The Larson Research Center

In his book, Lee Smolin identifies five, unsolved, problems of theoretical physics, but all of them are aspects of the one real problem: the unification of the continuous and discrete aspects of nature. The problem with string theorists’ enthusiasm for their approach, Smolin asserts, is that, while they don’t even know what it is, they believe that there is no alternative to string theory for solving this fundamental problem. In this view, we can either regard the fundamental entities of the standard model (SM) as 0D point particles, in which case we can’t unify the discrete domain of quantum physics and the continuous domain of general relativity, or we can regard them as 1D lengths, in which case unification of the discrete and continuous is possible, resulting in a unification of all the SM’s elementary particles and forces, as 1D motions, or vibrations, because string theory:

1. Explains existing gauge fields as open ended 1D vibrations
2. Explains gravitons as closed 1D vibrations
3. Explains unification of particles and forces with supersymmetry “sparticles”
   

“Here then is the dream that string theory seemed to make possible,” writes Smolin, referring to what is now known as the first superstring revolution. Before this revolution, resulting from the work of John Schwarz and Michael Green in the mid eighties, “some people doubted that string theory could ever be made consistent with quantum mechanics at any level…,” but now it “promised what no other theory had before - a quantum theory of gravity that is also a genuine unification of forces and matter,” at least in ten spacetime dimensions.

What? Yep, that’s right. For supersymmetric string theory to work, it needs nine space dimensions to go along with its one time dimension, ten spacetime dimensions in all. It can’t exist in three space dimensions. It needs six extra space dimensions to work. Smolin compares this to buying new car “option packages.” We can get the unification “option” we want, but only if we take the extra dimensions “option” too. “Much followed from this,” writes Smolin. “If the theory was not to be ruled out right away, there had to be a way to hide the extra dimensions.”

Ironically, as it turned out, there was a way to hide them. In fact, there were an infinite number of ways to hide them, and the problem became not one of how to hide the extra dimensions, but one of finding some reason why a particular one of the innumerable ways was preferred over the others! In effect, each way of folding up the hidden dimensions is a different string theory, with more and different constants and more and different unobserved particles and forces.

But, of course, a second string theory revolution was looming in the mid-nineties that would unify the many string theories that unified the particles and forces. Again, the basic idea was to increase the number of space dimensions. This time by just one, but this increase led to 11D M-theory, which includes so-called “branes,” or multi-dimensional entities that interact with the 1D strings, such as 2D surfaces. However, for this set of multi-dimensional objects to work it has to contain five types of string theories, including all the different ways the 6 extra dimensions of their geometries can be hidden, forming the specific background which defines the motion of the 1D strings and nD branes in a given theory. However, this means that the theory can’t be built on any one 10D background, but must encompass all backgrounds. In other words, M-theory must be background independent, but still consistent with the background dependent quantum theory. Smolin writes:

This is an important issue, perhaps the most important open question in string theory. Unfortunately, not much progress has been made on it. There have been some fascinating hints, but we still do not know what M-theory is, or whether there is any theory deserving of the name…M-theory remains a tantalizing conjecture. It’s tempting to believe it. At the same time, in absence of a real formulation, it is not really a theory - it is a conjecture about a theory we would love to believe in.

With the fundamentally different view of the nature of space and time that the RST provides, research at the LRC takes a completely different course than that taken by physicists in the LST community,  As we’ve been discussing in the New Math and New Physics blogs, instead of defining motion solely as a change of position against a fixed background geometry of space and time, as in quantum mechanics, or against a dynamic, background independent, geometry of spacetime, as in general relativity, the LRC’s researchers have three fundamentally different types of motion to work with, which promises to lead to an alternative to unification of the discrete and continuous faces of nature, which leading string theorists have no idea even exists.

