Introduction
Quantum Mechanics is the most difficult and complex branch of Physics I came across. To understand, we need a good foundation in various branches of mathematics - probability and statistics, linear algebra, complex variables, and advanced calculus. Personally, I think it also requires the skill to do thought experiments.
Luckily, I am not going to cover aforementioned in this article. I will focus on the simplified concepts of Quantum Mechanics and how they are used in our today’s technologies. And believe it or not, we come in touch with it many times in our daily lives.
Why I Write This
Because I am a nerd 😃. I am a software engineer nowadays, but I studied Physics, and I feel like it is a waste if I don’t share my knowledge. Plus, it’s my blog anyway 😆.
Background
Classical to Quantum
It is easier to touch upon classical mechanics first than explain the advent of quantum mechanics.
Speed limit signs in our neighborhoods, location of a coffee shop that we check in on social media, boxing matches with different weight categories - speed, position, and weight (consequently momentum) - we come across these measurements of classical mechanics in our every day lives. These measurements allow us to predict the states of our observables. If you drive at 80 mph in 50 mph zone, you are very likely to get into an accident. You can predict how long it may take for you to get to a mall from the coffee shop you are currently in. The point is that classical mechanics is a construct that we use to predict / model the behavior of matter or system at macroscopic scale.
Now, let us switch to matter at microscopic scale - we do the same (and also new types) of measurements and try to predict and model their behaviors. That is Quantum Mechanics. Most of the time, we are measuring light and its components, therefore we can also roughly assume that Quantum Mechanics is the study of light. Basically, we shine some kind of light on some matter, collect data and try to predict the behaviors of observables.
Properties of Light
We need to understand light before we dive into Quantum Mechanics. So here I go.
We all know that light is the fastest thing in our universe. At 186,000 miles per second, it can circle the earth 4 times in 1 second. High speed internet is possible because light coupled with signals is set up to travel via optical fibers, and we are able to stream sports matches from the other side of the world. Of course, the stream is not instantaneous due to limitations and interference in hardware, but we get the info within 2-3 seconds, which makes it near-live experience.
One less-known but important property of light is its dual nature of wave and particle. In other words, light travels in straight line like bullets from a bb gun as well as spreads like waves along its path. For example, we sit in a dark room with only a tiny source of light emanating from the door crack. After a few minutes, we can see the surroundings (or at least make out). This is because of the wave nature of light, which touches matter around its main path, making them visible to us.
Light carries energy, i.e. it carries heat - it is very obvious if we think that way 😆. There are different shades of light across a spectrum, and they are dependent on the amount of energy they carry. The frequency of light is directly proportional to its energy. Think of high UV light that tans our skin - it has high frequency, and it is hot! Basically, when UV light shines on our skin, it is syncing our skin atoms to its frequency. After some time, the subatomic particles in our skin atoms gets into some configuration or state that emits tan color. In extreme case, our skin gets burned.
Ultimately, light is the intermediary through which we see matter and its information. For example, the different colors we see are due to different configurations of subatomic particles. Light interacts with them and comes our eyes with such information.
Mathematics
Generally, in Quantum Mechanics, we want to track / predict the behavior of a system and its subatomic particles. In other words, we try to derive functions of each particle or observable and gather those into a system of equations.
To describe a subatomic particle, we use probability distribution functions (more on as to why later). To describe a system of subatomic particles, we use linear algebra which allows us to organize each function and solve at a high level. And finally to describe the evolution of a system with respect to time, we apply partial different equations.
The noteworthy major difference from classical mechanics is that the particles can only take up certain level of states. Consider this example, when a boxer throws in a punch, the impact of his punch can vary by the speed he executes it. In other words, the impact can be let’s say 1 to 5. It also be 1.2, 1.5, 3, (any number in between) etc. In quantum mechanics, those particles can only take up certain numbers, i.e. 1, 2, 3. There is no in-between states they can occupy. Mathematically, their measurements are discrete or quantized.
