Why a light-clock ticks, a Darwinian explanation

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) 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 a 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 incident 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…

Why-questions are dirty

I will share in this Blog some reflections on Physics (and in particular Special Relativity) that I also post in www.physicsforums.com, although here I will also be including comments on broader topics.

I intend to publish only ideas that are as widely acceptable and as little speculative as possible, but I do not guarantee that the scientific parts of this site are reliable, since I am no authority in this field.

The title of this first entry gives the tone of the series. I am addressing why-questions, admitting (half-jokingly) that they are "dirty"... because, yes, that has been the conclusion of a recent discussion in Physics Forums: to ask "why" is legitimate, but it simply means focusing on the details of a process, getting your hands dirty with the mechanics.

I have often complained, with regard to a number of Special Relativity issues, that the standard solution simply resorts to Einstein's postulates: this is so and so because the Principle of Relativity so requires, for example. I thus cried: that amounts to describing how nature works, but not explaining why it works that way. I was responded: you will find no scientific explanation that is not purely that, a description of how nature works.

When confronted with this answer, I was struck by my own complaint. I had written many pages defending the opposite of what I had just affirmed. I have been even more radical. I hold that we do not even describe nature. We interact with nature, we annotate the score of this sort of fight (we measure) and we interpret our measurements as clues for solving day-to-day problems. That is all.

What happened, then? Why did I speak against my conviction? I am afraid that the same thing happened as with my tennis. I have learnt new tricks, but in the heat of a game or a discussion, my doggish mind seeks refuge in the old routines. Realizing this helped me the trouble of losing energy in a useless fight. But I did feel that my complaint had "some" justification. So I decided to re-phrase it. I like semantics and I trust it is a powerful tool that can bring you out of a lot of trouble, both in life and in intellectual discussions.

Thus in the end we found an understanding.

I admitted that axioms like the Principle of Relativity cannot be labelled as "less profound". You cannot say that they must be put aside in favour of purportedly "deeper" truths. Granted: the more abstract that a principle is, the better it is. First, because it is beautiful in its slimness, which is the same as saying that it (probably) works. (We like handsome people because they were more apt to survive in old times. A different thing is that such evolutionary advantage may be useless today. But the idea still holds in the intellectual realm.) Second, a very elementary, fundamental principle is like a magic word, a master key that you can take anywhere to opens myriads of doors.

Yet I also found a better expression for my concern. I just wanted to descend to the details. Zoom in. Put on the working costume and stain my hands with the intricacies of the process in question, whatever it is. The helicopter view is necessary, but sometimes it is also convenient to turn into a little insect that dwells, with the devil, amongst the details. To sum up: the infamous why-questions do not lead you to a "deeper", but to a "lower" level.

I trust that this approach may be fruitful. My opponent in the discussion (now somehow siding with me…, though not for long: he is a tough guy!) commented that this way you often find connections between thing that might look unrelated before. I expect so. In particular, I intend to touch these issues, in the field of Special Relativity: why does the mechanical clock time-dilate, why does the photon hit the target in the light clock experiment, what is spacetime, why - to the dismay of book-sellers - nothing, not even faster than light travel can violate causality...?

It is not that I will always be so poetical. I promise some math and some geometry as well. But, yes, literature will be here, I will talk about Cinderella and the slipper. And I will also talk about law: when you look at the practical details, you realize that Einstein's theory is very "legal", very much in the line of that dirty art… lawyer's reasoning!