Tuesday, January 8, 2019

Taking your theory seriously

This blog entry is somewhat different than usual. Rather than writing about some particular research project, I will write about a general vibe, directing my research.

As usual, research starts with a 'why?'. Why does something happen, and why does it happen in this way? Being the theoretician that I am, this question often equates with wanting to have mathematical description of both the question and the answer.

Already very early in my studies I ran into peculiar problems with this desire. It usually left me staring at the words '...and then nature made a choice', asking myself, how could it? A simple example of the problem is a magnet. You all know that a magnet has a north pole and a south pole, and that these two are different. So, how does it happen which end of the magnet becomes the north pole and which the south pole? At the beginning you always get to hear that this is a random choice, and it just happens that one particular is made. But this is not really the answer. If you dig deeper than you find that originally the metal of any magnet has been very hot, likely liquid. In this situation, a magnet is not really magnetic. It becomes magnetic when it is cooled down, and becomes solid. At some temperature (the so-called Curie temperature), it becomes magnetic, and the poles emerge. And here this apparent miracle of a 'choice by nature' happens. Only that it does not. The magnet cools down not all by itself, but it has a surrounding. And the surrounding can have magnetic fields as well, e.g. the earth's magnetic field. And the decision what is south and what is north is made by how the magnet forms relative to this field. And thus, there is a reason. We do not see it directly, because magnets have usually moved since then, and thus this correlation is no longer obvious. But if we would heat the magnet again, and let it cool down again, we could observe this.

But this immediately leaves you with the question of where did the Earth's magnetic field comes from, and got its direction? Well, it comes from the liquid metallic core of the Earth, and aligns along or oppositely, more or less, the rotation axis of the Earth. Thus, the question is, how did the rotation axis of the Earth comes about, and why has it a liquid core? Both questions are well understood, and arise from how the Earth has formed billions of years ago. This is due to the mechanics of the rotating disk of dust and gas which formed around our fledgling sun. Which in turns comes from the dynamics on even larger scales. And so on.

As you see, whenever one had the feeling of a random choice, it was actually the outside of what we looked at so far, which made the decision. So, such questions always lead us to include more into what we try to understand.

'Hey', I now can literally hear people say who are a bit more acquainted with physics, 'does not quantum mechanics makes really random choices?'. The answer to this is yes and no in equal measures. This is probably one of the more fundamental problems of modern physics. Yes, our description of quantum mechanics, as we teach it also in courses, has intrinsic randomness. But when does it occur? Yes, exactly, whenever we jump outside of the box we describe in our theory. Real, random choice is encountered in quantum physics only whenever we transcend the system we are considering. E.g. by an external measurement. This is one of the reasons why this is known as the 'measurement problem'. If we stay inside the system, this does not happen. But at the expense that we are loosing the contact to things, like an ordinary magnet, which we are used to. The objects we are describing become obscure, and we talk about wave functions and stuff like this. Whenever we try to extend our description to also include the measurement apparatus, on the other hand, we again get something which is strange, but not as random as it originally looked. Although talking about it becomes almost impossible beyond any mathematical description. And it is not really clear what random means anymore in this context. This problem is one of the big ones in the concept of physics. While there is a relation to what I am talking about here, this question can still be separated.

And in fact, it is not this divide what I want to talk about, at least not today. I just wanted to get away with this type of 'quantum choice'. Rather, I want to get to something else.

If we stay inside the system we describe, then everything becomes calculable. Our mathematical description is closed in the sense that after fixing a theory, we can calculate everything. Well, at least in principle, in practice our technical capabilities may limit this. But this is of no importance for the conceptual point. Once we have fixed the theory, there is no choice anymore. There is no outside. And thus, everything needs to come from inside the theory. Thus, a magnet in isolation will never magnetize, because there is nothing which can make a decision about how. The different possibilities are caught in an eternal balanced struggle, and none can win.

Which makes a lot of sense, if you take physical theories really seriously. After all, one of the basic tenants is that there is no privileged frame of reference: 'Everything is relative'. If there is nothing else, nothing can happen which creates an absolute frame of reference, without violating the very same principles on which we found physics. If we take our own theories seriously, and push them to the bitter end, this is what needs to come about.

And here I come back to my own research. One of the driving principles has been to really push this seriousness. And ask what it implies if one really, really takes it seriously. Of course, this is based on the assumption that the theory is (sufficiently) adequate, but that is everyday uncertainty for a physicist anyhow. This requires me to very, very carefully separate what is really inside, and outside. And this leads to quite surprising results. Essentially most of my research on Brout-Englert-Higgs physics, as described in previous entries, is coming about because of this approach. And leads partly to results quite at odds with common lore, often meaning a lot of work to convince people. Even if the mathematics is valid and correct, interpretation issues are much more open to debate when it comes to implications.

Is this point of view adequate? After all, we know for sure that we are not yet finished, and our theories do not contain all there is, and there is an 'outside'. However it may look. And I agree. But, I think it is very important that we very clearly distinguish what is an outside influence, and what is not. And as a first step to ensure what is outside, and thus, in a sense, is 'new physics', we need to understand what our theories say if they are taken in isolation.