Illustrating the Higgs mechanism, Part 2

Part 1 is a prerequisite to this post.

Global gauge symmetry

Previously, I talked about the “direction” of the Higgs field, but what does that even mean? It doesn’t refer to a direction in space. There’s hardly any meaning to the direction at all. In fact, I could go ahead and change all the directions and it wouldn’t matter at all.

Two rows of circles. In the top row, labeled A, the Higgs field is pointing to the upper right. In the bottom row, labeled B, the Higgs field is pointing down.Figure 6.
[Read more…]

Origami: Snub Cube

IMG_0679 (small)
Snub Cube with Windows, from Unit Origami: Multidimensional Transformations by Tomoko Fuse.

The snub cube is one of those fancy Archimedean solids, for when you’re bored with the Platonic solids.  Each vertex lies at the intersection of one square and four triangles.  All together, there are 24 vertices, 60 edges, 32 triangular faces, and 6 square faces.  And can you imagine, it’s only made of 12 sheets of paper? [Read more…]

Illustrating the Higgs mechanism, Part 1

Most people are probably aware of the Higgs boson, long predicted, and recently observed by the Large Hadron Collider in 2012. The Higgs boson is was predicted by the Higgs mechanism, which is a theory that endows certain particles with mass.

Now, you might be wondering why I, a researcher in superconductivity, am talking about particle physics. In fact, the Higgs mechanism started out as a theory of superconductivity, and was soon imported to particle physics. I leave the historical details to your encyclopedia of choice.

To understand the superconductor/particle physics connection, consider the question: For which particles does the Higgs mechanism generate mass?

In particle physics, the Higgs mechanism generates mass for the W and Z particles, the mediators of the Weak force. The reason it’s called the Weak force is because it’s so short range, which is a consequence of the W and Z having mass. To my understanding, other elementary particles derive their mass from their interaction with the Weak force. (not quite correct, although link is correct.  See comments for details)

Transcript: There are four fundamental forces between particles: (1) Gravity, which obeys this inverse square law: F= G m1 m2 over d squared. (2) Electromagnetism, which obeys this inverse-square law: F = k q1 q2 over d squared and also Maxwell's equations (3) The Strong nuclear force, which obeys, uh... well, umm... it holds protons and neutrons together. It's strong. And (4) the Weak force. It [mumble mumble] radioactive decay [mumble mumble]--And those are the four fundamental forces!
From xkcd. Hover text: “Of these four forces, there’s one we don’t really understand.” “Is it the weak force or the strong–” “It’s gravity.” Accurate.

In superconductors, the Higgs mechanism generates mass for the electromagnetic field. This causes the electromagnetic field to be short range. Thus, if you apply an external electric or magnetic field, it will not penetrate into a superconductor of any appreciable size. The zero magnetic field is called the Meissner effect; the zero electric field leads to zero resistance current.

That’s the short explanation of what the Higgs mechanism does, but I wanted to explain how it works. Also, I wanted to try out this new doodling software…
[Read more…]

Love is chemicals, and I am grateful

The problem with a naturalistic world view is that everything is just a bunch of chemicals bouncing around, and nothing means anything. The only way to produce any meaning is if there are a few supernatural spirits bouncing around too.  You know, so they can moan about the meaning of life, the nature consciousness, and objective morality.  Or something like that.

But let’s be real. Chemicals are not “just” chemicals. Quarks and leptons can be quarks and leptons, while at the same time forming chemical structures. Likewise, a chemical can be a chemical, while at the same time forming a person. When we say that love is “just” chemicals, it is not a statement of fact, it is an aesthetic.

A common criticism of naturalism is that it forces us into the “just chemicals” aesthetic. But that’s just one of many aesthetics available to us. If you want to say “love is free yet binds us“, I don’t entirely know what that means, but it seems consistent with reality too. Aesthetics are a matter of preference.

“Love is just chemicals” is an aesthetic I prefer, and I think you should prefer it too. The chief point is that chemicals permit diversity. Love can be experienced in a variety of ways, or not at all, and that’s okay.
[Read more…]

Atheism within social justice

Miri Mogilevsky, blogger at Brute Reason, wrote an article called 5 Microaggressions Secular People Often Hear – And Why They’re Wrong, which appeared on Everyday Feminism.  Rather than discussing the content of the article, I wish to point out the framing.  Atheism is one social justice topic, just like any other.  Miri doesn’t just refer to microaggressions, but also the language of privilege and oppression.

In contrast, consider how PZ Myers responds to an article written by Dennis Prager, a religious apologist.  Prager is not so far off from the microaggressions in the listicle, but he’s not treated as such.  Instead, he is another kook proudly showcasing his ignorance of atheism.  He is an object of mockery and derision.

Going further back, consider how various bloggers responded to “10 questions for an atheist to answer”.  One of the questions asks if we are free to murder and rape without God, which is taken straight out of Miri’s list.  Bloggers chose to answer that one in earnest.

This makes me think about atheism, and its relation to social justice.  In the past several years, there has been much discussion about whether atheists should address social justice issues, but sometimes I wonder why atheism isn’t itself considered a social issue already.  Modern social justice discourse seems to include so many topics, from feminism to disabilities, to race, and sexuality.  Atheism is different from any of the standard social justice topics, to be sure, but the standard social justice topics are all so different from each other. [Read more…]

Paper: Cutting ties leads to cooperation

One field of study that greatly interests me is evolutionary game theory. The central question of the field is: how does altruism evolve? In a naive analysis, it would seem that uncooperative individuals can get ahead of the rest of their species, and uncooperative offspring will come to dominate the population. Nonetheless, in the real world we observe mixtures of cooperative and non-cooperative behavior.

In evolutionary game theory, “cooperation” is understood as a strategy in a two-player game. Most commonly, we consider the prisoner’s dilemma game, where two players each have the choice to cooperate or defect. “Defecting” is a strategy that benefits yourself, but hurts your opponent even more. And so if both players defect, then they’re both worse off than if they had cooperated.

The key to the evolution of cooperation is the ability to react to defectors. In particular, one needs to punish defectors, such that defection is no longer beneficial.

Here I’ll talk about one model that allows for such punishment, based on a paper titled, “Cooperation prevails when individuals adjust their social ties“. As suggested by the title, the mechanism for punishment is to cut off ties with defectors.

A network of cooperators and defectors
Figure 1 from the paper illustrates a network of cooperators and defectors
[Read more…]

What are topological defects?

This is a repost of an article I wrote in 2013, back when I was willing to take the time to explain physics stuff, and generate lots of images too.

Donut and Coffee
(image source)

It’s often said that topology is the branch of mathematics where they can’t tell the difference between a donut and a coffee mug. They each have a single hole (the mug’s handle and the donut hole), and that’s all that matters. If I may overanalyze this joke, the point seems to be that topology is so disconnected from our everyday experience. How is this useful?

I wish to explain one particular use of topology in physics: topological defects.

A topological defect is a sort of knot that exists in the microscopic structure of a material.* You can move the knot around from atom to atom, but you can’t untie it. We’ll get into how that works soon enough.

*Material is a vague term for “stuff”. Later I’ll discuss a few different materials including magnets, liquid crystals, and superconductors [Read more…]