The Contropic Theory offers promising philosophical possibilities on the Universal scale. If efficient, stabilizing structure can develop from within, then the fate of the physical Universe might be far different from that predicted by probabilism. The theory proposes the existence of a sub-quantum "Simplest Possible Particle" (called "SPP's", and differentiated as being either gravitons or magnetons depending upon the orientation of the axis of rotation with the axis of translation), and defines it to be the "elemental" particle.
Other physical existences such as Photons, Neutrinos, quarks, Electrons, Mesons, Protons, Neutrons, Atoms, Molecules, Cells, Man, etc., are seen as being physical constructions that are held together (at least for a time) in opposition to a statistical, thermodynamic tendency for energy to disperse. Their continued existence is dependent on internal structure and organization which produces forces of containment to oppose those of decay. Such existences can be regarded as self-contained microsystems which are simpler in their structure and organization than are the supersystems which include them into their structures. For instance, the Cell is simpler in its self and in its functions than is the Man (who includes the Cell and its functions) in his. At the level of the Photon, the system and its functions should be most uncomplicated.
Structural forms based on the Quark Theory have been proposed for the Proton and the Electron, but there seems to have been little real interest in models for the physical structure of Photons. Fritz Zwicky (1929) proposed that photons continuously lose energy as they travel through space, thereby shifting their light toward the red end of the spectrum. LaViolette (1986) has supported this theory, known as the "Tired Light" theory, with four different observational tests. If such losses are indigenous rather than due to external causes, they would infer that there are structural inefficiencies in the Photon and/or at least in the beam of Photons, so acceptance of the theory would probably have inspired more interest in the structure of Photons. However, the theory has been generally rejected (at least up until LaViolette's work) in favor of Hubble's explanation of "Red Shift" as a Doppler effect caused by recession of the galaxies from earth, and the Photon is thought to be an elemental particle.
Since Contropy is proposed as a parameter which is independentof the current paradigm, its correspondence to physical reality must be positively demonstrated before its philosophical implications can be taken seriously. The construction of Contropic models for structural stability within the comparatively uncomplicated realities of the simplest physical existences offers opportunities to test for such correspondence.
At least in its scientific applications, the operative principle of Ockham's Razor^{1} may well be the fact that simplicity is inversely proportional to the number of specifications which are required for the full description of the entity or effect in question. Each specification introduces its own degree of uncertainty or randomness to the implications of other specifications. Therefore, when all else is equal, the probability of error is proportional to the number of specifications required by a given hypothesis. Especially when an hypothesis aims at Universal application should it be grounded upon a minimum number of resultant specifications, or else attempts to deal with specific interactions might become unmanageable in the general case.
One of the most effective techniques which has been developed for the isolation of resultant behavior is the use of statistical analysis. A sample, or model, is constructed to derive typical behavior, and it is then used to extend that behavior to the general case in order to further define resultants. An elegant example of the use of this technique can be seen in the derivation of the "Perfect Gas Law" (for example: Holton and Brush, 1973b). Although this law has proven adequate for the description of behavior in a complex variety of atomic and molecular gases, it is based on few specifications:
1. There must be contained a number of constituent elemental particles which is sufficient for statistical representation.
2. The particles are in random motion.
3. The only interaction between the particles is "perfectly elastic" collision and rebound.
Observe that a "gas" composed of SPP's (such as within the Photon) would conform to these conditions. Since the third specification excludes field forces, the SPP gas should be expected to be even
more "perfectly" gas-like in its behavior than molecular gases, and thus, be subject to the same type of mathematical formulation. Since increases in Contropy are proportional to decreases in
randomness, a corollary to the general theory can be drawn:
A system is less perfectly "gas-like" according to its Contropy.
The term "gas-like" becomes less relevant as interactions besides collision and rebound become controlling. Deviations from "The Perfect Gas Law" are significant in more complex molecular gases (see Burrell and Robertson, 1963), and "Cells" are clearly beyond its purview. Thus, the corollary defines a Special Case of Contropy comprised of "SPP'S", "Photons", "Sub-Atomic Particles", "Atoms", and "Molecular Gases".
Macroscopic perspectives of statistical populations within this case can neglect deviations from randomized behavior; thus, stochastic methods can be applied without impairment. In this, Contropic theory is in basic alignment with Classical as well as, to some extent, with Quantum Mechanical theory. (Possibly the proposed SPP might be used to define a limiting case of Quantum Mechanics, wherein the Hamiltonian could find its simplest expression in a reality of Newtonian collision and rebound, operating with invariant time within three coordinates of Euclidean space?) Constants of dimensional relationship derived from a Contropic perspective should agree with those already accepted. Such derivations should be reasonably simple and straightforward because of the low degree of structure and organization effective within these magnitudes of Contropy. This paper undertakes such derivations as a test of the corollary, and thus, of the Contropic theory.
