Buckingham π theorem

This is a practical method used in applied mathematics, physics and engineering.

Let me start by stating that this article will be quite technical (unlike the other articles), and might be challenging for the lay public. Anyway, I invite you to read and ask 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 certain phenomenon. It relies on the principle of dimensional homogeneity which basically tell us that we can’t sum apples with melons.

I introduce this theorem here by means of an example. Let’s consider a pendulum, and suppose that we want to find movement’s period. So, we want to find an equation that tell us how the period depends on the physical quantities that affect the period.

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Questions & Suggestions

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You can use the comments to this post to comment and criticize this blog. You can give suggestions (concerning how the blog is managed, about the articles, and even suggest themes that you would like to read about). You can also ask questions. In essence, use this “space” to say whatever you want to say which is unrelated specifically to the articles that have been published (for questions related to published articles, ask instead in the comments of those articles).

If you prefer, you can contact me by email: m.lopes @ exeter.ac.uk.

Marinho Lopes

World of Particles II

Those of you who read Part 1 of this article may wonder: “so, the bosons are like this, fermions like that, and 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 distance” (force at distance) to explain 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 force also have their own mediators which are also bosons. Interestingly, we are still looking for a boson to mediate gravity (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 the String Theory (which I will talk about in another article).

(If you prefer to read this article in Portuguese: O Mundo das Partículas II.)

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World of Particles I

Some of you may already found some strange names which supposedly refer to particles… But what do these strange names mean? Sometimes you may even wonder if such small “things” exist, or if they are only the product of the imagination of some scientists.

In this article I will try to mention most of those strange names that populate the eccentric world of particles. We still don’t know 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 receives these new technologies, which open new avenues of exploration! It’s a positive feedback mechanism). I’ll be brief in my explanations, because otherwise this article would be too long. If you need any further clarification, please ask.

(If you prefer to read this article in Portuguese: O Mundo das Partículas I.)

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Black Holes

First of all, do black holes exist?

Yes, they do! (However, it’s true that there are still some mysteries concerning black holes. Some of them are related to the origin of the universe! Solving these problems will lead our knowledge about the Big Bang towards its first instants, the Planck time, but that’s another “story”.)

(If you prefer to read this article in Portuguese: Buracos Negros.)

Brief definition:

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Forces of Nature

Everybody knows what force is, however the definition you might be thinking of may not coincide with the definition used in Physics, which is a convention “imposed” by Newton.

(Note: if you learnt Physics in school, the first paragraphs may not be new for you, nevertheless, it’s important to find a common ground in order to explain the different known types of forces found in nature.)

(If you prefer to read this article in Portuguese: Forças da Natureza.)

What is the convention?

F = m\times a

F – force, m – mass, a – acceleration.

(This is the Newton’s Second Law.)

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Quantum Mechanics

In the late 19th century, many physicists thought that their job was almost finished, because well-understood 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, and soon it would be possible to describe the behavior of any system. (There is the story of a student who asked Lord Kelvin what would he advise him to choose to study in Physics, and Kelvin replied that he would better choose another area, because Physics was almost complete.)

(If you prefer to read this article in Portuguese: Mecânica Quântica.)

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