Islands of Stability Metastable water
Water can stay liquid well below its freezing point, waiting for something to start the ice. Diamond sits on an island it should not be on, and stays for ages.
Below 0 °C, ice is the stable form of water, yet a clean droplet can stay liquid far colder than that: small, pure droplets in clouds stay liquid down to about −38 °C before they freeze on their own. The liquid is not stable. It is stuck. To freeze, a droplet first needs a tiny crystal to form by chance, and a crystal that small costs more energy than it saves, so it usually melts again. Until one grows past that hump, the liquid persists. Diamond is the same story on a longer clock: at the Earth's surface graphite is the stable form of carbon, but the hump between them is so high that diamonds keep.
Why this is a clean case for the site. A supercooled droplet looks perfectly stable on every passive measure: it sits there, clear and liquid. Only a push, a speck of ice or a sharp knock, shows that it was never on the island it seemed to be on. That is proposition 2's evidence rule in its simplest physical form. And a tray of droplets freezing one by one is proposition 3's question, and its strongest objection, in a form you can watch.
Freeze a tray of droplets
Each blue dot is a supercooled droplet. It turns white when it freezes. Every droplet has its own chance per second of freezing, which never changes while it stays liquid. In the identical tray, all droplets have the same chance. In the mixed tray, some carry a speck of dust that helps ice start, so their chance is higher. The right panel shows, second by second, what share of the droplets still liquid freezes: the tray's hazard.
The tray: blue is liquid, white is frozen.
The tray's hazard: the share of still-liquid droplets freezing each second, against time.
With identical droplets the hazard stays flat: a droplet that has stayed liquid for a long time is no safer than one poured a moment ago. That is proposition 3's memoryless exit. With mixed droplets the hazard falls: the dusty droplets freeze first, and the longer the tray waits, the more of what remains is clean. No droplet grows safer with age, but the tray does. This is the same trap as the firm data, and ice-nucleation researchers argue about it in the same terms: whether freezing is stochastic, a constant chance per droplet, or singular, set by each droplet's own impurities.
The seed crystal is the push. Drop one into a supercooled droplet and it freezes at once, however long it had survived: its persistence was never evidence that it was stable.
Real droplets in a wind tunnel
The tray above is a simulation. Szakáll and colleagues measured the real thing. In a vertical wind tunnel in Mainz they floated supercooled droplets about 0.7 millimeters across, one at a time, each in a rising stream of air held at a single temperature below zero. Each droplet was water carrying particles of one material that helps ice start, a mineral dust or a plant fiber. Each run floated 70 droplets, one after another, and counted the share still liquid as time passed.
The record holds 34 such runs for six of the seven materials: kaolinite, montmorillonite, feldspar, Sahara dust, microcrystalline cellulose and fibrous cellulose. Each run held one temperature, from −11.9 down to −23.9 °C, and was followed for up to 34 seconds. The run that went furthest ended with 15 percent of its droplets still liquid.
On this scale a constant chance of freezing draws a straight line, as the identical tray does, and the authors read the runs that way, as the exponential fall the stochastic view of freezing predicts. From separate experiments in an acoustic levitator, where drops were cooled steadily, they also classed every material as a mixture of particles that start ice more or less easily, the multiple-component case, although for illite NX the difference from a single component was not significant. That is the mixed tray. Droplets that differ in what they carry differ in depth, the exception proposition 3 names, and here it is already shown. So these curves cannot test the proposition, and no test is drafted on them. A test would need the same droplet frozen again and again, which these experiments did not do. Jakobsson and colleagues (2022) did, tracking about 3,000 drops through repeated cooling and holds at one temperature. Their raw data were downloaded on 8 October 2026, and a test of proposition 3 on them is being drafted. The data stay unanalyzed until its rules are frozen.
Cost line and fragility line
Cost line. Nothing is spent to keep a droplet liquid or a diamond a diamond: the hump is a stock, like the nuclear and orbital islands.
Fragility line. A single speck: one ice crystal or one potent dust grain ends a supercooled droplet at once, and the colder the droplet, the smaller the speck that will do it.
How the propositions meet the water
| Proposition | On the water | Status |
|---|---|---|
| P2 The evidence rule | A supercooled droplet looks stable on every passive measure. Only a push reveals that it is not. The clearest physical example on the site. | illustration |
| P3 Exit statistics | Identical droplets freeze memorylessly. Mixed droplets show a falling hazard from frailty alone, the objection that withdrew the organizational reading. Real wind-tunnel runs are shown without a verdict: their materials are mixtures, a difference in depth already shown. | illustration, real data |
| P4 Cost | Does not transfer: the liquid's persistence costs nothing. It is held by a barrier, not bought. | does not transfer |
| P1, P5, P6 | Not applied here. | not applied |
Source and method
The real freezing curves: Szakáll, Debertshäuser, Lackner, Mayer, Eppers and Diehl, Atmospheric Chemistry and Physics 21, 3289-3316 (2021), doi:10.5194/acp-21-3289-2021, with the data behind its figures in Zenodo record 10.5281/zenodo.4436153 (CC BY 4.0). The page draws the six files of runs at one temperature as published, each checked against its SHA-256 checksum, and does not fit them.
The simulation: 400 droplets, each freezing in any 0.05-second step with probability 1 − e−r·0.05, where r is its constant rate per second. Identical tray: every droplet r = 0.1. Mixed tray: a quarter carry a speck, with r = 0.8, and the rest r = 0.05. These rates are illustrative, chosen so the effect is visible in under a minute. Real rates depend steeply on temperature and droplet size. The hazard is the share of still-liquid droplets that froze in each one-second bin. The −38 °C limit for pure droplets freezing on their own: Koop and Murray, Journal of Chemical Physics 145, 211915 (2016). The stochastic and singular views of ice nucleation: Vali, Atmospheric Chemistry and Physics 14, 5271 (2014).