The Foundations for My Modeling of Certain Creationary Concepts
The Special Theory of Relativity has been and still is a controversial theory. As pointed out in Herrmann (1992, 1995), the methods used by Einstein and those that followed him in the derivation of the basic aspects of this theory and its application to physical science actual lead to logical contradictions. As originally presented, Einstein used the abstract concept of universal time via the general term "clocks" restricted to coordinate systems. However, there is no such thing as a coordinate system within nature. Indeed, if there is no relative motion between two such systems, then his time concept is actually general universal time via the general "clock" notion. Such notions as coordinate systems (i.e. frames of reference) are human constructions. Restricting this theory to the physical-world, the use of the term "clock" indicates that it applies to all possible mechanisms that can be used as a "clock."
Einstein originally used partial derivatives in his derivation and, regardless of the derivation method used, the differential calculus is the major classical tool. Einstein had to synchronize his clocks using "light" signals via a reflection notion called, today, the "radar" method. This and other requirements signify that this theory and any theory that must reduce to the Special Theory under certain circumstances is but a light propagation theory. Many within the physical-science community hold this view.
In order to apply the differential calculus to any physical measure in a reasonably accurate many, especially for macroscopic behavior, one uses an ideal physical entity and measures that can be "infinitesimalized." Not all "clocks" corresponds to an "ideal" clock that can be infinitesimalized. Almost no clock that digitally displays time can be infinitesimalized in a reasonable manner. Further, since the theory uses the language of light (i.e. electromagnet) propagation, then, in order to avoid the model theoretic error of generalization, one should not generalize beyond this language. There is a physical mechanism that is digital, uses light propagation as its basic mechanism and can be infinitesimalized via the length measure. The clock is the light-clock.
One needs only consider two viewpoints relative to the implications of this theory to see that the use of the standard methods and incorrectly generalizing leads to contradictory yet viable philosophic views.
Herbert Dingle (1950) considers the contraction of "length" as physical nonsense. He states relative to the usual expression for length-contraction (*x' -x' =(*x- x)(1-v^2/c^2)^(-1/2)), "The implication of this choice is often expressed by the statement that a body contracts on moving, but the expression is unfortunate: it suggests that something happens to the body, whereas the 'movement' may be given it merely by our mental change of the standard of rest, and we can hardly suppose that the body shrinks on becoming aware of it" (p. 30). He also rejects the notion that "space" changes and contents that ". . . our province is simply that of physical measurements, and our object is simply to relate them with one another accurately and consistently . . . . this is completely achieved by a re-definition of length . . ." (p. 31) All this comes about since "length is not an intrinsic property of the body." (p. 30).
As to time-dilation, Dingle claims that is comes about only due to the way science defines velocity, a defining method that need not be used. A magnetic form of speedometer on a specific vehicle can simply be marked off in speedometer units as a measure of velocity is one of his examples. One then uses the length contraction statement and obtains the necessary time-dilation expression. Indeed, he claims for this time expression the following: "A very familiar expression of this result is that statement that the rate of a clock is changed by motion, and by this we are intended to understand that some physical change occurs in the clock. How false this is can be seen, just as the falsity of the corresponding statement for space-measuring rods, by remembering that we can change the velocity of the clock merely by changing our minds" (p. 39-40). Dingle gives specific examples of clocks that he claims cannot be altered in this manner. He claims that all evidence for the Special Theory time-dilation is evidence for changes that must be made in the "unit" of time via its relation to velocity and the required alteration in the "length" definition. He does not mention and explain in this book using his definition notion the Ives-Stillwell 1938 experiment (frequency changes in emitted "light" from hydrogen canal rays) nor changes in decay rates that are attributed to time-dilation.
Then we have Lawden's (1982) statements about length contraction. "The contraction is not to be thought of as the physical reaction of the rod to its motion and as belonging to the same category of physical effects as the contraction of a metal rod when it is cooled. It is due to a changed relationship between the rode and the instruments measuring its length. . . .It is now understood that length, like every other physical quantity, is defined by the procedure employed for its measure and it possesses no meaning apart from being the result of this procedure. [Notice the use of the term "quantity." Physical properties exist in reality. But, the properties are distinct from the methods used to measure the properties.] . . . [I]t is not surprising that, when the procedures must be altered to suit the circumstances, the result will also be changed. It may assist the reader to adopt the modern view of the Fitzgerald contraction if we remark that the length of the rod considered above can be alerted at any instant simply by changing our minds and commencing to employ the S frame rather than the S' frame. Clearly, a change of mathematical description can have no physical consequences" (p. 12).
