Tuesday, October 3, 2006

The quark's identity problem

All the big revolutions in physics in the 20th century, from relativity to quantum physics to chaos theory, have brought about some disturbing or at least fundamental changes to the way the world should be seen. Relativity told us crazy stuff about time, quantum physics assured us the world is not deterministic, and the chaos theory showed that small differences can indeed lead to very large differences (and one can speculate whether this allows quantum indeterminism to manifest itself in the macroscopic world). But there is another big revolution that has gone largely unnoticed: the quark revolution. What is this theory's the Big Idea?

In what follows, I will not talk about the specifics of quarks at all, but I'll just present the Big Idea. This can work fine because the theory is so mathematical that you can just take that math and apply it to virtually anything you want. The one who first had the Big Idea was the mathematician Hermann Weyl; the one who made the idea accessible to physicists was Eugene Wigner, and the first who realized that it can be used for describing the world of elementary particles was Murray Gell-Mann. This idea refers to the concept of identity – what does it mean that something is what it is? How can one define the identity of something?

This problem of identity has a long history in philosophy of course and it is one of the major issues people like Heidegger and his followers have been worrying about for the past 50 years or more. But although Murray Gell-Mann, the quark's inventor, is an unusually cultivated person for a physicist, the idea he used for defining identity is drastically different from everything any of these philosophers have ever thought about – fortunately. I would say, and hopefully I will manage to convince you as well, that Gell-Mann's idea is actually one of the most important philosophical ideas ever invented, especially as it is an idea one can use in practice (unlike the Heidegger-like metaphysical inquires about what identity means – or the "Dasein" as he calls identity).

What is identity?

When most people think about identity they think about grasping something which is supposed to be "the core" or the essential features of the thing. For example, for a biologist the biological identity of an animal is literally stored in the DNA that resides in the cells of the animal. This DNA provides the instructions for how everything inside the animal is supposed to take place and how the animal as a whole behaves in a given environment.

However, there is more to an animal than just its DNA. Besides issues such as those of symbiotic relations between two or more animals, one needs to account for the fact that most animals are sufficiently complex to learn stuff. This additional information is stored in the brain and somehow blends with the genetic information to influence the animal's behavior. But this learned stuff has no "core" like the DNA. (Richard Dawkins has actually proposed such a hypothetical "core" for the learned stuff, called "memes".)

Gell-Mann's idea offers a complementary solution to the problem. When one thinks of elementary particles this is the only solution available so it is no wonder that the idea has sprung from that field – the elementary particles have no DNA and no memes, no inner essential core, so how can you define them? The first draft of the idea is not very original: you have to define the identity based on how the things behave. But this is easier said than done. What behaviors should count as relevant?

So, instead of saying "these things are so and so and therefore they behave in such and such a way", Gell-Mann started saying that things behave in certain ways (which can be observed experimentally) and therefore they are this instead of that. The identity is caused by behavior rather than the other way around. This sounds similar to the idea that "nurture" is more important than "nature" for defining who somebody is. But such an idea is just empty unless you can specify what behavior exactly has to be taken into account.

What Gell-Mann had showed was that the "nature" and the "nurture" of the elementary particles do not so much contradict each other but are two different ways of describing the same thing – their "identity". In biology, the nature-vs.-nurture debate has been made obsolete by the discovery that the nature (the DNA) and the nurture (the environment) work together at every single step. Weyl's mathematical discovery has also unified the two perspectives into one in a similar way.

His idea was to look no so much for the behaviors that change the thing in one way or another, but to those that leave it unchanged. This was the Big Idea. To define a thing based on what you can do to it without changing it. It would be like identifying people not based on what their interests are, on what makes them "tick", but on what leaves them bored to death, on what doesn't create any reaction whatsoever!

You can see this idea at work with simple geometric figures. For example, you can define a (geometric) sphere as the object that can be rotated at any angle in any direction and still remain exactly as it were before. If I show you a sphere at two different moments of time, you cannot tell whether or not I have rotated it in any way from time 1 to time 2 (when you weren't looking) – this is what defines it as a sphere (rather than some other object) – the fact that you cannot tell the difference. A cube on the other hand can only be rotated at 90 degrees in certain directions so the difference isn't noticed – and this is what defines it as a cube. So, you can see that you can define the geometrical figures on the basis of what you can do to them while still leaving them as if you haven't done anything to them.

