Schrödinger’s Cat and Heisenberg’s Cut

No, Schrödinger’s Cat is Not Alive and Dead at the Same Time

There are at least two kinds of Schrödinger’s cat. There is Schrödinger’s cat parody or paradox, short details of which the physicist Erwin Schrödinger published in the German scientific journal Naturwissenschaften in 1935. And there is a Schrödinger’s cat of popular culture. According to the Google Books Ngram Viewer, the latter started to rise to prominence in the 1960s and 70s. The philosopher and historian Robert P. Crease credits science fiction author Ursula Le Guin as the first to introduce Schrödinger’s cat into a work of literary fiction in 1974 (see here), it and really took off in the 80s along with the expanding market for popular science, science fiction, and science fantasy, with the number of references continuing to increase to 2019.

It is not difficult to understand the cat’s cultural appeal. In this version, ‘quantum theory says’ that a cat trapped in a closed box with a radioactive substance and a flask of deadly cyanide becomes suspended in a weird superposition state. It is somehow both alive and dead at the same time. It continues in this state until we lift the lid of the box, and look. At that moment, ‘quantum theory says’ that the wavefunction of the cat collapses, and it is instantaneously projected into one or other of the physical states that make up the superposition. It is alive, or it is dead. The act of looking either kills it, or doesn’t. ‘Le Guin was entranced by the implied uncertainties and appreciated the fantastic nature of Schrödinger’s image’.

Schrödinger’s cat according to the AI image generator provided by Canva, the free-to-use online graphic design tool

What if?

The appeal lies in the ‘what if’ questions the quantum cat-in-a-box scenario provokes. It encourages us to ponder the ramifications of our very human choices. What if we don’t look? If we don’t look can the cat really be said to exist at all? Could we be just like the cat, but trapped in a much bigger box? If we are, who’s looking? Our decision to lift the lid is much like encountering a fork in the road. We choose a path. But what if we had taken the other path? The 1998 movie Sliding Doors delivers two parallel stories, one which unfolds when Helen Quilley (Gwyneth Paltrow) misses her train on the London Underground, and a second which unfolds when she manages to board it. Quilley’s life turns out very differently, depending on whether or not she beats the sliding doors and gets on the train. That such a trivial ‘sliding doors moment’ might profoundly alter the course of the future is deeply unsettling.

There is a related consequence of running with a very literal interpretation of quantum theory and expecting even more heavy lifting from the phrase ‘quantum theory says’. This is the ‘many worlds’ interpretation which offers us a multiverse of possibilities. The multiverse allows a much broader and more sophisticated range of ‘what ifs’ beyond the binary alive/dead-type questions relating to a sliding doors moment. What if the effects of our choices accumulate over time and conspire to change not just our future circumstances, but our personalities? In a multiverse of possibilities, is there a multiplicity of very different versions of you all living very different lives? Such questions are explored to great effect in Blake Crouch’s 2016 novel Dark Matter, for which the final episode of a nine-part TV adaptation dropped this week on Apple TV+.

The Schrödinger’s cat of popular culture feeds our innately human desire for mystery and gives licence for daring flights of imagination which help us to explore what makes us ‘us’. And, remarkably, it does these things in the name of science, because this is what ‘quantum theory says’.

But what does quantum theory say, really?

There is a widespread popular understanding that the scientific theory of quantum mechanics is both mathematically difficult and bafflingly weird. This understanding is justified. The theory emerged in the 1920s as physicists struggled to make sense of the results of experiments on atoms and sub-atomic particles like electrons. Heated debates erupted about how the new theory was meant to be interpreted.

Suppose a physical process leaves an electron in a certain quantum state. By ‘state’, I mean a physical state characterised by certain physical properties. We further suppose that previous experience suggests there are two different states that are equally possible. It doesn’t matter what these are so for simplicity let’s call these states ‘up’ and ‘down’. Quantum theory requires us to describe the electron as a superposition of the two possibilities, a combination of equal proportions of up and down. We perform an experiment to determine what the actual state of the electron is, and we find either up or down. If we repeat the experiment many times, we find we get up or down each with 50% probability. However, we can’t predict with certainty which result we’re going to get in each individual experiment. All we can do is calculate the probability of getting one result or the other from the proportions of each possibility represented in the superposition. We run the experiment, and look to see what we get.

