I. The Cat

1935. A paper. In its fifth section, a cat is put inside a steel chamber.

The arrangement exists on the page. There is a little radioactive material, a detector, and a lethal device linked to the detector. If a decay occurs during the chosen interval, the device operates and the cat dies. If no decay occurs, it lives. A minute event is amplified, step by step, until an animal's life depends on it.

Now let quantum theory describe the material, the apparatus, and the cat together. A difficulty appears. If the wave function of the whole still holds together both connected sequences of results, how do we get from that description to the one outcome we actually encounter?

Two lines can sit beside each other on a page. A cat is not two lines of writing.

Schrödinger called arrangements of this kind quite ridiculous. He was bringing a difficulty of interpretation within sight: what happens when the indefiniteness of a description is treated as the very appearance of the thing described? He was not declaring all microscopic superpositions impossible. Nor was this a proposal to perform an experiment on an actual cat.

Those turns in the argument proved harder to remember than the animal.

A cat. Alive and dead. The person opening the box seems to hold the key that will admit it to reality.

The image travels easily. So does a change in the question. What began as a demand to explain how a theory accounts for outcomes becomes a story about an animal waiting for human eyes to let it live.

The cat has wandered far from the paper. It has become a sign for superposition, although its inventor did not want a sign to bring explanation to a halt.

A person can leave behind a powerful image. He cannot keep every subsequent use of it in his hands.

II. The Man

Erwin Schrödinger. Born in Vienna on August 12, 1887.

His father ran a factory and cared about botany and art. The home contained books, German, and English. Schrödinger went on to the University of Vienna and earned his doctorate in 1910. The physics he entered was still working with Boltzmann's questions. Teaching, books, and research carried that connection.

He took up a post in Zurich in 1921. Around Christmas 1925, he was on holiday in Arosa. The papers on wave mechanics followed during the next year. In its first half he was thirty-eight. Four installments of “Quantization as an Eigenvalue Problem,” together with papers on the relation between two mechanics and the transition from microscopic to macroscopic behavior, are often grouped as six works.

On the page appeared a Greek letter: ψ.

The wave function. In the usual nonrelativistic description, it supplies the probability amplitudes of a quantum state. Those amplitudes allow the probabilities of measurement outcomes to be calculated. Given an initial state and the relevant dynamical conditions, the equation also specifies how the state evolves. Calculating that evolution is not the same as having a definite answer written in advance for each individual measurement.

The work brought him the 1933 Nobel Prize in Physics, shared with Dirac. That year he left Berlin for Oxford. In 1936 he moved to Graz. After Germany's annexation of Austria in 1938, he wrote a letter accommodating himself to the new regime; he was nevertheless dismissed and left the country. Appointments, letters, dismissal, and departures left different records. They do not fit a single straight route through exile.

He arrived in Dublin in 1939. The following year the Dublin Institute for Advanced Studies was established, and he worked there. Until his return to Vienna in 1956, a long stretch of his life finally had a relatively settled address.

He died on January 4, 1961, aged seventy-three.

The equation remained. So did a book about life, philosophical writings, and a life of which the cat has hidden quite a lot.

III. The Floor and the Plan

Throughout this series, Aristotle has been laying a floor.

Distinguish things. Find somewhere an explanation can begin. Stand there a while and look around. Later, Faraday lifts a corner and the field enters the picture; Boltzmann follows a temperature reading down to the movement of countless molecules. The needle stays steady, while underneath it things are far busier than we imagined. A floor can bear our weight and still be worth looking beneath.

Quantum mechanics brings another difficulty.

We are used to drawing a little ball, then tracing its path. Position here, momentum there: make both entries as precise as possible. But in a quantum state, the distributions of position and momentum cannot both be made arbitrarily narrow. Cutting finer marks into an instrument will not make that relation retreat.

A familiar manner of describing things has met a limit. It cannot fill every box as the old plan promised.

Schrödinger's cat carries that plan into ordinary life. We may tolerate abstract symbols when they refer to an atom. With a cat, we want to know how the symbols connect to a breathing body.

That demand does not require us to declare the floor nonexistent. Precisely because we can stand, read instruments, and encounter a result, there is something for the theory to explain.

Heisenberg's uncertainty relation and the cat problem are not identical either. One constrains the widths of quantum distributions. The other asks how a superposition describing the whole connects to a definite outcome. Call both “uncertainty” and the doorplates match. The problems inside have been shut away.

