Part II - Larson’s New System of Physical Theory


As explained in part I of this article, Larson realized that the definition of motion does not require a change in the location of a physical entity, measured in terms of a background of space and time. He understood that motion is the equivalent of a space/time ratio, marking the continuous march, or a progression, of space and time. Consequently, he posited the existence of such motion, or ratio of progressing space and time, as the sole constituent of a theoretical universe.

Since the entire Newtonian system of physical theory is based on the definition of motion as the change of a physical entity’s location, x, in some interval of time, t, or the function x(t), the change in this definition requires a new system of physical theory. One that is based on the new definition of motion. However, as mentioned previously, the new definition of motion does not replace the former definition. Rather, it expands the range and meaning of motion into a new realm, while preserving the results obtained on the basis of the former definition in the Newtonian system, even though some of these may now need to be reinterpreted in light of the new definition.

Needless to say, when one considers the significance of such a prospect, given the almost mind-boggling body of work accomplished in the Newtonian system, it’s rather difficult to assimilate it adequately, especially when one regards the level of technical sophistication, which modern theoretical physics has reached in the last 100 years. The disconnect between the practicing professionals in the Newtonian system, and the neophytes endeavoring to embrace the possibilities of the new system, is immense to say the least.

Fundamental Revolution

Yet, there is a crisis in the Newtonian system today, as Smolin points out so eloquently in the paper we’ve been discussing. Such a crisis is exactly the sort of development that, according to Thomas Kuhn, presages a scientific revolution. [4] In fact, the shift in paradigm that Kuhn describes as necessary to precipitate the revolution has been widely anticipated for many years, but no one in the community has had a clue as to what it might be, except that there seems to be a consensus that, whatever it is, it is likely to have something to do with our understanding of the nature of space and time.

David Gross, a recent recipient of the Nobel Prize in physics, and a leading light in string theory, discussed this subject with a PBS NOVA correspondent in an interview for the show “The Elegant Universe,” based on Briane Green’s book with the same title. [5] Gross clearly expects that the coming revolution will change our view of the nature of space and time. He said,

This revolution will likely change the way we think about space and time, maybe even eliminate them completely as a basis for our description of reality.

Gross, like many physicists today, places his bets on string theory, but he understands that string theory may only be a harbinger of what’s to come:

In string theory I think we’re in sort of a pre-revolutionary stage. We have hit upon, somewhat accidentally, an incredible theoretical structure, many of whose consequences we’ve worked out, many of which we’re working out, which we can use to explore new questions. But we still haven’t made a very radical break with conventional physics. We’ve replaced particles with strings—that in a sense is the most revolutionary aspect of the theory. But all of the other concepts of physics have been left untouched—a safe thing to do if you’re making changes.

Indeed. By the same token, however, it’s clear that the change needed must be a “sea change,” a revolution cannot be precipitated by a minor change. As Gross puts it:

On the other hand, many of us believe that that [replacing particles with strings] will be insufficient to realize the final goals of string theory, or even to truly understand what the theory is, what its basic principles are. That at some point, a much more drastic revolution or discontinuity in our system of beliefs will be required. And that this revolution will likely change the way we think about space and time, maybe even eliminate them completely as a basis for our description of reality—that is, leave us regarding them rather as emergent approximate concepts that are useful under certain circumstances. That is an extraordinarily difficult change to imagine, especially if we somehow change what we mean by time, and is probably one of the reasons why we’re still so far from a true understanding of what string theory is.

Clearly, the pursuit of string theory has raised some startling issues about our most fundamental assumptions regarding the nature of space and time. This implies in turn that a change in these assumptions, when it comes, will have an astonishing impact on the science of physics. Gross characterizes it as a new idea that breaks with the concepts of the past that have been the basis of physical theory historically:

In order to achieve a true understanding of string theory, some new idea will be required, and most likely, some break with the concepts on which we’ve traditionally based physical theory. This has happened before. In the last century, there were two such revolutions having to do with relativity and with the quantum theory, which was an incredible break with the classical notions of physics. Those revolutions were achieved in the end by discontinuous jumps that broke completely with the past in certain respects. It’s not too hard to predict that such a discontinuity is needed in string theory.

But Gross stresses the point that the nature of the coming change is impossible to predict:

What’s harder to predict is what kind of discontinuity is needed. Discontinuity jumps like that—revolutions—are impossible to predict. They require some totally new idea. A lot of us are waiting for such a new idea that will give us an alternate to our traditional notion of space and time perhaps—or perhaps some other new idea. Something is missing that is most likely not just another technical development, another improvement here or there, but something that truly breaks with the past. And all the indications are that it has to do with the nature of space and time.

So, a revolution is expected, one that entails a “totally new idea” that “has to do with the nature of space and time.” Moreover, it is expected that the impact of this new idea of space and time will cause “a break with the concepts” of the past “on which we’ve traditionally based physical theory.” Obviously, the new idea of the nature of space and time that forms the basis of Larson’s Reciprocal System is a perfect candidate to fulfill Gross’s prediction. However, to recognize the promise of Larson’s innovation across the huge disconnect that exists between the modern day practicioner, working within the Newtonian system, and the neophyte amatuer, embracing Larson’s system, is exceedingly difficult. To succeed, it seems that we must find some common ground that will entice those whose professional career is one large investment in the Newtonian system to risk their careers to investigate the promise of the new system. The most likely prospect for finding that common ground, I believe, lies in the principles of symmetry.

