Lesson Plan

The Cat

1927 to 1974, Bell Labs, Oxford, Berlin, Vienna • Vienna matter-wave lab, November 2025 (Pedalino et al, Nature 649): ultracold sodium clusters of 5,000-10,000 atoms placed in spatial quantum superposition; macroscopicity μ=15.5, an order of magnitude beyond any prior matter-wave experiment. • May 15, 2026

Before using this lesson plan: Read the full story or listen to the 5-minute narration (works as a bell-ringer).

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Lesson Plan: The Cat

Subject area

STEM with history and philosophy of science: quantum mechanics, experimental physics, the placebo / observer problem in measurement, and the development of matter-wave interferometry.

Recommended audience

High-school physics (Years 11-13 / Grades 10-12)

First-year undergraduate physics, chemistry, philosophy of science

General STEM enrichment for ages 14+, with some prior exposure to the basic concept of an atom and a wave

Lesson length

60-75 minutes (one period plus optional follow-up).

Learning objectives

By the end of the lesson, students will be able to:

Describe Schrödinger's 1935 cat thought experiment and explain why he intended it as a reductio ad absurdum rather than a serious claim about cats.

Define quantum superposition in plain language and distinguish it from classical "probability of being somewhere."

Explain the concept of decoherence and why it makes quantum effects normally invisible at human scales.

Outline the historical progression of matter-wave interferometry experiments from Davisson-Germer (1927) through C60 (1999) to the Vienna sodium-cluster experiment (2025).

Define macroscopicity (μ) as a figure of merit and interpret what a score of μ = 15.5 implies.

Articulate the technological consequences of matter-wave interferometry: atomic clocks, GPS, inertial navigation, gravity gradiometers, and gravitational-wave detectors.

Key terms

Quantum mechanics, Copenhagen interpretation, Göttingen school

Superposition, wave function, collapse, observation

Reductio ad absurdum, thought experiment, EPR paradox

Decoherence, thermal photons, environmental interaction

de Broglie wavelength, matter wave, wave-particle duality

Diffraction grating, interference pattern, interferometer

Macroscopicity, atomic mass unit (amu, dalton)

Buckminsterfullerene (C60), nanoparticle, cluster

Atomic clock, GPS, inertial navigation, gravity gradiometer

LIGO, Virgo, gravitational wave

Pre-class preparation

A printed copy of the abstract (in English translation) of Schrödinger's 1935 paper.

A simple diagram of a two-slit experiment.

A diagram of the Vienna 2025 three-grating sodium-cluster apparatus.

A timeline 1900-2030 with major matter-wave interferometry milestones blank for students to fill in.

Lesson outline

1. Hook (5 min): a cat in a steel box

Read aloud the cold-open passage. A 48-year-old exiled Austrian physicist, sitting in a borrowed Oxford study in November 1935, decides to bury a theory by inventing a cat. Ask: "If you read this in 1935, would you have believed the cat is half-alive? Why not? And what does that tell you about the theory?"

2. Quantum superposition in plain language (10 min)

The classical world: a coin is either heads or tails. Even before you look, it has a definite value; your ignorance is the only uncertainty.

The quantum world: an electron's position before measurement is genuinely undefined, not just unknown. The mathematics of the wave function says it is "in many places at once" in a sense that has measurable consequences (interference patterns).

The two-slit experiment: a single electron sent through two slits produces an interference pattern over many shots. This is wave behaviour. The electron has interfered with itself, meaning in some real sense it went through both slits.

Schrödinger wrote the equation that describes this in 1926. By 1935 he had decided the interpretation his colleagues were attaching to his own equation was nonsense.

3. The cat thought experiment (10 min)

The apparatus: sealed steel box, radioactive atom, Geiger counter wired to a hammer wired to a flask of hydrocyanic acid, cat. The Copenhagen interpretation says the radioactive atom is in superposition (decayed + not decayed) until observed. Therefore the cat is in superposition (alive + dead).

Schrödinger's argument: this is absurd. Real cats are either alive or dead. Therefore the Copenhagen interpretation must be wrong somewhere.

The thought experiment was developed in correspondence with Einstein. Einstein had described an unstable gunpowder keg in the same logical situation; Schrödinger replaced the keg with a cat because the absurdity is more vivid.

Discussion: students often hear "Schrödinger's cat" used as if the physicist believed it. He emphatically did not. What did he believe, and why did he die in 1961 still believing it?

4. Decoherence and the real-world barrier (10 min)

The cat's problem is decoherence. Any large warm object is in continuous interaction with the environment: air molecules collide with it, thermal photons strike it, its own body radiates infrared. Each interaction is a kind of involuntary measurement.

Decoherence collapses superposition. A cat in a steel box is in contact with ~10^25 air molecules; the superposition lifetime is far shorter than any conceivable measurement.

This is why we don't see quantum effects in everyday life. It's not that the wave function is "small": environmental interaction destroys it very fast for anything macroscopic.

