Quantum Communication and Heat Transfer

What problem led Max Planck to invent quantum mechanics and obtain the correct answer? Can we use the physics of communications to understand interaction between atoms on smallest scales? Professor of Mechanical Engineering at MIT Seth Lloyd explains why enthropy and communications are closely connected.

Laws of quantum mechanics that govern communication actually stem from the 19th century or rather from 1900 when Max Planck began investigating the laws of heat transfer. Plank was interested in the problem of how much energy and entropy could be radiated out of a hot body. It’s called a “black body”, because black body absorb and emit light at all frequencies. So a black wood burning stove, it looks black and when you heat it up it starts to glow red and if you heat it up even further (and I don’t recommend this by the way) it will glow white, because it’s emitting light of all frequencies. And when you do the calculation using Maxwell’s theory of electromagnetism about how much energy and entropy or heat could be emitted by a black body you get an answer, which is wrong. In fact you get the answer infinity.

What does heat transfer have to do with communication? Well, in fact communication is the transfer of information from one place to another. And information is measured in terms of bits. A bit is just the smallest chunk of information, you know. Two possibilities — yes/no, true/false, photon here/no photon there. A bit of information is transferred by say, if I say, no photon is zero, photon is one, then if no photon shows up in this time period my bit is zero. If a photon shows up, the bit is one. So where does the theory of information come from? Well, actually in the mid-twentieth century Claude Shannon of AT&T Bell Labs and subsequently at MIT developed what’s called the mathematical theory of communication.

We can imagine, for instance, an experiment and this is not an imaginary experiment, it’s a real experiment performed by my colleague Gang Chen down the hall in which you take a tiny sphere that’s only a few tens of nanometers in diameter, so it’s a few hundreds of atoms across and you move it to within a few atoms’ lengths of a solid surface and you can measure how much heat flows between the surface and the sphere, so-called nanoscale heat transfer because it’s heat transfer that’s taking place at the scale of nanometers, a billionth of a meter. Now, when you look at these experiments there are strange and weird anomalies, funny things that happened that you wouldn’t predict at all. The most remarkable and obvious thing is that Plank’s law of energy transfer from hot black bodies breaks down at this scale and once you get very close to an object the amount of heat transfer that you can get between these two objects is hundreds or thousands or even millions of times higher than the amount of heat transfer that Plank would have predicted.