A century and a half of scientific inquiry has yet to solve this one. It's clear that a thin layer of liquid water on top of solid ice causes the slipperiness. A fluid's mobility makes it difficult to walk on, even if the layer is thin. But there's no consensus as to why ice—unlike most other solids—has such a layer.
Scientists long reasoned that, since water has the unusual property of being less dense as a solid than as a liquid, its melting point can be lowered with an increase in pressure. While this is true, even the sharpest of skates raises the melting point by only a few degrees. The pressure theory doesn't hold water unless the ice is pretty warm already. Something else must be going on.
Some studies suggest that friction from a moving shoe, skate or tire causes the heat necessary to melt the ice beneath it. But what if the shoe isn't moving at all? A second theory proposes that ice inherently has a fluid layer, caused by the motion of surface molecules that have nothing above to bind to and so move around in search of stability. The slippery culprit may be a combination of these two theories.
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