Does God Sustain Fundamental Physical Behavior by Discrete or Non-smooth Processes?
Robert A. Herrmann Ph.D. 12 DEC 2007. Slightly revised 14 JAN 2016.
In physical science, it is well known, I hope, that acceptance of a model for physical-system behavior is driven by a world-view or personal philosophy. There are often different models that predict the same experimental results, but some selections will contradict an individual's world-view. Indeed, if the individual has an immutable world-view, in some cases, they cannot comprehend alternate models. It often takes extreme courage for an individual to select a model that requires an alteration in personal philosophy. Much of their previous work might be discounted. They can loose their authority, money, job and greatly damage their reputation. So, it's no wonder that a significant result, published in 1983, is known by very few and accepted by still fewer.
The GID-model interpretation of the GGU-model shows that the construction of and alterations in the behavior of all physical-systems within our universe are intelligently designed by a higher intelligence. The question as to what type of "control" is provided by the higher intelligence was actually answered first. As far as I can determine the paper (1) uses a process that had never before been employed to answer such questions.
When mathematics is used to describe behavior, it is not merely the basic numerical, etc. results that are stated. Indeed, it is actually often necessary that the mathematical results be interpreted in a physical language without any reference to the auxiliary mathematical quantities. A time dependent increasing function "measures" the "speed" of an entity. Physically one could simply state "over time the entity appears to be moving faster and faster." For our earth, one does not need to discuss the "processes" in-depth to state "a physical process is holding the earth in its orbit." Indeed, Kepler was the first to consider this as a radially directed "force."
As another example, consider the modern description for beta decay. Within the neutron, at time t, a "transition" takes place and a d-quark "changes" into a u-quark by emitting a W particle. (How does it do this?) Then another transition takes place at time t1 and the W particle changes or produces an electron and an antineutrino. (How does it do this?) Many consider these changes as "discrete" or sudden alterations. However, it was proposed that there should be a more detailed description for the "physical-processes" that yield these changes. The theory of propertons yields such a description. But, it does not further characterize the "gathering process." Indeed, when this paper was original presented, properton (subparticle) theory was not well developed. So, another rather unique method was used to characterize these processes, in general, where it does not require one to accept a specific "process."
What is done is that a collection of mathematical functions is used to represent a "neutron altering process," where numerical values are interpreted directly in terms of a physical process language. For a specific time interval [t,t"] at a transition time t0 contained in its interior, one unique function f with a value 2 for all times before the t0 and a 3 for all times after the t0, would be interpreted as modeling a "discrete altering process." Another function f' which is continuous and "smooth," that is the derivative exists and is continuous, and that has the value of 2 at t and 3 at t" is interpreted as a "classical altering process." A lot more stuff needs to be added in order to properly employ these functions and I won't go into this extra stuff. Obviously, it would appear that from the standard viewpoint, you cannot use both the f and f' functions as a model for these processes, whatever they might be, since they are contradictory. But, for some atomic-systems both process notions predict the same experimentally verified results.
One of the great "mysteries" is how is it possible that, in "the small," behavior is considered as discrete but "observed" macroscopic or large scale behavior is better understood and predicted using continuity and smoothness concepts? Biblically, it appears that it's the "observed" physical-system behavior that indicates God's invisible qualities. Thus, there has been a reluctance to accept the quantum physical notion of discreteness or a non-smooth concept as the correct view as to how God controls and sustains physical behavior.
Well, what does this paper show? It describes the mathematical results, an important part of which was later published in the J. of Math. Physics (2), that as viewed from a nonstandard substratum the altering processes can be characterized as hypercontinuous and hypersmooth within a substratum "time" interval. These two notions yield an higher-intelligence view for such behavior. These two notions give a type of continuity and smoothness that is "greater in quality" than in the standard case. But, when viewed from our standard world the process is discrete in character. Hypercontinuity or hypersmoothness, in this case, is not the same as the continuous or smoothness, respectively. Although standard continuous or smooth functions are also hypercontinuous or hypersmooth, respectively, this gives one answer for these two seeming incapable notions.
What about fractal behavior? This is behavior that is continuous and totally non-smooth in character. As first introduced in the 1880s, continuous functions defined on the entire set of real numbers exist that do not have a derivative at any real number. Of course, I cannot "graph" such a function. But, as shown in 1989 (2), for any n-dimensional fractal curve f, there is in the nonstandard physical world a function G that is hypercontinuous and hypersmooth, indeed ultrasmooth (it has derivatives of all orders). However, when G is viewed in the standard world, G and f coincide. Indeed, G can be *integrated to give meaning to a fractal measure for length, area, volume etc., something that is not so easily done for standard fractals. Also if one employs a model using manifolds, all of the above "hyper" results hold.
Thus, from the viewpoint of an higher-intelligence, there is no substantial difference between the discrete as well as non-smooth behavior, and these higher forms of continuity and smoothness. The mystery is solved, especially for those who hold physical-science to a strict Biblical standard. The difference is relative to the intelligence of the observer.
Once again these examples demonstrate, what I accept, that there are significant differences in the methods God uses to create and sustain His creation than the methods "imagined" by secular physical-science communities. I wonder if any of these results are employed when God's sustaining and creative power is discussed?
Finally, all of the immense amount of indirect evidence I have presented over the past many, many years for the existence of a created "substratum" interface (a foundational second heaven) between our physical world and God's pure supernatural world should not be discounted.
(1) Herrmann, R. A. "Mathematical philosophy and developmental processes," Nature and System, 5(1/2)(1983), 17-36.
(2) Herrmann, R. A. "Fractals and ultrasmooth microeffects," J. Mathematical Physics, 30(4) (April 1989), 805-808.
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