When most fish hear the words quantum physics or quantum mechanics, they try to swim away because they didn’t like math when they were in SCHOOL!

…Well. Physics can be accessed conceptually and mathematically, and many fish avoid studying the math in an attempt to save themselves from a headache; in your studies of physics you’ll find that math is unavoidable, but don’t worry! I’ll try to skip over the symbols as much as I can while I introduce quantum mechanics (QM) to you. 

First, let us discuss complex numbers, likely known to you as imaginary numbers. Many make fun of this because why even bother with something imaginary, but unfortunately it’s very real, and something you will come across often in QM. In grade school, you were introduced to a linear number line that went from 0 up to infinity. You later found out that there are numbers smaller than 0, negative numbers, that extend the number line, have magnitude, and the ability to be added, multiplied, and divided with other numbers. Then came coordinate planes with the y and z axes defining 3D space. 

Complex numbers exist on a plane known as the complex plane, and come from square-rooting a negative number, which arguably has no value since no two of the same numbers can be multiplied to result in a negative number (negative times negative = positive, positive times positive = positive). Negative numbers can undergo other operations though, so mathematicians’ solution was to introduce a symbol to represent the confusion, the number i. i is also represented by a circle...kind of.

Enough math for now–let’s divert back to physics. The vagueness of complex numbers reminds me much of the way measurements are approached in QM. In classical mechanics, we can calculate the location of a particle,x, and where it will be in t amount of time, etc etc. Everything is very exact and probability is 100%. In QM, if I find a particle at point A, do I know where it was before that? Was it at A, or somewhere close by? If something is not measured, does it exist? These are questions asked when QM was born–you can start thinking of measuring as creating a result, not finding one. 

We can define quantum mechanics as the study of the behaviour of energy and momentum packets (bursts of quanta, the smallest possible amount of something), where we look at particles on atomic and subatomic scales. These particles have energy so that they can satisfy Heinsenburg’s Uncertainty Principle, which states that the position and momentum of a particle can never be known at the same time. 

QM ultimately came to be because classical mechanics failed. Neils Bohr was a physicist who introduced the planetary model of the atom, the classic one we are all familiar with where the nucleus is in the middle and electrons orbit in circles around it. Bohr didn’t consider two things. One, electrons have negative charges which repel each other, so the electrons’ circular orbits don’t make sense–they would be wonky from avoiding each other when they got close. Second, if an electron is orbiting the nucleus, it is bound to lose energy and eventually crash into it. Since we fish exist, this clearly doesn’t happen. Everyone sighed…what now?

Light, for a while, was thought to (only) be a wave, rays that extend and extend throughout the Universe. Albert Einstein came along and said that light travels in particles called photons. If a wave could behave like a particle, then particles like electrons should be able to behave like waves. The Double Slit Experiment proved exactly that. I’ll attach some pictures so that you can visualize it better.

You see the two slits? When energy passes through it, it ends up bouncing against each other like light does, causing this wave pattern to form. When we try to observe this, it stops acting like a wave and forms just two lines, like a particle would. Hmm…fishy. It's quantum behaviour disappears. Physicist Erwin Schrodinger, with the idea that particles can behave like waves, believed the behaviour of each particle can be described with a function, which he named the wave function, denoted by Ψ (psi, pronounced as 'sigh'). 

With this, let’s go back to the atom. The quantum mechanical model of the atom accounted for repulsion by creating clouds (also known as orbitals, though they don't look like it) where the electron is thought to exist. We don’t know where though–the probability that it’s inside the orbital is 100%, but where exactly is another story. The wave function provides the probability that the electron is at x location. 

Recall Issac Newton, another physicist (there’s a lot of them). His second law, F=ma, is super duper important to classical mechanics. Schrodinger wanted to create something similar that showed how the wave function evolves over time. The wave function is set equal to 1, to show there is a 100% probability that the particle exists in the system. He adds an i to his equation, to keep the probability from increasing to infinity or decaying into nothing (recall, circular). 

If I continue, we really will get into math, which I’m not sure if you want. If you do though, I suggest reading this. It may seem like a lot, but QM is a lot! It took centuries of science to reach QM–don’t feel bad for not getting it quickly. I DEFINITELY did not. Here's the Schrodinger Equation if you’re interested in seeing what it looks like:

Most fish never get to study QM. It’s not the end of the world nor the key to happiness, but I have to say, physics has matured and humbled me in a way I never expected when I began my studies. That’s what you get for studying the branch of science that aims to explain all energy, movement, matter, space, and time, I guess!

One thing before we finish up–besides the common joke about particles acting differently when you look at them versus when you aren’t observing them, you may have heard of Schrodinger’s Cat. There is an idea in physics that something can exist in two states at the same time–this is called superposition. The cat is simultaneously alive, dead, and wanted dead and alive.

That’s enough for now! Hopefully I didn’t get anything wrong…whoops. Here is the Wiki page for QM just in case I did :P

-Val