Reflections on Special Relativity, with an inter-disciplinary approach.

# Why the light clock works, according to Darwin

Posted Feb25-12 at 08:42 AM by Saw
Updated Feb27-12 at 04:25 PM by Saw

In the previous entry I mentioned that why-questions are legitimate, but they have a humble goal: "explaining" is just zooming in and looking at the details of a process, showing step by step how it conforms to general principles.

A good example of this (in the domain of Special Relativity, which is the subject of this blog) is a very frequently asked question: why does the light work, why does the photon or light pulse hit the mid-point of the top mirror and bounce back to the mid-point of the bottom mirror?

The standard answer goes as follow: "Otherwise the Principle of Relativity would not hold: you would be able to ascertain whether you are in motion by measuring the degree of deviation of the light beam; in other words, the laws of physics would not be the same in all reference frames, since the same experiment (shining light upwards) would render a different outcome in different vehicles". That is true, although it is fun to develop how the mechanics of the process conform to such principle.

Of course, light, not being a sentient being, does not "choose" the right direction. Light is "imposed" its direction by the emitter. How?

Well, sometimes it is said that the emitter "aims" at the target, but I am not sure this is the right expression. If by that we mean physically orienting the light source in the appropriate direction, that is not accurate. Let us imagine that we have two identical laser guns pointing upwards, one on a train and another on the station. When the former passes by the latter, at a given instant, the two guns are perfectly lined up (top with top and bottom with bottom) and the same happens with the remote targets of the photons. Hence the two guns have the same orientation. A different thing is that, after this instant, the targets move away from each other and, in spite of that, each photon hits its own objective.

"Aiming" may, however, be an acceptable description if we mean by that using the light source, the apparatus for firing photons, in a different manner: we produce photons omnidirectionally but the gun automatically selects those that turn out to possess the appropriate direction. The gun is a tube, a reproduction at small scale of the path that the photons must afterwards follow in the outside world. If any of them reaches the exit hole of the gun, it is because it has already followed the good path, the one that will enable it to ultimately hit the top mirror of the clock. The smaller the hole, the better it will perform this sort of Darwinian process, where only the fittest photons survive.

This is quite apparent if we think of a "classical" source, like an incandescent bulb. Electrons bound to atoms are excited by collisions. After a short while, those electrons spontaneously relax and emit energy in the form of photons, with multiple arbitrary directions. If that is all, they go out in a spherical wave. But if we add a tube, then we sieve the photons to select only the apt ones and can thus create a more or less directional (non-diverging) light beam.

If we consider instead a "modern" source like a laser gun, the process is peculiar but not different in its essence. The laser ray can be made extremely thin, very directional. A reason for this is that here the phenomenon of "stimulated emission" intervenes. When the electron is excited, we do not wait until it releases its photon in a random direction. We hit it before with another photon that already has the right direction. The consequence is that the emitted photon is coupled with the incoming one, in several respects, including direction. But how did we manage to create those clever incident photons? Again, initially, we had to generate them omnidirectionally. It just happens that the physical display of the instrument favours that there are soon many apt photons, by virtue of a selection mechanism: there are two mirrors, one at the bottom and one at the top of the gun; the photons with an "evolutionary advantage" (those moving in parallel to the tube) keep reflecting back and forth, the others are absorbed by the walls; the reflecting photons act thus as "teachers" for the new-born photons to move in the successful direction, we could say that they introduce culture and nurture into the play…; finally, the top mirror is a half-silvered one, so when the number of fit photons calling at its door is very high, the mirror lets them out, in the form of an intense and thin beam. Hence this a clever trick to attain "direction" out of chaos, but with limitations: even laser rays are to some extent "non-directional" or "diverging", insofar as the gun cannot be made infinitely thin or long…
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