The Larson Research Center

Lee Smolin’s book is doing very well in the UK. One of the reasons is probably the exposure due to the ongoing debates between Smolin and string theorists organized at places like Oxford and the Royal Society of Arts (RSA), where Lee’s conclusions are frankly challenged in a typical English manner. Obviously, it makes for good publicity, but it also reflects the general interest in fundamental questions, I believe, even though the fundamental questions discussed most vigorously in these debates extend to those of a philosophical and a sociological nature, more than those of a physical nature.

In the RSA debate (mp3 audio file), chaired by Chris Isham, two professors, Michael Duff, a string theorist, and Nancy Cartwright, a philosophy professor, address issues raised by the book from the perspectives of offended physicists in the string theory community (Duff) and of a questioned assumption in the philosophical community (Cartwright).

Smolin’s defence is mostly to contend that the offense taken by string theorists, delineated by Duff, was not intended, and that the questioned assumption, raised by Cartwright, regarding the unification of nature, constitutes the gauntlet that nature herself has thrown down. However, he makes it clear that he is convinced that the discovered duality between the one-dimensional string objects and gauge theory is the deep, “core,” idea, as he puts it. Nevertheless, the current formulation of the idea in the context of a background-dependent framework, necessarily leading to nine or ten spatial dimensions and supersymmetry, is the “big bet,” he says. The issue of the unification of nature through higher dimensions and the challenge of how to treat the geometry and stability of the extra dimensions has “been in play” since the early 1920s, he notes, and without success.  Then he asserts something remarkable.  He states that with the

…development of the same idea [i.e the core idea of string theory] in a background-independent context, without the picture of strings moving in a classical geometry, but taking the whole geometry quantum mechanically, as the degrees of freedom that arise out of the dynamics of these extended objects, you get loop quantum gravity and spin foam models, precisely on the nose, that’s what they are.

But this comment, arguably the most valuable one in the whole debate, was his last utterance, at the end; it was not the point of departure at the beginning of the debate, as it should have been.

At one point, near the middle of the debate, Duff insisted that the triumph of string theory in uniting the particles of the standard model with gravity, was its chief justification, since no other theory has done that, but, in his book, Smolin clearly states that this is no longer true, that the other quantum gravity approaches, such as loop quantum gravity, have also succeeded in this. On page 254, he writes:

…one thing is clear. String theory is no longer the only approach to quantum gravity that also unifies the elementary particles…results suggest that many of the background-independent quantum theories of gravity have elementary particles in them as emergent states. And a given theory does not lead to a vast landscape of possible theories. Rather, it shows promise of leading to unique predictions, which will either be in agreement with experiment or not…Science done the old fashioned way is moving ahead.

This was news to me and I’m sure to most others, but because of all the fog raised by the offended string theorists, this point is not being made emphatically enough.  The loop quantum gravity approach and its associated variants, differ from the string theory approach in that they don’t require extra dimensions of space, in a fixed background that can be configured in a gazillion ways.  It is a background-independent approach that redefines space, and the geometry of space, dynamically.

However, the difference is that the particles in loop quantum gravity are emergent and they emerge from the way three 1D objects can be braided, which is something that Smolin and his colleagues learned from an Australian named Sundance Bilson-Thompson.  In his work, Bilson-Thompson shows that, using a toy model, one can represent fundamental objects with helons, which are 1D ribbons with left or right or no twists.  Ribbons with left twists are the inverse of ribbons with right twists, and, together with ribbons that have no twists, they form a group.  Thus, the same three part 1D structure that string theory uses, with its two end points and a vibration between them, analogous to the three part SUDR|TUDR structure of our work here at the LRC, arises once more.

