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.
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." [3] 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 fundament role, until today, "it serves as a guiding principle in the search for further unification and progress." [4]
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:
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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.
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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:
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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.
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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.
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 post, 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:
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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.
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In the light of space and time, however, we see that neither of these paradigms are descriptive of the true situaltion. Indeed, we find that the hidden beauty found in the 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.
References:
1) Thomas Kuhn,
Structure of Scientific Revolutions,
www.des.emory.edu/mfp/Kuhn.html
2) David Gross, "Viewpoints on String Theory," NOVA,
http://www.pbs.org/wgbh/nova/elegant/view-gross.html
3) David Gross, "Gauge Theory- Past, Present, Future?" psroc.phys.ntu.edu.tw/cjp/v30/955.pdf
4) David Gross, "The Role of Symmetry in Fundamental Physics,"
http://www.pnas.org/cgi/content/full/93/25/14256