Conjugate variables, in thermodynamics and elsewhere

When I wrote an explanation of cap and trade, I had a strong temptation to make a physics analogy, to an idea in thermodynamics. The trouble is nobody would understand the analogy, and I would be obliged to explain the physics instead of the economics. Well I’d still like to explain the physics, but in a separate article.

There are certain thermodynamic quantities that are considered to be paired with one another. For example, pressure and volume, or temperature and entropy. These pairs are called thermodynamic conjugate variables.

The concept of conjugate variables can be challenging for physics students to understand because the examples we use are unintuitive. The connection between pressure and volume is unclear, and most people don’t wholly understand what temperature or entropy even are. Therefore, I’d like to use a more down-to-earth example.

So, let’s consider a pool of water. The pool is described by two conjugate variables: the volume of water, and the height of the water.
[Read more…]

The black hole: Zoom in, enhance!

A few days ago, scientists announced the very first real image of a black hole (as opposed to one of those “artist’s conception” images that you see everywhere).

blurry ring of light

Black hole Messier 87 (aka M87) (credit)

This was a very nice surprise, because I was not aware any such project was underway, and I would have thought the obstacles were too great.  The main problem with imaging black holes is that black holes are really far away.  You would have to “zoom in and enhance” many many times to get the image above.  Let’s compare it to other examples of extreme zooming.

[Read more…]

Origami: Truncated octahedron

truncated octahedron

Truncated Octahedron, designed by me.  I kept this on my office desk.

Today’s model is one of my earliest original designs.   This is a truncated octahedron, which is the shape you get when you take an octahedron, and chop off the 6 tips.

I was interested in designing a model with this particular shape, because it has some special significance in condensed matter physics.  There’s a certain kind of crystal structure, called the “body-centered cubic structure”, which looks like this:

[Read more…]

That time IFLScience wrote about my field

As you can see, I took a brief blogging break… and during Asexual Awareness Week too.  But I don’t believe in apologizing for that sort of thing.

Two years ago, I spotted an IFLScience article about my particular field of research.  The article’s title?  Crucial Superconducting Theory Confirmed.  I remember chortling over the absurd idea that superconductivity would be solved, and that the first place I’d hear about it would be IFLScience of all places.

As I read the article, I realized how familiar I was with the research being discussed.  I knew Chandra Varma, a famous superconductivity theorist.  I had already read the scientific article they were talking about.  And one of the authors on the paper was a close colleague.  Small world, eh?

Anyway, I found the article interesting as a tiny little case study on science popularization.  Let’s go through the article, starting with the title.

[Read more…]

Explaining the light mill

 

A crookes radiometer, as described in the text

Image source: Wikipedia

The light mill, also known as the Crookes radiometer, is a little curiosity that can be found in stores at science museums, or in the offices of physics professors. It consists of four vanes, each painted white on one side, and black on the other. The vanes are placed in a bulb, under partial vacuum. When you shine light on the radiometer, the vanes spin around, with the white sides facing forward (counter-clockwise in the above image). A demonstration is shown in the video below.

Supposedly, the Crookes radiometer is an educational tool, but I can’t for the life of me determine what lesson it’s supposed to teach. Because if you ask how it works, the correct explanation is far beyond the ability for most people to understand. I have a Ph.D. in physics, and I still couldn’t understand it! There are numerous internet sources that identify “thermal transpiration” as the correct explanation, but fail to explain what that means or why it happens. So instead I found explanations in scientific literature,1 and now I will share the explanation with you.

[Read more…]

FTA part 4: Anthropic reasoning

This is the fourth and final part of a series discussing the Fine Tuning argument (FTA). The outline is here.

Mundane multiverses

A “multiverse” is a set of multiple sub-universes, which together comprise a single super-universe. The idea is that the universe that we know is a single sub-universe, and there are multiple other universes like ours. So we can imagine another sub-universe where everything is the same, except that ever coin flip comes up on the opposite side.  Or a sub-universe where everything is the same, but we’re all evil and have goatees. Or another sub-universe where

Typically, when physicists talk about parallel sub-universes, what they mean are non-interacting sub-universes. So, you can’t ever talk to the evil goatee’d version of yourself. Although, people sure like to imagine that sort of thing in sci-fi.  So let’s talk about the kind of parallel universe that we could, in principle, interact with. What if I told you that this kind of parallel universe is one we already know exists?

To travel to a parallel universe, just hop in a space ship, and travel 4 lightyears over to Proxima Centauri. You will find a universe exactly like ours, except that the sun is different, and the planets are different, and the constellations are different.

[Read more…]

FTA part 3: Ignorant hypotheses

This is the third part of a series discussing the Fine Tuning argument (FTA). The outline is here.

Uncertainty vs Ignorance

Earlier, I showed this plot showing probability distributions for three possible hypotheses of the universe. The FTA contends that the naturalism hypothesis predicts distribution A, and the God hypothesis predicts distribution B.

A graph showing three possible probability distributions. A is a very broad probability distribution. B is a sharp probability distribution centered at x_0. C is a sharp probability distribution centered away from x_0.

Three possible probability distributions. x0 marks the parameters of the universe that we have in the real world.

I will refer to a distinction that is commonly made between “uncertainty” and “ignorance”. “Uncertainty” refers to a situation where you don’t know what’s going to happen, but you at least have probabilities, a way to quantify how much you don’t know. “Ignorance” refers to a situation where you don’t know what’s going to happen, and you don’t even know how much you don’t know. When we compare probability distributions in the FTA, the probability distributions are just cartoons.  We don’t have any real probabilities.  We’re operating from a state of ignorance, not uncertainty.

Or, in other words, we pulled these probability distributions out of our asses.

[Read more…]