illuminating science

Just reading a neat paper on changes in length and time scales under special relativity. The idea of length (and time) scales is an important one in physics - it’s about asking what sizes “matter” to your system. For instance, is it a galaxy, thousands of light years across? Or is it an eyeballs, where millimetres is important? Or is it an atom, where we need to consider billionths of a metre?

It’s not just for fun, though - it helps you work out what’s important in your problem. If what you’re interested is on the scale of light years, you don’t need to worry about atoms. If you’re interested in how plants use photosynthesis, most of the interesting stuff is over in a millionth or even a billionth of a second - so don’t worry about leaves waving in the breeze, or maybe even the motion of certain proteins.

And of course, one place all this is really important is in computation - simulating physical systems on a computer. After all, if you you’re interested in how leaves blow in the wind, there’s no point in taking snapshots of your virtual plant a billion times a second. Save time, and just take 30, or 100, calculations “per second” of plant time. On the other hand, if you’re interested in how energy moves between different molecules, you’re going to need to simulate a much smaller scale and on much shorter timescales.

That’s one of the things that makes biology so hard to study - you’ve got “interesting” things happening on the scale of seconds, thousandths of a second, all the way down to billionths or trillionths. And sometimes, there’s things happening on much longer timescales as well! If some process takes 10 seconds to happen, but you need to increment in steps of 0.0000000001 of a second, it’s going to take a very long time! Similarly for distances - if I need to simulate every molecule of a plant, it’s physically impossible on any computer we have to do this before the sun runs out of fuel…

Enter this paper. In special relativity, time and space can change depending on how fast you’re moving. Clocks can run slower when they speed up (tested with airplanes!), rulers can appear shorter, etc. The upshot of this is that the important lengthscales and timescales can also change - if you simulate your particles moving very fast, you might find that you can be more “pixelated” in your model, and still get all the info you need. Everything kind of gets “compressed”, if you like. This means that choosing a different speed for your simulated experiment can cut a week long calculation down to just 30 minutes!

Apparently, other researchers are so impressed because no-one had found this before, despite special relativity being very well understood (by some ) It’s a simple discovery, in essence, but it might make previously impossible calculations very realistic - and who knows where that will lead?