Free The Universe Within by Neil Turok

trouble was that Maxwell’s theory allows electromagnetic waves of all wavelengths, down to zero wavelength. There are only so many ways to fit a wave of a given wavelength inside a cavity of a certain size. But for shorter and shorter waves, there are more and more ways to fit the waves in. When we include waves of arbitrarily short wavelength, there are infinitely many different ways to arrange them inside the cavity. According to Boltzmann’s principle, every one of these arrangements will carry the same average amount of energy. Together, they have an infinite capacity to absorb heat , and they will, if you let them, soak up all the energy.
    Again, let me try to draw an analogy. Think of a country whose economy has a fixed amount of money in circulation (not realistic, I know!). Imagine there are a fixed number of people, all buying and selling things to and from each other. If the people are all identical (not realistic, either!), we would expect a law of equipartition of money. On average, everyone would have the same amount of money: the total amount of money divided by the total number of people.
    Now imagine introducing more, smaller people into the country. For example, introduce twice as many people of half the size, four times as many a quarter the size, eight times as many people one-eighth the size, and so on. You just keep adding people, down to zero size, with all of them allowed to buy and sell in exactly the same way. Now, I hope you can see the problem: if you let the tiny people trade freely, because there are so many of them they will absorb all the money and leave nothing for anyone else.
    Planck’s rule is like imposing an extra “market regulation” stating that people can trade money only in a certain minimum quantum, which depends inversely on their size. Larger people can trade in cents. People half as big can trade only in amounts of two cents, people half as big again in four cents, and so on. Very small people can trade only in very large amounts — they can buy and sell only very expensive, luxury items. And the smallest people cannot trade at all, because their money quantum would be larger than the entire amount of money in circulation.
    With this market regulation rule, an equilibrium would be established. Smaller people are more numerous and have a larger money quantum. So there is a certain size of people that can share all the money between them, and still each have enough for a few quanta so they aren’t affected by the market regulation. In equilibrium, people of this size will hold most of the money. Increase the total money in circulation, and you will decrease the size of the people holding most of the money.
    In the same way, Einstein showed, if you imposed Planck’s quantization rule, most of the energy inside a hot cavity would be held by waves just short enough to each hold a few quanta while sharing all the energy between them. Heat up the cavity, and shorter and shorter waves will share the energy in this way. Therefore if a hot body is placed inside the cavity and allowed to reach equilibrium, the wavelength of radiation it emits and absorbs decreases as the cavity heats up.
    And this is exactly how hot bodies behave. If you heat up an object like a metal poker, as it gets hotter it glows red, then yellow, then white, and finally blue and violet when it becomes extremely hot. These changes are due to the decrease in wavelength of the light emitted, predicted by Planck’s quantization rule. Human beings have been heating objects in fires for millennia. The colour of the light shining at them was telling them about quantum physics all along.
    In fact, as we understand physics today, it is onlyPlanck’s quantization rule that prevents the short wavelength electromagnetic waves from dominating the emission of energy from any hot object, be it a lighted match or the sun. Without Planck’s “market regulation,” the tiniest