Aristotle can keep laying boards. Setting one down need not be a declaration that everything beneath the bridge has now been drawn.

IV. Schrödinger and Heisenberg

Two sheets of paper. Both are calculating the atom.

Heisenberg's work, developed with Born and Jordan, became matrix mechanics: arrays of numbers, operations whose order cannot casually be reversed. Schrödinger began from de Broglie's matter waves and worked toward differential equations. Waves rise, meet, and combine. They call up things we have seen more readily than a table of numbers does.

What is easier to picture is not necessarily what the thing ultimately is.

With several particles, in particular, a wave function uses the coordinates of all of them. It cannot simply be drawn as a sheet of material rippling through a room like water. The picture can show us a way in, then lead us astray.

In 1926 Schrödinger wrote a paper specifically about the relation between his mechanics and that of Heisenberg, Born, and Jordan. He established connections between their calculations. The same energy values could emerge from different forms of writing. Later formulations made the correspondences more complete; the first argument had a scope of its own and connections still to be worked out.

“I prefer waves” or “I prefer numbers” could not settle the matter. The calculations had to be set beside one another. Did they yield corresponding results, and under what conditions?

Faraday and Maxwell have already shown us something of such a meeting. One person's work is taken up in another language and develops things not previously written down. The likeness lies in the passage between them, not in assigning four men to opposing teams called intuition and reason.

The correspondence between equations and matrices did not make Schrödinger and Heisenberg agree about physical meaning from then on.

The calculations on the pages could meet. Their authors could still ask what the pages were saying.

V. The Cat and the Act of Looking

What is inside the box when you are not looking?

First, consider a coin hidden in my hand. It has already landed. I have not told you which face is up. Your equal probabilities describe what you do not know. That does not exhaust the meaning of quantum superposition.

In an arrangement such as a double-slit experiment, amplitudes for different paths can add and interfere. Arrivals become more likely in some places and less likely in others. That is different from first assigning each event a definite path and then adding two ordinary probabilities. The two calculations leave different patterns.

We cannot reduce superposition to a result already fixed but not yet glimpsed. Nor can we leap to the opposite claim, that a human glance creates the whole of reality.

Looking in an experiment involves apparatus. Light interacts with the system being measured; a detector leaves a record. That record may be there before an experimenter comes back to read it. Remove human attention from the room and you have not thereby removed every physical interaction.

An actual cat breathes and has a body temperature. There is air and light around it. Closing a lid does not disconnect it from its entire environment. Later work on decoherence explains how such connections can make interference between branches extraordinarily difficult to detect locally. We no longer readily obtain the patterns familiar from microscopic experiments.

Suppressing interference, however, does not by itself select the single outcome we experience. Accounts of outcomes include approaches that retain the usual state evolution, approaches that modify the dynamics, and approaches that add to the physical description. Each has assumptions and consequences to explain. “Looking makes it collapse” cannot stand in for all of them.

The cat remains in the question. But no person outside the universe has been given responsibility for its on-off switch.

Leave the laboratory and return to an unopened letter. “Seeing” becomes an ordinary act again.

You open a letter, learn of another person's difficulty, and decide to reply. Your action may alter his circumstances. His reply may alter yours. But he had a life before you broke the seal. Not seeing him did not mean he did not exist. Seeing him at last does not authorize you to fill in everything on his behalf.

What works here is a reply, waiting, an actual offer of help—not a quantum equation. Once a person enters your life, things you could previously leave alone suddenly have a name on the envelope.

VI. What Is Life?

February 1943. Dublin. Schrödinger lectures on life at Trinity College, under the auspices of the Dublin Institute for Advanced Studies. The lectures become What Is Life? the following year.

The question starts very small. How can hereditary material pass certain traits on with considerable stability? Material inside a cell is also exposed to thermal motion. Why is it not easily disrupted? How can it accommodate so many different arrangements?

He proposes an “aperiodic crystal.” Imagine wallpaper with the same design repeating, then a tapestry whose different parts do not repeat. The wallpaper is regular. The tapestry can have structure too, while carrying different content in different places. The comparison comes from his book. It helps a reader hold two requirements together: stability, and a capacity for difference.

He was not the first to investigate genes as material structures. Delbrück and his colleagues appear explicitly in the book. Schrödinger entered a room where people were already working. He brought questions from physics and submitted them to biological facts.

