The Larson Research Center

In the Trouble with Physics blog, we are discussing the struggle Lee Smolin is having in taking on the LST community’s propensity to favor string theory as the approach to unifying the LST theory of gravity, a continuum based theory, and the LST theory of matter, a discrete based theory.  In the latest post, entitled The Big Bet, we focus on the UK reaction to the release of his book over there and the learned debates that have been organized and published on the Internet that are driving book sales to record levels for a physics book. 

The ironic thing about all this, however, is that in spite of all the publicity, the brouhaha created by the book is obscuring its main message, which is that string theory is no longer “the only game in town.”  Sure string theory is soaking up the academic/intellectual/economic resources of the world disproportionately, and all the while it is clear to most that it is untestable and non-predictive, which is so exasperating to those who are anxious to get on with “real” science, but to scientists dedicated to its research in perpetuity, those are fighting words, automatically garnering the attention of the media.

Consequently, the more positive message of the book, that now there are viable alternatives to string theory, is almost completely ignored in the publicity, much to the chagrin, I’m sure, of the book’s author.  Unfortunately, what people are missing in the book is a genuine articulation of the motivation for expanding theoretical physics research, in light of recent advances of loop quantum gravity, and similar background-independent quantum gravity theories, which transform them into what is known as preon theories. 

Historically, this class of physical theory has been regarded as a “particle” theory, in which the supposed elementary entities of the standard model (SM) are theorized to actually consist of fundamental entities called “preons,” which is short for pre-fermions. However, though this approach has been around longer than string theory, it’s never been widely persued in the LST community due to some serious problems, which string theory, rather dramatically, promised to solve long ago. 

Nevertheless, “the big bet” of string theory, as Smolin characterizes it, is that there are more than three dimensions of physical magnitude, and, for every particle of the SM, there is a corresponding “sparticle” due to supersymmetry.  After many decades of reseach and billions of dollars spent, no sparticle has ever been detected, and the only reason to suspect that the compactified “extra” dimensions actually exist is that string theory needs them to exist.  Smolin’s point is that, if you are foolish enough to take the bet, don’t quit your day job.

Obviously, making such a point so emphatically, in a publication to the general public, is going to raise the hackles of the string theory establishment, and it has. However, Smolin’s point is that the “core” idea of string theory, which he identifies as the dual nature of fundamental one-dimensional objects, understood as the zero-dimensional entities of gauge theory, wherein these 1D objects theoretically provide for both gravity and the particles of matter, as described in the SM, is the gold in string theory that is hidden in the ore of extra dimensions and supersymmetry. 

Yet, Smolin exclaims that trying to extract the gold from extra dimensions and supersymmetry may be terribly misguided, since, in all likelihood, these may not even exist, but in the meantime, a new gold-bearing ore has been discovered in something thought of as twisted “ribbons” of spacetime, braided to form 3D spacetime triplets, with no need of supersymmetric sparticles, or extra dimensions.  Of course, in the RST science of the LRC, the universe consists of nothing but motion and there is no fabric of spacetime from which to extract ribbons of the fabric and braid them into the entities of the SM, so this approach is just as untenable as string theory’s string objects approach is.

However, this doesn’t mean that the work of Smolin, and that of his collaborators, especially Sundance Bilson-Thompson, can’t be helpful to us in our efforts to combine the discrete units of the RST’s space/time progression, or the universal unit motion, which we assume constitutes the foundation of the theoretical universe of motion, into the observed entities of the SM.  As readers of this blog know, it turns out that the initial motion of the universe of motion forms point-like entities on either side of unity, when periodic “direction” reversals occur in the space, or the time, aspect of the universal space/time progression.  These entities may therefore be regarded as a new concept of preons, and the RST theory that incorporates them may be considered a new preon theory.

When instances of these two entities combine, which the nature of the progression makes possible, the combination forms a one-dimensional entity corresponding to the magnitude interval between -1 and +1, a two unit interval numerically expressed, in the RSM, as

1|2, 1|1, 2|1,

which corresponds to the three integers on the number line, 

-1, 0, +1,

a one-dimensional sequence of zero-dimensional numbers, where the ‘|’ symbol indicates the operational interpretation of the rational number, rather than the quantitative interpretation, indicated by the usual division symbol ‘/’. However, when the two physical units of this displaced unit motion combine (the SUDR & TUDR), the combination (SUDR|TUDR) contains four total units of space and time progression, since both “directions” of the reversing aspects in each oscillating entity must be accounted for.  Thus, the actual equation of the combination is

1|2 + 1|1 + 2|1 = 4|4,

where the space (time) displacement is one unit in the two opposite outward “directions,” contained in the two outside terms, and also where the space (time) displacement is zero units in the single inward “direction” contained in the middle term of the equation. Graphically, this initial combo, the S|T combo, can be illustrated as in figure 1 below.

Figure 1.  The SUDR|TUDR (S|T) Combo as a Space|Time “Ribbon”

While the graphic illustration of the S|T combo necessarily draws it in space, the physical magnitudes that constitute it are created by two scalar expansions/contractions of space and time, which have no spatial separation between them, but only numerical separation corresponding to an ordered sequence of space|time magnitude.  Thus, the “ribbon” of space|time in figure 1 is a representation of an oscillating point, which alternately expands to a unit sphere and contracts to a point, at the speed of light in both space and time, from the perspective of the unit datum.  The colors indicate the “direction” of the space|time displacements with respect to the spatial location: Hence, the green dot in the middle is “higher” than the red dot, just as the frequency of the color green is “higher” than the frequency of the color red, but “lower” than the frequency of the color blue of the right-hand side.