But isn’t this just the same as tossing a ‘fair’ coin, and getting heads or tails with equal probability? We wouldn’t normally choose to describe the coin as being in a superposition of heads and tails as it spins through the air, though in principle there’s nothing to stop us from doing this. We don’t do this because of course we know that both sides of the coin continue to exist unchanged throughout the entire process. So, by the same token, can’t we just assume that each electron exists in one or the other of the two states? We might be ignorant of its actual state before measurement, hence the need to reach for probabilities, but surely the measurement simply tells us which one we had all along? The answer is an unequivocal and rather disturbing ‘no’. Many experiments have been conducted which demonstrate that making this assumption gives predictions which conflict both with quantum theory and with experiment. We can’t do without the superposition, or the probabilities. Quantum theory is indeed weird.

Why are we left to deal only with probabilities? Quantum theory doesn’t say. How does the state change from a superposition of up and down to a mixture of outcomes up or down? Quantum theory doesn’t say. Where in the process of measuring and recording the actual state of the electron does the state change from a superposition of up and down to final states of up or down? Quantum theory doesn’t say. Now, this is not the way in which classical (pre-quantum) physics works, so at what point in the process of measuring and recording the actual state of the electron do we stop applying quantum theory and switch to theories of classical physics? In other words, at what point does the weirdness stop? You guessed it. Quantum theory doesn’t say.

Heisenberg’s cut

The founders of quantum theory nagged away at these problems and arrived at solutions that many deemed satisfactory, but some deemed deeply unsatisfactory. One of the more intractable problems concerns the point at which it ceases to be okay to apply quantum theory and we turn to theories of classical physics instead. This is the point of the quantum-to-classical transition, also known as ‘Heisenberg’s cut’, named for the physicist Werner Heisenberg (of uncertainty principle fame).

How we think about the placement of the cut depends on what we make of quantum theory itself. What does the superposition and, more broadly, the quantum wavefunction, represent? One view, associated with Niels Bohr and known generally as the ‘Copenhagen interpretation’, is that these are calculation devices not to be taken literally. They are purely symbolic. The superposition simply represents what we know about the electron, and we use the algorithms of quantum theory to predict the probabilities for various expected outcomes. So, when we talk about an electron being in a superposition state of up and down, this doesn’t necessarily mean that the electron literally possesses both properties simultaneously. In truth, we don’t know what the state of the electron really is, or how to describe its real physical situation. But if we represent this state as a superposition, we know we will get predictions consistent with experiment.

Heisenberg was a member of Bohr’s group, although in some of his pronouncements he diverged substantially from Bohr’s philosophy. As far as he was concerned, it does not matter where we choose to place the cut. As the concepts of the theory are purely symbolic and deal only with our knowledge of the situation, it makes no difference to the answer if we assume quantum theory applies all the way up to the point at which our distinctly human knowledge is acquired: ‘… there must, within limits, exist complete freedom in choosing the position of the dividing line [the cut]’.

Quite ridiculous cases

Both Albert Einstein and Erwin Schrödinger believed this was unacceptable. They refused to believe that quantum theory could be the last word on the description of physics at the atomic scale. In a series of letters they exchanged through the summer of 1935, they sought to highlight to each other the absurdity of the theory using ‘thought experiments’ in which Heisenberg’s cut is extended to a classical scale. From their exchange, Schrödinger developed his parody of the cat.

‘One can even set up some quite ridiculous cases,’ Schrödinger wrote. Suppose we build a steel chamber. Inside this we place a small quantity of radioactive substance with a ‘half-life’ such that, in one hour, there is a 50% probability that one atom of the substance will decay. Schrödinger wasn’t specific about the nature of the radioactive process (because this isn’t important) but, for the sake of illustration, let’s choose beta decay. In a radioactive beta decay process, a neutron inside the atomic nucleus transmutes into a proton, kicking out a high-speed electron (the beta particle). Now, the chemical identity of a substance depends on the number of protons in its atomic nuclei, so beta decay changes one kind of substance (let’s call this A) into another (B), plus the escaping electron (e). According to quantum theory, after one hour the correct description of the atom in question is a superposition of the state characteristic of A and of a composite state comprised of B and the electron e, which in quantum theory we write as the product B x e.

If the atom decays it triggers a Geiger counter, also placed inside the chamber. So, after one hour, the two possible states of the Geiger counter are not-triggered (G) and triggered (G⁺). Clearly, if the Geiger counter is not triggered this must mean that the atom is still intact. We write this composite state as A x G. Likewise, if the Geiger counter is triggered, the composite state is B x e x G⁺, and we might suppose that the superposition now involves the states A x G and B x e x G⁺.

Schrödinger proposed we also place a ‘diabolical mechanism’ in the chamber such that, if the Geiger counter is triggered, a relay releases a hammer which smashes a small flask of hydrocyanic acid. Let’s keep things reasonably simple by representing the state of this diabolical mechanism using the collective symbol D. The two possible states are then not-triggered (D), and triggered (D⁺), and we might suppose that the superposition now involves the composite states A x G x D and B x e x G⁺ x D⁺.