In 1953, three papers on DNA structure appeared together in Nature. Watson and Crick proposed a model; Wilkins, Stokes, and Wilson, and Franklin and Gosling, reported their structural studies. Put the pages together and the double helix is no longer a diagram conjured out of nothing after one book awakened two readers.

The helical backbone is regular; the sequence of bases can vary. “Aperiodic” does not mean the entire molecule lacks any regularity. Nor had Schrödinger already drawn the later structure. A book can make someone want to enter a subject. Beyond that entrance lie experiments, data, models, and many people's work.

The book also discusses life and entropy. An organism sustains its activities by exchanging matter and energy with its environment. Schrödinger used “negative entropy” to help explain this, then responded to colleagues in a note to chapter six, acknowledging that free energy would have been the more suitable concept for a technical audience. Food is not a mysterious medicine called order. The body has not stepped outside thermodynamics.

Boltzmann's question has found another entrance here. The gap Faraday crossed acquires another echo in this series.

A gap can be a passage. Reach across, however, and the other side is not empty. Other hands are already reaching from there.

VII. Consciousness

There is an epilogue at the end of What Is Life? From heredity, matter, and bodies, the discussion turns toward “I.”

Schrödinger considers a unity of consciousness, the relation between the individual self and the whole in Vedantic thought, and Schopenhauer. This is a direction in which he chooses to keep thinking, not a final formula automatically deduced from the experiments in the earlier chapters.

Imagine two people by a window looking at the same tree. One remembers a childhood garden. The other notices only the leaves turning over. The tree can enter a shared description. Adding more pages of information about it does not, by itself, finish describing each person's present experience.

Between describing that tree and describing how this person is seeing it now, there seems to be some distance left. We can keep investigating. We can also listen. As the description grows more detailed, the person looking at the tree is still by the window.

Ramanujan has brought this series close to Indian traditions. Schrödinger also found his way there. Their backgrounds and questions differ. A shared place name cannot write the same answer for them both.

On Emily's moor there is another sentence.

In chapter nine of Wuthering Heights, Catherine tells Nelly, “I am Heathcliff.” She has just discussed marrying Edgar, including her plan to use that marriage to help Heathcliff. Nelly does not simply hear her out and nod. Intimacy, social standing, misunderstanding, and other people's lives crowd the room.

The sentence lets us hear a feeling that refuses to confine the self within the body. It remains a character's speech in a particular situation, not a theorem about consciousness submitted by Emily. Heathcliff and Edgar still have circumstances of their own.

Now turn back to Schrödinger himself. The Dictionary of Irish Biography records his approaching underage girls as a private tutor, grooming one over time and later entering into a sexual relationship with her. It also notes earlier attempts to connect such behavior to his genius. That explanation cannot reduce a girl to a place from which he obtained inspiration.

Believing in a deep connection does not supply another person's consent. With an underage pupil, the adult has a particular responsibility to maintain boundaries. He cannot leave the entire burden of self-protection to the girl and wait for her to say no.

VIII. Seeing and Thinking

Schopenhauer placed one difficulty of thought here: what everyone sees may still not have been thought through. Discovery does not belong only to the first pair of eyes to arrive somewhere.

A sky, a falling apple, water cooling, a cat in a room: how many people have passed them by? Van Gogh stops and picks up a brush. Newton asks about motion. Boltzmann asks how countless molecules produce a steady reading. The familiar thing is still there. A question makes someone stay.

Schrödinger puts a cat into an apparatus on paper, making a difficulty about description harder to pass over. There is imagination in that act, and patience with a question that will not go away. The animal's appeal cannot validate a calculation. A calculation's success cannot silence every question of interpretation.

Turn back to the preface of What Is Life?

He acknowledges that no one can master every field firsthand. An attempt to connect knowledge must use some indirect, incomplete material and risk being wrong. Then he thanks several people who helped him with his English. A native language is like a garment that fits; a change of clothes is not always comfortable. The comparison is his.

A man who can write an equation may still need another person's help to settle a sentence into place.

Reading these acknowledgments, one almost sees another chair drawn up to the pages. Someone will sit down and find a better word for a sentence, or point out an inference that does not yet hold. Across the gap between fields is not only new knowledge. There is also a person willing to take your paper and read it.

See the same thing. Think something different. Then put the thought on the table.

