Imagine you’re holding two equal-size dice. Is it possible to bore a tunnel through one die that’s big enough for the other to slide through?
Perhaps your instinct is to say “Surely not!” If so, you’re not alone. In the late 1600s, an unidentified person placed a bet to that effect with Prince Rupert of the Rhine. Rupert — a nephew of Charles I of England who commanded the Royalist forces in the English Civil War — spent his sunset years studying metallurgy and glassmaking in his laboratory at Windsor Castle.
Rupert won the bet. The mathematician John Wallis, recounting the story in 1693, didn’t say whether Rupert wrote a proof or bored a hole through an actual cube. But Wallis himself proved mathematically that, if you drill a straight tunnel in the direction of one of the cube’s inner diagonals, it can be made wide enough to allow another cube through. It’s a tight squeeze: If you make the second cube just 4% larger, it will no longer fit.
If there’s one law of physics that seems easy to grasp, it’s the second law of thermodynamics: Heat flows spontaneously from hotter bodies to colder ones. But now, gently and almost casually, Alexssandre de Oliveira Jr.(opens a new tab) has just shown me I didn’t truly understand it at all.
Take this hot cup of coffee and this cold jug of milk, the Brazilian physicist said as we sat in a café in Copenhagen. Bring them into contact and, sure enough, heat will flow from the hot object to the cold one, just as the German scientist Rudolf Clausius first stated formally in 1850. However, in some cases, de Oliveira explained, physicists have learned that the laws of quantum mechanics can drive heat flow the opposite way: from cold to hot.
