INTERFACE RELATIVITY Interface between special and general relativity PLEASE NOTE: This document has ascii characters. It reads fine at Dos or in any compatable editor but not in Windows. In Windows the ascii characters are substituted by Ansi surrogates such as capital letters and strange looking symbols. In a Windows Browser you cannot read this document's equations, since the strange codes surround and change the equational content's appearance too drastically. The best view is in any Dos environment such as an editor. This file is written in Dos ASCII format. A helpful sonic stereo experiment reports contains possible insights casting more light on Interface Relativity, see the reports here in the 'appendix.txt' page ABSTRACT: A step toward unifying the forces. The gravitational force, and electro-magnetic forces (strong, electro-weak, and charge) are unified through Interface Relativity equations which join general and special relativitist effects into a fundamental equality. The interface specifies the principles and properties by which the general (gravity) and special relativity (radiation) modes are unified into a single set of of coherent balanced equations. ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± ±±±±±±±±±±±± ±±±±±±±±±±±± ±±±±±±±±±±±± INTRODUCTION TO MASS INCREASES BY ±±±±±±±±±±±± ±±±±±±±±±±±± GRAVITATIONAL RELATIVITY ±±±±±±±±±±±± ±±±±±±±±±±±± ±±±±±±±±±±±± ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± The following proposes that steady state relativistic effects can be understood to occur pursuent to gravitational fields. The wider range of distortions in space embraced by the GENERAL THEORY OF RELATIVITY are put aside and certain specific effects are studied in detail. These specific effects are understood to come under the heading of GRAVITATIONAL RELATIVISTIC EFFECTS. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY THEORY ±±±±±±±±±±±± º º CONNECTS CERTAIN SOLAR PLANET MASSES. º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ͹ º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ͹ º ALSO, GRAVITATIONAL AND SPECIAL RELATIVITY THEORIES º º ARE INTRINSICALLY RELATED º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ By assuming a mass and spacial effect in general relativity, a proposed gravitation relativity is evident, in which there is a direct tie-in between effects seen in Special Relativity and in Gravitational Relativity. In fact, properties commonly factored for a star or black hole in Gravitational Relativity, can also be factored in Special Relativity, and visa versa. This suggests not necessarily a unified field theory, but definately a connection betweeen certain properties in gravity, and in electro-magnetism. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º ABSTRACT º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ Several facets are to be discussed in the following. (Part 1) Arguments demonstrating an increase in mass by the effects of gravitational relativity are shown through events which occur in the solar system. (Part 2) Effects for gravitational and special relativity are shown to be synonymous for a given mass. Critical limits are uncovered in the behaviors of both relativities. In specific situations, mass is locked to a ceiling which is less than, but is determined from, black hole mass equivalents. In this, it is found that the maximum original mass which can be gathered before gravitational relativistic effects are maximized, is that of a black hole's mass divided by a factor of 1.618034 (a number constant known as the Golden Harmonic Ratio). The maximum velocity attainable by this mass when moving in special relativity, is the speed of light divided by the Golden Harmonic Ratio. (Part 3) It is found that for any visible mass, there is a maximum special relativistic limit on the mass. This limit can be known in advance by knowing the maximum velocity the moving mass can attain and still remain visible in the normal sense, when observed by a stationary observer. The maximum effect is a derivative of the speed of light reduced by the relativistic effect of the mass's gravity. This is shown to define an upper limit velocity at which any given mass can appear in the same state of the universe as the stationary observer. Any rest mass reaches this barrier at a plateau that is predictable, and so the mass cannot visibly expand to infinity. (Part 4) Innuendos of a unified field theory are harking loudly, popping out of the framework of relativistic physic. There is a universality in obvious behaviors working directly between the one field's venues (gravity) and the other field's venues (electromagnetism). As to whether these equalities can constitute segments of a full fledged unified field theory is not to be addressed at this time, in the scope of the following disclosures. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º part 1 ±±±±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY ±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ A little known (entirely unknown) fact is that certain solar planetary masses can be connected as a direct consequence of gravitational relativity. This is shown to be true when it is surmised that relativistic effects of gravity may include an intrinsic increase in the mass comprising the source of the gravity. The relativistic increase for the Sun mass is very small compared to the mass of the Sun itself. Even though the increase in mass is small at roughly 4.23 x 10 to the power 27 grms, the increase is nevertheless nearly 7 times the mass of Mars, and is marginally less than the mass of Venus. Such an increase in the Sun mass, when calculated to advanced accuracy, is found to be exactly equal to the mass difference between Venus and Mars. Another discrete relativistic potential includes 1/2 the mass of Jupiter added to the mass of the Sun. The existence of states makes it possible to infer a more accurate estimate for the existing mass of the Sun. The radius of the Sun is considered to be a constant for various manifestations, shown to correspond to parameters which operate between solar mass equivalents up to the masses of black holes. In this, a link between gravitational and special relativity is shown. The link is the subject of part 2. