ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º PURE MATH CONNECTORS º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ Terms Nx, Egs, and Ess, can be shown to be mathematically connected by direct steps which bypass the physical dynamic terms. This does not mean the physical dynamic terms do not exist, it only means that it is possible to quickly work back and forth between Ess, Egs, and Nx, when a few connector rules are known. These rules include the following: Given an Nx term: then: Egs = û(1 - 1/Nx) and: Nx = root 1/(1 - (Egs)ý) and: Ess = root 1 - (Egs)ý and: Ess = û(1/Nx) = 1/ûNx These connector rules can be more readily shown in a table, as follows: TABLE 8 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ FOR EXAMPLE, GIVEN THAT Nx = û3 = 1.732050807 ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Then: for GRAVITY relativity ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ ³ 1 ³ ³ 1. Egs = ³ 1 - ÄÄÄ = .650115167 ³ ³ \³ û3 ³ ³ ³ ³ ³ ³ 1 ³ ³ So that: Nx = ÄÄÄÄÄÄÄÄÄÄÄ = 1.732050807 ³ ³ 1 - (Egs)ý ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Cont. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ Then: for SPECIAL relativity ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄ ³ ³ ³ 1 ³ ³ 2. Ess = ³ ÄÄÄÄ = .759835685 ³ ³ \³ û3 ³ ³ ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ ³ 2G M ³ ³ Ess = ³ ÄÄÄÄÄÄ = .759835685 ³ ³ \³ Cý R ³ ³ ³ ³ ³ ³ 2G M ³ ³ And: Essý = ÄÄÄÄÄÄ = .577350269 ³ ³ Cý R ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Cont. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ Essý Cý R ³ ³ So that: M = ÄÄÄÄÄÄÄÄÄÄÄ ³ ³ 2G ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ And: Ess = \³ 1 - (Egs)ý = .759835685 ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ And: Egs = \³ 1 - (Ess)ý = .650115167 ³ ³ ³ ³ 1 ³ ³ And: Ess = ÄÄÄÄÄ = .759835685 ³ ³ ûNx ³ ³ ³ ³ 1 ³ ³ So that: Nx = ÄÄÄÄÄÄÄ = 1.732050807 ³ ³ (Ess)ý ³ ³ ³ ³ And: Vx = C / 1/Egs = Velocity ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ NOTE: There are specific similar distinctions ³ ³ between the Nx terms for the two relativities, ³ ³ and first given Egs and Ess terms, shown in ³ ³ TABLE 8 as 1, and 2. ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ These above shown pure math permutations are ³ ³ true when given any value for Nx, or Egs, or Ess. ³ ³ ³ ³ With these rules it is possible to freely move back ³ ³ and forth to arrive at key terms for gravitational ³ ³ and special relativites. ³ ³ ³ ³ For instance, given a special effect (Ess) for a ³ ³ body moving at a high velocity, then equivalent ³ ³ gravitational effect (Egs) in relativity is directly ³ ³ known by a single step calculation, for instance ³ ³ by: ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ Egs = \³ 1 - (Ess)ý ³ ³ ³ ³ And what portion the given moving body's mass ³ ³ is to a black hole silent partner equivalent, ³ ³ is directly known by a single step calculation, ³ ³ for instance by: ³ ³ ³ ³ 1 ³ ³ Nx = ÄÄÄÄÄÄ because: Nx = Mbh/M ³ ³ (Ess)ý ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ When dealing with real events which occur at the critical mass limit Mc, where then Mbh/Mc = GH (the Golden Harmonic Ratio 1.618034), then pure math connectors can appear slightly confusing, in that certain pure math factors exactly occur through functions of the Golden Ratio, rather than through relativistic field dynamics. For instance: TABLE 9 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ GIVEN THAT Nx = 1.61803398875 = The Golden Ratio ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ Then also: ³ ³ ³ ³ Egs = 1/GH = GH - 1 = .6180339 ³ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ And: Egs = \³ 1 - (Ess)ý = .6180339 ³ ³ ³ ³ ³ ³ And: Nx = Egs + 1 = 1.6180339 ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ And: Ess = ûEgs = .7861514 ³ ³ ³ ³ And: Nx = (Ess x 1/Egs)ý = 1.6180339 ³ ³ ³ ³ And: Nx = Essý + 1 = 1.6180339 ³ ³ ³ ³ Etcetera ³ ³ ³ ³ ³ ³ BUT THESE ARE TRUE ONLY WHEN NX = THE GOLDEN RATIO ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º WHY Egs AND Ess ARE INTRINSICALLY RELATED º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ In a closer look at the preceding, some further facets are learned. In particular: EQUATION Z-18 For example: Taking data for Ess and Egs from EQ Z-17-3 ; and: M+ from table 6 then: in EQ Z-18 ; ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Ess = \³ 1 - (Egs)ý where: M+ = ûNx ; when: Nx = Mbh ÄÄÄ ÄÄÄ M M and so: in EQ Z-18-1 ; EQUATION Z-18-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Ess of .003161416 = \³ 1 - (.999995002)ý because: (M+/M) = ûNx as when: in EQ Z-18-2 ; EQUATION Z-18-2 (1.482558107 x 10 to 36 grms) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ = 316. 