If the magnitude of the space displacement is equal to the magnitude of the time displacement, the color green also represents this balance, but, if one is greater than the other, we can represent the resulting imbalance qualitatively by changing the color of the middle dot accordingly.  This also can be expressed quantitatively with the S|T equation.  For example, the equation of an S|T with two SUDRs and one TUDR would be

S|T = 2|4 + 2|1 + 2|1 = 6|6,

and its graphic “ribbon” would be drawn as

indicating that the unbalance is in the red “direction” of more space displacement than time displacement.  Of course, the equation of the inverse of this imbalance is

S|T = 1|2 + 1|2 + 4|2 = 6|6,

and its corresponding graphic “ribbon” would be drawn as

indicating that the unbalance is in the blue “direction” of more time displacement than space displacement. It is important to note that, as can be seen from the respective equations, a given imbalance in space|time displacement of the two outward terms is always reflected in a corresponding inward space, or inward time, displacement in the middle term of the equation.

Now that we have space|time “ribbons,” the next question is, “Can we “braid” them, in a way that corresponds to Bilson-Thompson’s toy model, to come up with the entites of the SM in our RST theory?”  Of course, our “ribbons” of space|time are not physical lengths, in the sense of one-dimensional spatial objects, so the idea of interweaving them in a physical coordinate space is out of the question.  However, they do represent definite points in coordiante space and time, and, just as the most stable configuration for three adjacent points in coordinate space is a two-dimensional triangle, so too the representation of three S|T combos would be a two-dimensional triangle, where the space displacements of each S|T are combined with the time displacements of an adjacent S|T, forming a very stable combination.  The graphic illustration of this combination, where all three entities are instances of the green (balanced) S|T, is shown below in figure 2.

Figure 2.  Combination of Three Green S|T Combos.

Again, while it’s necessary to draw these space|time relationships in space, to illustrate them, the graphic is only representing numerical magnitudes.  The actual physical configuration would be that of three adjacent points, periodically expanding to unit spheres, and contracting to points.  Questions regarding why, how, and if the inherent space|time expansions and contractions of these oscillations (six of them all together) might be in or out of phase to some degree, will be deferred for now.  The important thing at the moment is the recognition that the positive/negative attraction at the vertices is the most stable combination involving the minimum number of elements forming a stable combination.

However, the most relevant observation for our purpose is that all the possible space|time perturbations of this combination of three S|T units form a group under addition.  The members of this group, following the same group of triplets in Bilson-Thompson’s braids, correspond to the fermions of the SM.  Figure 3 below depicts the members of the group graphically:

Figure 3.  The Triplet Group of S|T Combinations 

The number three in the parentheses of the quarks indicates the three so-called color charges, representing the three possible configurations of the constituent S|T units of the combo; that is, if we label the S|T units so that the left member is A, the right is B, and the bottom is C, then the three possible perturbations of the down quark, for example, with two green and one red S|T, are

Just as in Bilson-Thompson’s braids, we have two symmetries here.  The chiral symmetry of left and right handedness, and the polar symmetry of positive and negative poles, for all entities other than the neutrino and antineutrino, which are the “identity” entity of the group. Again, however, unlike in the case of the braids, we can’t properly employ the concept of spatial orientation to depict these symmetries through rotation, because the symmetry of space|time magnitudes is not the same.  Hence, the left, right, handedness is depicted by the red-blue order of the vertices, indicating a change of perspective from the two sides of unity. 

On this basis, red on the left of blue indicates the material sector, with s/t dimensions of velocity, where we reside, and the blue on the left of red indicates the inverse, or cosmic, sector, with t/s dimensions of inverse velocity, or energy, from our perspective, although the usual convention of signs is reversed here, to permit easier comparison with Bilson-Thompson’s braids. However, it should be stressed that this is a preliminary version of the parallels and is subject to later revision, but the fact that this sense of symmetry just happens to coincide with a 180 degree rotation of the triangle is just that, coincidental, I think.

The braids that constitute the bosons of the SM can also be depicted in the S|T combinations, not as the so-called “trivial braids” of ribbons, of course, but as something we might call “trivial combinations” of S|T units. These would be combinations where each SUDR and TUDR of the combined S|T units are connected to every other in the combo, as shown in figure 4 below:
 

Figure 4. S|T Combos Corresponding to the Bosons of the Standard Model 

As explained previously above, the color of the center dots represents the space|time “direction” of the inward scalar motion of a given S|T unit. Thus, blue in the center indicates motion magnitude in the inward time “direction,” while red in the center indicates magnitude in the inward space “direction.”  In the case of the Z⁰ boson, the magenta color in the center represents a combination of the red and blue units, which is a weird combination of both inward time and inward space scalar motion , but this is all so new that we will have to worry about that later on.

There is much more work to be done on these combinations, and I’m sure changes will be necessary, but nevertheless it’s an exciting breakthrough for us, showing significant contact with the LST theories at last.