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º part 2 ±±±±±±±±±±±±±±±±±±±± SPECIAL RELATIVITY ±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ It can be easily demonstrated that a visible mass moving at velocities nearing the speed of light, can never grow to infinite quantities and remain visible in the normal sense, and so can never achieve a velocity equal to the speed of light, in the normal sense. This is because gravitational relativistic effects have to be considered for a moving mass, if it is assumed that gravitational relativity includes an effect that increases the original state of the mass which is the source of the gravity's relativistic effect. It is readily shown that such gravity effect has significance to special relativity. There is a boxed in limit, where the moving mass (bumped in value in special relativity) assumes a value equivalent to the mass of a black hole, when the original rest mass is expanded by the effect of special relativity, in direct accord with the mass's radius contracted by the effect of special relativity. When assuming the mass of a black hole equivalent, the moving mass effectively drops from sight in the normal physical view as seen by a stationary observer. (See Appendix A at the end of this document, for a related discussion involving elementary particles such as the proton). One of the finite limits to which a mass can be accelerated in special relativity, and to which a mass can be accumulated in gravitational relativity, can be explicitly expressed for both modes of relativity as factors of a number constant known as the Golden Harmonic Ratio, 1.61803398875 . In this, the Golden Ratio's significance is to the existence of black holes. Specifically, a black hole's mass includes both an original mass and an augmentive portion from the relativistic effect of gravity, to comprise the total mass involved. The relationship between original, gained, and final black hole mass aggregations, can be expressed in exact terms of the Golden Harmonic ratio. In particular, however, in the dynamic behaviors of both relativities, important boundaries are reached at a certain critical limit whose mathematical significance is the Golden Harmonic Ratio. The parameters here include a black hole's mass aggregate and event horizon. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º part 3 ±±±±±±±±±±±±±±± THE GOLDEN HARMONIC RATIO ±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ The effects of gravitational relativity can be generally related to the effects of special relativity, to the extent that relativity effects of gravity and of special relativity can be shown to be equated through a single common factor. The maximum velocity attainable by a visible moving mass, is the speed of light reduced by the proportionate effect of the gravitational relativistic effect in the mass being accelerated. The critical limit (maximum velocity) possible, is restricted by bounds achieved in special relativistic effect when the rest mass has increased, and radius has contracted, to a point where the moving entity reaches a state where it forms a black hole and effectively disappears from view, relative to a stationary observer. The barrier limit is easy to calculate and to mathematically confirm, when given the original rest mass and radius. It becomes clear that, generally a visible mass accelerated to relativistic velocities cannot theoretically achieve an infinite mass, and the velocity can never theoretically equal the speed of light. The traditional interpreted statements in special relativity which say any visible mass continues to expand toward infinity, and the velocity continues to the speed of light, are in error about such things. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±± GRAVITATIONAL RELATIVITY THEORY ±±±±±±±±±±±±± º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±± GENERAL INTRODUCTION for part 1 The Solar System ±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ In the following, the existing orbits of planets are not considered as terms, and all of the events are shown to occur as within a constant confinement radius which is the existing radius of the sun. A general relativistic equation is in common use for gravitational effects. Such an equation has been around in physics since 1916. Variations of the equation are also in common use. Given a known mass for instance, a Schwarzschild radius for that mass confined as a black hole can be immediately calculated. Conversely, given a radius, how much mass would be needed to be confined within that radius as a black hole can also be calculated. Such effects are a steady state system. It is the amount of mass within a specified radius which counts. The effects are constant per given mass and radius, since no outside velocity or acceleration is involved with the masses sitting stationary. The same is true for mass aggregates which are not a black hole, but which have mass sufficiently large, and a radius sufficiently small, for gravitational relativistic effects to be discernible. For stars the size of the Sun, for instance, there are discernible effects, even though they appear to be very slight at first sight. In a closer look, however, the slight effects can reveal many major properties in the fundamental relativistic behavior of gravity. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ GRAVITATIONAL RELATIVISTIC EFFECT ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In principle, gravitational relativistic effects are calculated via the standard equation, for varying mass and radius, until a meeting point is reached at which the mass and radius correspond to the formal parameters of a black hole. In the standard equation, a term for the relativistic effect results, which has been mainly used to determine the slowing of time in closer vrs more distant proximities to the field generating the effect. The same term can be used to find out how much a gravitational mass's radius can further contract relativistically per given increase in mass, when assuming that gravity relativistically contracts its own confinement radius. The same term can be used to calculate the gravity's relativistic effect on its own mass. This term can be called E (for effect). The value of term E suddenly nose dives toward 0 when the mass is sufficiently large, due to a sudden relativistic upsurge in pull in the greater power of the gravity itself, at which point the existing mass becomes a so called black hole and the existing mass's radius no longer appears to contract, rather, it will begin to increase given further increases in mass. This mass and radius stabilization is considered a physical boundary called the Schwarzschild radius, or event horizon. The stabilization is discussed in 'A Comparison Between Gravitational And Special Relativity' (found directly under the 'General Introduction for Relativity' Part 2', below), and is formally described in Equations 3 to 5 in APPENDIX B at the end of this document. