## Monday, March 06, 2006

### Theory of everything from trinions

Since the very first moment when Lee Smolin informed me that loop quantum gravity would become a real competitor of string theory because it would include not only quantum gravity but also the rest of particle physics, I was looking forward to the preprint.

It's because the probability that a new and truly important idea is found by an original thinker is higher than the probability that a randomly chosen background in the set of 10^{350} vacua describes the Universe around us. And in the case that the paper is set to confirm the expectations, at least we can have some fun.

Ladies and Gentlemen, the paper by Lee Smolin, Fotini Markopoulou, and Sundance O. Bilson-Thompson (čo bolo, to bolo, terazky som majorom) has arrived.

The paper is a followup of a previous paper by Sundance O. Bilson-Thompson

in which the buzzwords of loop quantum gravity are taken into account. The first detail about the new paper you will notice is that unlike most of the average papers, only the PDF file is available. This is the first sign that the paper is really special. For example, you can see that while Jack Sarfatti's paper, available in PDF only, is exceptional, the reply to him, written in TeX, is just another paper.

On the first page of the paper by Lee Smolin et al., the reader is reminded of many great and not-so-great paradigms such as loop quantum gravity, discrete spacetime, preons, quantum groups, and especially noiseless subsystems. Noiseless subsystems turned out to be very useful for physics of loop quantum gravity. When the entropy of the black holes calculated from loop quantum gravity was shown to disagree with the semiclassical expectation, most physicists thought that it was just another piece of evidence that loop quantum gravity was inconsistent as a theory of quantum gravity. However, Lee, Olaf, and Fotini proposed a better explanation.

For example, if loop quantum gravity calculates the entropy to be S=1917 while the correct result should be S=1776, you don't give up. Instead, you say that the part "141" of the S=1917 result is politically incorrect and only the subset S=1776 is the right "noiseless subsystem". This method has allowed loop quantum gravity to solve all contradictions you may ever encounter. In fact, this method is more powerful and universal in forgiving your errors, sins, and discrepancies than Jesus Christ (PBUH & SAW).

Trinions

But the noiseless subsystems are not the only fascinating idea that is promoted in this preprint. The authors have discovered a completely new and revolutionary method to divide a two-dimensional surface into pieces. This method involves the so-called trinions.

If you want to hear how these ideas explain the existence of quarks and leptons and their chiral gauge interactions, I ask you for more patience. ;-)

What is a trinion? As the term suggests, a trinion is a generalization of 0nion. The only difference is that while 0nion has 0 straight line intervals on its boundary, trinion has three of them. The "open string version" of a trinion is a hexagon, but saying that a trinion is a hexagon would obscure the real depth of the new discovery. The "closed string version" of a trinion is a pants diagram - a sphere with three finite punctures. A surface may be regarded as a union of trinions.

Although this observation goes well beyond the scope of the paper ;-), you may notice that a trinion is one half of a genus 2 Riemann surface. The Euler character of a genus 2 Riemann surface is "2-2g = -2", and therefore a trinion has the Euler character equal to "-1". However, you must always use an even number of trinions to cancel the boundaries which means, after a minute of thought, that you can generate closed Riemann surfaces with arbitrary negative Euler numbers, i.e. all surfaces of genus 2 or higher.

The usual "fascinating game" of loop quantum gravity-like physics is getting started. You associate Hilbert spaces to trinions while gluings create tensor products. The figures in the paper are irresistable. Some of them look like a handcuffed octopus or Roman numerals IX and XI. Maybe it is not an octopus but rather kalamari, to remind you of one of the authors.

If you are still waiting how these things are related to particle physics, let me already give you a glimpse of the answer. For example, one can conjecture that a normalization of a U(1) charge, if one appears, may be renormalized by an integer. Which integer? What is the most fundamental integer in the theory of trinions? Yes, it is three. This is why the quarks could have charges that are multiples of 1/3, the page 4 argues. Do you want to ask why did not we use tetranions? Be careful about heresy: the God is also composed of three forms - the Father, the Son, and the Holy Spirit and you better not ask these questions.

The number of pictures is growing. How do you get fermions and their chiral gauge interactions, you may still want to ask? For example, the muon neutrino is an octopus handcuffed in one way. Other particles correspond to other kind of knots created from trinions. Surely, the more advanced questions - why do the particles live in three dimensions as opposed to a string with defects, why are the animals fermions, why are they described by spinors, why there are any gauge groups at all, why the fermions have the right representation properties, and why there is any del-slash, any covariant derivative, the Lorentz invariance, or anything else for that matter - are details that will be fully resolved in a simple followup of this paper.