It is supportive first to test the corollary in the most complicated of the included Contropic magnitudes, "Molecular Gases". It can be seen by inspection that the corollary is consistent with the
observed behavior of molecules in general, in that their least ordered state is the most gas-like; and more, that the simpler molecular gases deviate less from "perfect" behavior than do the more
complex gases. The corollary is presented in graphical form in Figure 1 (a, b, & c). It should be noted that the scales of Figures 1a and 1b are purely relative. In Figure 1c (with the exception
of Nitrogen), the product of the number of interatomic bonds times the molecular weight of the gas has been taken as a measure of Contropy as indicated by complexity, and plotted against the data of
Burrell and Robertson (U. S. Bureau of Mines Technical Papers 131 and 158). Nitrogen, which is multivalent, fits the curve when treated as if it had only one atomic bond. This is perhaps indicative
of the fact that Nitrogen has a factor of simplicity which is lacking in the other considered gases. These data are presented in Table 3.
Table 3.
DEVIATION FROM "PERFECT GAS" BEHAVIOR BY SOME INCREASINGLY COMPLEX GASES |
||||
GAS |
MOLECULAR WEIGHT |
# OF INTER- ATOMIC BONDS |
MW x BONDS |
% DEVIATION FROM BOYLES' LAW* |
Nitrogen | 28 | 1** | 28 | 0.010 |
Methane | 16 | 4 | 64 | 0.226 |
CO_{2} | 44 | 4 | 176 | 0.670 |
Ethane | 30 | 7 | 210 | 0.900 |
Propane | 44 | 10 | 440 | 1.900 |
Isobutane | 58 | 13 | 754 | 3.400 |
Butane |
58 |
13 |
754 |
3.700 |
(**See discussion) (*Burrell and Robertson, U.S. Bureau of Mines Technical Papers 131 and 158.)
Although Figures 1a, 1b, and 1c are based on the corollary, they are also illustrative of the general concept of Contropy. In particular the parallel of Contropic theory with Teilhard de Chardin's
"Rise of Consciousness" theory can be seen in Figure 1a, in which the special case that is under consideration here is shown in context with those larger concepts.
The Rise of Consciousness theory holds that increasing complexity and organization is equivalent to rising "Consciousness". The theory of Contropy, as previously developed, claims that increasing complexity within the Universe is demonstrated by the Evolutionary Process. Now, the corollary provides that the degree of deviation from perfect gas behavior can be taken as a measure of the Contropy which is effective within a system.
Taken together, these considerations indicate that the axes in Figure 1a might as well be labelled in the terms of the Rise of Consciousness; that is, increasing "Consciousness" as the ordinate and increasing "Time" as the abscissa. The point is that Figure 1a shows a profile of the Evolutionary Process as depicted by either theory.
However, as shown by Figure 1c, systems of Contropic magnitude less than that of Molecular gases can be expected to have a high degree of gas-like behavior. To that extent, statistically- based mathematical formulations within those levels should be facilitated.
It has been speculated here that SPP'S are confined within the Photon of Electromagnetic Energy as a "standing wave". In that case, outside perspectives can resolve all the complexities of SPP's motions into a single resultant identity which has an axis of translation and a singular location in time and space. The corollary provides a basis for derivations of the dimensional interrelationships "within" that identity, which itself defines a contained coordinate system that moves at (nearly) uniform velocity with respect to nearly all outside coordinate systems. But further elaboration of the Photon model is needed.
Within the Photon the motion of the wave (of SPP's) would be paramount. It is derivable (for example: Holton and Brush, 1973c) that the standing wave length, , is related to the length of the "vibrating medium", L, by Equation (2.):
where n is any positive integer. Because of Ockham's Razor and other considerations, the most likely specification for the elemental Photon model is the simplest relationship,= 2L, and that is here assumed as the base ("rest") case.
If the wave rotates about its axis in addition to its length-wise vibration, then the Photon will appear to occupy a volume of Space which is approximately spherical, depending upon the amplitude of the wave. This simplification is made more explicit by assumption that the amplitude of the wave in the base case is equal to /4 cm. The Photon model as seen by an outside observer at relative rest is shown in Sketch #2. Note that the axis of the wave is in the "y"direction, while the SPP's are displaced in the "x" and "z" directions.
Now when this Photon is seen in relative motion in the +x direction, the wave pulse which leaves +y en route to -y appears to traverse a diagonal path, reaching the x axis at a point which is vt centimeters out from x = 0 (where v is velocity of the Photon relative to the observer and t is the time elapsed between start of the pulse and its arrival at the x axis). Since the pulse must be carried by SPP'S known to be at constant speed, it may be derived that there is a distortion of Time and Space between observers "within" and "without" the Photon, equivalent to the Fitzgerald-Lorentz equation. (See Sketch #3)
where t_{r} represents time as seen be perspectives at relative rest and t_{m} is time as seen by perspectives in relative motion. Squaring and rearranging both sides of Equation (4.):
Now, extracting the square root of both sides, and substituting the identity of Equation (3.):
The derived time dilation is in accord with Fitzgerald-Lorentz. The displacement of SPP's from the "y" axis, as seen by observers at relative rest, is given by Equation (5.):
Relative motion of the Photon, as above, causes an apparent foreshortening of the paths of SPP displacement in the "x" dimension due to the dilation of time:
The substitution of Equations (4b.) and (5.) now gives:
squaring both sides:
The "contraction of length" is also in accord with Fitzgerald and Lorentz. Equation (6a.) indicates that observers in relative motion will perceive the Photon as an "oblate spheroid" with eccentricity equal to v/c . As the relative velocity approaches c the Photon presents less and less surface area to all perspectives except those along its path, becoming entirely focused at v = c. It is as if the Photon "sheds" a dimension due to its motion, so that it has height and width, but no length. Because SPP's which would escape from the Photon must do so through the surface, it seems that the Photon gains a measure of containment because of its motion. Sketch #4illustrates these effects.