There are many aspects to the new approach, but the one aspect that is most relevant to string theory is the dimensional aspect.  In string theory, the extra dimensions are necessary to get the various combinations of vibrations of strings that go into the calculations of n-dimensional magnitudes.  However, in addition to the problems with the huge variety of possible forms this approach can take, there is still the fact that there is no motivation for resorting to extra dimensions, other than that the mathematics of string theory requires it. Smolin quotes Nobel Prize winner Sheldon Glashow’s protest on this point:

But superstring physicists have not yet shown that their theory really works.  They cannot demonstrate that the standard theory is a logical outcome of string theory.  They cannot even be sure that their formalism includes a description of such things as protons and electrons.  And they have not made even one teeny-tiny experimental prediction.  Worst of all, superstring theory does not follow as a logical consequence of some appealing set of hypotheses about nature.  Why, you may ask, do the string theorists insists that space is nine-dimensional? Simply because string theory doesn’t make sense in other kind of space. 

In contrast, the RSt under development at the LRC is “a logical consequence of an appealing set of hypotheses.”  That set, known as the fundamental postulates of the system, assumes that everything in the universe consists of one component, motion, existing in three dimensions, in discrete units, with two reciprocal aspects, space and time.  However, In the chart of motion, we see that, mathematically, four dimensions of magnitude exist, the 0D point, the 1D line, the 2D area, and the 3D volume, and we see that there are three types of motion that can define each of those magnitudes in different ways.  The first way is via the change of position of the familiar vectorial motion, the only form of motion recognized by LST physics.  The second way is via the change of interval inherent in electromagnetic radiation, and the third way is via the change of scale inherent in a scalar expansion/contraction.

However, we know too that, mathematically, no new phenomena, beyond these four dimensions (0, 1, 2, 3) exists, thanks to Raul Bott’s proof of the periodicity theorem. So then the question is, “Why do string theorists need five more than this?”  Apparently, the reason is that in higher dimensions the quantum corrections (read “cheating” terms) in the wave equations have to cancel out, and this only happens if everything is symmetrical, which happens at d=10.  Nevertheless, the whole edifice depends on how motion is defined in gauge theory, and this involves complex numbers and the use of rotation in the complex plane; that is, a two-dimensional motion (rotation) is transformed into a one-dimensional motion using complex numbers.  Moving to this type of motion in two and three-dimensions, then, requires higher than four dimensions of space.

The chart of motion simplifies all this, but only if the concept of motion is understood to embrace much more than the M₂ motion, or change of position motion.  As we increase dimensions beyond three dimensions (four counting 0), the Bott periodicity theorem tells us that no new phenomena exists beyond these initial three (four) dimensions; that is, at dimension four (five) things change.  What we’ve discovered is that the nature of the change is that the tetraktys simply repeats.  That is to say that whereas 1, 2, 3, and 4, raised to the 0, 1, 2, and 3 powers successively, corresponds to the space magnitudes of point, line, area, and volume, the next four dimensions just repeat this.  Thus, for M₂ motion,

1. 2⁴ = point
   
2. 2⁵ = line
3. 2⁶ = area
4. 2⁷ = volume

However, now the point has the value of 2⁴ =16, and the volume has the value 2⁷ = 128, and so on.  This doesn’t make much difference in M2 motion, because nothing changes in terms of calculating change of position magnitudes, but, in M₄ motion, it is very significant, because it means calculating change of scale magnitudes in terms of higher densities, if you will; that is, a 4⁰ = 1 point, is much less than a 4⁴ = 256 point from a scalar magnitude point of view.

What this means, then, is that the higher dimensions, in the chart of motion, don’t have to be hidden, and that there is definitely only one way to get these magnitudes, not an infinite number of ways.

The title of this blog, The Trouble with Physics, is the name of Lee Smolin’s new book, the full title of which is, The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next.  This title implies that the rise of string theory and the fall of “a science” go together; that is, it seems that Smolin asserts that string theory is responsible for the lack of real progress in fundamental physics for the past quarter century.