Interestingly, however, unlike the strings of string theory, the structure of these braids is very close to the structure of our SUDR|TUDRs! For example, each twisted helon consists of two, 1 pi, twists, just as each UDR consists of two, 1 unit, progressions of space|time.  Thus, the three types of helons, braided together, constitute four units of positive and negative pi twists, but Bilson-Thompson doesn’t ever braid left-twisted helons with right-twisted helons.  Instead, left-twisted helons are only braided with untwisted helons, or other left-twisted helons, and the same for right-twisted helons.  Only untwisted helons are braided with both types of twisted helons, or with each other. 

On this basis, the three-helon braid of two left-twisted helons, with a neutral helon, has a complemented version of the same thing, with the pattern of the braided helons reversed, and, of course, the three-helon braid of the right-twisted version also has its corresponding complemented braid.  In other words, there is a left and a right-handed braid, consisting of left, neutral, or some combination of these two types of helons, and the inverse of these, the left and right-handed braid, consisting of right, neutral, or some combination of these two types of helons.  Hence, there are chiral versions of braids and anti-braids (positive and negative magnitudes in left and right-handed versions).

Bilson-Thompson’s paper contains the graphic depiction of the braids just described, as shown in Figure 1 below. 

Figure 1.  Bilson-Thompson’s Braids and Antibraids of Positive and Negative Helons 

In the figure above, the left-handed and right-handed versions of each braid of left-twisted (positive) helons are on the top row, while the left and right-handed versions of each antibraid of right-twisted (negative) helons are on the bottom row.  As indicated in the graphic, each type of braid, or antibraid, equates to a particle of the first generation of the standard model, or it’s antiparticle.

As soon as Smolin read Bilson-Thompson’s paper, he knew it was what they had been looking for, because they could use these ideas of braids in loop quantum gravity to represent the emergent particles of the standard model in the theory.  He writes on page 254:

As soon as I read the paper, I knew this was the missing idea, because the braids Bilson-Thompson studied could all occur in loop quantum gravity. This meant that the different ways to braid and knot the edges of the graphs in quantum spacetime must be different kinds of elementary particles.  So loop quantum gravity is not just about quantum spacetime - it already has elementary-particle physics in it.  And if we could discover Bilson-Thompson’s game working precisely in the theory, it would have the right elementary-particle physics.

Eventually they managed to do it, though the achievement certainly isn’t being heralded in the LST community as much as would seem warranted, in part, evidently, because the string theory controversy is eclipsing the real message of Smolin’s thesis: String theory is not the “only game in town.”  He writes:

Plainly, there are different approaches to the five fundamental problems in physics.  The field of fundamental physics beyond string theory is progressing rapidly, and in several directions…While there aren’t as many people (perhaps two hundred, all told) in these [alternative] research programs as there are in string theory, it’s still quite a lot of people to be tackling foundational problems on the frontiers of science.  The big leaps of the twentieth century were made by far fewer.  When it comes to revolutionizing science, what matters is quality of thought, not quantity of true believers.

Of course, at the LRC, there are even fewer people, far fewer people, working on these foundational problems.  However, we are undaunted in our determination to move forward with the new system of physical theory, the RST, exploiting our recent discovery of the Chart of Motion (CM), which is providing phenomenal insight into concepts of numbers and magnitudes of motion and the way to unite them into a single concept that addresses the enigma of the continuum versus the discrete faces of nature. 

However, we are not developing the RSt in a vacuum, understanding the LST community’s challenges is an important part of our work here at the LRC, and there is no greater example of the value of this than what we have been discussing in this post.  To wit: Bilson-Thompson’s work promises to a be a great help to our own efforts in developing the SUDR|TUDR combinations that lead to the standard model’s entities.  Of course, what we bring to the table is an immense advantage over any other approach, because the new system is not only completely background-independent and discrete, but it also is completely free of the conundrum of starting with a definition of the length of space as something with tangible properties.

We don’t need to start with strings; we don’t need to start with ribbons, and we don’t need to start with graphs, in order to discover emergent entities of matter, radiation and energy.  All we need to start with is the definition of motion and the properties of natural numbers.  What a thought!