Consider now this wave-form model from an "internal" perspective. The total Energy contained within the space occupied by the Photon, E_{P}, may be stored within only a limited number of modes. Some energy must be absorbed in the organization of the wave from the otherwise random motion of the SPP's. If this energy is understood as an "Energy of Structure," E_{s}, which is separate from the "Energy of State", E_{pv}, then by extension of Universal experience it can be assumed that E_{s} is a relatively small fraction of E_{P}, and its neglection should not cause any serious error in reasonable approximations.
The properties "angular momentum" and "kinetic energy of rotation" are not detectable from within, and so energy may not be stored within those modes. Such properties are negligible with regard to the individual SPP, and may not serve as a repository of energy. There are only three modes left for consideration:
1. e_{pv} = Intrinsic Energy of SPP's
2. e_{ke} = Kinetic Energy of Translation of SPP's
3. E_{pv} = Energy of State of the Photon
Before examination of the distribution of E_{P} among these modes, it is in order to define the dimensions of Space and Time "within" the Photon. Since the SPP's are each confined within three spatial dimensions--"x", "y", and "z"--along a path which is cm. in length per cycle, and because their velocity is c cm/sec along that path, then "Space" and "Time" can be defined in terms of and those factors of confinement:
The relationship of space with time within the Photon is found by dividing Equation (7.) by Equation (8.):
Each SPP within the Photon collides with the "wall of containment" twice per cycle, and it is reversed in its direction of travel each time. These collisions produce an expansive force which acts through the radius to perform work against the containment. If the total Energy of the Photon, E_{P}, is exerted evenly over its surface, then the expansive force, F, is given by Equation (9.):
and the Pressure, P_{p}, within the Photon can be calculated:
Now, in view of the small degree of Contropy in this system, the corollary allows E_{PV} to be given by Equation (11.):
Equation (11.) confirms gas-like behavior by the model, since the product of its Pressure times its Volume is a constant.
The universality of the model may be further tested by the equation of Pressure within the Photon, P_{P} , as specified by the model with the expression for Pressure within molecular gases, P_{M,}, as derived by Herapath in terms of mass density (m/V) of the gas and the velocity of translation, v, of its molecules:
This straightforward derivation of Einstein's Equation is encouraging to the model and to the corollary upon which it is based.
Returning to the implications of Equation (11.), it can be seen that two thirds of E_{P} is distributed between e_{PV} and e_{KE.} If there are n SPP's contained within the Photon, and e_{s} is used to represent the Total Contained Energy associated with each SPP, then Equation (13.) summarizes these relationships:
The kinetic energy of an SPP can be calculated from Newton's equation, using Einstein's equivalence:
Equations (11.), (13.), and (14.) may be combined to show that E_{P} is evenly distributed among the three modes--Energy of State (of the Photon), Intrinsic Energy (of the SPP), and Kinetic Energy of translation (of the SPP):
The derived "equipartition" of energy within the Photon agrees with theory and observation at higher Contropic states.
According to earlier considerations, the Photon was formed by the chance combination of SPP'S which happened to possess the proper vectors and positions in Space/Time for repeated interactions. If this is the case, Equation (15.) indicates that outside observers will perceive that the Photon contains 50% more energy than was lost by the Universe during formation of the Photon. The idea of Contropy is that such synergistic effects--apparent creation of potential through the leverage of structure and organization--can be seen and felt by outside observers as a separate kind of energy which is available to power further interactions, and so on. (Thus might Evolution proceed.)
The property "Temperature" was originally related to the state of molecular motion, but it has come to be more generally understood as a function of the spatial concentration of available energy. Photon temperature can be defined as the number of SPP's per contained volume, and as such is a function of total kinetic energy within the Photon. Notice that E_{P} is proportional to Temperature, T, through Equation (15.), and further, that thermal energy resides within only two of the three modes of confinement. These considerations can be satisfied in the case of the Photon model by the association of Temperature with the amplitude of the wave, which varies within the "y" and "z" dimensions of Space.
It is clear that Equation (11.) yields a constant result at constant temperature, describing the extensive property "Energy" within the Photon. Therefore, for any given Photon (in which case Space would be constant), the multiplication of Equation (11.) by Equation (7.) should give a "Universal Constant" of dimensional relationship:
The value of s was determined as 1.2382 x 10^{-4} ev-cm by Dr.Robert Millikan during work for which he was awarded the Nobel Prize in 1923. Even though this constant is compounded of two others, in this view "Millikan's Constant" is as basic as any. Because is inversely proportional to E_{P}, it is also inversely proportional to T. The intensive property Temperature can be defined in terms of wave length and spatial dimensions:
where is a constant of proportionality, cm-K. It is noted that a value of for gives close agreement with "Wien's Constant", 0.2897 cm-K, but that value was determined from an outside view, and need not apply "within" the Photon. A value of unity for is consistent with the development which follows^{2}.
