Cats In Boxes

The game is called Cat in the Box and applies quantum mechanics principles to a simple card game, making it really interesting and fun to play. I heard about this game from a theoretical physics friend, and we found the theme fun and had a good time trying to figure out the hidden physics principles they included in the rules (very nerdy, I know).

I will not even attempt to try and teach you the game here, there are people far better at that all over the internet. However, to aid your understanding of the parts I talk about, I will describe how a round is played. In a 5-player game, each person gets dealt 9 cards. These cards can be numbered from 1 to 9, and there are 5 cards of each number in the deck. These cards only have a number and don’t have a suit or ‘colour’. To start the ‘trick’, you will play a card and declare the ‘observed’ colour of it, “Five of Blue” You then place your token on that space on the board. Now, no one else can play that same blue 5. The next person has to follow suit or declare that they have no blues. This is where the game gets confusing because since there are no suits on the cards and you instead declare the suit, how can you not be able to follow suit. This is a fair point, but if you play the game, you’ll understand why declaring that you can’t follow suit is really useful. After each person has played one card, the person with the highest value card in the stack wins the trick, and they begin the next round. This repeats until all spaces on the board are filled or a paradox is caused, then scoring begins, the cards are shuffled, re-dealt and another game is played.

Now that you have some understanding of the game let’s talk about quantum mechanics. Wooo!

So, this game makes fun of Schrödinger’s cat thought experiment, which goes like this: A cat is put in a box with a piece of apparatus. This apparatus houses a radioactive isotope of unknown half-life; once the isotope decays, a sensor will trigger the release of a poisonous gas into the box. Schrödinger states that if the box is perfectly sealed, there is no way to tell if the cat is dead or alive until you open it; therefore, it is both simultaneously. This idea feels a bit ridiculous, and upon further reading about the subject, I have found that this is the point.

In 1935, Schrödinger, while talking to Einstein, suggested this thought experiment to point out the flaw in the Copenhagen interpretation of quantum mechanics. The Copenhagen interpretation states that a measurement of a quantum system is only a single state of a superposition of a wave function. Schrödinger and Einstein agreed that this was fundamentally flawed because no attempt was made to suggest what was happening when the system wasn’t directly observed. The cat can’t be both alive and dead at the same time.

The Von Neumann interpretation fixes this issue by stating that there is the need for a conscious observer to ‘collapse the wave function’. Wigner later developed this idea through the ‘Wigner’s friend’ thought experiment, where he asks a friend to open the box and not to reveal whether the cat is dead or not. Now, Wigner’s friend is part of the wave function and has seen the cat both dead and alive. This can be expanded to another observer as Wigner learns of the cat’s state, and Wigner becomes part of the wave function. This can continue indefinitely.

This causes a paradox where the solution feels rather mundane; Wigner states that the Geiger counter-measuring the decay of the radioactive isotope already has collapsed the wave function, and no amount of observing and remeasuring will change that. Roger Carpenter devised an experiment that serves as a proof of concept; the experiment in the box shows one of two colours depending on the outcome, and an observer who is unaware of the meaning behind the colours is shown what the colour result was. This information is relayed to the person who set up this experiment, who then opens the box to reveal the actual state, which, as a result of being observed by the Geiger counter, was the same as the information relayed.

There are many other interpretations of what happens at the quantum level, one of my favourites being the many-world theory, which is expertly described by Sean Carrol in the book ‘Something Deeply Hidden’

This board game is encased in references to multiple quantum mechanic principles. One of the more obvious ones is in direct reference to Schrödinger’s cat, how the cards don’t have a suit and instead need to be ‘observed’ when declaring their suit. This also leads to the colour property given to fundamental particles such as quarks as an additional quantum state, so the Pauli exclusion principle still stands. While the quantum colour property only had three colours, Red, Green, and Blue, the game uses a fourth colour, Yellow, to mirror a standard deck of cards with four suits.

In my eyes, the Pauli exclusion principle (PEP) steals the show of the most utilised quantum principle in this game. The PEP states that, in an atom or molecule, no two identical particles with half-integer spins can occupy the same quantum state. This formed a problem when looking within protons and neutrons at their quarks; these particles have to follow the same PEP, but they seem to share quantum states; this caused the idea of colour to resolve this conflict. This is the reason why, in the game, you cover the number-colour combinations that have been used already.

I’m going to have to stop there. I could easily talk about this for a while longer. I hope you enjoyed hearing my rant. Let me know your thoughts, and feel free to suggest other games or media that have a physics theme to them; maybe I’ll include it in a future post.