What does Schrödinger’s cat tell us about ourselves?
You probably already have a hazy idea about Schrödinger’s cat — the one that is both dead or alive until you open the box — but when was the last time you really thought about it. What if it isn’t a cat and you are in the box? How would you feel to be both dead and alive at the same time?
At the end of last year I wrote a series of posts introducing some of the concepts of quantum mechanics for the purposes of understanding quantum computing. A number of people asked me how the cat relates to the ideas that I outlined so now I am going to attempt to unpack some of the issues around the popular thought experiment, both in terms of how it relates to practical quantum computing, but also about how it relates to our selves and our experience of the world.
What is the cat doing in the box?
Erwin Schrödinger came up with the thought experiment in 1935 now known as Schrödinger’s cat to try to explain the idea of quantum superposition, but in terms that make sense at our scale of the world. In the experiment the cat is put in a box with a radioactive source, a Geiger counter and some method of dispatching the cat, eg poison. If the source decays then the decay is detected by the Geiger counter and the poison is released. The radioactive source has a superposition in which decay or not are equally likely and until the system is observed, the decay has both happened and not happened. This means that the cat is both dead and alive simultaneously. When we open the box then the quantum superposition collapses and we see the cat either dead or alive.
This experiment was proposed to highlight the problems with the idea that a quantum system can be in two opposing states at the same time. With a stretch we can imagine this to be the case when thinking about mysteriously small subatomic particles, but it seems bonkers when we apply the same reasoning to the cat.
What defines a quantum measurement?
A key aspect of the thought experiment is where we draw the line for quantum measurement. My initial instinct was to say that the Geiger counter performs the measurement so the cat is never both dead and alive, but it turns out that the definition of a quantum measurement is not so straightforward. Why do some interactions give rise to quantum entanglement, preserving quantum superposition, and others constitute a measurement, collapsing the waveform? In other words, why do some interactions preserve quantum superposition, and others collapse the waveform. Being able to maintain quantum superposition until we are ready to measure the results is a central pillar of quantum computing, but how do we do one and not the other?
This is a question that physics has yet to answer. Mathematically we characterize a measurement as the collapse of the wave function, but this an aspect of our model of quantum mechanics, designed to explain the results we see in real life. Physicists have yet to identify a physical process where the wave form collapses. There are various competing theories for when the collapse happens or whether it happens at all, but nothing that has been proven to be correct or indeed practical.
A common and useful interpretation of measurement is that the quantum entanglement is spread to a larger system. This is a concept called quantum decoherence where information about the quantum system is lost into the wider environment. This makes sense when you think about the effect that one particle generally has on systems are large as us. However in the case of the cat we have constructed a system in which the state of a single quantum particle can have a large effect on a whole cat.
This is how this interpretation of measurement gives rise to the related idea that large systems (such as a cat) can be in multiple states at once. The collection of theories along these lines is called the Copenhagen interpretation. If true, the Geiger counter itself takes on a superposition of two states: one with decay detected and one without. This in turn puts the cat into a quantum superposition of being both dead and alive. We then reach a problem — when we observe the cat, do we collapse the quantum superposition by our observation or we ourselves take on a superposition of seeing our beloved pet both expired or alive and well at the same time?
The idea that we can be in multiple states at once gives rise to even more wacky ideas. One theory is the many worlds interpretation: every time a particle interacts the universe splits into multiple versions, one where the cat is alive and another where it is dead. We always find ourselves in one version of reality, but in fact both take place in parallel universes. This idea doesn’t clear up quantum mechanics entirely neatly because the particle is still a superposition of waveforms in our universe. Essential for quantum computing, and demonstrable with the double slit experiment, is the idea that a particle can be in a superposition of opposing states, |0⟩ or |1⟩. The multiple world theory needs the universes to diverge at the point where we measure the qubit in a state of either |0⟩ or |1⟩, which is later. Whether or not this is the case, this theory seems somewhat unsatisfactory since no one has been able to prove or disprove it. It is also a little depressing to think that every time I get a bit of good luck there are billions of versions of myself having a really bad time.
Are we in a superposition or not?
