you like. The two tallies drift toward the same share of dead cats, and the difference between them is the scatter of tossed coins, nothing more. At one hour, both boxes come up dead half the time. That is not bad luck; it is arithmetic. Everything a box can show you is in a small table of numbers, the density matrix, and for these boxes only three of them matter: the chance that nothing happened, the chance that it did, and a third number, the coherence, which ties the two together. In a “both” box at one hour the coherence is 0.5; in a “decided” box it is 0. Opening a box asks each part which state it is in, and the answer's odds depend only on the first two numbers. The verifier checks this the long way, in a simulation of the parts written separately from this page: for one, three and five parts, every possible pattern of answers comes out with the same probability from both boxes, to twelve decimal places.

So the question “is the cat both alive and dead?” cannot be settled by looking at the cat. Opening the box is a measurement guaranteed not to see the difference.

The question that can

There is a measurement that sees the coherence. It is the kind real laboratories use on their own small cats. Turn a dial that shifts the phase of every part by the same angle, then ask each part a different question, not “nothing or it happened?” but one whose two answers are the two states added and subtracted, and multiply all the answers (each is +1 or −1) together. Repeat on many fresh boxes and average. Chao Song and colleagues, who made such states with superconducting circuits in 2019, write the average as ⟨P(γ)⟩ = 2 |ρ_{00...0, 11...1}| cos(Nγ + ϕ), where ρ_{00...0, 11...1} is exactly the coherence, N is the number of parts and γ is the dial. A “both” box swings as the dial turns, N times per turn; a “decided” box averages zero at every setting. Press run the interference test on each box above and look for the swing. With the box's five parts and no strays, the “both” box swings from +1 to −1 five times in each turn of the dial, and the decided box sits at zero, apart from a scatter of about 0.1 at 100 shots a point. Push the parts to 20 and the swing gets faster, which is what Omran and colleagues saw with 20 atoms in 2019: “the frequency of the measured parity oscillations grows linearly with N”.

Notice what the test demands. Every part must be brought back and asked: the atom, the counter, the hammer, the flask and the cat, and anything else that ever carried a trace of what happened. Tick one part escaped above and run the test again.

One bounce

That box is at the heart of why this test has never been run on anything the size of a cat. A part that gets away cannot be asked, and the test on what remains reads exactly zero. It is worse than that: the verifier checks that once one part is lost, the remaining parts of a “both” box are identical to a “decided” box under every measurement there is, not only this one. The same happens if anything outside the box picks up a record of the outcome. Model a stray particle that bounces off the box and leaves in one of two states depending on what happened inside. If its two states can be told apart perfectly, one bounce is enough: the coherence is gone, and again no measurement on the box can tell it from a decided one. If they overlap, each bounce multiplies what is left of the coherence by the overlap.

Strays that learn almost nothing still add up. With an overlap of 0.99, a stray that can barely tell the two outcomes apart, 100 strays leave 0.366 of the fringe, and it halves every 69 strays. In the box game, set the strays to 300 at 0.99 and try to pick the “both” box: the swing is down to a twentieth of its height, smaller than the scatter at 100 shots a point, and you are guessing. Raise the shots and you can win again, for a while; the next few hundred strays take that away too.

This process is called decoherence. Its key idea was first put down by H. Dieter Zeh in 1970, and it was developed in the 1980s, chiefly by Zurek, with the first estimates of how fast it happens worked out by Joos and Zeh and by Zurek. Nothing in it is added to quantum mechanics: the strays obey the same equations as the cat. What it shows is that the information that would let anyone tell “both” from “decided” leaks into the surroundings, fast, and cannot practically be gathered back.

How fast, for something big

How fast is fast? Zurek gave a rough estimate for an object put in two places at once, a distance Δx apart, in surroundings at temperature T. The coherence between the two places dies in (λ_T/Δx)² of the time the object would take to settle back to rest, where λ_T = ħ/√(2Mk_BT) is its thermal de Broglie wavelength, a length that shrinks as the mass M grows. Pick a body and a separation:

For his own example, a gram at room temperature in two places a centimetre apart, the formula gives a thermal wavelength of 3.7 × 10⁻²³ metres and a ratio of 1.3 × 10⁻⁴¹; Zurek states it as “approximately 10⁴⁰ times faster than relaxation”. He adds that these estimates “should be taken with a grain of salt”: the simple model behind them often does not hold, and the rate cannot really be faster than the rate at which the superposition was made in the first place. A cat's alive and dead are not two positions, so the formula does not describe Schrödinger's box. It gives the scale. At 300 K a 4 kg cat has a thermal wavelength of 5.8 × 10⁻²⁵ metres; an electron's is 1.2 × 10⁻⁹ metres, about 2 × 10¹⁵ times longer.

The cats that have been made

Physicists now make Schrödinger cats on purpose, small ones, and watch them decohere. The name is now used for a superposition of two clearly different states of a system of many parts. A few, with what each paper itself reports:

None is a cat, and nothing in them suggests anyone will ever do this to one: a cat breathes, radiates heat and scatters light, and every one of those is a stray. But every one of these experiments shows the coherence the way the box game does, by a test that is not opening.

What this does not settle

Decoherence explains why you will never see the swing for a real cat, and why, for anyone who cannot round up every stray, the box behaves in every respect like one whose fate was settled. It does not say which outcome happens, or why there is an outcome at all. Maximilian Schlosshauer, in a 2019 review, is flat about it: “The measurement problem as just defined cannot be solved by decoherence.” Guido Bacciagaluppi puts the gap in one sentence: decoherence “does explain why we do not observe superpositions of measurement results, it does not explain why we do observe measurement results in the first place.” What fills that gap depends on the interpretation: Bohm's, Everett's, the collapse theories, versions of Copenhagen. Some of those differences can be tested. Collapse theories modify the Schrödinger equation itself, and interference with ever heavier molecules, as Fein and colleagues write, places “more stringent bounds” on them.

So the cat still does the job Schrödinger and Einstein gave it, nearly a century on. It is not evidence that a cat can be alive and dead. It is a question about what the ψ-function is, the one they were asking, and this page cannot answer it. What it can show is narrower and certain: opening the box was never the test, and the test that would work is undone by a single molecule that carries the outcome away.

A note on two dates. The day Schrödinger first described the cat to Einstein is given two ways. The Stanford Encyclopedia of Philosophy's entry on the EPR argument says his reply was dated 19 September 1935; David Kaiser, citing Arthur Fine's The Shaky Game, dates it 19 August and dates Einstein's “Your cat shows” answer 4 September, which a letter of 19 September could not have prompted. August is the better supported, but neither book was read here, so the page says only that Schrödinger answered. Nor was the original German of the essay read: it is behind a paywall, and the German quoted above is German Wikipedia's transcription.

Sources

1. E. Schrödinger, “Die gegenwärtige Situation in der Quantenmechanik”, Die Naturwissenschaften 23 (1935) 807 to 812, 823 to 828, 844 to 849. doi:10.1007/BF01491891 (part 1, November 1935), BF01491914, BF01491987. Not read in the original; the German phrase is from German Wikipedia's “Schrödingers Katze”, fetched 11 October 2026.
2. J. D. Trimmer, “The Present Situation in Quantum Mechanics: A Translation of Schrödinger's ‘Cat Paradox’ Paper”, Proceedings of the American Philosophical Society 124 (1980) 323 to 338, sections 5 and 6, pp. 327 to 328 (JSTOR 986572; read in a scan hosted at unicamp.br, checked against the page images).
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