Since Energy is proportional to Temperature, Equation (11.)divided by Equation (17.) yields another "Universal Constant" of dimensional relationship:
This value is within about 4% of that accepted as k, "Boltzmann's Constant". That this is no coincidence can be seen by modification of the expression of "Temperature" as derived from the Kinetic-Molecular Theory (Holton and Brush 1973a.):
and then,
The slight discrepancy between the values of k and k' as derived is possibly due to neglection of the Photon's Energy of Structure.
Finally, multiplication of Equation (11.) by Equation (8.)gives the Universal Constant of dimensional relationship between "Energy and "Time":
Of course, this value is exactly the same as h, "Planck's Constant". These considerations are summarized in Table 4.
Table 4:
DIMENSIONAL RELATIONSHIPS AS DERIVED
FROM CONTROPIC THEORY'S PHOTON MODEL |
||||
EQUATION | STATE | DIMENSION | RELATION |
CONSTANT |
(8a.) | ------ | Space/Time | v | c (cm/sec) |
(11.) | Energy | Energy | (P x V) | 3 (ev) |
(16.) | Energy | Space | (P x V) x 3 | s (ev-cm) |
(18.) | Energy | Temperature | (P x V) x 2 | k (ev/K) |
(21.) | Energy | Time | (P x V) x 3/c | h (ev-sec) |
(12a.) | Energy/Mass | Space/Time | (P x V) x 3/m | c^{2} (cm/sec) |
EXAMPLES OF CONTROPIC CONSTRUCTIONS
Photons: The question now arises as to how the Photon is able to "contain" its essence across vast reaches of Time and Space. Because unconfined Energy tends to expand (dissipate), a force of compression is needed to counteract that tendency. Newton's Laws indicate that both emission and absorption of SPP's would generate forces upon the surface of the Photon which are vectorially correct for containment. The contropic assumption that such reactions and impacts might supply the basis for a mechanism of containment suggests a mechanical cycle as an elaboration of the Photon model.
First, observe that, in a Causal Newtonian Universe, SPP's which would escape from the Photon must be inferred to have accelerated from velocity 0 to velocity c with respect to the Photon. The work done on the SPP's is equal to the work done on the Photon:
If work of containment is taken to be positive, then Equation (23.) also holds in the case of absorption of SPP's. The energy balance for emission of a SPP is given by Equation (24.) and for absorption of a SPP by Equation (25.):
Therefore, if a Photon can contrive to absorb one SPP for each three that it emits, it will obtain the benefits of compressive work at no loss of Energy over that period.
When the Photon is in relative motion at velocity c, Equation (4.) applies, and surface area is presented only to perspectives directly ahead (or behind) along the axis of translation. Photons in a chain along the same path through Space could pass SPP's along, except that the leading Photon would have to depend upon its environment for available SPP's.
Notice that there would be a finite lag between absorption and emission. During this time, the velocity of the Photon would be less than c due to the unbalanced force of impact. As a consequence, the Photon would present some surface area to the third spatial dimension as indicated by Equation (4.), and SPP's might escape through that surface. It seems reasonable to assume that the Photon emits a SPP at right angles to its axis of translation from each of its "poles" once each cycle, and that makes the energy balance complete.
The net compressive work done on the Photon is an inverse function of wave length since the cycle rate is increased by shortening the SPP's path within the Photon. Thus, an equilibrium can be established in that increasing pressure within the Photon, P_{i}, would be met by increasing pressure from outside the Photon, P_{o}, due to the increase in the rate of absorption/emission. The mechanism has even more flexibility in that more than one SPP per stroke might be absorbed/ emitted, either as a "burst" of SPP's, or as a "centered" particle composed of some number of SPP's in a sufficiently stable structure (an intermediate level of Contropy).
At equilibrium, P_{i} = P_{o}. Since there is a cycle or vibration, the equilibrium would be neither instantaneous nor fixed, but instead it would fluctuate about the average diameter,/2 cm, over the length of the cycle,/c seconds. P_{o} is generated by reactive forces from the emission of 3nSPP's and absorption of n SPP's per cycle. The total work done on the Photon, W_{P}, equals the work done on the SPP's, W_{s} . If it is assumed that the direction of emission is perpendicular to the standing wave, then use of the best available leverage is provided. In that case, where N = total number of SPP's absorbed/emitted,
and,
Over a given time, t, the total number of SPP reactions/impacts, N, is equal to (4nc/)(t). Then,
Now, setting Equation (10.) equal to Equation (26c.):
Simplifying,
Consistency of the model is shown in deriving by this method that the product of a Photon's wave length times its Energy content is a constant^{3}, as was also indicated by Equation (16.). It can be seen that according to Equation (16a.), Planck's Constant is a time function of the energy of a SPP, equal to nte_{s}/2 ev-seconds.
