You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
John Baez (Oct 03 2020 at 20:12):Just for fun, an article on the properties of water:
Actually this is part of my long-term project to learn more condensed matter physics. There's a lot of modern condensed matter physics that makes explicit use of categories, especially modular tensor categories, but I like the whole subject.
John Baez (Oct 03 2020 at 20:13):Someday I'd like to write a book of essays on strange forms of matter. And water is strange.
Morgan Rogers (he/him) (Oct 03 2020 at 21:14):I absolutely adore phase diagrams, and it made me feel bad that I never got to do material sciences (or, apparently, condensed matter physics!) because I missed out on these lovely beasts. Finding out where and when phase lines merge and split is especially exciting. Could it be that the liquid region of the phase diagram for what is completely closed, so that at ridiculously high temperatures and pressures we find a new sublimation transition!? That's the kind of thought I couldn't have had without seeing a diagram like this.
John Baez (Oct 04 2020 at 15:59):Actually the line between the liquid and gas phases ends at 373.946 Celsius and 217.8 atmospheres:
John Baez (Oct 04 2020 at 16:03):This point, at the right edge of the picture, is very interesting. It's a "second-order phase transition" which means that water is approximately scale-invariant there: it consists of droplets of water containing bubbles of air containing droplets of water... etc., in such a way that if you zoom in it looks just the same.
John Baez (Oct 04 2020 at 16:06):This phenomenon is called critical opalescence.
John Baez (Oct 04 2020 at 16:08):So the right way to formulate your question is whether the "fluid" phase of water (the combined liquid-gas phase) ever ends at high temperatures. And it does: the water molecules break apart into a plasma at some point!
Morgan Rogers (he/him) (Oct 04 2020 at 23:00):I did wonder what "critical point" meant! Are there pictures of this?!?
John Baez (Oct 04 2020 at 23:19):The Wikipedia article on "critical opalescence" has a not-too-charismatic picture, but there are also videos on YouTube:
https://www.youtube.com/watch?reload=9&v=DIGdbmJvFUw
John Baez (Oct 04 2020 at 23:19):Since making movies of extremely hot water at 217 times ordinary atmospheric pressure is difficult and dangerous, and critical opalescence is a general phenomenon, this movie shows critical opalescence for a mixture of methanol and cyclohexane heated to about 75 C, when the two liquids, immiscible at lower temperatures, blend into one.
John Baez (Oct 04 2020 at 23:21):The Wikipedia article gives a pretty good explanation of what's going on. I guess it also helps to know why opals look the way they do.
Nikolaj Kuntner (Oct 05 2020 at 13:57):Youtube has a bunch of very nice demos of supercool water