313878376 = û100054.469653 (4.686984066 x 10 to 33 grms) where: û100054.469653 = ûNx x 100,000 because: Nx is ratio 1.000544617404 and: Mbh / 1.000544617404 gave Mass1 for our study model and: Mass1 / 100,000 gave Mass2 for our study model NOTE: The true value of û(Nx x 100,000) = 316.313865868 = û100054.4617404, is slightly departed from the actual Nx value for Mass2 shown immediately above. The departure is due to intrinsic truncation in accuracy, where a few digits are clipped from the tail end of the HIGH special relativity Ess term .003161416, and the LOW Egs term .999995002. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±± SPECIFIC CONCLUSIONS ±±±±±±±±±±±±±±±±±±±±± º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ It is now clear, according to the above derivations which begin with EQ T and continue through EQ Z-18-2, that a fundamental barrier exists in physics, which limits special relativistic effects on a visible moving mass entity to a pre-determinant black hole gravitational mass equivalent, gained by a pre-determinant limit in velocity. The pre-determination on the entity is as seen by a stationary observer watching the mass entity move at relativistic velocities. At its pre-determinant limit in velocity, the mass entity transfigures into a black hole and disappears from view. (This does not mean that the black hole cannot keep acceler- ating. What it means is that the possibility of such further acceleration is not addressed in any way, in the scope of this disclosure. This exploration ends with the original radius R transfigured into an event horizon R- = R'. And so as an event horizon radius R- will thereafter behave in dissimilar ways than in the physical form of a radius R. Such dissimilarity in behavior of radii is discussed further above at the start of Part 2, as Items 1 and 1A under: 'A Comparison Between Gravitational and Special Relativity'). In outlook, a visible mass is any mass of radius R. The visible mass has to be capable of radiating light to be seen in the universe. Its black hole M+ and R- equivalent at the relativistic limiting barrier does not radiate light, and so no longer physically exists in terms of basic electromagnetic radiation. Generally, a visible mass accelerated to relativistic velocities cannot achieve a theoretical infinite visible mass, and the velocity of the visible mass can never theoretically equal the speed of light. The interpreted statements in special relativity which say a mass (obviously visible) continues to expand toward infinity, and the velocity continues to the speed of light, are wrong, when they do not take into consideration the black hole barrier effect. The maximum velocity attainable by a visible moving mass, is the speed of light reduced by the proportionate ratio of the gravitational relativistic effect of the mass being accelerated. The velocity barrier limit (maximum velocity) possible, is restricted by the bounds achieved in special relativistic effect when the mass has increased, and its radius has contracted, to a point where the moving entity forms a black hole and effectively disappears from view. As already said, this point is easily calculated, as being the velocity resulting when the speed of light is divided by the proportionate effect of the mass's gravitational relativistic effect. This point will vary from mass to mass, and from radius to radius per given mass, but will inevitably appear somewhere before the speed of light is reached, when the visible mass is being accelerated to relativistic velocities. A further limiting factor is reached, when the original mass factors and augmented mass factors are summed, to reach an absolute prior limit at which the total mass transforms into a black hole equivalent in single bumps, which are proportionate factors of the Golden Harmonic Ratio 1.618034. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±± GENERAL CONCLUSIONS ±±±±±±±±±±±±±±±±± º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ The fundamental point of view adapted for much of the preceding, is to consider that gravitational relativistic effects are steady state. Ie., the gravitational source is simply sitting there doing its relativistic thing. And so there are no gravitational accelerations of a kind which involve motions of points of center, when understanding certain of the effect's basic properties, such as the effect on the original mass of the gravity causing the effect. Throughout the gravitational relativity explorations of Part 1, the perspective was entirely from the perception of different mass aggregates being squeezed within the same unchanged radius. In practice, the only radius used was the radius of the Sun, as it is presently measured empirically in this solar system. That the Sun's radius can be presumed to be reduced slightly by the relativistic effect of gravity has been taken into consideration, but has not been explored through any of the possible permutating effects that changes to the radius might have. In short, the studies involved variable densities. The very nature of gravitational relativity implies