Lawden takes the time-dilation expression as the one that has physical significance ". . . all physical processes will evolve more slowly when observed from a frame relative to which they are moving" (p.13). Dingle and Lawden agree that the length-contraction expression only relates to measurement and the proper way one must define length based upon the circumstances. However, we have a direct and absolute contradiction between these two philosophic views relative to the time-dilation notion. However, are these time-dilation alterations actual physical changes or are they but observational illusions? (This is answered below.)
It appears significant that there was no rigorous basis for the philosophic stances of Dingle and Lawden. This all changed with the use of infinitesimal light-clock theory. In Herrmann (1992, 1995), infinitesimal light-clock measurements are expressed entirely in terms of the counter numbers and an "arm" length, where two distinct physical interpretations are possible rather than one. The length of the "arm" can be reasonably infinitesimalized in the same manner used to measure "lengths" of a many curves via classical calculus. In order to have a light-clock model using the most basic light propagation properties and do so in the simplest possible way, it is necessary to select the interpretation that states that the "arm" is not physically altered by relative motion, but the infinitesimal light-clock count numbers can be altered. In all cases, the numerical value of a coordinate position in the basic Cartesian system is obtained from the basic relation for the infinitesimal light-clock counts of the observed (that is reflected) pulse from a third point P, where we have uniform substratum velocities or potential velocities. I point out that relative to the standardizing methods used in Nonstandard Analysis this becomes an exact real number measure for coordinate locations.
When infinitesimal light-clocks are used to measure the length of a rod with respect to linear relative motion, the trivial case shows that there is no change in infinitesimal light-clock length measure. But, under a specific change in circumstances (i.e. parameters), an equation (6.13 (p. 38)) shows that there is a change in the measure of "length" due to alterations in the infinitesimal light-clock counts. Indeed, (a), in Herrmann (2005), shows how any other changes in circumstances also yields different expressions for the infinitesimal light-clock defined length. Hence, since there is no fixed expression for such length "contraction" independent of the parameters, the notion is not universal and the idea that the expressions simply imply altered definitions is viable.
On the other hand, with respect to linear relative motion, (b), in Herrmann (2005), shows that the alterations in the infinitesimal light-clock counts used to measure "time" are independent from the circumstances (i.e. the parameters) and is a universal requirement. Hence, the assumed non-physically varying "arm" assumption yields the Dingle-Lawden philosophic length notion. However, the mathematics (equation 6.14) rejects the Dingle notion that (infinitesimal light-clock measured) time-dilation is simply a problem of measure and definition and verifies that it must represent actual physical or observed alterations in behavior if such a notion is actually applicable to the physical world.
There are also other philosophic problems with the Special and General theories. For example, what is physical space or spacetime in modern physics? "Physical space is, then, nothing more than the aggregate of all possible coordinate frames" (Lawden, 1982, p. 127). Indeed, Lawden claims that this is the only way that physical space can be scientifically defined. But, since within nature there are no coordinate frames, then under this definition physical space does not exist as a physical-science entity. Indeed, under this definition spacetime is not a physical entity and neither is "time" a physical entity. Dingle notes that many don't accept such a Lawden statement when they consider such notions as 'curved' spacetime. "Thus a complicated set of misinterpretations of symbols, . . ., has been presented as a great discovery of a physical truth. . . . All of the inconceivable statements that have been made about it [General Relativity] are the result of confusion of symbols with what is being symbolized" (p. 87).
Dingle gives various examples as to exactly what he means. He shows that specific terms used to discuss mathematical expressions do not correspond to real physical behavior; indeed, expressions in terms of "curvature" where the term does not correspond to physical reality. However, many modern scientists apparently consider "time" as an actual physical entity related to propagation. (Super)string theory seems to require "time" to be considered as a physical entity. This seems to come about by equating motion with time. This is a rather old idea since this is how Aristotle defined time. The basic philosophical problem is that we are dealing with paper-and-pencil humanly constructed models using mathematical constructs. Are the models we construct analogue (it rationally represents behavior and properties where the actual objects used may be different from those presented) or fully analogue (only represents behavior by assuming entities none of which correspond to the actual objects) or concrete (the objects used are claimed to be the real objects)? With the possible exception of overwhelming indirect or observed evidence, I personally reject many physical models for natural-system behavior as being concrete models. I'll discuss more of my philosophy of this sort of science later.
Let's return to the Special Theory where it appears that the use of light-clocks or equivalent devices is the proper measuring device.
Using various procedures, attempts were made to derive the Special Theory based only on the light propagation notion and the radar method. They all failed until Prokhovnik (1967) was able to achieve the desired results. However, Prokhovnik's work is incomplete and an aspect of his interpretation (i.e. space expansion) is faulty. He presupposes that a certain differential equation models one aspect of light propagation.