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ GENERAL MASS QUANTA EFFECT ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In variations of the equations, when a quantity of mass is given and the radius containing it is also known, then a simple solution using term E can denote how much of a mass increase may occur in the mass, due to a relativistic augmentation by the mass's gravity. The augmentation can be conjectured to occur in two ways. Either a measured mass is naked (original with no relativistic augmentation), or is augmented (the measured mass includes the augmentation). Hence the augmentation can be conjectured to be in two modes; either a decrease upon the originating mass, or an increase. In keeping with special relativity effects, a mass increase in gravitational relativistic augmentation can be presumed with no difficulties. For instance the Sun (given its mass and radius) is surmised to have a visible radius which is marginally reduced by relativistic augmentation (shrunk), and so the Sun's apparent mass is also surmised to be marginally augmented (expanded) in a mass increase by an equivalent relative proportion. The problem is that such a conjecture (relativistic augment- ation in mass) is hard to prove, since it is not possible to actually separate a given mass from its gravity and so observe any change in the apparent mass, when the mass is compared with vrs without the relativity of the gravity. In which case, any evident mass augmentation will have to be learned by some secondary means. In this solar system such a means is provided mechanically, by the fact that the amount of solar mass augmentation is a meaningful quantity in company with the existing mass of some of the planets. The mass augmentation has a value which is in a quantum correspondence to the existing masses of Venus and Mars. This makes the mass augmentation clearly visible. The fact that the relativistic mass is involved with these planets (in relationship with small particles external from the Sun) is very curious. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ GRAVITATIONAL RELATIVISTIC EFFECTS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The standard equation for gravitational relativistic effect is described as follows: EQUATION A ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mass) E = ³ 1 Ä ÄÄÄÄÄÄÄ \³ Cý R The square root of ((1 - the product of 2 times the gravitational constant G, times a mass), divided by the radius of that mass times the speed of light squared), yields a gravitational relativistic effect factor, termed E. EQUATION B The radius of the mass times the reciprocal of the E factor, gives the originating radius of the mass, ie., before contraction of the radius by the mass's gravitational relativistic effect. ÚÄ Ä¿ ³ ÚÄ Ä¿ ³ Where Re is the ³ ³ 1 ³ ³ amount of space ³ R x ³ ÄÄÄ ³ ³ - R = Re by which the Sun's ³ ³ E ³ ³ radius is contracted ³ ÀÄ ÄÙ ³ by the relativity ÀÄ ÄÙ in the Sun's mass ÚÄ Ä¿ Ro is the original ÀÄ Ro ÄÙ radius before effect. R is the existing radius (the radius we see) which includes effect (Ro + Re) These (Equations A and B) are well known and nothing new has been so far stated. The relativistic collapse in the Sun's radius is very slight, hardly 1« kilometers. This is learned as the difference between the originating Sun radius Ro, minus the existing (augmented) radius R. The difference seems to be a remarkably close approximation of « the Schwarzschild radius needed for the Sun mass to be a black hole. However this is not surprising, in that the smaller the mass and/or the larger the radius, the closer the radius augmentation is to « the Schwarzschild radius. The 1/2 approximation grows closer, the less the mass aggregate is a black hole. In principle, with little mass and a large radius, there is very little augmentation. Conversely, a very small radius for the small mass is needed as the event horizon for the small mass to become a black hole. The point intended is that as the mass to radius ratio approaches the primes of a black hole, the rates of change due to gravitational relativistic effects climbs up a steepening gradient. At solar quantities, the effects are so slight as to be normally thought of as negligible. But this is not so. If for instance 1/2 the mass of JUPITER is added to that of the Sun, and this enhanced mass sum is regarded as being within the confines of the existing Sun radius, the relativistic mass augmentation effect when applied to the mass of the Sun minus 1/2 the mass of Jupiter, equals the previously noted congress involving Venus and Mars masses, (at the end of 'General Mass Quanta Effect', above). Such state arrays reveal a previously unsuspected property, of relativistic mass quantal arrangements displaced at long distance from the source generating the relativistic mass effect. A first suspicion is that: 'THERE IS AN INCOMPATIBILITY BETWEEN A GRAVITATIONAL FIELD AND THE RELATIVISTIC EFFECT IT GENERATES'. The appearance is that some aspect of the relativistic mass effect generated in a field of gravity, does not stay within the field generating it. In supposition, it appears that some relativistic component is expunged (externalized) from the originating field of gravity. In the case of our solar system's example, the masses of Venus and Mars, along with Jupiter, are external and yet relativistically tied to the Sun mass. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ ESTIMATED ACCURACY OF SOLAR MASSES ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Masses in the solar system are traditionally published in two ways. A mass for each planet is given as a ratio between it and the mass of the Sun. Since comparative ratios can be inferred to considerable accuracy, the Sun to planet mass ratios for most of the planets are well known. On the other hand estimating the actual mass of a planet or the Sun in terms of (say) gram units, is not so easy, since there is no way of actually sitting a planet on a scale. For that matter, estimating the real mass of the Sun (in say grams) is also difficult since the Sun cannot be weighed on a scale. The problem is compounded in that in order to know a real weight (in grams) requires that the universal gravitational constant (G) be known to high accuracy, which it is not. Whereas determining the mass influences of one body on another, as a ratio, is easier since (G) is not a critical factor for the accuracy. For these reasons the real mass of (for instance) the Sun (in say grams) cannot be stated with great accuracy by ordinary measuring methods. The Sun's mass is currently given as somewhere between 1.989 x 10 to 33 grms, and 1.991 x 10 to 33 grms. Whereas planet masses are currently given in gram figures accurate to between 4 and 5 significant figures. The greater accuracy for planet masses is assisted by the fact that the planets tend to subtlety bounce each other around in orbit, and their bouncing can be closely watched. Whereas the Sun is hardly bounced by the less hardy influence of the planets. The Earth - Moon combination gives the best look at bouncing. But rigorous real weight analysis for the Earth is not so easy when tried, because both the Earth and Moon also subtlety bounce around as a unit. If the