permuting effects due to gravity on all of the parameters involved, for instance on all of the terms in EQ W. The sheer magnitude of the job of trying to explore all possible combinations of permutations involving just R vrs M for this solar system, for instance, has not been explored here. Which leaves wide open a very important question. In the circumstances so far described, there is no proof that the radius of a mass aggregate is the bottom line through which important gravitational relativistic manifestations are to be observed. This in no way suggests that a proof should not be forthcoming. It so happens that a constant radius (in this case the radius of the Sun) is very convenient for displaying many important manifestations of gravitational relativity and black hole correspondences. It appears to hold together a thread of logic though many physically dissimilar events, including standing stark still (gravity relativity) and in motion (special relativity). Such stark realism between the relativities would be a hard (if not impossible) task to monitor if the confinement radius was allowed to be mutable. So, the Sun radius is freely used as a constant for exploring different stark manifestations. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ MASS DENSITIES IN A CONSTANT RADIUS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ It is clear (as shown in many of the preceding demonstrations) that the existing Sun radius might in some way be of fundamental importance. Not necessarily in core physics of the universe as a whole, but at least in core physics of the solar system. This is seen in the interphased mass congress states involving « units of Jupiter's mass, as discussed in Part 1. In the various relativistic explorations, the Sun's radius has been willfully maintained as a constant value through different discrete changes in mass aggregates studied. (This applies to the corresponding planet masses explored, and is not meant to apply to any special relativistic effects explored). Dynamically, a change in mass within the same radius usually translates into a change in density of the aggregate. In other words, density pressure may be a part of the cause and effect, or at least may have originally been a part of the cause and effect, prevailing at the time of this solar system's formation. This may be a clue regarding the unusual solar characteristics observed; where different discrete units of mass (including mass particles said to be a part of total mass aggregates) are seen externalized as planets orbiting far from the major field of the Sun. The mystery is that the particles are orbiting well beyond the significant radius of the inducing effect. The external factors include planet masses which are a part of the mass aggregate inducing significant effects. One particular planet is Jupiter. Other planets are clearly related to the induced effects, but their masses do not seem to be included in the mass aggregates. These planets are Venus and Mars. It may be that concomitant to gravity relativistic effects gained with the Sun's mass, special relativistic effects are also gained. But rather than being produced in the form of increased mass per se, the special effects become produced in the form of velocity which can translate directly into angular momentum, resulting in at least some of the induced influences being flung into orbit thus carrying away discrete units of relativistic effect in the form of discrete quantities of angular momentum. This is only a thought, probably ridiculous. (In a casual thought, if a gravitational body also induces a synonymous relativistic effect (motion) the motion has no real way to go forth in itself, since ideally all of the effect of motion is equidistantly applied to a sphere (the gravitational body). In this scenario, the motion portion is thrown off (externalized) in order to be expressed). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ A QUESTION REGARDING RELATIVISTIC ³ ³ MASS EFFECT AND QUASARS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ These following remark are purely conjectural. Let's suppose that certain relativistic effects induced by gravity seem to be incompatible with the basic gravity itself. In other words there are two aspects to gravity: the original (naked) gravity for any material, and the relativistic effects caused by that gravity. In this supposition, some relativistic nature cannot exist within the naked nature, and so is externalized at long distance. The externalizing is guessed as either by a throwing off (forcibly casting forth) or by a remake (as if in leaping from here to there, where 'there' is a predetermined position in some kind of latent underscore pattern involving the gravity field). (In high energy physics, many sub atomic particle interactions are depictable as occurring simultaneously in two places at once, where an event at one place