In order to complete a light propagation derivation without logical difficulties, one needs to restrict the "clock" notion to include the actual language used in all standard derivations including the usual simple one first suggested by Minkowski, often using imaginary time, where the wave-front property of light is employed. The only appropriate "clock" that incorporates all of the needed propagation requirements is the light-clock. Further, the differential equation used by Prokhovnik needs to be derived from "physical" properties. The new derivation using only light-clocks, and the modern theory of infinitesimals was obtained in 1992 (Herrmann, 1995). Besides rigorously establishing the physical significance of time-dilation, the derivation establishes via indirect evidence the existence of a "substratum." (This is not the "ether" as was previously hypnotized.)
All of the basic Special Theory transformations, in terms of infinitesimal light-clock counts, are obtained. It rigorously shows that, in terms of infinitesimal light-clock measures, relative velocity is not dependent upon the location of the observer and much more. A totally new interpretation as to meaning of the transformations immediately emerges. No speculation is required. What the transformations imply is that, relative to this substratum, relative motion alters only one mechanism. It alters the infinitesimal light-clock "counts." Thus, as an immediate conclusion, for both the General and Special theories, you have a pure physical cause for all such actual or merely observed physical alterations in behavior that previously were attributed to general time-dilation. The cause is a type of electromagnetic interaction with the substratum. As mentioned, the controversy between whether "length" or "time" is altered when viewed from the appropriate system is eliminated since such "length" is also measured by the infinitesimal light-clocks and light propagation. The only alteration is in light-clock counts and "physical" time is not altered.
For intuitive reasons, substratum time and a relative velocity with respect to the substratum are used as a basis for the derivations in Herrmann (1995) without considering any mode of measurement. After this, the Einstein measures are introduced. These are actual physical measures represented by infinitesimal light-clock counts. These measurements are operationally obtained and correspond to infinitesimal light-clock counts that are operationally approximated within the natural world. Thus, the substratum times are determined by expressions that involve only operational Einstein measures. The real world relative velocities are also obtained operationally and can be used to calculate substratum velocities. These substratum velocities are a type of absolute velocity that are measured by real world processes.
To avoid the model theoretic error of generalization, each apparent alteration in physical behavior due to this interaction would need to be individually derived and the derivations should only use the timing light-clocks. Further, these are relative alterations. In the real world, one makes measurements for the properties of a fixed body, considers these measurements as a standard and then compares them with any altered measures for the same properties of a similar object that has non-zero relative motion with respect to the standard. Of course, relative to the Special Theory, any alterations due to gravity would need to be mathematically removed or experimentally eliminated. If these alterations were verified as physically real, then this would indicate that the physical objects involved have some sort of coupling with electromagnetic entities. (This coupling would be particular significant for gravitational alterations.) Towards this goal, a totally new method to derive the notion of line elements (metrics) is developed. These are general line elements that contain a single parameter that represents a type of velocity or potential velocity. Although if one wishes these line elements can be related to geometry and the classical General Theory by simply changing the notation used for coordinate time and position, such a relation it is not necessary. Indeed, many of the line elements used in the General Theory are obtained not from the Einstein-Hilbert equations, but by selecting specific and physically determined potential velocities.
One of these line elements is called the "linear effect" line element and is the one used to derive individually the Special Theory apparent alterations in physical behavior using only the notions of operator styled "separation of variables" and universal functions. By these methods all the basic verified relativistic (apparent) alterations in physical behavior for the Special Theory have been derived. But, using the line elements associated with the General Theory, the exact same infinitesimal time-light clock differential expression is obtained as used for the Special Theory. The exact same derivations yield the gravitational relativistic alterations in behavior where the "velocities" are but potential. Few doubt that the gravitational alterations are physically really. This yields additional very strong evidence that the Special Theory alterations are physically real as well. All of these basic results were developed under a 1993 federal government research grant and were published in journal form as well as in Herrmann (1995). The fact that these new derivations were obtained was announced to the CRS in the Quarterly of March 1994. These results present a real world mode of measurement since infinitesimal light-clocks can be approximated within the real world by equivalent devices.
One aspect of these new discoveries is that the line elements could also be used with a process emanating from the substratum to obtain the locally altered rates of change of various physical quantities and other corresponding measures of pure quantities such as mass or energy. This all depends upon the location of line element application. The rates of change and associated measures of physical quantities could be made to decrease or increase. Using the local decrease aspects, I developed the "hot firmament model" with the exceptional slowing of these physical rates of change so that the entire exterior universe would develop over the appropriate external time period during one earth-time day. I point out that these alterations should only be considered as comparative in character. Since one of these line elements happens to be the Robinson-Walker line element, then, if one wishes, this leads to an actual textural expansion of our universe via an expansion of the substratum. I accept that there is an actual real world center for this expansion that corresponds to a position within the substratum. In theory, such a center might be inferred from indirect evidence. Physical objects at, or "near," this center would essentially be stationary as viewed from the substratum. In the sense of Popper by using this location and Einstein measures, absolute motion with respect to the substratum could be measured. This contradicts the major assumption of the Einstein approach with respect to the ether. But, I mention again, that the substratum does not have the same properties as the assumed ether.