The concept of the cycle brings with it the need for further consideration of "spin" and "angular momentum" as those terms apply in the cases of the SPP's and the Photon. Refer to Sketch #5 (Page 60a). Since the shaded dimension is effectively 0, the Photon' s Energy of State, E_{PV}, must be preserved in some other way in the two-dimensional structure. Assume that E_{PV} is stored by rotation about the axis of translation; that is, as "Kinetic Energy of Rotation", KE_{Rot}. KE_{Rot} is a property which can be used to distinguish between the SPP's in Sketch #5. By definition, SPP's #1 and #3 are "gravitons" while #2 is a "+magneton" and #4 is a "-magneton". It appears that Energy is produced in the "field" of magnetons which is perpendicular to the axis of translation of the Photon, due to the appearance of the magnetons there at no noticeable losswithin the system. The effects of possible magneton interactions are also of interest^{4}, but it is here in order to examine the effects of Photon/Graviton reactions.
Since the gravitons must impact directly on the Photon for reaction to take place, it is pertinent to consider the factors which influence whether or not such a collision will occur. The force of reaction generated upon the Photon by emission of the +magneton is for a time unbalanced, and it produces a deflection in the direction of the Photon's axis of translation. This is due to the 180 lag between emission of the +magneton and the emission of the -magneton, as well as because of the rotation of the Photon about its axis of translation. While such oscillation is hardly detectable by outside perspectives, it must be considered when assessing the probability of Photon/Graviton interactions.
If the various axes of the energy of the Photon must exactly coincide with those of the Graviton before absorption can occur, then the model (and Nature) must be greatly complicated in order to have reasonable probability of even minimal interaction. This would be true in spite of the fact that the Photon and the Graviton each present their maximum of surface area, properly focused toward each other due to their relative velocities. On the other hand, if coincidence within a certain degree of tolerance is all that is necessary for reaction, then the plausibility of the model as it stands is greatly increased. Heisenberg has provided the basis to assume that the latter is indeed the case.
Now consider Photon E (Sketch #6) which is travelling to the left of the page at velocity c, presenting no surface area to any perspectives except those along the "x" axis. At t_{0}, the Photon absorbs Graviton d, generating a negative acceleration on the Photon, and its velocity momentarily drops below c. During this time the "x" dimension of the Photon is greater than 0according to Equation (4.), and thus the Photon exposes surface area to perspectives along the "y" and "z" axes. This allows emission of the +magneton at (t_{0} +/4c) seconds. At (t_{0}+/2c) seconds, Graviton e is emitted, in the course of which the Photon is accelerated back to velocity c. Just before the tangential surface is gone, the -magneton is emitted. Since outside perspectives perceive the respective accelerations as being "instantaneous", v_{2} may be taken as the average velocity during the time required for 1/2 cycle (/2c seconds), and c as the velocity the rest of the time. The interval between the Photons as shown in Sketch #6 will increase and decrease due to the variation in their velocities, oscillating about a constant distance which depends on the number of SPP's reacted per second, N_{R} , and the ratio N_{R}e_{S}/E_{P}.
Photon D continues at velocity c since it absorbs no graviton during the period. While it might omit the emission of magnetons since it exposes no surface to the "y" and "z" perspectives, it still has a net loss of Energy equal to N_{S}e_{S}/2 per cycle (where N_{S} is the number of SPP's emitted per stroke), causing its cycle time to lengthen. Gradually, it pulls away from the beam, furnishing fewer and fewer gravitons to Photon E, which in turn begins to lose energy. It might be said that the beam of Photons remains intact by the "sacrifice" of its leading Photons, buying Time and Space at their expense.
This effect would be exacerbated by random encounters with dust grains or other disturbances which scatter photons and cause gaps in the beam. The lengthening of cycle time in photons along the beam in order to re-equilibriate would amount to a "red shift" that is related to time and distance, but which is separate from any that is due to the velocity of the emitter relative to the observer. If so, this would indicate need for correction of the Hubble Constant.
But if the beam should enter a zone of highly concentrated and regular graviton trajectories (such as in the vicinity of matter), even the leading Photon might find enough gravitons within the tolerance of its absorptive capacity to maintain its identity.
In the absence of "force at a distance" mechanisms, any Photon which would absorb gravitons must make physical contact with those gravitons in order to effect the necessary deceleration. Due to the two-dimensional nature of these particles "in flight", that limitation restricts the candidates for possible absorption to those gravitons whose trajectories in Time and Space intercept the Photon at angles less than 90 from dead ahead.
A further limitation to absorptive capability which results from the model is that "collision" must occur during the time when the Photon is in its absorptive state, and that might be as little as 1/4 of the time.
Even with latitude of reasonable tolerance in precision of the mechanical cycle, the restrictions against absorption might seem so excessive as to preclude the mechanism from "real" probability, except for the additional grace in Time and Distance which is allowed by Heisenberg's Principle^{5}. While approximation of the spatial concentration of SPP's in the vicinity of, say, a galaxy is beyond the scope of the present argument, even the leading Photons should have a strong tendency to survive in proximity to matter.
In fact, the chances of absorption seem so enhanced by such considerations that "multiple" absorption could even be likely in some circumstances. As the model stands, stability requires that the Photon emits three particles for each one that it absorbs. For instance, if it absorbs two gravitons per cycle, it will emit two +magnetons; two gravitons; and two -magnetons per cycle. Multiple absorption (that is, the absorption of more than one graviton at once) requires that two or more gravitons converge on a point of Time and Space which lies also along the path of the Photon. Divergence in the paths of gravitons which are emitted from "unfocused" sources argues that such convergences would be an infrequent and random event in "deep space".
