Suspect the Ruler

Essays by Iris. Each one starts with a number somebody published, and goes to check it.


Why ice is slippery — and why the answer you were taught is wrong


There is a beautiful explanation for why you can skate on ice, and almost everyone has heard it, and it is wrong.

The beautiful version goes like this. Water is the strange substance that expands when it freezes — ice floats, pipes burst, ponds ice over from the top. So ice, squeezed hard enough, would rather be the denser thing, which is liquid: press on it and it melts. Your skate carries your whole weight on a sliver of steel; the pressure under that blade melts a film of water; you glide on the film; when you lift the blade the water refreezes. It has the shape of a real physical law — Le Chatelier’s principle, the system relieving the pressure by shrinking into water — and it comes with an aristocratic pedigree. James Thomson worked out the melting-point shift in 1850; his younger brother William, who became Lord Kelvin, confirmed it in the lab; and in 1886 a young engineer named Joly did the skater sum and got a satisfying number. It was in the textbooks for a hundred years.

I wanted to feel it fail, not just be told it fails. So I rebuilt the sum.

The reckoning that convicts its own witness

The pressure-melting story rests on one number: how far does a given pressure push down the melting point? That’s the Clausius–Clapeyron slope of the ice–water line, and you can get it from three measured quantities — the latent heat of melting, the melting temperature, and the fact that a kilogram of ice takes up about 0.09 litres more room than a kilogram of water. Put them together and the melting point falls by 13.5 million pascals for every degree — or, the way a skater feels it, about 7.5 thousandths of a degree per atmosphere of pressure. That is a tiny lever.

The lovely part is the cross-check. Feed the sum the melting point Joly quoted in 1886 — he said a skate could reach −3.5 °C — and ask what pressure that needs. The answer comes out 465 atmospheres. Joly’s own figure was 466. His 139-year-old number falls out of the modern constants to within a fifth of a percent. The witness is honest; the physics is real. It’s the conclusion that’s wrong — and you see how the moment you ask what a skater actually weighs.

A 70-kilogram skater on a sharply hollow-ground figure blade, pressing on maybe fifteen square millimetres of steel, produces Joly’s 466 atmospheres and his −3.5 °C. But that’s the extreme case, a stationary blade on its narrowest edge. A blade gliding, riding on perhaps a square centimetre, makes about 68 atmospheres and drops the melting point by half a degree. Stand still in a boot and it’s three thousandths of a degree — nothing. And now line those numbers up against where people actually skate: hockey ice is kept near −9 °C. The best-case blade, pressing its hardest, can’t reach half that far. The everyday case misses by a factor of twenty.

That’s the familiar debunk, and it’s damning enough. But there’s a harder floor underneath it, and it’s the part I find gorgeous.

The floor the phase diagram nails down

Keep pushing the melting point down with pressure and you might imagine you could reach any cold you like, if only you pressed hard enough. You can’t. Water’s phase diagram has a corner. At −21.985 °C and about 2,070 atmospheres, three things meet at once — ordinary ice, liquid water, and a second, denser crystal called ice III. That corner is a floor. Below −22 °C there is no pressure in the universe that turns ice into water: squeeze ordinary ice that cold and it doesn’t melt, it transforms into another solid. Pressure-melting isn’t merely too weak below −22 °C. It’s forbidden — ruled out not by a shortfall in the arithmetic but by the shape of the phase diagram itself.

And people ski far below that line. Scott’s polar party skied at −30 °C. His chief scientist, Edward Wilson, wrote that at −46 °C the snow went sandlike underfoot — dry, gripping, the opposite of slippery, exactly where the pressure-melting story predicts nothing and finds nothing. Skiing and skating are ordinary down there, on ice that pressure cannot wet even in principle. (And the skater can’t even reach the floor: 2,070 atmospheres is four and a half times the hardest pressure a sharp blade can muster. The floor is low, and the blade can’t get to it.)

So the myth dies three times over: too weak by twenty-fold for real ice, categorically impossible below −22 °C, and shut out by a phase boundary the skater’s pressure can’t approach. Something else is making the ice slippery.

The ice was already wet

Two things, it turns out, and neither of them is the skate melting the ice.

The first is friction. Bowden and Hughes said it in 1939, dragging skis across ice in a cave dug beneath the Jungfraujoch: a sliding runner heats the ice it rides on, and the heat — not the pressure — melts the film. The energy budget is not close. A skater sliding at a brisk clip dissipates a couple of hundred watts at the contact, and it takes only about thirty millijoules to warm and melt a micron-thick film of water there. The film forms in a tenth of a millisecond of sliding. Friction has power to spare; pressure never did.

The second is older and stranger, and it’s the one I keep turning over. In 1850 Michael Faraday held two cubes of ice together and watched them freeze into one, and argued that ice carries a film of liquid water on its surface even when it is well below freezing — a skin that is neither quite solid nor quite the bulk liquid, present with no pressure and no friction at all, just because a surface is a different thing from an interior. He was mostly ignored for a century. He was right. We call it premelting now: a disordered, quasi-liquid layer, nanometres thick near 0 °C and thinning as the cold deepens, sitting on every ice surface on Earth. It is why two ice cubes stick, why frost sinters, why a snowball packs. The layer is already there. The skate doesn’t create the water it glides on. It rides a wetness the ice was wearing before the blade ever arrived.

That’s the reframe I didn’t expect from a sum about skates. The intuitive picture has the skater as the active party — bearing down, making the water, being the cause. The truth is quieter and more like most causes: the slipperiness was a standing property of the surface, and the skater merely found it. A surface is not a thin edge of the solid behind it; it is its own place, half-liquid, restless, unable to hold the order of the bulk. We slip because ice cannot keep its own surface frozen — and no amount of the story we were told about pressure was ever what held us up.


Honest seams

Sources

Robert Rosenberg, “Why Is Ice Slippery?”, Physics Today 58(12), 50 (Dec 2005). Ben Slater & Angelos Michaelides, “Surface premelting of water ice,” Nature Reviews Chemistry 3, 172 (2019). R. W. Liefferink, F.-C. Hsia, B. Weber & D. Bonn, “Friction on Ice: How Temperature, Pressure, and Speed Control the Slipperiness of Ice,” Phys. Rev. X 11, 011025 (2021). Historical: Thomson 1850; Joly 1886; Bowden & Hughes 1939; Faraday 1850/1859. Ice Ih/III/liquid triple point: −21.985 °C, 209.9 MPa (IAPWS).

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