Fun day: Groundhog Day and quantum mechanics

Right, so despite my delayed post yesterday, I still want to seize the day and talk about a fun topic. This time, it’s the turn of quantum mechanics. Nevertheless, instead of trying to explain the advanced math behind it, which I don’t even think I’m qualified to discuss, I will use the movie Groundhog Day to illustrate the superposition principle from quantum mechanics. But before introducing this fantastic film from the 90s, let’s start with the general idea of this weird type of mechanics.

Phil and Phil on Groundhog Day

Quantum mechanics got its name from the term quanta, a concept used to describe a fundamental unit; this is, a primary unit that cannot be divided into further elements. There are different types of quanta, but perhaps the most famous one is that of light, the photon. Of course, nowadays, we are familiar with this concept; however, in the early 20th century, this was a revolutionary idea. The notion of a minimum unit of energy was introduced by Max Plank, who believed that matter could store energy, and such energy was composed of a discrete number of packets of a predefined size, a quantum. Einstein later expanded this idea by proposing the wave-particle duality and got a Nobel price in the process. Under this principle, quanta behave as a wave or as a particle. However, when scientists tried to identify which one was it, the quanta collapsed into one of the two states. And I know this is getting out of hand, so I’ll leave it here. For now, what I want you to remember is that matter and energy can behave both as a wave and as a particle, but when you tried to know which one, it will immediately behave just as one or the other, not both.

Now, quantum mechanics, among other things, propose the idea of superposition, and it is a weird thing because it means that quantum could be experiencing multiples states at the same time. A state could be anything; for example, a light bulb could be in an ON or OFF state. In computer sciences, a state could be a voltage level or a piece of information such as 1 or 0, and the unit storing this value is called a bit. In quantum mechanics, the ON or OFF information is stored in a unit called a qubit. But unlike its digital counterparts, a qubit can be on and off at the same time. These states are equivalent to the notion of behaving as a wave or as a particle. The principle of superposition is complicated to conceive. Even Schrödinger tried to ridicule this idea in his famous thought experiment with the cat in a box, both dead and alive at the same time. However, I believe the events occurring on Punxsutawney, Pennsylvania during Groundhog Day could help us understand quantum superposition.

I hate to spoil movies, so I’ll try to reveal as little as possible, but If you haven’t seen this gem in the past 27 years, well, that’s on you. Groundhog Day starts by introducing Phil Connors, a local TV weatherman that travels to Punxsutawney to report on the local celebrity, a weather-predicting groundhog also called Phil. Now, the story begins when Phil, the weatherman, gets trapped in a time-loop, reliving Groundhog Day over and over again. During his misfortunes, we see him do all kind of things, going crazy after noticing the time loop, committing some mild vandalism, getting to know members of the community, and even learning new skills. Then, after countless iterations, Phil manages to do the right things and can break the look, finally moving to the next day. Now, as far as I am aware, I don’t think the writers ever intended to use the movie to explain quantum mechanics, but there are some distinct parallels.

In the movie, there isn’t any apparent reason why the loop started, but we can deduce that it happens because Phil began to feel uncertain about his life. Something similar happens to quanta; when we are not sure what state they are in, they can be in several states at the same time. Now, humans can not perceive the effects of quantum mechanics, since this only occurs at sub-atomic scales; this means that we cannot appreciate the superposition state. In the movie, the various states (ways to spend Groundhog Day) are shown to us linearly; this is one after the other. However, if we consider that everything is happening on the same day, we can equate this to a superposition state, when everything, every iteration of the same day occurs at the same time.

Re-arranging the story to the expected occurence of superposition

In the movie, we can see two or three dozen versions of the same day, but it is implied that there were many more versions that happened off-screen. Similarly, quanta could be in infinite positions at the same time. Finally, quanta collapse into one single state once we are certain of the outcome we are looking for. This situation is also depicted in the movie, as Phil wakes up the next day, certain of the type of person he wants to be. We can deduce this is the case from all the dedication and commitment the character puts into the outcome of the last version of the Groundhog Day we get to see.

And there you have it. These are the reasons why I believe Groundhog Day is an excellent example of the principle of superposition or at least one that we can relate to. I could try to stretch this explanation a little further to describe the principle of entanglement. Suggesting that every for every “good day” that Phil had, he should also have a proportional amount of “bad days”, but we don’t get to see this principle accurately depicted. In any case, as I mention, I don’t think the creators intended this movie to be a 101 on quantum mechanics.

In all seriousness, quantum superposition is a very relevant concept in real life. It underpins one of the main advantages that quantum computers possess over traditional systems. Imagine we could use the superposition effect to try to guess your email password, virtually trying millions of possibilities at the same time. Superposition could also help us understand the world better. With our current systems, we are only able to simulate a few thousand atoms at the same time. Still, with quantum computers, we could simulate cells or simple living organisms, facilitating the discovery of life-saving drugs or treatments. However, it is good to carry out this type of exercises to try to grasp such counterintuitive concepts, and I hope to find another great example. For now, I’ll leave here, and I’ll come back tomorrow with a new topic for the week.

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