Rewinding a little, we don’t know if the cat is in a superposition of being both dead and alive and we also don’t know if we are placed in a similar superposition when we open the box. It seems weird to think that we could be in two states at once, but what if we climbed into the box with the cat?This is an experiment called Wigner’s friend. It was devised in 1961 by Eugene Wigner, much later than Schrödinger’s cat, but involves two people, no animals, and no one has to die. Instead Wigner waits outside a door for his friend to tell him the outcome of some experiment which is equally likely to be |0⟩ or |1⟩. For those uncomfortable with abstract quantum states, lets call those states spin up and spin down. At one point the friend knows the outcome, but Wigner doesn’t. Is the friend in a quantum superposition? It seems unlikely, but from the point of view of Wigner the state of the system, which includes the whole lab containing his friend, is still in a quantum superposition because no observation has been made. This differs from the experience of his friend who thinks the waveform collapsed when she measured some state as being either |0⟩ or |1⟩, up or down. In this way the collapse of a waveform looks like the dissipation of knowledge and two people, or agents, can have a different view of what intuitively feels like same system.
A key part of this thought experiment is that each person can apply quantum mechanics to large systems such as the lab, but they do not include themselves in the system. This allows them to have differing views of the world. Wigner’s friend experiment can be extended in various ways to give rise to a number of contractions as we try to extrapolate quantum uncertainty to real life sized systems such as ourselves. It is something that physicists have been arguing about for 60 years.
How does it feel to be in a superposition?
Many issues with these theories of quantum mechanics draw us back to how we feel about the world. We don’t experience a quantum superposition, even when observing an isolated quantum event, so it seems unlikely to us that the universe works in this way. If we reach a point where we are able to extrapolate an updated version of quantum mechanics to the deterministic macro world then this poses a problem for free will: if everything in the universe is deterministic then we make no decisions and everything we do is predetermined by the current state. I feel like I do have free will so I don’t like that idea.
Roger Penrose, as well as making lovely tiles and contributing enormously to modern physics, was also very concerned with the idea of whether consciousness is computable. He theorized that if consciousness is real then it cannot be computable and there must be something else going on beyond our understanding of the world. He liked the idea that quantum mechanics is also not computable in the classical way with a Turing machine and proposed that perhaps consciousness and free will are linked to the collapse of quantum wave forms in the brain. Subsequently Stuart Hameroff has suggested that structures in our cells called microtubules could be the location of this quantum behaviour and that quantum effects within these structures are what give rise to consciousness.
Am I a quantum computer?
If consciousness is caused by a collapse of the waveform then perhaps we are all quantum computers and with enough qubits we can build an inorganic conscious computer. It is a wild idea and I find it hard to empathize with the feelings of the quantum computers that we have today. Maybe if the human race lasts long enough to build a person-scale quantum computer my decedents will feel differently, but for the moment our ambitions stretch to thousands of qubits which is a very long way away from the quantum complexity of me.
At the moment it is not clear whether we will ever build a quantum computer the size of a person. One of the challenges when building quantum computers is avoiding decoherence where the qubits interact with the wider system and loose their carefully constructed quantum superposition. This is why many implementations need to be super cooled to within a few milli kelvin of absolute zero and even the other implementations of quantum computers are usually very cold indeed. Qubits must be isolated in this way for us to be able to manipulate their state an implement our quantum algorithms with a reasonable degree of accuracy. As soon as qubits interact with the outside world the state of the system no longer is known and the computer stops being useful.
Maybe the quantum computers of future generations will deal with decoherence differently and we will be able to build computers that have the complexity of ourselves without having to isolate every qubit to such a degree. For the moment though, quantum mechanics cannot be applied to large systems and classical mechanics cannot be applied to sub-atomic particles. The next question is where the cross over is. Clearly we are large and a photon is small. Various attempts have been made to entangle the state of single particles with laser beams that have millions of photons and they have been successful, but this is still a far cry from putting a cat or ourselves into a demonstrable quantum superposition.
Where does this leave us?
We obviously have a long way to go to explain quantum measurement and the many paradoxes around it, but for the moment it seems that our model is good enough to explain the world as needed for quantum computing. Physics does not yet tell us whether we are real or what reality is. It does not yet tell us if we have free will and it has nothing to say about the possibility of an afterlife.