We can see where this is leading. We have also placed a cat (C) inside the chamber, and the release of the hydrocyanic acid will most certainly kill it (C). We might therefore suppose that the superposition now involves the composite states A x G x D x C and B x e x G⁺ x D⁺ x C. This represents a superposition which consists of the live and dead cat. Schrödinger wrote: ‘The [wavefunction] 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’. This is what we get if we exercise complete freedom in where we place the cut.

Schrödinger’s tongue was firmly in his cheek. He understood that under no circumstances could his cat be considered to be both alive and dead at the same time. He invented his parody as a way to expose the apparent absurdity of quantum theory, not by suggesting that ‘quantum theory says’ that a superposition consisting of a live and dead cat is a real possibility, but by suggesting that what quantum theory doesn’t say can lead logically to an absurd possibility. Einstein replied: ‘… your cat shows that we are in complete agreement’.

An irreversible act of amplification

Perhaps we’re asking too much of quantum theory. We know the theory works extraordinarily well in the quantum domain of atoms and sub-atomic particles. It is right that we apply quantum theory to the radioactive atom and, after an hour, describe the result as a superposition of the states of A and B x e. But a cat is a large-scale classical object. It clearly does not belong in the quantum domain, and there is certainly no observational evidence for quantum-like quirks, such as superposition states, applying to classical objects, no matter how appealing such a scenario might be. So, at what point in the chain of events from the atom to the cat must our description change? Where should we exercise our freedom and place Heisenberg’s cut? Quantum theory doesn’t say, but why should it? We do not expect our theories of classical mechanics to say where they cease to apply, but they clearly cease to apply in the quantum domain. It’s surely up to us to figure this out.

I suspect a good place to look is inside the Geiger counter, especially the element which senses ionising radiation, called the Geiger-Müller tube. In the event that the radioactive atom A decays, the high-speed electron e enters the Geiger-Müller tube, which is filled with low-pressure inert gas, such as helium, neon, or argon, across which a large voltage is applied. If the electron e collides with one or more atoms of inert gas, it may dislodge further electrons from these. The freed electrons are accelerated by the high voltage, and may collide with other inert gas atoms. As more and more electrons are dislodged and accelerated, the result is ‘avalanche multiplication’ and something called Townsend discharge, which significantly increases the electrical conductivity of the gas and is readily detected as an electrical pulse. This can be recorded using a counts display and, if the Geiger counter possesses a small speaker, through an audible click.

We could expect to be able to apply quantum theory to the first collision between the high-speed electron and an atom of inert gas and possibly a few further collisions. But as the avalanche builds, there comes a point where quantum theory is no longer useful, or necessary. Bohr placed the cut – the quantum-to-classical transition – at the point of the ‘irreversible act of amplification’ associated with a measuring device. That we can’t be specific about precisely where or when in this process of amplification we should replace the and of quantum superposition with the or of classical outcomes doesn’t invalidate the conclusion that by the time the counter advances by one or the Geiger counter clicks, all the apparent quantum weirdness has ended. Don’t jump to the further conclusion that this seems to tie everything to ‘measurement’. It doesn’t. The key is not measurement, but scale.

There is today considerable interest in the quantum-to-classical transition, driven largely by efforts to build functioning quantum computers. Avalanche multiplication in semiconductor materials is also fundamentally important in the production of commercial remote sensing devices. We can expect a lot more scrutiny of instances of Bohr’s ‘irreversible act’, and further clarification is a distinct possibility. Quantum theory doesn’t say, but we may yet find an answer.

The fork in the road

Schrödinger ends his 1935 paper with the observation: ‘The simple procedure provided for this … is perhaps after all only a convenient calculational trick, but one that today, as we have seen, has attained influence of unprecedented scope over our basic attitude toward nature’. In other words, we are faced with a choice. We can recognise that quantum theory – with all its extraordinary superpositions – is a purely symbolic framework for predicting the probabilistic outcomes of measurements. It is indeed a calculational trick, not to be taken literally, which allows us some ability to get a handle on an otherwise unfathomable atomic and sub-atomic realm.

Or, we can recognise (with Einstein and Schrödinger) that quantum theory is at the very least incomplete, and deeply unsatisfactory. A theory capable of fathoming the atomic and sub-atomic realm is possible, if only we have the wit to look for it.

This is the fork in the road. Which path will you take?

Jim Baggott is an award-winning science writer and co-author with John Heilbron of Quantum Drama: From the Bohr-Einstein Debate to the Riddle of Entanglement, published by Oxford University Press.