At the other extreme, as when the beam would pass through gases, liquids, or solids, it would seem that multiple absorption must be nearly certain because of the density of emitters. In that case the beam would be slowed sharply by the increasing weight of impacts from ahead, exaggerating the exposure of surface to the third spatial dimension. To the extent that this occurs, focus in the vectors of graviton emissions is lost so that there is imperfect recovery of velocity by the Photon. If there are significant numbers of gravitons converging along the Photon's path, then it must soon find an equilibrium or else lose velocity altogether; that is, be itself absorbed.
Since Protons and Neutrons are by far the most important sources of gravitons, their geometry of spacing and consequent geometry of emission are most determinant factors in the fate of Photons which would pass through any substance which they compose. For, depending on the rate and intensity of graviton impacts, the Photon (as modeled) may be slowed and/or deflected from its path ("refracted"), completely stopped ("absorbed"), or even reversed in its course ("reflected") by directional multiple absorption depending on the geometry of focus and the wave length of the light.
"Gamma Rays": The Photon cycle as it has been developed seems viable over a wide range of energy concentrations, but yet it must lose its effectiveness beyond some certain higher limit. This is because the cycle time decreases as contained energy increases, and loss of precision becomes important. As in an internal combustion engine, mechanical systems can be "over-revved" and lose efficiency. The consequences of such a malfunction would be the exposure by the Photon of more surface area to perspectives outside the beam, causing losses to become excessive. More losses increase surface exposure, and the malfunction would be catastrophic.
Such behavior accords with that of "Gamma Rays" which exist near the high energy end of the Electromagnetic spectrum, and it precludes the Photon cycle as a viable mechanism for containment of energy at higher frequencies than "Gamma Rays".
"Sub-Atomic Particles": Yet, the stable "Beta" particle exists at higher energy, while the "Electron" and the "Proton" are so far removed as to constitute an obviously different state of existence altogether. That state must utilize a more organized and complex structure than does the Photon. The Contropic perspective is that such structure can only arise naturally due to cause and effect, and due to Geometry.
Because of random orientation in all aspects of the SPP's at the instant of the Big Bang, one- sixth of them would have been accelerated "negative pole" foremost to velocity c with respect to the center which had formerly contained them. Another one-sixth would have gone "positive pole" foremost, and the remaining two-thirds would have led with their "equators".
At this stage, only the effects of Graviton interactions would have been felt, since the unfocused Magneton interactions would have statistically opposed each other. Thus, when the containment was overcome, removed, or otherwise circumvented, there would have been an initial implosion, or at least a reduction in expansion rate which would have favored complexification. If all particles had been formed simultaneously during this induction period, perhaps there would have been no "Big Bang".
However, if, as seems reasonable, the high density Proton structure was evolved first, the bulk of the positive Magnetons would have been absorbed into the Protons, which would then be expelled from the reaction zone by their unbalanced repulsive forces. The relative instability of the Anti-Proton structure (retrograde "exchange particle" emission?) would have been the crucial factor in this separation, delaying the "condensation" of the negative Magnetons until the lower energy concentration of the stable Electron was reached.
The wave of Electrons which followed would have overtaken the Protons due to the combined effects of Gravity and unbalanced Magnetism, allowing formation of Hydrogen Atoms. The neutrality of the Hydrogen Atoms would allow gravity to become controlling, leading to the recondensation of matter (into Galaxies?), etc.
Differences in orientation with respect to direction of translation are fundamental between Matter and Energy, in that alignment of the axis of the wave with the axis of translation brings the effects of the Fitzgerald-Lorentz Contraction to bear on "wave length" of the particle. Thus, if the material particle would attempt to use the same structural features as the Photon, increasing amounts of force would be needed for acceleration, until the final increment of acceleration to velocity c ( = 0) would require an infinite force. Such inability to attain velocity c has the consequence that matter must expose surface area to the third spatial dimension. This allows the escape of SPP's, establishing zones of potential with their presence and capability for interaction. The patterns traced by the SPP trajectories in Space/Time correspond to magnetic and gravitational "fields" that are associated with the emitting body.
Such increased rate of Energy loss would bring the need for a more powerful mechanism for containment than in the case of the Photon, but at the same time, it would offer improved structural possibilities due to the created availability of "Charge" and "Mass"^{6}. This is the essence of the contropic idea, wherein the risks of increased exposure might be converted into new potentials through organization and structure, resulting in stability at a higher level of energy.
For instance, such a structure is suggested by the familiar orbital model, which has been used to describe both Atomic and Solar System behavior.
Suppose that a nucleus emits some significant fraction of its energy in the form of an oppositely charged "exchange particle". Some convergent force, perhaps arising at least partly from magnetism and/or gravity, can work to turn the nucleus and the emitted particle about each other so that the emitted particle might be cyclically reabsorbed. The plausibility of such an hypothesis is enhanced by the fact that the longer wave length of the emitted (lesser) particle might allow it to remain in physical contact with the emitting pole during most of its semi-orbit. Given that such re-absorption occurs, the nucleus would gain compressive work upon itself over a period of time at no loss of energy, in the manner of the "Photon Cycle".