The experimental challenge of the last century: how do you isolate something massive enough that the result is interesting, for long enough to see the wave behaviour?

5. The historical progression (10 min)

1927 Davisson and Germer at Bell Labs scatter electrons off a nickel crystal and observe an interference pattern. Wave behaviour of single electrons confirmed.

1974 Helmut Rauch and colleagues at the Atominstitut Vienna demonstrate the first neutron interferometer. Wave behaviour of single neutrons.

1999 Markus Arndt and Anton Zeilinger's group at Vienna demonstrate wave behaviour of C60 buckyball molecules (60 carbon atoms, 720 amu).

2013 Arndt group reaches molecules of approximately 800 atoms (~10,000 amu).

November 2025 Sebastian Pedalino (Vienna) with Klaus Hornberger (Duisburg-Essen) puts sodium clusters of 5,000-10,000 atoms (>170,000 amu) into spatial superposition. Macroscopicity μ = 15.5, an order of magnitude beyond any prior experiment.

6. Macroscopicity, the figure of merit (5 min)

Macroscopicity (Stefan Nimmrichter and Klaus Hornberger, 2013) is a number that measures how seriously an experiment tests the Copenhagen prediction against alternative theories (e.g., spontaneous collapse models) at the scale of the object.

It is roughly logarithmic in the mass of the object times the duration of the superposition.

An electron in superposition for one nanosecond gets a very small μ. A 10,000-atom cluster in superposition for a hundredth of a second gets μ = 15.5. To match Vienna's μ using only single electrons would require keeping that electron in superposition for nearly 100 million years.

7. What we use this for (10 min)

Atomic clocks rely on matter-wave interference of laser-cooled atoms (typically caesium or rubidium). They are accurate to ~1 part in 10^16, the most accurate measurements humans have ever made.

GPS satellite navigation depends on atomic clocks aboard the GPS satellites to broadcast precision time signals. Without matter-wave interferometry, no smartphone navigation.

Inertial navigation systems on nuclear submarines, intercontinental aircraft, and ICBMs use atom interferometry to measure acceleration and rotation. The submarine sails for months underwater and knows where it is without surfacing.

Gravity gradiometers using atom interferometry are being deployed on satellites to map subsurface water tables, mineral deposits, and tectonic structure.

LIGO and Virgo detect gravitational waves using laser interferometry (a related but distinct technique). The same family of measurement physics.

8. Wrap and assignment (5 min)

Pose: "Schrödinger meant the cat as a knockdown argument against the Copenhagen interpretation. Ninety years later, his thought experiment has become the foundation of GPS, submarine navigation, and gravitational-wave detection. What does this tell you about the difference between a physicist's philosophy and the technology his equations enable?"

Optional homework: write a 500-word essay arguing whether the Vienna 2025 experiment "answers" the philosophical question Schrödinger raised. Use specific terms from the lesson (decoherence, macroscopicity, superposition, collapse).

Discussion questions

Schrödinger said his cat case was "burlesque" or "ridiculous." Why did the rest of the physics community take it seriously? What does this tell you about how scientific thought experiments work in practice?

The 2025 Vienna experiment placed 10,000 atoms in superposition for 1/100 of a second. A real cat has roughly 10^26 atoms. Is the gap between the experiment and the thought experiment a difference of degree or of kind?

Decoherence is sometimes presented as "solving" the measurement problem. Read about it in more detail and decide: does the existence of decoherence answer Schrödinger's worry, or does it just rename the problem?

The technology underlying GPS depends on quantum behaviour that Schrödinger personally believed was an artefact of an incorrect theory. What other examples are there of a scientist's philosophical position being contradicted by the engineering consequences of his own equations?

The Vienna group's stated next benchmark is a 10-million-atom cluster. What would the next-but-one benchmark look like? At what mass does the experiment become indistinguishable from the cat?

The figure of merit μ rewards both mass and duration. Suppose you had a fixed budget. Would you rather make the particle heavier or hold it in superposition longer? Argue both sides.

Extension activities

Calculation: the de Broglie wavelength of a particle is h/p, where h is Planck's constant and p is the momentum. Calculate the de Broglie wavelength of a Vienna sodium cluster (mass 170,000 amu) travelling at 1 m/s. Compare with the de Broglie wavelength of a single electron at the same speed.

Reading exercise: read the English-translation abstract of Schrödinger's 1935 paper. Identify the three places where he uses the word "ridiculous" or "burlesque" or their variants. What does the choice of language tell you about his intent?

Writing assignment: write a 1000-word essay comparing the philosophical positions of Bohr, Einstein and Schrödinger on the interpretation of quantum mechanics. Use the cat thought experiment, the EPR paper (both 1935), and the Bohr-Einstein letters as the central case studies.

Critical reading: read the press release for the Vienna 2025 paper and the Nature paper itself. Identify three claims in the press release that go beyond what the paper actually demonstrates, and three claims that the press release softens or omits.

Time Rhymes