Fundamental Symmetry

One of the most important developments in the field of physics in the last hundred and twenty years is the understanding of invariance principles. These principles underlie the processes of theory development in the Newtonian system of physical theory, in a deep and intriguing manner. They began to be applied as it became clear that the validity of physical laws, explaining the regular behavior of physical phenomena, had to persist across transformations of space and time separately, as in different locations in space, and at different moments in time, as well as together, as in moving frames of reference. However, it soon became apparent that these tests of invariance of physical laws could be expressed as laws in and of themselves. Invariance leads to laws of conservation of energy, momentum and charge, for instance, as first proven by Emmy Noether.

Eventually, the idea of invariance grew to include the concept of scale as well, which as it turned out, led to a great increase in the ability to classify force laws, and to identify those that are fundamental by means of symmetries that could be seen to exist in group theory, and they enabled the prediction of events based on laws whose invariance arises from the principles of symmetry in these groups. Since the grand goal of the Newtonian program of research is the classification of these force laws, in terms of a few fundamental particles and a few fundamental interactions, the effacacy of this approach has had a major impact on the philosophy of physics.

In fact, Gross, following Wigner and others, asserts that “the primary lesson of physics in this century is that the secret of nature is symmetry;” that is, that “symmetry dictates interactions.” [6] Gross attributes this deep understanding and appreciation of symmetry to Einstein, whose “great advance in 1905 was to put symmetry first, to regard the symmetry principle as the primary feature of nature that constrains the allowable dynamical laws.” Gross stresses that such a change in point of view “is a profound change of attitude,” that enabled Einstein to “score a spectacular success” ten years later, with general relativity. GR is based on a local symmetry, the principle of equivalence between inertial and gravitational mass, which dictates the dynamics of gravity. Then, as quantum mechanics emerged in the 20th Century, principles of symmetry assumed an even more fundamental role, until today, “it serves as a guiding principle in the search for further unification and progress.” [7]

However, there are two kinds of symmetry that have been the focus of modern physics, global symmetry that embodies the invariance of space and time separately as locations, and the invariance of space and time together, as motion, and local symmetry, which has to do with the scale of space and time. Thus, global symmetries express the invariance of physical laws in different physical situations, such as the locations of events that are translated or rotated, or the timing of events that occur at different times, or events in a moving frame of reference, a so-called inertial frame of reference.

Local symmetry transformations, however, do not change the location or time or move the frame of events. Local symmetry transformations change the description of the event in terms of the scale (gauge), or phase of the event. For instance, an EM field can be changed by merely introducing a vector potential, but the values of the E and B fields are not affected by the potential. At first, these local symmetries were not regarded as real, eventually, however, they came to dominate the thinking of physicists, and in fact, are now believed to be more real than global symmetries. Gross states:

Indeed today we believe that global symmetries are unnatural. They smell of action at a distance. We now suspect that all fundamental symmetries are local gauge symmetries. Global symmetries are either all broken (such as parity, time reversal invariance, and charge symmetry) or approximate (such as isotopic spin invariance) or they are the remnants of spontaneously broken local symmetries.

The dramatic success with symmetry has led to the inquiry as to why nature should be so symmetrical as this, and to the search for the “fundamental symmetries.” As Gross puts it:

When searching for new and more fundamental laws of nature we should search for new symmetries. Current theoretical exploration in the search for further unification of the forces of nature, including gravity, is largely based on the search for new symmetries of nature. Theorists speculate on larger and larger local symmetries and more intricate patterns of symmetry breaking in order to further unify the separate interactions.

Of course, the most famous of these, and the one string theorists have searched for decades to find, is supersymmetry. But they haven’t found it. Many think that this is because it doesn’t exist, but others are convinced that it will be found at higher energies, which is why the LHC at CERN is so important.

Perfect Symmetry

Meanwhile, however, a new, fundamental, symmetry has been found. It is the symmetry of space and time as the reciprocal aspects of scalar motion. This symmetry is both local and global; that is, changing the scale of the discrete units that form the space/time ratio does not alter the symmetry, but altering the symmetry of the space/time ratio has the global effect that creates the physical constituents of radiation, matter, and energy, together with their properties such as propagation, gravitation, and entropy.

In the next part, we will explore the mathematical aspects of this symmetry and show how it is broken, the consequences that follow, and how it answers Gross’s question, “Why is nature symmetric?” In regards to this question, Gross explains:

There are at least two views. The first is based on the paradigm of condensed matter systems where unexpected and new symmetries often occur, although they are not present in the fundamental laws. The prime example is the appearance of symmetry in the behavior of long-range fluctuations of a system undergoing a second-order phase transition. Here one has the phenomenon that at the fundamental, short distance or high energy, level there is no symmetry. Rather the symmetry emerges dynamically at large distances. Could this be the reason for the “fundamental symmetries” that we observe in nature? Could they be dynamical consequences of an asymmetric physics? I believe not. The lesson of the history of physics in this century points to the opposite conclusion. As we explore physics at higher and higher energy, revealing its structure at shorter and shorter distances, we discover more and more symmetry. This symmetry is usually broken or hidden at low energy. I like to think of the first paradigm as Garbage in—Beauty out, and the second as Beauty in—Garbage out.

In the light of space and time, however, we see that neither of these paradigms are descriptive of the true situation. Indeed, we find that the hidden beauty found in the perfect symmetry of scalar motion is manifest over and over again as the source of the beauty of nature’s plethora of physical forms.

(See also: Larson’s New System of Physical Theory - Part III - Larson’s New System of Physical Theory - Part I - Larson’s New System of Physical Theory - Part IV - Larson’s New System of Physical Theory - Part V)