However, the most relevant message of the book is not the failure of string theory, but the fundamental crisis in theoretical physics that the pursuit of string theory has exacerbated.  Smolin and others, like Peter Woit, whose anti-string theory book, Not Even Wrong, has just now become available in the U.S., are worried that, based on ideas coming from string theory, physicists are abandoning hope that a unique, unified, solution to five fundamental problems in theoretical physics actually exists, while disregarding, or denying, the severe impacts the implications of this thinking have on the science of physics itself.

Smolin discusses each of these five problems in the first part of his book, entitled the “Unfinished Revolution,” referring to the second major revolution in the science of physics and mathematics.  The first revolution is so ancient that it is not normally mentioned by Smolin or other physicists.  They usually just focus on the second, modern, scientific revolution, started by Planck and Einstein, which initiated a turn away from the physics of the continuum, to the physics of the quantum, at the beginning of the 20th century. 

Nevertheless the first revolution occurred when the Pythagorean secret of the square root of 2 got out and turned mathematics from the quantum of integers to the continuum of real numbers, which finally took off in a big way with the advent of the calculus, many centuries later.  While, at this point, the second revolution, that turned mankind back to the quantum, may seem unfinished to the impatient modern physicists,  maybe they should reflect on how many centuries it took to finish the first revolution, in order to put things in a better perspective.

Clearly, however, the key issue at the heart of the modern trouble with physics is not string theory per se, but rather the mystery as to how nature can be both discrete and continuous at the same time.  The modern physics of the continuum is embodied in the classical mechanics of vectorial motion, and the most erudite and exotic form of classical mechanics is found in Einstein’s theory of general relativity, while the modern physics of the quantum is now embodied in quantum mechanics, and the much heralded theories of quantum fields, and quantum colors. 

Of course, the trouble with this modern concoction of physical theory is that these two forms of physics, one continuous and one discrete, are fundamentally incompatible, and while the hope of reconciling them in string theory grows fainter in the minds of some, it nevertheless continues to soak up almost all the manpower and resources of the theoretical community, because of the influence and tenacity of those who remain optimistic that it can eventually reconcile the differences and heal the schism of modern physics.  This has led to mighty confrontation and polarization in the LST community.

Recently, Lee Smolin and Briane Green, a popular string theorist, discussed the trouble with physics with Ira Flatow, the host of the NPR series, Science Friday. After discussing, at length,  Smolin et al’s criticism of string theory’s inability to predict physical phenomena that could verify it, and the effective suppression of new ideas due to its thorough domination of academia, these gentlemen finally began to discuss the real problem. 

As Green explained how that testing the consistency in the calculations of string theory, and its consistency with the established concepts of past physics, shows that the “theory comes through with flying colors every step of the way and keeps us thinking that things are at least headed in the right direction,” Flatow turned to Smolin and asked, “Well, Lee, what would be wrong with that, if things are working like that?”

Lee’s answer is very telling, and it’s well known in the community. Essentially, it is that in spite of these favorable things that one can say about string theory, there are some very important things “it doesn’t come close to doing.” Then Lee hit the nail squarely on the head:

If you really put quantum mechanics together with the description of space, then we know, from general considerations, that the notion of space should disappear.  Just like the notion of the trajectory of a particle disappears in quantum mechanics, …the same thing should happen to space and the geometry of space.

“So far, string theory doesn’t address this very directly,” asserts Smolin, “while other approaches do,” but before he could explain this further, Flatow took a call from a lady who suggested that “thinking outside the box,” is what’s required, which distracted Smolin into stating that, while he agreed with her, he definitely feels that it has to be the trained minds of professional physicists that do the “out of the box” thinking, who “go back in the decision tree,” looking for new answers to foundational questions, because only they are prepared to readily scale the true mountain of knowledge, once the location of the highest peak in the landscape is discovered.  Whereupon Flatow interjected,

Are we at a point now, where you just have to sit and scratch your head and think, “We need some revolution, don’t we?” I mean, we need a revolution in physics, maybe we need a new physics!