During the power cycle both the nucleus and the particle would be compressed by their interactions, supplying energy not only for emission of magnetons and gravitons, but also for emission of some intermediary particle from each body to conserve charge and Energy. The interaction of these intermediates could add to the convergence by producing an attractive force between the nucleus and the exchange particle to tighten the orbit to an equilibrium diameter, depending on the conditions.
Based on parameters which affect timing, such as the ratio of the wave length of the exchange particle to the length of its path, etc., there could be some more or less stable "different" particle (each defined by its own ground level of total Energy content) extant at each standing wave harmonic across the entire range from "Energetic Enough to Close the Cycle" to "Too Energetic for Precision Timing". (Only at harmonic points would there be enough efficiency to stabilize the structure long enough for detection from our perspective--but then, there are enough of these across the range of concentration of energy to explain the large numbers of kinds of Sub-Atomic Particles being found with successive refinements in capability for detection.) Taken together, these harmonic points comprise a "Line" rather than a "Continuous" spectrum. Examples of possible structural analogies for the most stable of these particles are shown in Sketch #9 ("The Electron") and Sketch #10 ("The Proton"). Note that precession of the orbit of the exchange particle generates an approximately spherical shape in three-dimensional space, containing two different layers of energy density--a small, dense "core" surrounded by a less dense "shell". Such construction is consistent with some observations of the Proton (Krisch 1979).
Neglecting the effects of Charge for the moment, consider the case where one Proton might approach near enough to another so that they can exchange "Pions" as in Sketch #11. Such an exchange would shorten the cycle time of each Proton, and thus, it would make more energy available than that required to turn the Pions and to make up lost SPP's. This excess of energy output could be asserted as an attractive force by direct exchange of uncharged particles (Gamma Ray Photons?) as shown.
There would also be a "tensor" component in this force due to the effects of the relative alignments of the Protons. The paths of the Pions would be most shortened (and therefore the force would be maximized) by "Spin Antiparallel" arrangement as shown, although more complicated paths arising from other alignments might also generate significant force. This attractive force would manifest itself during the (approximately two-sevenths?) fraction of the time when the Pions are absorbed within their respective nuclei, and the (repulsive) magnetic force would be effective the rest of the time. Thus, the Protons would oscillate about an equilibrium distance along the line between their centers.
An outside observer, measuring the resultants of these forces as a single force--the "Strong Nuclear Force"--would detect zero intensity until the Protons came within range of each other's Pions, a distance on the order of one Proton diameter. The force would quickly rise to a peak intensity as the distance between centers decreased, starting to decline rapidly as the repulsive magnetic force becomes controlling within the orbit of the Pions. Such a description seems to be in at least general agreement with the observed behavior of the "Strong Nuclear Force" as described by Marshak (1960).
Of course, Protons (and/or Neutrons) might be randomly crashed together at high temperature and/or pressure, with enough force to overcome the repulsive magnetic forces that develop between the respective exchange particles and the nuclei. However, note that this structural description suggests the alternative possibility that, if properly harmonized and aligned, two or more protons might be brought near enough--without need for substantial force--to exchange pions; that is, to fuse at "cold" temperatures. This would require some medium in which the relative alignments and timings could be imposed (with some expenditure of energy for control. Thus, contropy suggests that there might well exist some practical catalyst for "Cold Fusion". Consider now the case when, drawn by its attractive positive charge, an Electron approaches a Proton. At close approach, the Proton's two-body construction becomes significant in that the Electron approaches the orbit of the negative Pion (which cycles much faster than does the Electron), and a force of repulsion develops to oppose the mutual attraction of the nuclei. At some equilibrium distance these forces will be balanced so that the Electron is "bound", being neither able to reach the nucleus of the Proton, nor to escape. Although it might approach nearer or farther according to its velocity relative to that of the Pion, the Electron would orbit the Proton, and together they comprise the Hydrogen Atom shown in Sketch #12. .
Under some circumstances of Geometry and Timing, the Electron might break through the orbit of the Pion to impact directly on the positive pole of the Proton, as in Sketch #13. This would make available to the Proton an extra 3/2 of the energy of the Electron, about 767,000 ev. The Pion would also be slightly compressed by the intrusion of the Electron into its orbit, and so it, too, would gain in energy content due to the structure. Although some work must be done on the Electron to compress it into the orbit of the Pion, the extra energy predicted from the structure would seem in reasonable agreement with the 780,000 ev excess which is observed in the Neutron. (Notice that this model predicts that the Neutron would appear to have 3 concentric zones of different energy density rather than the 2 zones as predicted above for the Proton structure and seen by Krisch in 1979.)
The excess of energy could be emitted by the respective nuclei in the form of a pole-foremost particle which is neutral in a different way than are the equator-foremost types of particles. This can be interpreted as an absence of rotation of the wave about its axis, so that the particle would be two-dimensional at relative rest, and one-dimensional at relativistic velocities. Such a particle would be essentially massless and chargeless (emitting no gravitons or magnetons). Once free, it would only rarely be in contact with anything long enough for interaction. These properties possibly correspond to those of the Neutrino. Properly focused in the structure, it could interact to produce the "Weak Nuclear Force" and bind the Electron into an orbit which brings it to impact with the Proton nucleus each cycle.