gram weight of the Earth (5.976 ñ .004 x 10 to 27 grms) is multiplied by the Sun to Earth mass ratio (332,995.9 ñ .4), then the Sun's gram weight results as (1.9899834 x 10 to 33 grms). This value is actually deemed low to a very minor degree for the equations which follow below. In the following, a Sun mass in the vacinity of (1.990993 x 10 to 33 grms) is explicitly inferred. Another problem in any advanced accuracy is inherent in the weak solar gravitational relativistic effects per se. Because the effect for solar mass quantities is so slight, there is a loss of some accuracy due to inherent truncation in doing the calculations. In the equations which follow, accuracy has been maintained to 13 significant digits, but inherent truncation results at the 7th significant digit of certain of the terms. Such truncation is diminished when dealing with larger masses confined within small radii. The truncation disappears completely when dealing right at the range of black hole masses. Hence, black hole limits can provide a tool for comparing calculations, to determine which calculations produce exactitudes and which produce close approximations only. This is actually more straightforward than it sounds. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ BASIC CONVENTIONS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In the following, the existing orbits of planets are not considered as terms. All of the events are shown to occur as within a constant confinement radius, which is the existing radius of the sun. For the sake of convenience, the mass of the Sun is shown as a standard term labeled (MM). In the following, the calculations are accomplished at an accuracy of 10 to the 13 significant digits. Zeros are used to fill gaps between available digits and the 13th significant digit. As already mentioned, some of the terms are accurate only to the 7th significant digit. In fact, some terms cut off at the 7th digit. For this reason, the highest maintained accuracy possible is very important. For the universal gravitational constant G, a recent revision having a digital value of 6.6720 x 10 to -8 is used. The speed of light C of the following value is used: 2.99792458 x 10 to 10 cms/sec. The radius of the Sun is used as a constant R, having the value 6.96265 x 10 to 10 cms. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ MASS CONVENTIONS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The following mass aggregates have been adopted as standards for the involved quantities. The high accuracy given them has been by the adjusting of repeated pure math experimental results until a semblance of coherency in the mass standards looked viable. The term 'aggregate mass' is used for denoting a mass (such as the Sun, plus or minus another mass (such as 1/2 the mass of Jupiter). 'Aggregate mass' is also used to denote any apparent mass, since the mass is assumed to include relativistic augmentation due to gravity. Hence, the original mass before augmentation is termed 'original mass', or 'originating mass'. K has been adopted as a term to explicitly denote the relativistic mass augmentation in the Sun's mass due to the Sun's gravity. In determining aggregate mass values, the value of MM for the Sun's apparent mass was first determined, based on an assumed equality that a so called K augmentation factor for the Sun mass is indeed the mass difference between planets Venus and Mars. Without doubt the real values for the mass aggregates (given in grms for instance) will marginally change depending on future adjustments of the universal gravitational constant, and perhaps sharper astronomy techniques. (For that matter, mass MM may not be the true real mass of the Sun. It may turn out that MM is the mass of the Sun ñ something else). It is anticipated that any such changes would nevertheless prove to continue to be coherent within the realms of the gravitational relativistic state equations which involve them. Several tables and basic equations follow. Following these, a discussion begins on how a mass of MM was inferred for the Sun, via gravitational relativistic effects. Table 1 which follows, lists important mass aggregations, and the highest resolved real mass values possible as used to explore their relativistic highlights. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º INFERRING A GRAVITIONAL RELATIVISTIC º º AUGMENTED MASS VALUE FOR THE SUN º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ TABLE 1 INFERRED VALUES ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ MM = Existing Sun mass, presumed to include ³ ³ original mass plus mass augmentation K ³ ³ ³ ³ = 1.9909930 x 10 to 33 grms ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ K = Gain in original mass of the Sun, the ³ ³ amount of relativistic augmentation ³ ³ due to the Sun's gravity ³ ³ ³ ³ = 4.226490 x 10 to 27 grms ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Mbh = Mass of a black hole having an event ³ ³ horizon equal to the Sun's radius R ³ ³ ³ ³ = 4.689536679 x 10 to 38 grms ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ TABLE 1-A ESTABLISHED VALUES ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ R = Existing Sun radius ³ ³ = 6.96265 x 10 to 10 cms ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ C = Speed of light ³ ³ = 2.99792458 x 10 to 10 cms/sec ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ G = Universal gravitational constant ³ ³ = 6.6720 x 10 to -8 cms3/grms secý ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ CR = A physical constant for Mass/Radius ³ ³ ratio of a black hole ³ ³ = 6.735275620 x 10 to 27 grs/cm ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ GH = Golden Harmonic Ratio ³ ³ = 1.61803398875 ³ ³ û = 1.272019649 ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ TABLE 2 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ Planetary masses - Data is from tables found at the ³ ³ back of the following reference: ³ ³ ³ ³ UNIVERSE by Don Dixon, Houghton Mifflin Co., ³ ³ Boston, 1981 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 TABLE 3 Certain terms are used to generalize certain types of masses: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ Low mass - Masses in the range of those found ³ ³ in this solar system ³ ³ ³ ³ Enhanced mass - Solar mass aggregates other ³ ³ than the Sun, added or subtracted ³ ³ to the Sun mass ³ ³ ³ ³ - Specifically the mass of the ³ ³ Sun plus 1/2 Jupiter, and mass of ³ ³ the Sun minus 1/2 Jupiter, also mass ³ ³ of the Sun minus mass of Venus ³ ³ ³ ³ Higher mass - Mass of a black hole, and in mass ³ ³ range of a black hole ³ ³ ³ ³ - Specifically the mass for a ³ ³ black hole whose event horizon ³ ³ is the radius of the Sun ³ ³ ³ ³ ³ ³ Originating mass - Original mass accumulation without ³ ³ any relativistic augmentation ³ ³ ³ ³ Augmented mass - Existing