Smolin’s reply revealed how difficult it is for the trained minds of professionals to think “outside of the box,” in that he referred to the need for more experiment, not clearer thinking.  “Nothing can happen without experiments,” he asserts.  Yet, surely the trouble with physics is not that there is not enough empirical data, but that there is no satisfactory explanation of the existing data from many, many experiments.  In Smolin’s view, however, the pressing need is to complete the revolution that Einstein started, by putting the existing theories together somehow, not that a revolution in existing concepts is needed that would make it possible to explain both the quantum and the continuum nature of reality in a consistent, new, way. 

Yet it is this latter meaning of “new physics” that Flatow had in mind, so he turned to Green to get his comments, and Green seemed more willing to admit that something truly revolutionary in physical concepts is needed in our conception of space and time:

I full well believe that we will, when we do complete this revolution that Lee is referring to, have a completely different view of the universe.  I totally agree with Lee, that everything we know points to space and time not even being fundamental entities…We think that space and time…rely upon more fundamental ideas…What those fundamental entities are…that make up space and time, we don’t know yet, …but, when we get there, I think that we will learn that space and time are not what we thought they are.  They are going to morph into something completely unfamiliar, and we’ll find that, in certain circumstances, space and time appear in the way we humans interpret those concepts, but fundamentally the universe is not built out of these familiar notions of space and time that we experience.

Flatow stumbled a little, trying to get his head around an idea of what this might mean in terms of changes to existing concepts, which prompted Green to state:

It would change the very notion of reality…We all think about reality existing in a region of space and taking place through some duration of time, but we’ve learned that those basic ideas of the arena of space and the duration of time are not concepts that even apply, in certain realms, and if the notions of space and time evaporate, then our whole conception of reality, the whole container of reality will have evaporated, and we’ll have to learn to think about physics and the universe completly differently.

At the LRC, we have already “learned to think about physics and the universe completely differently,” in just this way. In our work, space and time have no meaning apart from that which they have in the equation of motion.  Space is not something that can be warped, or curved. Time is not something that that can be treated like space, as if it were a fourth coordinate in a spacetime continuum.  Indeed, just as these gentlemen suspect, space and time are not regarded as fundamental entites, with their own, independent, properties, but merely as the reciprocal aspects of the truly fundamental component of the universe, scalar motion. 

Space means nothing except in relation to time, and the only known relationship of space and time is motion.  The familiar concept of space, upon which the principles of geometry depend, are the result of motion.  Discrete units of scalar motion, once they are defined, occupy definite locations relative to one another, and a set of such locations satisfies the postulates of geometry, but, without the prior scalar motion, such locations cannot be identified.

Thus, with these ideas, the concept of reality changes radically.  It changes from a concept of space and time as a container of matter, where the universe begins with a single location of infinitely dense matter and spreads out to infinity, to a concept of space and time as an eternal increase, where all we can say is that when two locations exist, one farther away than another, there is alway a third, farther out than they are, and when two events exist, one later than another, there is always a third, later than they are.

This new concept of the eternal progression of space/time, or scalar motion, as the sole component of the universe, is something completely unfamiliar, as Green predicts it will be, but Larson has shown that it is capable of leading to an astounding array of consequences that seems to explain the observable structure of the universe.  Larson was the first to discover it, and the first to investigate its consequences, but the work based on this new concept has barely commenced. 

The LRC was established to take Larson’s initial work to a new level, by engaging professional scientists and mathematicians in the task of applying the new physics.  These professionals, as Smolin points out, must have the requisite skills and training to climb the new mountain peak, discovered by Larson, but the task of convincing them that the universe of motion, unveiled by the new physics, is by far the highest peak in the physical landscape is not an easy one.  However, at the Larson Research Center, we are dedicated to accomplishing it.