RandaMinor aka johnreed Dec 4 1999, 12:00 am When I was a boy, I suspected that there was a common thread that ran through all physical systems, and connected all physical laws. The more I learned, the closer I came to identify it. A recurring image, a momentary insight, a sudden panoramic view, but again and again, it disintegrated and was gone. Defining this thread, putting my finger on it precisely, was for a long time, just outside the range of my consciousness. The most difficult physics problem at that time was the conceptual understanding of atomic structure. A new mathematics had been conceived, and refined, by Bohr, Heisenberg, Schrodinger, Born, Dirac, Feynman, and others, that had been developed expressly for the operational, or scientific analysis of atomic phenomena. Actually, atomic structure is but a part of the larger realm of natural phenomena that the new mathematics was eventually applied to. However, our view of atomic structure remained rife with conundrum and paradox, with or without, the new mathematics. Today much of the new mathematician’s description of the world on the blackboard and in the published papers, is abstract and devoid of any conceptual connection to physical reality. Steven Weinberg, an accomplished contemporary physicist, wrote, ... it is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. With the phrase, ...something to do with the real world, Weinberg reveals that the mathematician has only an unformed idea as to what his abstractions represent conceptually, and no idea why they apply to the universe so well. Consider the words of the late Hungarian mathematician and physicist, Eugene P. Wigner, ... the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious ... there is no rational explanation for it. It is in the contemplation of the remarkable, and on the face, extremely fortunate connection, between the mathematics and the operation of the stable systems in the universe, that I found the thread that had so long eluded me. It turned out that there is, in fact, a rational explanation for it. Galileo may have been the first to formally assert that, ... the laws of nature are written in the language of mathematics. Today we may elaborate. Stability in the field requires economy in cyclic motion.The invariant aspects of the stable systems within the physical universe, toward which we necessarily direct our investigative efforts, function from the principle of least action. Equivalence and symmetry are intrinsic to the principle of least action. Mathematics in general, as is evident from Euclid, and when applied through theoretical physics, feeds on equivalence and symmetry. It is illuminating to note that what the mathematics represents well, its area of focus, is precisely the action stable systems must follow to maintain perpetuity in the field. The rules and laws and generalizations that result from the economic mathematical abstractions, derive necessarily, from a physical systems potential for stability, and not from a separate reality, for any of its postulated or experimentally observed operational quantities. The mathematics fits the stable universe because mathematics and equations can easily represent the economic properties of stable systems. As a result, all our classical conservation laws speak to the economic orders of form attendant to stable system action. This is not to say that there are no causes or underlying reasons for the order we observe in the universe, beyond the principle of least action. Rather, it is to say that our laws and principles are derived solely from, and speak solely to, the principle of least action. Consider the continuing words from Eugene Wigner, ... it is just this uncanny usefulness of mathematical concepts that raises the question of the uniqueness of our physical theories. The extent of the uniqueness of our physical theories is defined by the properties they retain after ultimate reduction to their most basic state. In this form they are consistent with, or reduced to, the static orders of form attendant to an instant or complete cycle of stable system action, be it as in the inverse square property of an economic sphere, the circumference line segment ratio to, its radially enclosed area in the Euclidean circle, or the planets trajectoral time interval ratio, and its swept out area of the economic orbital conic. These are all encompassed by the principle of least action. The consequence of these observations, is the realization that we can create an abstract, bare bones, mathematical system that fits experimental measurement reasonably well, solely by utilizing operational quantities that are economically compatible, symmetrically consistent, or otherwise without effect, with respect to the invariant kinematic orders of form attendant to stable system action. Wigner approaches the idea that one can mathematically define an experimentally verified conserved quantity, complete with a local numerical magnitude, and if that quantity operates according to the principle of least action, without further influence, or effect, it can be proportionally applied to any other stable ystem, utilizing its locally derived magnitude, by virtue of the invariant, economic, time-area, or frequency-wavelength aspects, common to each stable system. This suggests that with any inaccurate, seminal, a priori knowledge assisted dynamic assumption, one can add too, subtract from, and in many ways modify the seminal assumption, in order to maintain a fit with the experimental evidence. Aside from the kinematic quantities common to stable systems, our operational quantities are products of our assumptions and expectations, which in turn are derived from, and limited by, our sense perceptions. The consequence of this, is that all mathematical models of stable physical systems, are at some point, conceptual creations of the observers. This suggests that devising an operationally effective mathematical scheme based on the idea of mass, or high energy particle collision data and principles of symmetry, does not necessarily raise the operational quantities to the level of a physical reality. The fact that we can alter the energy of a proton into primarily transient energy states we collectively call bosons and fermions causes us to conclude that a proton object is composed of quark objects, whereas, by our argument so far, this does not even reasonably follow. The quarks have a physical justification that is dependent on the trails of transitory atomic fragments, created by high energy collisions in the atmosphere, or in the laboratory. I introduce the question here. Of what significance is an isolated transitory (unstable) energy state? Murray Gell-Mann put the theory together from the host of data available, but he never believed that it truly mirrored, real world quantities. Consider Steven Weinberg’s words again. ... it is always hard to realize that these numbers and equations we play with at our desks have something to do with the real world. Before the publication of The Physics Preview, the ... something to do with the real world aspect of the mathematics, had not been clearly articulated. As a result we assumed a too literal interpretation, for the operational quantities within our theoretical constructs, and the mathematicians and physicists were taught, and accepted the physical reality of the theories they learned. What this meant for the rest of humanity was: absent a clear understanding of the connection between the mathematics and the stable systems in the universe, and as long as the physicist had something that worked as a mathematical model for a physical system’s action, humanity was stuck with the operational quantities used within that model. Quantities that are the conceptual nomenclature for the new mathematical constructs that define the action in stable systems. These operate within an idealized operational representation of stable physical systems, as perceived aspects of those systems, and are subsequently conceptually applied to the real universe, describing it solely in terms of the stripped down rarefied model. We are given these quantities as real objects, and we are told that they are fundamental aspects of the universe. The most recent additions are the logical result of an unquestioned, never verified, one hundred year old seminal assumption. That assumption was and is that the electron exists inside the atom as a granular object. Colored quarks have no real existence in the universe, yet, today the academic humanist must reason from a theoretical reality, composed of colored quarks, joined together with gluons, within a time dilating, curved space universe. Why? Because mathematics has something to do with the real world. johnreed members.aol/randaminor
Posted on: Mon, 09 Jun 2014 08:42:10 +0000
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