mass assumed to include ³ ³ a change from the originating ³ ³ mass due to relativistic effect ³ ³ of gravity ³ ³ ³ ³ Existing mass - As physically measured, with ³ ³ any assumed augmentation present ³ ³ in the measurement ³ ³ ³ ³ Real mass - A real weight, in terms of a ³ ³ physical weight, for instance ³ ³ measured in grms as if weighed ³ ³ on a scale ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Certain equations are used to generalize mass effects due to gravitational relativity. Certain term conventions are adopted for the sake of convenience in bookkeeping: EQUATION C Determining a relativistic effect factor Em for a mass aggregate, in particular the Sun: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM) Where MM is the mass Em = ³ 1 Ä ÄÄÄÄÄÄÄ of the Sun, and R is \³ Cý R the radius of the Sun EQUATION C-1 Determining how much mass augmentation relativistically occurs in the mass aggregate of the Sun: (MM) - ((MM) x Em) = Km Where K is the actual mass augmentation increased on the Sun's original mass due to gravity EQUATION C-2 Determining a relativistic effect factor for a mass aggregate, such as the Sun plus X, where X is anything: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM+X) Ex = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ \³ Cý R EQUATION C-3 Determining how much mass augmentation relativistically occurs in a mass aggregate, such as the combined mass of the Sun + X , when both are confined in radius R : (MM+X) - ((MM+X) x Ex) = K+x EQUATION C-4 For example, determining a relativistic effect factor for such as the Sun plus 1/2 Jupiter combined: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM+1/2j) E+1/2j = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ \³ Cý R EQUATION C-5 Determining how much mass augmentation relativistically occurs in a mass aggregate, such as the combined masses of the Sun and 1/2 Jupiter, when both are confined in radius R : (MM+1/2j) - ((MM+1/2j) x E+1/2j) = K+1/2j ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º VERIFYING A MASS OF MM FOR THE SUN º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ An aggregate mass MM (being the mass of the Sun) found to have intrinsic relativistic consequences, can be easily verified. If starting with an estimated Sun mass, for instance; (1.989 x 10 to 33 grms); and assuming that the Sun mass is already relativistically augmented, the gravitational relativistic mass increase of a Sun mass of (1.989 x 10 to 33 grms) is found (using Equations C and C-1), to be slightly less than the mass difference between Venus and Mars. That is: Venus mass is 4.8683 x 10 to 27 grms Mars mass is .64181 x 10 to 27 grms Venus - Mars is 4.226490 x 10 to 27 grms whereas the mass augmentation Km of a Sun mass of (1.989 x 10 to 33 grms) is (4.218033 x 10 to 27 grms), which is low. If the Sun's mass is gradually increased, eventually a mass aggregate will be found, in which the relativistic mass augmentation K is precisely (Venus - Mars), that is: K = 4.226490 x 10 to 27 grms. The point of agreement occurs when the mass aggregate for the Sun MM is found to be (1.990993 x 10 to 33 gms). For instance, suppose arbitrary units of Neptune's mass are systematically added to a base mass of (1.989 x 10 to 33 grms). A break point will be reached. At + 18N units of Neptune's mass the relativistic augmentation (Km) of the aggregate mass will be marginally less than (Venus - Mars). And at + 19N units of Neptune's mass, the relativistic augmentation (Km) of the aggregate mass will be marginally more than (Venus - Mars). And so somewhere between (base + 18N) and (base + 19N) is a solar mass component whose resulting augmentation (K) is exactly equal to (Venus - Mars). The search can now be narrowed to (base + X), where (+ X) falls somewhere between (+ 18N and +19N). Fine tune fiddling back and forth using smaller and smaller increments for X, eventually closes in on a result for; (base + 18N + X) in which the relativistic mass augmentation from (base + 18N + X) when using Equation D below, equals (Venus - Mars) exactly. EQUATION D Where b is a base mass ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ (1.989 x 10 to 33 grms) ³ 2G (b+X) E = ³ 1 Ä ÄÄÄÄÄÄÄÄ And so (b+X) - ((b+X) x E) = K, \³ Cý R and K = (Venus - Mars) exactly, when (b + X) is exactly (1.990993 x 10 to 33 grms) EQ D can be written so that (b+X) is standardized as MM, so that: EQUATION E Where MM is an inferred Sun ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ mass, so MM - ((MM) x Em) = K ³ 2G MM where K = (Venus - Mars), Em = ³ 1 Ä ÄÄÄÄÄ and Em is the relativistic \³ Cý R effect factor for mass MM In other words the inferred Sun mass MM presents a solar mass factor whose relativistic gravitational augmentation (K) is exactly equal to the mass difference between Venus and Mars. That is: Equation E determines Em and: MM - ((MM) x Em) = K and: K = 4.226490 x 10 to 27 grms which is precisely (Venus - Mars) which also is: 4.226490 x 10 to 27 grms This instantly presents an interesting situation. The inferred mass of the Sun MM appears to involve a relativistic gravitational mass amalgamation which is greater than the mass of the Sun alone. The interesting kink is that the masses of Venus and Mars are found expunged into space, at long distance orbits around the Sun. This orbital existence is not explained at this point and so is noted only as a comment. The other interesting point of view is that although the mass of Mars for instance is very small compared to the mass of the Sun, the mass of Mars is nonetheless highly visible. This is something like the high visibility of the electron's tiny binding energy unit in comparison to the mass of the Proton. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º SPECIFIC MASS QUANTA EFFECT º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ As described under 'A Comparison Between Gravitational And Special Relativity' (found directly under the 'General Introduction for Part 2', below), gravitational relativity includes at least two variable source terms for its effect. These source terms are the aggregate mass, and the mass's confining radius. It means that different quantities of mass can be said to occupy the same area. In which case there can be (in result) different or identical relativistic mass augmentations, depending on discrete combinations of how much mass is said to be added or subtracted to the initial mass aggregate, confined in the same or in different radii. For instance in mass aggregates which are in the range of the size of the Sun, here, discrete extra mass in the same radius (the Sun's radius) can produce a relativistic factor Ex which when arbitrarily applied to yet another discretely different mass aggregate, can produce a K augmentation which is otherwise gained from yet another different mass aggregate. For instance, the