I was looking at today's xkcd, and am reminded of a Terry Pratchett quote: [The science of Discworld, Terry Pratchett, Ian Stewart & Jack Cohen, ISBN 9780091886578, chapter 22 "Things That Aren't"]


It's a reasonable question. Let's see where it leads.

In the 1960s a biological supply company advertised a device for scientists who used micro-scopes. In order to see things under a microscope, it's often a good idea to make a very thin slice of whatever it is you're going to look at. Then you put the slice on a glass slide, stick it under the microscope lens, and peer in at the other end to see what it looks like. How do you make the slice? Not like slicing bread.

The thing you want to cut - let's assume it's a piece of liver for the sake of argument - is too floppy to be sliced on its own. Come to think of it, so is a lot of bread.

You have to hold the liver firmly while you're cutting it, so you embed it in a block of wax. Then you use a gadget called a micro-tome, something like a miniature bacon-slicer, to cut off a series of very thin slices. You drop them on the surface of warm water, stick some on to a microscope slide, dissolve away the wax, and prepare the slide for viewing. Simple ...

But the device that the company was selling wasn't a microtome: it was something to keep the wax block cool while the microtome was slicing it, so that the heat generated by the friction would not make the wax difficult to slice and damage delicate details of the specimen.

Their solution to this problem was a large concave (dish-shaped) mirror. You were supposed to build a little pile of ice cubes and  'focus the cold' on to your specimen.

Perhaps you don't see anything remarkable here. In that case you probably speak of the 'spread of ignorance', and draw the curtains in the evening to 'keep the cold out' - and the darkness.

It occurs to me that it would surely work as you would expect. Whilst you cannot focus cold on to something, you can cover part of the area that would radiate heat from the environment to something with a mirror, and that mirror pointing at ice cubes means that not as much heat is radiating from the ice cubes via the mirror to the target as would be otherwise. But heat from the target is radiating to the ice cubes that absorb that heat. The net flow of heat would be from the sample to the ice cubes for a large chunk of the area surrounding the sample.

But this would mathematically be the same as considering cold radiating from the ice cubes to the target via the mirror. I suspect the maths works out exactly as you would expect for focusing cold just the same as it does for electron holes.



  1. Yeah, I think that's true. It's perfectly sensible to discuss the laws that 'emergent phenomena' like holes. phonons, etc obey and sometimes these are very similar, or mathematically the same as, the laws that actual particles obey.

    Also, consider that most laws of physics are time-symmetric, and anything that can focus - like a lens - is usually also reversible. from a time reversed perspective, photons move 'from' the source of 'cold' in exactly the same way that in the normal-time perspective photons move from a heat source. So a lens or focusing apparatus should focus 'cold' in exactly the same way that it would focus 'heat'.

    This reminds me of Jayne's story about formal systems. He mentioned a mathematics professor who used to blow the minds of his students by integrating (pr maybe it was differentiating) both sides of an equation with respect to pi. How can you integrate with respect to a constant? Well, the point is that once you have interpreted your problem in terms of a formal system, the definitions of your original problem need not control your manipulations. Anything that the formal system says is logically implied by your original statement (as translated into the formal system) holds once you translate back. The intermediate manipulations need not have a valid interpretation in reality.

  2. Your premise is correct. Radiative cooling paint can cool a surface below ambient temperatures when pointed at a clear sky. Search "Novel CaCO₃ Microsphere Synthesis" on youtube for a homebrew paint recipe.


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