The new authors can already build on precious insights of this paper. For example, the gauge structure of the fermions is explained as follows: one can draw at least 30 different types of octopi, so we can also understand them as 30 complex components of 15 Weyl spinors that appear in one generation of the Standard Model. ;-) The question why the manifestly different octopi should transform as a representation of a group is not explained, but it is surely another detail that will be fully resolved soon.

The fundamental, most important ideas have already been found: the muon neutrino is an octopus made of trinions. Moreover, the authors even explain on page 10 that the mass of the elementary particles may arise from the number of self-crossings of the octopus arms, much like the mass of an octopus who has just eaten three onions.

My 1988 model of elementary particles

When I was 14, I had the very same theory. It was completely dumb and reflected my complete misunderstanding of quantum field theory at that time, but it still seems to have more content than this paper. What did I think about elementary particles in 1988?

Elementary particles were classical topological defects on the fabric of space, I thought - although the language I used was less modern. In the case of closed two-dimensional orientable manifolds, all new topologies can be constructed simply by adding handles. Is there a corresponding procedure for three-manifolds describing the real space? Yes. One can construct some kinds of local topological defects by adding handles. You may remove a solid torus or a solid manifold whose boundary is a genus "g" Riemann surface. Remove the same solid torus or another filled surface elsewhere, and glue the boundaries of the two "holes".

You can't probably get all topologies by this construction (can you prove it or disprove it?) but you can get many new topologies. The topology of the defect is determined by the topology of the boundaries that you identified. When they are spheres - when you remove two balls from space and identify their boundaries - the resulting particle will behave as an electron. When you remove two solid tori and identify their toroidal boundaries, you will obtain a neutrino. The toroidal structure is probably related to its inherent spin. When you remove two filled genus 2 surfaces and identify their boundaries, you obtain a proton. Moreover, there is a way to draw a genus 2 Riemann surface so that it has a Z3 symmetry, which I argued was an explanation why the dumb physicists thought that there were 3 small elementary quarks inside a proton. Holes with genus above 2 were more massive or less important, I believed.

Let me admit that for some time I was really excited with this idea, much like many others, thinking that it was the next revolution in physics. ;-) But I would have never gotten excited had I known the actual sharp, well-defined facts from the experiments that our theories are supposed to explain in the first place.

You see that I was talking about topologies of 3-manifolds that can't be embedded into a flat 3-space. Lee et al. only talk about 2-dimensional octopi that are simply embedded into a flat 3-space but surely, there must be some other depth.

I did not have an explanation of antiparticles, the possibility for particles to annihilate, or other facts about elementary particles - whose list I believed to be fundamentally composed of the electron, a single neutrino, and the proton only - but it was a sufficiently attractive theory to satisfy my desire for elegance, at least for some time. Had I published it, the new preprint would be my followup. The new preprint is really unusual even though there are certain groups of thinkers where such papers are not so unusual. Needless to say, their theory contradicts everything that my theory disagreed with. For example, you can never annihilate two particles because all of their "particles" have a negative Euler character and you will never find a sufficient positive Euler character to get to zero.

Sorry, Lee, but I simply can't believe that you're serious.

Figure 1. Muon neutrino according to the new theory of everything based on loop quantum gravity. This description of weak interactions is a highly improved version of mating doughnuts accupuncture.

This paper may be viewed as a culmination of all the wrong things that have been a part of loop quantum gravity more or less from the very beginning, for example:
• completely naive, classical visualization of physics
• the opinion that completely non-fundamental, emergent, shallow, ad hoc characteristics of objects - such as the shape of an octopus - are fundamental
• the inability (or lacking will) to grasp or study the actual mathematics that is known to be relevant for the real world, especially quantum field theory and its methods
• the tendency to make dozens of different random and unjustified (and unjustifiable) choices
• the inability to see that the facts that are claimed to be "consistency checks" tautologically reflect the assumptions, and there is no non-trivial output whatsoever

I am sure that this paper is so tough that others in loop quantum gravity will distance themselves from this work. However, this work is indeed a characteristic example of many aspects of the wrong thinking of our colleagues in this troubled subfield of theoretical physics.

On the other hand, I am equally certain that crackpots will embrace it as a great idea. Sorry to say but this is exactly the way they think.

#### 1 comment:

1. I'm a layman, so I started reading this post thinking it was about a genuine new theory...

Then I got the feeling that it might be a spoof, a physicist in-joke... and when "onions" were mentioned, I got sure.

Very funny post. :)