Someone else may take it up. Someone else may point to the place where it has not yet joined.

IX. Superposition

The encounter at the bridge that follows is a work of literary imagination.

Someone else has arrived. He holds a cat, with several sheets of paper tucked under an arm.

The animal shifts. He changes his grip so its hind legs have somewhere to rest. A corner of paper slips out: a sketch of a box. The lid in the drawing is shut. The cat in his arms is sniffing the wind.

Its whiskers stir. It turns its nose the other way, as though the wind is more interesting there.

Socrates stands in the clearing. Plato crouches over his blueprints. Hume attends to a backgammon board. Schopenhauer looks beneath the bridge. Kierkegaard has made his leap. Turing looks at the apple in his hand. Chekhov leans against the railing. Cantor looks at the sky. Copernicus has put down his book and walked away. Sartre paces with his pipe. Beauvoir holds a mirror. Quine has said a quiet sentence.

Tesla listens to a hum. Edison holds an unlit bulb. Heisenberg's position is uncertain. Bohr holds an unsent letter. Tolstoy faces Chekhov with a prescription. Shakespeare is not there: he is the water below the bridge. Spinoza has glass dust on his hands. Aristotle crouches to lay the floor. Faraday lifts a plank. Maxwell stands writing equations.

Joan of Arc carries fire above the bridge. Wilde stands with easy elegance, holding that sentence. Ramanujan has emerged halfway through a gap. Oppenheimer walks on with his burden of ash. Charlotte holds a pen. Emily is out on the moor beyond the bridge; the wind comes from where she is. Boltzmann cradles the stone bearing his equation. Van Gogh is covered in paint, his brushes still dripping color. Dickens stands over the crack with pen and matchbox in his hands. Churchill has the flag on his shoulder and still holds his pen. Roosevelt sits in his wheelchair, the pen with its two inks within reach, a gentle ramp joining the bridge.

Schrödinger takes his place beside Aristotle.

Faraday holds up a corner of the floor. The letters on the stone in Boltzmann’s arms lie quiet. Heisenberg’s position makes Schrödinger look twice. His own papers slip; he presses his elbow against them.

Aristotle sets a board level and runs a hand over the join.

The cat wants to get down. Schrödinger crouches and lets it reach out a paw first. The board bears its weight. It walks along the edge, stops beside a gap, and turns an ear toward the water.

The board gives a faint creak. The cat finds its footing, its tail sweeping above the gap.

Schrödinger gathers the slipping papers. The drawing of the box has not vanished. Neither have the parts of it that remain unexplained.

Kant stands in the distance.

Schrödinger looks up toward Kant, then down at his papers. There is still a stretch of bridge between them. He squares the edges, ready to go over.

Hume moves a piece. Under Dickens's feet, paper makes a faint sound. The cat walks a little way along Roosevelt's ramp, then returns and brushes against Schrödinger's shoe.

He puts the papers in his pocket, freeing both hands, then picks up the cat.

He walks toward Kant. The cat yawns in his arms and rests its head in the crook of his elbow. A few steps on, its small weight begins to relax.

The wind turns a corner of paper in his pocket.

The question is still awake. The cat is asleep.

Notes

^[1] The published cat passage is in §5 of the 1935 paper. Probability amplitudes are not ordinary probabilities; uncertainty, decoherence and definite outcomes are different questions. Observation involves physical interactions, not human eyes granting the world permission to exist.

^[2] Four installments with one title and six related works count different sets of 1926 papers. What Is Life? grew from the 1943 lectures. The aperiodic crystal did not anticipate the complete DNA structure; the three adjacent papers of 1953 retain the contributions of the different research groups.

^[3] The consciousness discussion follows the epilogue of What Is Life?; Catherine’s words follow chapter nine of Wuthering Heights. Conduct involving underage girls is attributed to the signed DIB biography, not excused through genius. The seeing-and-thinking maxim follows traceable attribution to Schopenhauer, not a quotation assigned to Schrödinger.

^[4] Section IX is literary imagination. The cat, planks and Kant are neither physical experiments nor proofs of one another. An unresolved theoretical question does not replace another person’s life or boundaries.

Sources: translation and original publication details · Dictionary of Irish Biography · MacTutor biography · Zurich Central Library archival exhibition · study · §§1–5 to 1–7 · §2–1 · author's preprint · reformatted English text · original pages · novel · quotation-history investigation