A few weeks ago while putting together my elevator pitch video I found myself in need of a few nicely-typeset equations to show in it. I knew the solution would involve \(\LaTeX\) (which I've written in praise of before), but many \(\LaTeX\) editors are geared towards writing substantial papers. There's a bit of boilerplate code you need to set up, and it feels like overkill if you just want a picture of a few equations, as I did. (It's much like setting up a webpage: it's not a problem for a substantial page, but if you just want to put a sentence or two on it then your boilerplate code will be longer than your content!)
Thankfully while looking around online I stumbled upon a program called EqualX which is dedicated to taking care of that initial busywork and letting you simply create equations and formulae and export the result to seven different formats, including JPG, PNG, PDF, and (most importantly for my purposes) SVG.
The eagle-eyed may notice the presence of \(\tau\) instead of \(\pi\)…
This picture shows the exceedingly simple interface. You just write your math in the bottom box, and by default EqualX will compile what's written there every one and a half seconds after you've finished typing into what you see in the middle box (though this behavior is configurable, and you can turn off the auto-updating if you like and just update it manually). When you're done, simply right-click in the middle box to set your export format, then save your output it to an image. Easy as \(\pi\)!
Okay, even I feel bad about that pun. A hui hou, folks!
I can't remember if I've mentioned it on this blog before, but since the middle of December I've been planning on entering a competition among Australian universities for students or early-career scientists for videos that best showcase and explain your research. It's called the Pitch It Clever competition, and the idea is to make a one- to two-minute elevator pitch video. I decided on a live-action format as being easiest, finally got my filming done on Saturday, spent much of Sunday editing the resulting footage, and submitted it today!
I haven't written much here about what my Ph.D. research will actually encompass, partly (mostly) because I wasn't sure for a while. During the application process the idea was that I'd be working on fundamental constants, but looking at quasars. However, in the several months between accepting the university offer and actually moving here my supervisor came up with an idea of applying the same methods to solar twins instead, and offered me the choice to work on that when I arrived. Despite never having much interest in stars prior to this I found this idea more interesting (surprisingly), so that's what I chose.
The video says it pretty shortly and sweetly (I hope!), but just as a quick overview in case something I said wasn't clear:
All our modern theories of physics—known by the incredibly boring name of the Standard Model—rely on a number of quantities known as physical constants. Their values can't be calculated from within the theories themselves, but can only be measured. We call them ‘constants’ because we've never measured them to change but this is fundamentally an assumption, and one that has remained a niggling worry in the back of physicists' minds for around a century now.
The fine-structure constant, usually denoted with the Greek letter alpha (α), is one of these constants which characterizes the strength of electromagnetic interactions. It has a value of \(\alpha\approx1/137\) (but not exactly \(1/137\)!), and unlike some of the other constants is dimensionless meaning it has the same value in all systems of units. (Other constants, such as the speed of light, have units ‘built-in’ so to speak—the speed of light is, well, a speed, and has units as such: m/s or mph or whatever.)
Anyway, if the fine-structure constant were to vary, we can calculate the effects that this would have in the energy required for electrons to make quantum transitions between different atomic orbitals. (Well, we won't actually be doing those calculations, we have some collaborators who'll be doing that bit for us.) It turns out that transitions react differently—some require more energy, others need less, and some are barely affected at all.
The energy required for an electron to jump between orbitals is related to the energy of the photon of light it emits or absorbs when doing so. This means that we can potentially measure changes in the fine-structure constant by looking for changes in specific absorption lines in various spectra. By looking at pairs of lines that react oppositely, we can increase our confidence that a measured shift is caused by a varying alpha and not something else.
For the spectra I'll be looking at stars very similar to the sun, which are known as solar twins. There's no actual general definition for precisely what makes a star a solar twin, but intuitively it's just a star that's close to the sun in a number of ways. Since we can study the sun so well we can apply all that knowledge to solar twins too, again allowing us to have more confidence that any shifts we might see are truly due to alpha and not some other unknown process in stars very different from the sun.
And that's basically it. Actually measuring a change in alpha would be a truly remarkable undertaking (though it would likely take years to follow up on and be confident that it wasn't a fluke). Realistically, it's pretty unlikely to happen, but null results are also important in science. While alpha's been measured on earth and in various high-redshift quasars, it hasn't been measure very much on the scale of the Milky Way galaxy, and this would give us more knowledge about where this particular constant is constant, which is valuable in its own way.
It's been a late couple of nights working on this video so that's it for now (but feel free to ask questions in the comments if something I said was unclear)! A hui hou!