Sun mass MM, plus 1/2 the mass of Jupiter, can provide via EQ C-2 an effect factor (E+1/2j) which when applied to the same mass aggregate, via EQ C-3, results in K+j . But if E+1/2j is applied to a different mass aggregate, for instance to MM-1/2j, a value slightly departed from K+j must result. The resulting slightly lower value in fact once again happens to be K exactly (the mass difference between Venus and Mars). The formal description for this enhanced mass state is: EQUATION E-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ (MM+1/2j) is the ³ 2G (MM+1/2j) aggregate of the Sun E+1/2j = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄ mass plus 1/2 the mass of \³ Cý R Jupiter, confined in the existing Sun radius R EQUATION E-2 (MM-1/2j) - ((MM-1/2j) x E+1/2j) = K where K equals the mass of (Venus - Mars), and (E+1/2j) is the relativistic effect of the slightly denser aggregate of the inferred Sun mass MM plus 1/2 the mass of Jupiter, when confined in the Sun's radius R. In keeping with state-like mass aggregates, if EQ E-1 is rewritten so that the initial mass aggregate used in EQ E-1 is now MM-1/2j, and a resulting effect (called E-1/2j) is used in a rewritten form of EQ E-2, then a relativistic mass augmentation equal to K once again results; that is: EQUATION E-3 (MM+1/2j) - ((MM+1/2j) x E-1/2j) = K where K equals the mass of (Venus - Mars). EQUATION E-4 The bifurcation of Jupiter mass around the mass of the Sun to form coherent relativistic states can be generalized as: E+1/2j of mass M+1/2j applied to M-1/2j yields K Em of mass MM applied to MM yields K E-1/2j of mass M-1/2j applied to M+1/2j yields K EQUATION E-5 Such a bifurcation around the mass of the Sun can be generalized as: E+x of mass M+x applied to M-x yields Kx E of mass M applied to M yields Kx E-x of mass M-x applied to M+x yields Kx However, the augmentation quantity Kx only equals known augmentation value K, when M+x and M-x are specifically MM+1/2j, and MM-1/2j. That is, when 1/2 quantas of Jupiter's mass are added, and subtracted, to the inferred mass MM of the Sun. (It should be noted that the bifurcation results of EQ E-4 are not perfect exactitudes. The three resulting values of K happen to look the same for masses in the range of this solar system. For higher mass densities for example MM times 1000, confined in the same radius R, the three K values (shown as Kx in EQ E-5) are noticeably separated). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ VERIFYING THE COHERENT 1/2j STATES ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Equations E-1, E-2, E-3, and E-4, were not easily found without a prior insight and a discovery. In question is how come a unit of 1/2 the mass of Jupiter has been arbitrarily used to arrive at a seeming non arbitrary result, this result being where K is twice again calculated, as summarized in Equation E-4. An original intention was to see if the total mass of the solar system could be inferred to be in any way involved in some sort of interphasing between different mass aggregates in this solar system's gravitational relativity. This thought itself came from an original impression that the real mass of the Sun was in the range of base (1.9891 x 10 to 33 grms), and inferred mass MM would be the real Sun mass (base) plus Jupiter's mass, since (MM - base) closes in on an excellent approximation of Jupiter's real mass at (1.901 x 10 to 30 grms), when using EQ D to infer mass MM. For a while it was looking good. It seemed that if MM was the mass of the (Sun + Jupiter), and a mass value just slightly larger than the total mass of the solar system was substituted in EQ C-2, then a mass augmentation of K was again found when the factor Ex of EQ C-2 was substituted in EQ C-3, when Jupiter's mass was subtracted from the solar total mass aggregate and the result of this reduction substituted for MM+X in EQ C-3. In the exploration, a mass term Mt was adopted for the solar mass total, plus some little extra, to give mass term Mtx. And mass term Mtx-j denoted the solar total minus the mass of Jupiter. The value of Mtx could be rigorously inferred, as being exactly the mass aggregate needed in EQ C-2 to result in a mass augmentation effect equal to K in EQ C-3, when mass aggregate Mtx gave augmentation effect Etx, which was used to find the augmenting effect on mass Mtx-j, as in: EQUATION F ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G Mtx Etx = ³ 1 Ä ÄÄÄÄÄÄ \³ Cý R and a mass aggregate of (Mtx - Jupiter) was substituted in EQ C-3, giving: EQUATION G (Mtx-j) - ((Mtx-j) x Etx) = K In other words, the thinking was heading along a line that a sort of formal relativistic interphasing might be occurring, whose boundary was spread between the base mass of the Sun, and the total mass of the solar system. For instance between the Sun, and (Sun + Jupiter), and (Sun + planets + moons), and (Sun + planets + moons - Jupiter). The problem was in that little extra mass bit, (the x of Mtx). What might it represent? It was suddenly and unexpectedly found that the value of Mtx as rigorously inferred, turned out to be exactly (MM + 1/2 Jupiter). This was not a percentage of error type of equality. The figures that suddenly appeared on hand were identical to 8 significant digits. In other words, the rigorously determined value for Mtx, and MM+1/2j, were identical to 8 significant figures. Which dramatically changed the picture. It was now easy to think that MM instead of being a (Sun mass + Jupiter) aggregate, represented the real mass of the Sun itself. In other words, MM could well be the real mass of the Sun. It was also easy to perceive a formal verification for the quanta bifurcation factor involving 1/2 the mass of Jupiter. By using Equations F and G to find a result equal to K, a mass quanta increment of (+X) added upon MM eventuates in an interphase involving (MM-X) for the K result, only when X is exactly 1/2 Jupiter, when using the same inferencing technique as was used to infer MM in the first place, as described above under 'Verifying a Mass of MM For The Sun'. A slightly more accurate inferencing for MM itself was thus made possible. In order for Equations E-1 to E-4 to yield results definitely equal to K, the value of MM is adjusted to the greater accuracy of (1.99099305 x 10 to the 33 grms). It made the explorations involving solar mass total aggregates Mt and Mtx not important. This avenue of reasoning was dropped, and is mentioned above only to reveal how a quantal value of ñ 1/2 Jupiter as displayed in Equations E-1 to E-4 came to be an issue. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ OTHER MASS AGGREGATE STATES ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In applying such interphasing logic to the solar system, the study is narrowed to include only mass quantities which currently exist; these being the Sun, and certain planets. In the case of a bifurcated Jupiter mass, a theoretical attribute is identified. This is where mass aggregates and resulting gravitational relativistic effects can phase in and out (in a continuation of certain coherent effects), through a range of mass densities confined within a single constant radius. A form of harmonic interphasing through a realm of masses is definitely sensed. In gist; a higher relativistic effect from an enhanced mass aggregate is applied to a lower mass aggregate, such that the resulting augmentation is lower or different than would be expected for either the originating enhanced mass, or the reduced mass. This type of reasoning should only be speculative, except that the mass augmentation which actually results when +1/2 Jupiter and -1/2 Jupiter are involved, is already a recognized quantity, this being mass term K, already independently seen for a mass aggregate which is other than an effect that is expected straight across for an enhanced or diminished sum of the Sun plus or minus 1/2 Jupiter. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ OTHER MASS EFFECT COHERENCIES ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Other mass effect coherencies seem to occur. One involves the mass of the Earth (Me), which, when subtracted from mass MM, yields an aggregate mass whose relativistic effect factor (herein called Ee), which when applied to mass aggregate MM, results in a discrete mass split which is precisely equal to the mass of the Earth Me minus K. This formula (as exemplified in EQ H and I below), might at first seem tautological until further studies show that a relativistic factor Ex for any mass aggregate (M + X) or (M - X) does not phase in perfectly to an exact result for (MM - (MM x Ex)) = X - Kx for any value assumed for mass X. Only certain precise values of ñ X are seemingly phased in a coherency. For instance when: 1. X equals the mass of Earth 2. X equals the mass of Venus 3. X equals ñ 1/2 the mass of Jupiter The case of X being equal to ñ 1/2 the mass of Jupiter has already been demonstrated in Equations E-1 to E-4. When X equals the mass of Venus, then a mass split resulting in a discrete relativistic augmentation, also incorporates the mass of Mars. This is shown further below in Equations Q to S. A formal description for the interphasing state involving the Earth is as follows: EQUATION H ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM-Me) Where (MM-Me) is mass MM Ee = ³ 1 Ä ÄÄÄÄÄÄÄÄÄ minus the mass of the Earth Me. \³ Cý R MM is the mass of the Sun EQUATION I MM - ((MM + Me) x Ee) = Me - K Where Me is the mass of Earth, and K is (Venus - Mars) This formula (as exemplified in EQ I), might at first seem exciting until it is recognized that it is rather a sort of strange tautology. That is, further exploration shows that a relativistic factor Ex for any low mass aggregates in the range available for this solar system, for instance (MM + X) or (MM - X), phases in to a seeming predictable result where: when Ex is determined as the relativistic effect factor for mass MM-X (for instance using EQ H), then: MM - ((MM+X) x Ex) = Xx = (X - K) where Xx = (X - K) results for any reasonable value assumed for mass X. But for higher masses (much beyond MM), the equality actually breaks down, demonstrating that there was no tautological equality to begin with. A formal description for showing the breakdown is: EQUATION J ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (M-X) Where (M-X) is mass M minus Ex = ³ 1 Ä ÄÄÄÄÄÄÄ any other mass X, and radius \³ Cý Rx Rx is the same for any values of (M-X), then: EQUATION K M - ((M) x Ex) = Kx And: EQUATION L M - ((M+X) x Ex) = Xx And: EQUATION M Xx - X = Kx Where: Xx + Kx = X And: Xx = X - Kx Where X is the original arbitrary mass that was subtracted from M in EQ J, and was then added to M in EQ L ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ STRANGENESS IN A SEEMING TAUTOLOGY ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ This section covers general ground and seems to ramble, rather than to leap straight ahead from one event to a next. Read if interested. This section concludes with information of importance to the following section 'A Coherent Phase in This Solar System'. The discussion resumes in earnest in PART 2 a few pages further below. Do not be fooled by the implied authority of Equations J to M. Equations J to M are not a perfect tautology. Even though they are presented above as such. Instead, they are strange, in that their results can actually vary in several ways, under the microscope of vigorous scrutiny. For instance terms X and Xx begin to noticeably separate for larger values of M, for instance when M begins to assume a mass approaching that of a black hole having radius Rx. In these higher mass regions, the value of Kx can begin to rapidly escalate over and above any amounts of increase given to mass M. In other words Kx begins to itself take on high value (pursuant to gravitational relativistic augmentation), but always is less than the value of M. The value of Kx is in fact somewhat periodic in two ways. (Kx is said to be the mass augmentation due to the gravitational relativistic effect of mass M acting on itself, ie. on mass M). Firstly: the digital value of Kx is dependent almost entirely upon the digital value of M. For example a Kx digital value ranging from (4.21 x 10 to the power 27) up to (4.79 x 10 to the power 37) is found for mass M values ranged from (1.989 x 10 to the power 33) up to (1.989 x 10 to the power 38), when the confinement radius Rx is held constant at (6.96256 x 10 to 10 cms), through greater and greater magnitudes in the concentrations of mass M. Secondly: it will be seen that for every increase of M by a factor of 10, the value of Kx increases by a power of 100 (actually just slightly more than 100), until the Value of Kx vrs M closes suddenly in a very rapid crunch toward unity as the value of M approaches a last iota in becoming the mass of a black hole. The power of just above 100 in the increases of Kx, is due to the modest increase in the digital value of Kx identified in the previous paragraph. At the junction at which the confinement radius Rx becomes the same as an event horizon of a black hole, Then the augmentation Kx vanishes from the picture, because when M is the mass of a black hole having a radius Rx, then Kx can no longer be calculated. Related events can be closely watched for permutations by keeping certain parameters constant. For instance Rx is the same constant radius, in Equations O to O-4 which follow. Then, given the basic equation: EQUATION O ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mh) Where Ex is the relativistic Ex = ³ 1 Ä ÄÄÄÄÄÄÄ effect factor of a high mass Mh \³ Cý Rx having a confinement radius Rx, and: EQUATION