Weyl generalized this idea so it could be applied not only to geometrical features but to any kind of properties. This operation of doing something to some thing but which leaves it as it were is called a symmetry (or an operation of symmetry). What Gell-Mann then did was finding some specific symmetries that allowed him to define a few new particles, the quarks, and to describe the entire "zoo" of hundreds of known particles with these newly invented entities. It was really incredible. The quarks are in a certain sense the DNA that resides inside particles such as the protons or the neutrons (as well as many others – known collectively as "hadrons") and they have been discovered via their symmetries.

It is interesting to note that there are some symmetries which are shared by all things in the universe and this could offer a definition of the universe as a whole. For example, such an apparent universal symmetry is the rotation with 360 degrees. If you rotate anything with 360 degrees it would be as if you haven't done anything to it. Thus, because this applies to everything, such a rotation describes the universe rather than the thing you are rotating. (One of the crazy quantum mechanical discoveries was that electrons don't have this symmetry – you have to rotate them 360 degrees twice to get them in their initial position!)

Moreover, it can be demonstrated that all the conservation laws are true because there are some universal symmetries – so, the conservation laws are clues for these symmetries. For example the energy is conserved because you obtain the same results in any experiment no matter when (at what moment in time) you are doing the experiment – this is called "time symmetry", the moment at which you are doing an experiment doesn't influence the outcome. Or the electric charge is conserved because the thing (called "electromagnetic potential") that defines the electromagnetic forces can be changed in a certain arbitrary way without provoking any change in the real world (the forces remain exactly the same). The connection between symmetries and the conservation laws has been discovered by Emmy Noether, one of the first major women mathematicians.

Using symmetries in practice

One of the most important results of this theory of symmetries (called "group theory" by the way) is that the following two actions are equivalent:

  • (a) changing an object in a certain way while maintaining a constant perspective (an unchanged "frame of reference" from which the object is being observed) and
  • (b) changing the perspective in a certain way (the "frame of reference" from which the object is observed) while the object remains unchanged.
For example, it is the same thing to say that the unit of measurement has been inflated twice or that the object you are measuring has halved in size (relative to your constant unit). This has even been tested with an interesting virtual reality experiment. Or it is the same thing to say that a thing is rotating in front of you or that you are moving around it (supposing we disregard all other things in the world). This allowed the 16th century astronomer Tycho Brahe to have a funny model of the solar system, with all the planets revolving around the Sun rather than the Earth and the Sun revolving around the Earth, which was supposed to be at the center of the Universe. (Mathematically speaking, this model is entirely equivalent to the Copernican system that has the Earth moving around the Sun; from a physical point of view, however, the model is not correct because, according to mechanics, both the Sun and the Earth are moving around their common center of mass and this center of mass happens to be deep inside the Sun, because the Sun is so much heavier than the Earth - so, from a physical point of view, Earth is truly revolving around the Sun, while the Sun doesn't not revolve around the Earth.)

The fact that (a) and (b) are equivalent has very interesting philosophical consequences. For instance we are used to thinking that something is objectively true if it is seen in the same way by various people. (If I'm the only one that sees that UFO, that UFO doesn't exist objectively – it exists only subjectively.) But how can then discoveries happen? With such a social definition of objectivity, how can one become convinced that everybody else might be objectively wrong?

The answer is that a change of perspective is equivalent to a certain change of the observed thing. So you can obtain objectivity even all by yourself by applying various changes to things. Actually, this is exactly what physicists are doing when they test various symmetries. That's why they are doing it. To give you a very simple example: how can you know that you are seeing some object in the same way as me, given that you are always seeing it from a different angle? Easy: you take the object and you rotate it – this is how you can see it from my perspective. (Then, you can rotate it back.) Even if I'm not present, or even if I don't care to look at your stupid object, you can still take the object and rotate it and see for yourself how I would see it.

Of course, in other cases the symmetries are more complicated than the mere rotation. To make the point that this works even in complex cases, let me give you two examples, one from cognitive science (the example is discussed at length by Daniel Dennett in Consciousness Explained, although he doesn't seem to be aware of the generality of the method he employs), and one from economics.

Example 1.

Dennett discusses the situation when you remember something differently from what has actually happened. For example you remember that some lady had glasses but actually she didn't. The question is: Did you experience a perceptual hallucination and then you remembered correctly what you had perceived, or did you saw her correctly but then experienced a memory alteration? (It might seem absurd but there are a lot of people debating this issue!)

