The Least Action Consistent Stable Universe and the Mathematics November 20, 2009, Modified November 23, 2009 John Lawrence Reed, Jr. Section 4a
Angular Momentum Angular mass momentum is the spin analog of Newton’s first law. We start an object spinning in free (unencumbered) space and it will continue to spin at uniform velocity, perhaps forever. We start an object moving rectilinearly in free space and it will continue to uniformly move, perhaps forever. We have angular and linear momentum. So my question was “How do we get from the first law single body, spin angular momentum, to a two body orbital angular momentum”? Obviously something must support such a “jump”. Section 4 in this series subsumes angular momentum in terms of Kepler’s law of areas, and Newton’s uniform motion, describing a perfectly circular orbit. Recall that Newton used a perfect circle and uniform motion as the basis for the derivation (See Section 4, this series of posts). A 2D perfect circle in a uniform spinning motion is the 2D kinematic equivalent of a 3D solid, uniformly spinning sphere, and a 2D solid, spinning disk. Recall that Newton used Kepler’s least action consistent, law of areas, to support his supposition for a mass derived centripetal force, as his mathematical argument that carried that force to the entire universe, as the means to generalize our “feel” of “gravity”, as the cause of the least action order we observe in the celestial least action universe (See Section 4, this series of posts). Kepler’s law of areas is the naturally occurring, celestial orbit, least action consistent, kinematic analog, of the uniform spinning circle, and the kinematic properties of the spinning sphere and disk. The common constant kinematic connection between the four is angular velocity, which is an artifact of the uniformly spinning circle and spinning sphere, and spinning disk, and is met by the celestial, least action consistent, more general (conic section) orbital motion. These are all least action consistent properties. Three of which are artifacts of a uniformly spinning circle, sphere and disk. One of which (Kepler’s law of areas) apparently obeys a time function independent of mass, to maintain a constant angular velocity. I asked, “So how do we get planet surface mass into the celestial time controlled orbits”? Well, we just multiply two sides of a least action consistent equation by unity in the form of [m/m]. In other words we hitchhike (Hijack or commandeer are perhaps better terms). The least action consistent angular velocity, picked us up (gave us a ride), and became least action consistent angular momentum, by mathematical decree. So again I asked a question: “What is it about the mathematics that allowed us to commandeer the least action consistent celestial motion? The answer here is: the least action itself. Our least action consistent mathematics, carried our conserved planet surface object mass, to the least action consistent, celestial universe motion, in general. Note that our planet surface object mass (this includes our artificial satellites) is conserved, and operates within the least action consistent, time controlled orbits, without an orbit causal effect. We just put planet surface object mass in the least action consistent orbit. Isaac Newton justified this operation by writing, “Since it is true for all objects we can measure, it is true for all objects whatsoever”. Paraphrased. I agree with the idea that since mass is conserved for all objects we can measure, it is probably conserved for all objects whatsoever. Nonetheless, I again asked a question, “Does this mean that all objects with mass, that we cannot measure, have a mass that is proportional to the mass of the objects that we can measure?” And then, what do we mean by “proportional”? Proportional by volume? Proportional by length? Proportional by time? Proportional by area? Proportional by moles…? Here we can gauge precisely what we mean by “proportional” through the units we use to define the gravitational constant. However, we need only know that the experiment we used to determine its value involved only the objects we can measure. Any constant calculated from this experiment applies proportionally only to the objects we can measure. And when we use that constant to proportionally define celestial mass magnitudes, we are merely, once again, commandeering the least action consistent celestial orbit motion, and defining it in terms of the quantities we apply to planet surface objects, to duplicate that motion. Not that far removed from the Pacific Islanders who after the war, painted wooden boxes white to make refrigerators. Since the Earth attractor does not act on mass during orbit, during escape velocity and during freefall (we apply a force to a resistance), we can easily quantify its celestial presence, solely in terms of what we (planet surface mass objects) act on. That is: planet surface mass objects, which we qualify as. Consequently, the idea for angular momentum as a causal descriptor for celestial orbital motion, is kinematically consistent with the celestial angular, time controlled velocity, and the conserved but celestial, velocity independent, planet surface object mass. Here angular orbital momentum does not speak to a controlling mass, much less a proportional to planet surface object, controlling mass. Nor does it speak to a universal force called gravity. The idea for planet surface object angular momentum, as a proportional causal descriptor for celestial orbital motion, is kinematically consistent with the angular time controlled velocity, and the conserved, but independent, planet surface object mass momentum, that we measure. Planet surface object mass momentum can be applied proportionally to the celestial objects that we cannot measure, because planet surface object mass and momentum do not enter into the least action consistent celestial object mathematics, and remain conserved across the universe with respect to planet surface object interactions. Again, where we qualify as planet surface objects. Conclusion Impacting planet surface objects reflect the conserved cumulative resistance of each object’s atoms. We quantify this resistance in terms of planet surface mass. We apply a force to a resistance that is an equal and opposite resistance to the force we apply. From here we conclude that we are responding to an equal and opposite universal force, which we call gravity. Consequently, we define the universe in terms of the force we exert to duplicate the least action consistent celestial events. Where planet surface object mass and momentum do not enter into the celestial mathematics. This is regarded today as Newton’s Great Syntheses. The principle has been incorporated into the atomic study known as particle physics. I say, the Earth attractor acts on atoms. We act on the conserved cumulative resistance of those atoms (mass) and we call our action a force we respond to. Afterword The tendency for the massive orbital body to fly off into space is a consequence of mass and possibly the cause of the eccentricity in orbit, but in the natural satellite celestial case, is not necessarily proportional to planet surface object mass, and is subject to the time function of the least action consistent, attractive celestial mechanism, probably initiated by electromagnetic causes. Therefore the idea for angular momentum as a causal descriptor for orbital motion is kinematically consistent with the angular time controlled velocity, and again, the conserved, but independent planet surface object mass momentum, that we measure, but is not the physical cause of the celestial least action consistent motion. A supremely functional working “subjective” quantitative concept, that initiated the scientific age for mankind. Even with the qualifying statements Isaac Newton increasingly put forward as he aged, those who followed, ultimately led us to conceptual flights of frivolous fantasy, as well as intellectual dead ends, like; Big Bangs and Black Holes, etc. All of it based on our tactile sense, or “feel” of force. johnreed, November 23, 2009 -- You received this message because you are subscribed to the Google Groups "Epistemology" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. 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