## Schrodinger’s Cat Is Stuck In His Box.

How much do you know about Schrodinger’s Cat? Not his actual cat – I do not know if Schrodinger ever owned a moggy of his own, although his casual mental cruelty towards cats would probably mark him as more of a dog person – but his famous thought experiment. You have a cat locked in a box along with a vial of poison gas and a molecule of a radioactive isotope which has a half-life of t. If the isotope decays it will release a radiation particle which breaks the vial of poison gas and kills the cat. If we wait for a time t after the box has been shut then the chances of the isotope decaying or not are exactly 50/50, and consequently the chances of the cat being gassed or not are also exactly 50/50.

To properly explain Schrodinger’s Cat, we have to delve into some of the fundamental concepts of quantum mechanics.

• Schrodinger’s equation is the fundamental equation of quantum mechanics. It describes how the quantum state of a system changes over time.
• The quantum state of the system at a particular time is described by the system’s wave function.
• The quantum state is a series of quantum numbers that describe the quantum attributes of a given system. For example, an electron has four quantum numbers which describe its position in the general hierarchy of electrons making up the shell of an atom along with the electron’s spin.

Schrodinger’s Cat focuses on the wave function of a system. The wave function does not describe an object in terms of discrete values that would accurately describe its quantum state. Instead the wave function (or more correctly the square of the wave function) merely supplies a probability that, at a given time, a particle may be found in a quantum state A. It will also supply a probability that at that same point in time, the particle may be found in quantum state B. This can go on and on for as many quantum states as it is possible for the particle to be found in, but for now we’ll just deal with the two states A and B.

Now, obviously when you look at a particular object it is not occupying states A and B at the same time. It can either be in state A, or state B, but not both. In other words, at some point in between you calculating the wave function and you looking at the object you did something that increased the probability of the object being found in state A (for example) to 100%, and decreased the probability of the object being found in state B – as well as any other state – to zero. This is known as wavefunction collapse, and eighty years after Schrodinger first came up with his equation and his cat it’s still the most debated aspect of quantum physics.

What all physicists agree on is that wavefunction collapse is a real thing. Before we “look” at a quantum object it is indeed “smeared” out into a collection of quantum states and behaves as a wave (hence the wave function describing its behaviour), but after we look at it and collapse the wave function it behaves as a particle, only showing up in one discrete place at a time. This is wave-particle duality, and it can be easily demonstrated by a simple double-slit experiment. The agreement ends there, though, because although we know it happens nobody can figure out what wavefunction collapse actually is.

This is down to Schrodinger having figured out his equations to fit what he observed happening without ever understanding what was happening. As an analogy there was a codebreaker called William Friedman who built a working replica of a Japanese cipher machine based on signal intercepts of its output without ever setting eyes on the machine itself, and it’s the same with Schrodinger’s equation. Schrodinger saw the results quantum mechanics was spitting out and devised an equation that described those results, but while the equation is mathematically robust and reproduces observed results perfectly we have no way of knowing if it’s describing what’s actually going on, or if it’s just a working replica like Friedman’s cipher machine.

^Watch this play if you have the time, it’s pretty good.

The thing with probabilities and quantum states that I have just described is one particular interpretation of the quantum events the Schrodinger equation describes known as the Copenhagen interpretation. The Copenhagen interpretation was – and still is – the predominant interpretation of quantum physics during the period when most of the groundwork was being laid for quantum theory, but there were many prominent scientists who had a big problem with it. Their problem was this: the Copenhagen interpretation does not make any effort to explain why wavefunction collapse happens, or why observing (or measuring) an object precipitates this.

Einstein was amongst those who attacked the Copenhagen interpretation as an incomplete theory because of this, but Copenhagen’s detractors also included Schrodinger himself, who came up with Schrodinger’s Cat as a way of demonstrating wavefunction collapse taken to an absurd extreme. His argument was that according to the Copenhagen interpretation there was no reason why the cat could not exist in a superposition of two states at once, alive and dead, until the box was opened and an outside observer collapsed the cat’s wavefunction. An object as large as a cat cannot (according to our everyday experience) exist in this superposition of states, and so in Schrodinger’s view the Copenhagen interpretation was lacking since it could not adequately account for the privileged status of the act of observation, or even what “observation” and wavefunction collapse actually entailed.

Schrodinger’s Cat and the EPR paradox have stimulated a lot of debate over quantum theory over the years, and while Copenhagen has survived more-or-less intact (although it mutated into the theory of quantum decoherence along the way) there are several competing interpretations of quantum physics that also attempt to explain Schrodinger’s Cat in a satisfactory way. For example, Copenhagen holds that once the wavefunction is collapsed the “dead” cat will wink out of existence and the “alive” cat will only ever remember being alive, while the many-worlds interpretation instead theorises that both dead and alive states persist, albeit in different worlds/universes. There are other interpretations, and lab experiments have further shown that it is sufficient for an automated instrument to measure a particle and subsequently collapse the wavefunction without a human being ever getting involved meaning that the process of observation is a little better defined than it was is Schrodinger’s day. Nevertheless we still don’t know what exactly goes on on the quantum level when something is observed and the wavefunction is collapsed, and I suspect that we never will. All we can do is predict the result: that, when we open the box, the cat has a 50% chance of being alive and a 50% chance of being dead, but not both at the same time.

P.S. — My quantum physics isn’t as good as it could be, which is one of the reasons why I’m reading about it now. If I’ve made any horrible scientific mistakes in this post then do feel free to let me know.

## 2 thoughts on “Schrodinger’s Cat Is Stuck In His Box.”

1. innokenti says:

Thanks for this! It’s pretty much how I’ve understood this bit of Quantum Mechanics, so I am glad that I’ve not missed anything or misunderstood.

Excellent.

2. [...] counterintuitive, and it isn’t helped by many of the popular misconceptions about it such as Schrodinger’s cat. I originally wanted to explain how quantum entanglement and the quantum eraser works because [...]