He argues at length that it is literally impossible to distinguish between the two cases – therefore, using the physicists' jargon, the change from one perspective to the other is a symmetry. But due to the fact that a symmetry in the change of viewpoint is equivalent to a symmetry in the observed thing (in this case the brain that does the error) this tells us something about the brain!

More exactly, it tells us that our consciousness isn't a "point" where all the information gets centralized – if that would have been so we could have found out which error happened, because we could have had a clear cut narrative story of the perceived situation and we could have detected where the error "intervened". Instead, if this symmetry is indeed real, we have to conclude that consciousness is made of different parallel processes and that the error didn't intervene in some given "point". Dennett calls these parallel processes "multiple drafts" that describe what has happened but which never really settle into one single final version of the "story" – into a linear "stream of consciousness".

Example 2.

In the communist states it was assumed that if the state controlled all the prices and all the production (what to be produced and in what quantities) than the laws of the capitalist economy would be abolished. In particular, the law of supply and demand – which sets the price for something based on what the supply and demand is – would also be abolished. Other economists thought that this is insane, because they thought the laws of economics are not specific to a certain political system, but are objective. However, how could they argue that?! (They tried of course but to no avail.) Only the reductio ad absurdum demonstration in the communist states could have really settled the issue.

The fact that the laws of economics still applied was indeed observed. For example, based on the law of supply and demand one can compute what would happen when price controls are put in place: shortages. One can even compute how large the shortages would be. And, although the law of supply and demand was supposed to have been abolished, this is exactly what was observed in the communist states (as well as each time a smart government anywhere had imposed price controls). Thus, we have a symmetry: that law remains unchanged when the political system has changed. This is strong evidence that that law is indeed objective and not subject to political control.

From such examples you can see the power of this idea – the idea that the identity of something is given by its symmetries and that one can use symmetries to demonstrate empirically whether some law is objectively true or not. Many philosophical issues can be settled this way, and this is why I think this idea is one of the greatest ever invented. But there is more.

Broken symmetries

As a final point, I want you to think about how things combine together to form more complex things. What would happen to their symmetries? And how could we use what happens to their symmetries to define the idea of "relation" as well? (The question of what a relation between two things is has been as difficult to answer as the question of what the two things are.)

As long as the things that combine preserve their identity inside the structure, their symmetries remain intact. But the structure as a whole doesn't necessarily inherit all their symmetries. For example suppose you place a triangle on top of a square and you obtain a "house". The "house" is much less symmetric than either the triangle or the square. We are saying that the symmetries have been "broken". Generally speaking, the breaking of a symmetry is an indication that some interaction has happened. This is how one can define a relation in this Gell-Mann perspective.

Another example: Suppose there is a ball on top a Gauss-like hill. This situation is symmetric to rotations around the vertical axis that passes through the top of the hill (and through the center of the ball on the top of the hill). But now suppose the ball slips from the top to the bottom of the hill. The symmetry has been broken – it is no longer possible to rotate the landscape around that vertical axis. The reason why the ball falls is gravitation. But how about defining gravitation as that kind of symmetry breaking – or the set of all such symmetry breakings? Although it sounds very unusual, it is one way in which physicists are thinking about gravitation - although it hasn't proved very successful (at least not yet).

In the late 1960s Steven Weinberg and Abdus Salam have applied this idea to describe the electromagnetic force and the weak force (the one responsible for radioactivity). Their theory unified the two forces and predicted the existence of three new particles, called W+, W- and Z, which were detected. These particles are similar to the photons. In the early 1970s the same idea was applied to the strong force - that keeps the protons and neutrons together - and predicted the existence of gluons. These particles are responsible for the interactions between quarks.

What's interesting about this perspective on how things relate to each other is that the identity of the smaller parts is literally a part of the identity of the larger structure. Both identities are defined using the symmetry operations and the distinction between the complex and the simple is that the complex has broken many its components' symmetries – the ones that are left define its identity. This is indeed the idea Ilya Prigogine had used to define complexity in chaos theory.

Moreover, the way sketched above for defining the universe as a whole, and which is a very precise way of doing that by the way, gives new meaning to the idea that the whole universe is part of every single thing that exists in it. As far as I can tell this slogan has meaning only from this perspective.

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