I know all you coffee enthusiasts have always wanted to know the exact mathematical description of your cup of coffee when you swirl it with a spoon! Here I introduce the principles of fluid mechanics so that I can answer this burning question of yours. Approx 15 min read, or just 5 mins if you want to see the solution, without the derivation of the governing equations of fluids.
A bit of an update on where I have been this past year and why there have been no posts since March. Approx. 5 min read.
One of my favourite theories ever, classical electrodynamics deserves as high a place on this blog as any other fundamental physics. I'm just going to be giving an overview of Maxwell's equations. In this post I introduce the electric field and derive some of its properties, and finally give a simple use of Maxwell's equations to solve a problem.
Approx 20 min read
In today's post, we're finding out what special relativity is and in good form; I introduce the notion of a metric tensor, and do my best to generalize Euclidean geometry to Minkowski space, and discuss the fantastic way of looking at special relativity as a bunch of new symmetries. This also happens to be my longest post ever. Approx 25 min read, probably.
Taking a little time out of the day to tell you about one of my favourite things: symmetries. Approx 5 min read.
You may have heard of the Pauli exclusion principle. It's supposedly one of the most important things in the universe, and after reading this post you may see why, and more improtantly where it comes from. If that fact alone doesn't tempt you, there's also a few cheeky paragraphs about the Dirac equation, and a meme. Approx. 5:47.36671 minute read.
This post will be wrapping up our adventures through Hilbert space for the time being, and in grand fashion. This is a very dense post, with a lot of incredible physics. As a result it is also a bit longer than others. But if you have an emptiness inside you that is screaming for beauty, symmetry, geometry, abstraction and concreteness at the same time, put everything you're doing aside and read this one. Approx 15-20 min read.
Topology is one of the coolest things I've ever studied and in this post, I'm going to tell you about one of the core concepts of the subject - that of the fundamental group. I'll be talking about loops and transformations a lot, but we do have a bit of ground to cover. Luckily for you, any closed subset of the reals is compact, so we can find a finite subcover of this ground, which is precisely what I've tried to do here. It ain't a party without a sick as proof though, but party animal that I am, I'm bringing the goods. And it's gonna be fun. Approx 15-25 min read.
Did you ever just lie in bed wondering why you can't actually know position and momentum simultaneously? Spent hours awake wondering what the structural relation between the position and momentum representations of abstract quantum states are? Well, here I am to finally put you to sleep. Approx 10 min. read.
When quantum mechanics first came around, the race was on to find out just what the hell it meant, and how to do it. Dirac won that race, and today we all speak his language. In this post, we're laying down the foundations of the Dirac notation, and consequently, the foundations of everything in quantum mechanics. Approx 15 min read.
We're finally wrapping it up with classical mechanics, and in true spirit, we need to finish with a bang. Poisson brackets, Phase space, and Liouville's theorem satisfy this prerequisite with flying colours if you ask me. Approx 15 min read.
Hamilton's equations are two stunning statements of symmetry between position and momentum. Due to their beauty, and some of the things coming up in the next few posts, I have decided that I need to tell you about them.
Approx. 10 min read.
A little maths once again. This is supposedly topology or differential geometry.. one of the two. Maybe both? I don't know. All I know is, it is very pretty.
Approx 15-20 min read.
Have you ever wondered what would happen if you took Schrodinger's Cat and squished it into an unimaginably, horrendously, pitifully, and inescapably tiny box? Well, look no further, and strap yourselves in ladies and gentlemen, because today's post answers that question and motivates the need for quantum field theory.
I'd say, 5-10 minute read probably.
[Spoiler: the cat will die, whether the box is poisoned or not.]
In this post you will find out about one of the coolest things in all of physics. From a mathematical standpoint it's not really that big of a deal, but from a physical perspective it absolutely kicks ass. This is a slightly long post with a lot of maths, but if you can get through it all and understand it, it will have been worth your while! Approx. 20-25 min read depending on how much maths you skip through or follow.
I want to tell you about one of my favourite theorems. It is a theorem in the subject of real analysis, which deals with analyzing the properties of real numbers, their sequences, series, and functions. Real analysis is a very pure subject and is very fun if you have an appreciation for aesthetic and enjoy mental gymnastics. This proof is typically seen seen at the beginning of a lot of analysis classes and I think it is very pretty, so I will show you it. Approx. 5 min read. But just like all other maths, if you want to understand it, that means an extra 3 hours thinking time, if you are so inclined.
I'll show you how easy physics becomes when you possess the Euler-Lagrange equation, and you will see first hand just how fundamental it truly is.
Not only that, but I will explain to you a very interesting phenomenon that you no doubt are aware of yourself but perhaps don't fully understand, as well as show you some very nice double pendulum systems in gif form! There's a lot of maths but also some nice summaries if you don't know maths. Approx. 10 min read.
Today I will show you a strikingly beautiful principle of physics (which just so happens to be the bedrock of all laws, from Newton's second, to string theory) - the principle of least action, and one of my favourite equations of all time, the Euler-Lagrange equation. Approx. 10 min read.
A little about one of the most successful equations of all time, Newton's second law, and how it works. You'll also see an introduction to the one of the most fundamental and beautiful ideas in all of physics - symmetries, which I will talk about a lot down the track. Approx. 5 min read.