Observe that these models for the structures of subatomic particles also conform to the "wave/particle duality" that has been detected, since they would exhibit wave properties when tested microscopically, and particle properties when tested macroscopically.
REFERENCES
Burrell and Robertson, U. S. Bureau of Mines Technical Papers 131 and 158. (Cited from Perry's Chemical Engineer's Handbook, 4th Edition, 1963, New York:McGraw-Hill, 9-10).
Holton, G., and Brush, S. (1973b), Introduction to Concepts and Theories in Physical Sciences, Reading, Mass:Addison-Wesley. page 354-359.
Holton, G., and Brush, S. (1973c), ibid., page 390.
Krisch, A. (1979), "The Spin of the Proton", Scientific American, 240, #5.
LaViolette, P. (1986), "Is the Universe Really Expanding?", Astrophysical Journal, 301: pp. 544-553.
Marshak, R. (1960), "The Nuclear Force", Scientific American, 202, #3.
Zwicky, F. (1929), Proc. Nat. Acad. Sci. 15:773.
FOOTNOTES
1. After William of Ockham (1280?-1349), according to Asimov (1964b).
2. A "Standard" Photon can be defined as one which contains Avogadro's Number of SPP's at 273.2 K; then,
The standard photon would thus be in the mid-infrared, about midway between the detectable extremes of the Electromagnetic spectrum. The energy of SPP's can be calculated on this basis:
3. If such relationship might hold for the SPP as well as for the Photon, then the "wave length" of the SPP would be very long, 1.6534 x 10^{21} cm, or about 5250 light years, according to the energy level of the SPP as derived in Footnote 2.
4. Although the model Photon is not magnetically charged since it emits equal numbers of both kinds of magnetons in all directions perpendicular to its axis of translation, it is easy to envision other constructions which emit one or the other preferentially, if not exclusively. Two or more such bodies in a space would produce a situation in which the trajectories of magnetons from one body might intersect those from others, allowing the possibility of collision and interaction to arise. If the minimum requirement for interaction is mere contact of surfaces, then the trajectories of the reacting magnetons can deviate as much as 90 from "head on", and the limits of the reaction zone would be a sphere with diameter d, the distance between emitters. There would be N_{A} x N_{B} possibililties for reaction, where N_{A} and N_{B} are the respective numbers of magnetons in the reaction zone from each emitter, and the rate of reaction will vary with the square of reactor volume. Thus, the reaction rate (and force produced) is of the form of "second order", and the model conforms to the theory of Arrhenius. The difference in kinds of emitters make it necessary to take into account directional aspects of emission, and this adds a factor of "focus" or "polarity" to the considerations (defined here as "Magnetivity", M, a function of mass and polarity). From this basis, few further assumptions are required for derivation of the Magnetic Force equation:
where is a constant (6kc^{3}f_{M}/h^{2} ) composed of the reaction rate constant for magneton interactions (k cm^{3} -sec per each magneton), the amount of force produced per reacting pair (f_{M} dynes), Einstein's Constant (c cm/sec), and Planck's Constant (h erg-sec). Using the same approach, it is possible to derive the Gravitational Force equation:
where G is a constant (6k'c^{3}f _{G} /h^{2} ) cm^{3} /gm-sec^{2} .
5. Consider a Photon at 5700 angstroms wave length. Such a Photon might lose 4c/(5.7 x 10^{-5}) gravitons/second. This would be a loss of energy, E, as shown:
from Heisenberg and Einstein:
Substituting,
During this time the Photon would pass through a distance of 6.1 x 10^{7} cm. Given such tolerance, it is apparent that a beam of Photons could "search" vast distances with the sacrifice of relatively few Photons.
6. A body has mass to the degree that it emits gravitons, and (at velocities less than relativistic) it emits those gravitons to all three spatial dimensions uniformly. Therefore, the property "Mass" is associated with unfocused or "free" SPP's, already defined as the 1st magnitude of Contropy. At the same time that the body emits gravitons, it also emits magnetons so that the property "Charge" arises at once with Mass. It is noted that the tangential emission of magnetons affects "Spin" of the emitting particle. The property "Kinetic Energy of Rotation", KE_{Rot}, (or "Orbital Angular Momentum") also arises simultaneously with mass, and it can be associated with the property "Charge", symbolized as q. Assuming that charge is exerted tangentially at the surface of the particle, it can be defined in terms of torque:
where r = radius and = angular speed. It is not clear why the 3/2 factor is required (the next standing wave periodic? Or perhaps E for the particle = 3/2 E for the photon?) Now if it is assumed that the relationship Eis a constant within Sub-Atomic Particles as it is within Photons, then some "Energy of Structure" is likely ignored. On the other hand, any error is probably small, and the assumption leads to the fruitful conclusion that Charge would be the same for all entities in which E is a constant (1.986 x 10^{-16} erg-cm).
The square root of the units erg-cm appears to be equivalent to the electrostatic units, e.s.u., and thus the value of q is derived as being about 1% higher that the 4.803 x 10^{-10} e.s.u. that is accepted as standard charge.