directly effects the event in another place even though nothing but thought can transfer between the two places). A third form of ejection might be by the simple virtue of an outthrow of discrete bits by angular momentum. In the workings of gravitational relativity, several things are at issue. There is an original mass, plus the original mass's augmentation due to the relativity of the mass's gravity. There can also be more mass added into the conglomerate at any time. Which results in a hike in the augmentation effect due to strengthened relativity. It can be supposed that if an increase in mass takes place within a given radius, resulting in a hiked relativistic mass augmentation due to the added mass, which in turn causes jitters so that something of the hike has to be expunged or externalized from the gravity field which is generating the effect in order to satisfy an esoteric yearn to solve the jitters, then where added mass is accreting into a large black hole some of the relativistic gain is transferred to an external position outside the black hole. Since very high energy effects are involved with the black hole anyway, it is not difficult to picture that the expunging can appear highly energetic. What the mechanism is that could transfer the effect to an external place is not here conjectured but can be supposed. For instance: A long arm recurrence (here and also there) is one mode. An intense radiating away (or bleeding away) of some of the change upon the event horizon boundary, in alternative to allowing a change to go ahead in the relativistic regions of the boundary size itself, is another mode. This is made more viable if it is suggested that the black hole yearns to maintain some form of internal density which has no further relativistic influence inside the black hole. And finally, a conversion of units of intrinsic spin as energy, (conversion from spin to propagational energies), is another, if possible. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ A QUESTION REGARDING RELATIVISTIC ³ ³ EFFECT ON THE GRAVITATIONAL CONSTANT ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ There is also the prospect that the gravitational constant itself is modified by the relativistic effect of gravity. In retrospect, it is not readily apparent as to whether the gravitational constant would weaken, or strengthen, relativistically, given larger and larger masses. The present day mode of thought is to consider that the gravitational constant might grow relativistically stronger. On the other hand, Equations Y to Y-2 above suggests that the gravitational constant relativistically weakens through increasing mass aggregates. On yet another hand, it has not been proven that a mass relativistically increases (as opposed to decreases) by gravitational relativity. A stable picture should ensue, albeit not exactly the same as the picture described in Equations T through Z-11-4, if a mass decreases by its gravitational effect, such that the mass's confining radius might increase, or decrease, and the gravitational constant also might increase, or decrease, etc. Such possibilities are not considered in the above shown mass congresses involving the Sun and certain planet masses. If the gravitational constant is in fact modified by relativity, then the apparent mass of the Sun is still valid, but the original mass should not be precisely that as determined by the apparent mass MM, minus the apparent mass times the effect; as shown in EQ W-1. In fact all of the parameters of Equation 1 below in APPENDIX B (except for the speed of light) might be in states of modification. These parameters include G and M, where a mutable value of G therefore is internally influencing the value of M. In any case, the resulting gravitational relativistic mass congresses between the Sun and planets as viewed herein are in their resultant apparent states (involving the masses as seen in the domain of the solar system and empirically measured). And finally, the direct tie-ins between gravitational and special relativity are balanced correctly anyhow, according to the parameter choices selected for the preceding, to infer then portray their handshake nature. In a casual thought, if a gravitational body also induces a synonymous relativistic effect (motion) the motion has no real way to go forth in itself, since ideally all of the effect of motion is equidistantly applied to a sphere (the gravitational body). In this scenario, the motion portion is thrown off (externalized) in order to be expressed. It is not hard to speculate that the special relativistic mass gain for the stationary object (gravity source) can be (at least in part) thrown off in the form of energy, since e=mCý. In which case a lot of energy will be visible per small quantities of involved gain in mass. In this speculation, there is a pure (rather than nuclear) conversion of mass to energy. In unstated allusions are hints that gravity and special relativistic effects work hand in hand, with perhaps the special relativity effects being more and more suppressed the higher the gravity. But as already said, any special relativity associated seems to be incompatible within the naked gravity itself and so ends up externalized (for instance) as certain planets, as if a velocity is induced in a gravity mass at rest which can leave its source, via angular momentum in the velocity. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ A QUESTION REGARDS THE GRAVITATIONAL ³ ³ CONSTANT AND THE GOLDEN HARMONIC RATIO ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Whereas in another conjectural possibility, going in the other direction, it may be possible that the apparent quantum jump in relativistic effects seemingly embodied in operators involving the golden section ratio (the golden harmonic), do not actually occur in the physical universe. For instance if the universal gravitational constant did change in value under increasing relativistic influence, it may result in a situation where such things as mass and space increase smoothly toward infinity after all, with the quantum leap from a plateau straight to black hole parameters smoothed out or voided by relativistic changes in the power of the universal gravitational constant. Ho hum, speculations can be rather boring. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX A ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º ELEMENTARY PARTICLE MASSES º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ In high energy physics experiments, particles such as the electron or Proton are being accelerated to velocities said to be virtually at the speed of light. How is this possible? This is possible because the Mass/Radius ratio of the proton (as an example) is extremely small, compared to the Mass/Radius ratio of the Sun for instance. The Mass/Radius ratio of the Sun is: (Mass 1.991 x 10 to 33 grms) / (Radius 6.963 x 10 to 10 cms) = (2.859 x 10 to 22 grms/cms) which itself is very small compared to the ratio of a black hole having the Sun's radius, in which the Mass/Radius ratio is then: Mass = (Cý x R) / 2G = (4.689 x 10 to 38 cms) And: (Mass 4.689 x 10 to 38 grms) / (Radius 6.963 x 10 to 10 cms) = (6.735 x 10 to 27 grms/cms) = CR Note that value (6.735 x 10 to 27 grms/cms) = CR is actually a physical constant for every black hole, and is equal to the ratio of the speed of light divided by twice the universal gravitational constant, as in: (Cý/2G) = CR = (Mbh/Rbh) when Mbh and Rbh are the Mass and Radius (event horizon) of a black hole, C is the speed of light, and G is the universal gravitational constant. When, otherwise, a normal M and R are transfigured by special relativity into a new black hole having mass M+ and radius R-, then: CR = (M+/R-), where, CR still has the constant value: (6.735 x 10 to 27 grms/cms). In the large scale world of normal events the magnitude of the Sun's mass at (10 to +33 grms) is well above the magnitude of the Sun's radius at (10 to +10 cms). In the world of the very small, the situation is quite reversed. For example the mass of the proton is: 1.672 x 10 to -24 grms whereas its radius is reverse in magnitude, in the much larger range said to be about: 1.32 x 10 to -13 cms. This produces a Mass/Radius ratio (proton Mass/proton Radius) of: = 1.239 x 10 to -11 grms/cm. Clearly, a proton will have to accelerate to an extremely high velocity, virtually to the speed of light, in order for special relativistic effects to transfigure the proton's effected mass M and radius R into the (M+/R-) = CR parameters of a new black hole. The Mass/Radius ratio of the proton will have to grow by a magnitude of (5.435 x 10 to the 38), in order for the accelerated proton to take on the look of a black hole having mass M+, and radius R-, and a (M+/R-) ratio equal to CR. A calculation to determine what velocity the proton needs to move in order for the transfiguration, is impossible to complete with devices having mediocre accuracies good to only (say) 13 significant figures. The calculation to determine the proton's velocity first requires knowing what the gravitational relativistic effect Eg is for the proton's mass and radius. Effect Eg is too small by many magnitudes to be mechanically calculated by a device of 13 significant figures. Given a device with greater accuracy, the resulting Eg effect for the proton is divided into the speed of light, to give the velocity at which the proton must travel to relativistically transform into a black hole. The velocity will be the same as the speed of light to many significant figures, before the digits begin to deviate. (Unless there is (previously unsuspected) a gate in the velocity of light, at which a particle (for instance a proton) might in fact make a quantum leap to black hole magnetudes at a point that is at some measurable factor less than a total 100 percent of the speed of light). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Proton Comparative Mass Density ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ To give a comparison on just how nebulous is the mass density of the Proton (how little in the way of gravity that Proton matter presents), the mass density of a Proton is on par with about 1 gram of matter wisping in a shell whose width is equivalent to 10 times the full diameter of the orbit of the Moon around Earth. If the on par Proton mass were gathered together for the protion which occupied the actual orbit of the Moon, it would be a moon weighing about .48 grams circling the Earth. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX B ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º BASIC EQUATIONS º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ Advanced details of a black hole, such as a paradigm model of a charge membrane for instance, are not considered. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º RELATIVISTIC MECHANICS º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ EQUATION 1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G M Finding gravitational relativistic Eg = ³ 1 Ä ÄÄÄÄÄ effect Eg, for a given mass M and \³ Cý R a given radius R EQUATION 2 (1 Ä (Eg)ý) x Cý R Finding mass M for a given M = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R and a given 2G relativistic effect Eg EQUATION 3 2G M Finding radius R for a given R = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ mass M and a given gravitational Cý (1 Ä (Eg)ý) relativistic effect Eg EQUATION 4 2G M Finding the Schwarzschild R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's Cý event horizon. When effect E = 1, then factor (1 Ä (E)ý) is 0, which drops from EQ 3 leaving EQ 4 EQUATION 5 Cý R' Finding mass M' needed for a M' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as R' ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º GRAVITATIONAL MECHANICS º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ EQUATION 6 Vý R Finding the mass M for M = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ sustaining a body orbiting the G mass at a given velocity V at a given orbiting distance R EQUATION 7 G M Finding the orbit R of a R = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ body around a given mass M Vý at a given orbital velocity V ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX C ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º PURE MASS CONGRESS º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ This information is presented as a separate tableau and has no self evident bearing on any of the explorations and conclusions of the above statements. The following shows that generally: (« THE SUM OF THE MASSES OF MERCURY, VENUS, EARTH, MARS), PLUS THE MASS OF THE MOON, EQUALS THE MASS OF THE EARTH. (« the sum of masses N1 to N4) + N5 = N3 TABLE 10 Masses + N1 Mercury = .33020 x 10 to 27 grms + N2 Venus = 4.8683 x 10 to 27 grms + N3 Earth = 5.9760 x 10 to 27 grms + N4 Mars = .64181 x 10 to 27 grms ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ = 11.81631 x 10 to 27 grms ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ « = 5.908155 x 10 to 27 grms ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ + N5 Moon = .07350 x 10 to 27 grms ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ Equals N3x Earth = 5.981655 x 10 to 27 grms ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄÄÄÄÄ ÄÄÄÄÄÄÄÄ ÄÄÄÄ Inequality N3x - N3 = .005655 x 10 to 27 grms There is an extra (+ .005655 x 10 to 27 grms) in the N3x result, which is unexplained. There is no other Moon in the inner region of the solar system for instance. The aggregate mass of the asteroids seems to be too small by a factor of 10 to be this inequality. So the extra (.005655 x 10 to 27) does not meaningfully represent the mass of the asteroids. What the mass inequality may represent is not clear at all. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º GENERAL MASS CONGRESS (summary) ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ The Sun's mass plus « the mass of Jupiter added, can be shown to induce a gravitational relativity mass increase effect which is exactly equal to the mass difference between the planets Venus and Mars. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G x (Sun mass + 1/2 Jupiter mass) (Sun effect ratio) = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý x R C = Speed of light G = Gravitational constant R = Radius of the Sun K (Mass augmentation) = Sun mass - [Sun mass x (Sun effect ratio)] K (also equals) = Venus mass - Mars mass The same result is handled (in a slightly different way) in the section beginning with TABLE 1 of file RELATIVE.1 . See TABLE 11 next below. TABLE 11 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ K = 4.226490 x 10 to 27 grms ³ ³ = (Venus mass - Mars mass) ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ C = 2.99792458 x 10 to 10 cms/sec ³ ³ G = 6.6720 x 10 to -8 cms3/grms secý ³ ³ R = 6.96265 x 10 to 10 cms ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Planetary masses Data is from Table 1 in ³ ³ the file RELATIVE.1 ³ ³ ³ ³ Moon = .0735 x 10 to 27 grms ³ ³ ³ ³ Venus = 4.8683 x 10 to 27 grms ³ ³ Earth = 5.976 x 10 to 27 grms ³ ³ Mars = 6.4181 x 10 to 26 grms ³ ³ Jupiter = 1.901 x 10 to 30 grms ³ ³ ³ ³ Sun = 1.9888 x 10 to 33 grms ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ APPENDIX D ÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º FOOTNOTES º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 1 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ RELATIVITY EQUIVALENCE PRINCIPLE ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-21 1 - Egý = 1 - Esý One minus the square of gravity's relativity effect, equals one minus the square of special relativity's effect. ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ EQUATION Z-22 1 1 ÄÄÄÄÄÄÄÄÄÄ = ÄÄÄÄÄÄÄ = Nx 1 - (Eg)ý (Es)ý The reciprocal of one minus the square of gravity's relativity effect, equals the reciprocal of the square of special relativity's effect. This equality is equal to the ratio of a gravitational mass divided into the mass equivalent of a silent black hole partner for the gravitational mass. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 2 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ There is recent speculation that events in electroweak theory and gravitational theory may converge to similar kind at very small distances of the order of (10 to -28 cms) to (10 to -33 cms), said to be possible at the time of a so called big bang. Whether or not the unified field behaviors as disclosed in the above equations are favorable or distasteful to such a big bang outlook is not in any way considered to be of our concern, here. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 3 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In use of the Sun's radius as a constant confinement delineator for various mass aggregates and equivalent black hole masses, it is acknowledged that the amount of extra mass poured into the existing size of the Sun has to be very large to make a black hole. For example the amount of mass is about 235,000 times the mass of the Sun, poured into the space occupied by the Sun, to make a black hole. This is of course physically unrealistic, (that that mass can pour into the Sun and the Sun stay the same size). But having a constant radius makes it far easier to keep track of various effects. The physical universe is actually quite different. For instance the radius of the Sun will dramatically expand with any appreciable amount of mass poured into it. But this is iffy. For example if the extra mass is iron, the Sun's area will expand according to high material density. If the matter is helium or hydrogen, the enlargement of the Sun's radius will be substantially more. In either case, since the radius is expanding (with more matter poured in), a black hole mass plateau will be eventually reached at a much different enlargement in mass than the factor of 235,000 times mentioned above. As you can see, pinning down parameters into 'look and see' constants, with this sort of thing going on, is like trying to pin down the behavior of silly putty. And so events herein have been scrutinized in detail from the point of view of a single unchanged basic radius (the Sun radius), used as a convenient point of reference to compare significant related events that involve that single radius. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 4 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The Golden Harmonic Ratio 1.61803398875, cited in this disclosure, is an absolute number value gained as (« of û5) plus .5. This number is also known as the Golden Section. The number can functionally permutate through a bewildering array of directions on its own, with many particular permutations appearing in the construction of 5 sided geometrical figures. A particularly well known physical manifestation of the Golden Section is the proportion of a Golden Rectangle. Other well known manifestations include spirals and progressions occurring in nature, some based on the Fibonnaci number series. These are said to include galaxy spirals and Bode's Law for the solar system, however some researchers think the astronomy occurrences appear to be as much a case of co-incidence as anything. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 5 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The Constant Ratio CR cited above as being M+/R- = Cý/2G also gives instant readout on such curiosity questions as: 1. How much mass is contained in a black hole whose radius is 1 cm? The answer is: 6.735275620 x 10 to 27 grms In that: Cý R Finding mass M needed for a M = ÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as R = 1 cm Note that the mass has the same digital value as ratio CR 2. What confinement radius is needed for a black hole whose mass is 1 grm? The answer is: 1.484720234 x 10 to -28 cms Note that this is the digital reciprocal of the value of the mass M of question 1, in that: 2G M Finding the Schwarzschild radius R = ÄÄÄÄÄÄÄÄÄÄ R event horizon of a black hole Cý whose mass is 1 grm ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 6 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In the most unusual circumstance of a velocity ratio V/C being equal to a mass proportional ratio M1/M2, then gravitational relativistic effect Egs is equal to ratio M2/M1. For instance, let the ratio of one mass M1 divided by a smaller mass M2 be called Rn. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ (C/Rn)ý ³ Vý Then: Ess = ³ 1 - ÄÄÄÄÄÄÄ = ³ 1 - ÄÄÄÄ \³ Cý \³ Cý And: Egs = 1/Rn ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Footnote 7 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In case there is a concern over what has been done above, (in the conjecturing of major effects as seen wrapping around changes in the rest state of masses through two different synonymous modes of relativity), there are no rules that exclude a direct synonymous tie-in between both gravitational and special relativistic effects. For example, it has been experimentally confirmed that time slows in the proximity of a gravitational field. A main question which can be asked is: At what velocity does a mass have to be moving, to induce a slowing of time (time dilation), that is equivalent to the field effect from the gravity generating a relativistic effect of equal magnetude on the flow of time? The time dilation effect of a velocity in special relativity is straight forward. That is, at a given velocity, events in time for the moving object will seem slowed by a specific amount as seen by a stationary observer. In the case of gravity effect, the situation is more ambiguous. The effect of time dilation depends on where the object is in the vacinity of the field generating the effect. Closer to the field means a greater time dilation. But in large scale objects such as the Earth or more so the Sun, closeness empirically means close to the surface, for example, rather than close to a mathematical data point or to a fixed velocity. In our explorations above, real time positions moving here or there in the embraces of a varying gravity field are not at all in the picture. The basic 'need to know' speaks through simple statements consisting of 'how much mass' in 'how much radius' to result in 'how much effect' in the gravity will effect time. The main point of view has been in terms of gravity as a mass source extending in a boundry termed the gravity body's radius. In this view, events can be measured from the radius and extending outward from the radius, according to a mass total located at the radius, where the radius itself is measured from a single point of center. In questioning a mass augmentation effect in the gravity, the issue can be more clear cut. Specifically, given a finite mass and a finite radius, what gravity relativity effect is generated, and how much does the effect increase the original mass generating the effect?. From this steady stateness, it is easy to ask across to special relativity wishing to know what velocity is required to generate an identical effect. However, in closer introspect, a greater question has also been asked. And that is, given a mass enhancement and space contraction in special relativity, at what velocity does a mass have to be moving in order for it to transfigure into a black hole? Looking at things from another point of view the question can be put in yet another way; to wit: At what velocity does the mass have to be moving in order for special relativistic effect (increasing the mass's mass and collapsing its radius) to cause the mass's flow of time to come to a standstill? The answer is found in an M+/R- ratio, which is calculated through special relativity using the mass's gravitational effect to state the equivalent relative velocity. This type of thinking is out in the open in the material of Part 4. It is summarized in the relationships enclosed in TABLE 8 under 'Pure Math Connectors' above. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± FINISHED ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Planetary Data is from the following reference source: UNIVERSE by Don Dixon, Houghton Mifflin Co., Boston, 1981 (References found at the back of the book) ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Signed: Rhae. S. Livingstone Address: 78072, Cityview, Nepean, Ont, Canada K2G 3J0 Phone number: Area code: 613 820-9450 (C) 1990 Introduction to Mass Increases By Gravitational Relativity. Rhae S. Livingstone. Canada. Copyright March 16, 1990 All rights reserved. Peace Power and Plenty everyone. ALL DONE