These methods were not developed for theological application but, of course, such an application can be made. From a theological viewpoint, this substratum is an interface between the ultranatural world and our natural world. In general, the ultranatural world need not be the theological "supernatural." Such a supernatural world is on yet another level of comprehension. For the ultranatural world, we have specific knowledge as to the behavior of the processes. This is not the case with the supernatural world. As with other interface notions, there can be information available within the ultranatural world as to the rules for application, the ultranatural laws, theories and the like are predicted to exist. However, such information is not comprehensible in detail since in-depth explanations require a "higher" language. Theologically, the entity that has designed and applies the ultranatural operators is a supernatural entity termed as God. God would use these processes and needs to only select the value of a single parameter. Indeed, a single process can also be used to produce the Genesis Flood. Although these results are not related to Humphreys' method of gravitational time-dilation, the final results are the same. The "stars" either "appeared" during day-four or they are created during day-four. But, after applying this process to Biblical descriptions in 1993-1994, do I actually accept this as the basic method that produced the Genesis 1 creation scenario and the Genesis Flood?
It has often been said that when creationary scientists spend some effort in developing various Genesis theories, they will not reject them even in the light of a better one. The better one appears in the book "Science Declares Our Universe IS Intelligently Designed (Xulon Press 2002). It can be stated in a single sentence. "This is easily accomplished by adding billions upon billions of additional steps over the primitive time interval. Within the bounded region, this would give the appearance, in comparison, of retarding all day-three (or day four) developing processes that are represented by time rates of change" (p. 214). Such a pre-designed event sequence would exist covirtually. It only needs to be realized. I state on my web site that whether you consider a day-three or day-four star formation depends upon what your consider to be the "local environment." It must, at the least, include the Earth. Thus, a "simple" selection of a pre-designed event sequence with the realization operator applied is all that is required. I now reject the Special or General theories physical alteration processes as a model for Genesis 1 and the Flood, although I accept my derivation of the Special and General theories via infinitesimal light-clocks and its causal implications. I accept this event sequence form for Genesis 1 and the same approach for the Genesis Flood based upon the modeling notion often called Occam's Razor. So, although I no longer accept these Special and General theory processes as the actual Divine method that verifies a literal Genesis 1 creation scheme, it appears that I do have a certain priority when the notion of creation and reduction of rates of change are concerned. One wonders why, my work in this area has been so completely ignored. Maybe because I only minored in physics at Johns Hopkins, the first university within the United States dedicated to research.
Many do not appreciate the complexity of modern theoretical physics. Mostly "modern" mathematical structures are employed for this theoretical work. For theorists in "supergravity" and "superstring" theory and elsewhere, the basic structure is the manifold. Then generalized gauge theories, conformal field theory, various abstract topological structures, unusual algebras and even cohomologies are utilized. It turns out that the basic structures just mentioned can be recast in terms of sets of infinitesimals or generalizations such as the topological monads. I contend that as long as any dimension greater than 3+1 is required no matter how one might "fold" them into a final result, that all such endeavors are not related to reality. They are but paper-and-pencil activities that might partially model the behavior of a developing event sequence in terms of imaginary entities. In almost all cases, they are even unnecessary. I further contend that all such theoretical constructs must eventually converge to a "first-level" theory of actual macroscopic world measurements for properties of real world entities. Among all of its other attributes, the theory of infinitesimal light-clocks is such a theory of measurement.
H. Dingle. (1950). The Special Theory of Relativity, Methuen's Monographs on Physical Subjects, Methuen & Co, London, John Wiley & Sons Inc. New York.
R. A. Herrmann. (2005). Remarks (1) on the Theory of Infinitesimal Light-Clocks www.arxiv.org/abs/math.GM/0502092
R. A. Herrmann. (1992, 1995). Nonstandard Analysis Applied to Special and General Relativity - The Theory of Infinitesimal Light-Clocks www.arxiv.org/abs/math.GM/0312189
D. F. Lawden. (1982). An Introduction to Tensor Calculus, Relativity and Cosmology, John Wiley & Sons, New York.
S. J. Prokhovnik. (1967). The Logic Of Special Relativity, Cambridge University Press, Cambridge.