This is a method used in applied mathematics, physics and engineering.
Let me start by saying that, unlike the other articles in this blog, this post will be quite technical, and it might be challenging for the lay public. Anyway, I invite you to read and ask me questions in the comments if something is unclear.
The Buckingham π theorem can be used to find the “hidden” relation between physical quantities that describe a given phenomenon. It relies on the principle of dimensional homogeneity which basically tell us that we can’t sum apples with melons.
I will use an example to explain the theorem. Let’s consider a pendulum, and suppose that we aim to find its period (i.e. the time that the pendulum takes to complete an oscillation). Our purpose is to find an equation describing how the period depends on the physical quantities involved.
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If you read Part 1 of this article you may wonder: “so, the bosons are like this, fermions like that, so what? What are the consequences of that?” Actually, these particles differ in something very important: while fermions interact with the forces, the bosons mediate the forces!
Newton introduced the idea of “action at a distance” (force at a distance) to formulate gravity. It was an extremely important concept to understand gravity and later electromagnetism. Then, it was discovered that electromagnetism is mediated by the photons (which are bosons), and that the weak and strong forces also have their own mediators which are also bosons. Interestingly, we are still looking for a boson to mediate gravity (the graviton), which constitutes a very important open problem in particle physics (within the Standard Model). In fact, the Standard Model is not compatible with the graviton, because this particle brings some contractions into the model. The most famous theory to solve these (and other) problems is String Theory (which I will talk about in another article).
Have you ever found some strange names which supposedly refer to particles? No idea what do these strange names mean? Sometimes you may even wonder if such small particles actually exist, or if they are only the product of the imagination of some scientists.
In this article I will try to talk most of those strange names that populate the eccentric world of particles. We are yet to uncover much about this world, but we are on the way to explore and conquer it, using increasingly better technology. (First science improves, which allows the technology to improve… In turn, science takes advantage of these new technologies, which open new avenues of exploration! It’s a positive feedback mechanism). I will be brief in my explanations, for otherwise this article would be too long. If you would like any further clarifications, please ask in the comments.
Yes, they do! (However, it is true that there are still some mysteries concerning black holes. Some of them are related to the origin of the universe! Solving these problems may expand our knowledge about the Big Bang towards its first instants, the Planck time, but that’s another “story”.)
In the late 19th century, many physicists thought that their job was almost finished, for well-understood mathematical laws could explain most of the observed physical phenomena. There were only a few things lacking explanation, but physicists thought that they were just details. They believed that soon it would be possible to describe the behavior of any system. (There is the story of a student who asked Lord Kelvin what he would advise him to choose to research in Physics, and Kelvin replied that he should choose another area, for Physics was almost “complete”.)