O-1 M - ((Mh) x Ex) = Kx But when Mbh is the mass of a black hole of radius Rx, then: EQUATION O-2 2G (Mbh) ÄÄÄÄÄÄÄÄ = 1 And therefore: Cý Rx EQUATION O-3 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mbh) Ex = ³ 1 Ä ÄÄÄÄÄÄÄ \³ Cý Rx Is no longer valid, since: EQUATION O-4 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ Ex = ³ 1 Ä 1 The square root of 1 - 1 = 0 \³ is impossible. However, in looking back to Equations J through M, where terms X and Xx are featured, certain important distinctions can be observed to occur for high masses M that are not yet a black hole. For instance if variable amounts of mass M ñ X are confined within the same radius Rx so as to provide a consistent point of view via a constant Rx, then in particular: ITEM A. If X is closer in value to the higher value M, (for instance if X is 1/100th the value of M), then Xx of EQ L can be substantially lower than X, and Xx can also be substantially lower than Kx. ITEM B. If X is substantially lower than the higher value M, (for instance if X is 1/100000th the value of M), then Xx can increase substantially above X. In fact Xx approaches the value of Kx for the mass M (as will be found when in using Equation K, above). These above mentioned 'drifts' are inherent in the gravitational relativistic arena. It was possible to see them only because for the instances of ITEMS A and B above, the value of radius Rx was held constant, so that the consequences of different masses (M-X) and (M+X) through different values of M and X can be followed in the varying results. The above 'drifts' have been discussed here at length because if their insights are not known, certain confusions may seem to occur in doing high mass calculation in the denser levels up to that of a black hole, vrs doing low mass calculations involving values of mass M that are on par with the mass aggregates available in this solar system. In such low mass calculations, conditions similar to ITEM A above are found. Except in low mass calculations for this solar system, the value of Xx can be rather close to the value of Kx, and Xx + Kx can be rather close to the value of X. In fact in mass regions on par with this solar system, any difference between X and (Xx + Kx) of Equation M above, in which the Earth mass Me is X, is hardly discernible, so indiscernible that X and (Xx + Kx) seem the same, (as indicated in EQ I above, where Xx would be Me - K). But X and (Xx + Kx) are not truly identical. Yet there are certain precise values phased in a certainty for all values of M right up to that of a black hole. For instance there is a condition in which Xx and Kx can both turn out to be identical. This is as follows: EQUATION O-5. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mass) Ex = ³ 1 Ä ÄÄÄÄÄÄÄ \³ Cý Rx And: Mass - ((Mass) x Ex) = Kx Then: EQUATION O-6. (A zero result occurs in using the reciprocal 1/Ex) Mass - ((Mass - Kx) x (1/Ex)) = 0 This is true for both low mass and high mass calculations ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ A COHERENT PHASE IN THIS SOLAR SYSTEM ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In this solar system there is one precise value of X which seems phased in a genuine coherent certainty, when viewed through the scope of Equations J through L. Specifically, when the mass aggregate equals MM, and X equals the mass of Venus (Mv), the strange tautology of Equations J through L become a seeming genuine equality, wherein the resulting X = (Xx + Kx) mass split in relativistic augmentations, also incorporates the mass of Mars. Specifically, Xx is the mass of Mars. The formal description for this state is as follows: EQUATION P ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM-Mv) Where (MM-Mv) is mass MM Ev = ³ 1 Ä ÄÄÄÄÄÄÄÄÄ minus the mass of Venus Mv. \³ Cý R MM is the mass of the Sun, and R is the exiting radius of the Sun. EQUATION Q (Determines a value K) ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MM) Ek = ³ 1 Ä ÄÄÄÄÄÄÄ \³ Cý R This is the same as EQ E, so that: MM - ((MM) x Ek) = K Such that: EQUATION R MM - ((MM+Mv) x Ev) = Ma Where Ev is the effect factor of EQ P above, and Ma is the mass of Mars, so that: EQUATION S Mv - Ma = K In which also K + Ma = Mv With Equations P to S there is established a formal second (albeit obvious) identification for the previously noted condition; that the relativistic augmentation (K) of the inferred mass of the Sun MM is identical to the mass difference between planets Venus and Mars. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± PART 2 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º ±±±±±±±±± GRAVITATIONAL AND SPECIAL RELATIVITY THEORY ±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 2 ±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ A COMPARISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ It is traditionally thought that gravitational relativistic effects differ in kind from special relativistic effects, in that in special relativity, an approaching equality between a velocity and the speed of light is theorized to lead to an escalating mass increase which continues toward infinity as the velocity closes in on the speed of light. In this view of special relativity, there is only the one ultimate source of the effect, this being the varying velocity. The velocity of light can never be reached in an onrush of mobile matter, due to the infinity in mass which would result. In gravitational relativity, at least two source parameters are variable. Specifically, there is a given mass and a given radius, each of which can change independently, and so can ultimately combine in combinations where various equalities exist. For instance a radius of a mass can vary depending on ambient mass density, for example between a gas such as hydrogen, and a solid such as gold. But for any mass of sufficient size, gravitational collapse can theoretically lead to a black hole. 1. In a mathematical convenience, more mass added to the same radius can produce the collapse. In this sense there are equalities involved. The equalities are when the mass's existing radius is normal and when the same radius is the boundary of a mass's black hole event horizon. 1A. A sort of double flip flop occurs at this boundary. If extended beyond this equality, any increase in mass in the black hole results in an increase in radius (rather than decrease in radius). But conversely a decrease in a black hole's radius results from a decrease in mass, ie., if the mass does not decrease the radius does not decrease). 2. This stable equality can exist because both the input terms for mass, and confining radius, are variable. For instance a low density gas cloud can have a high mass but large radius, resulting in very weak relativistic consequences, whereas the same mass concentrated in a very small area can have substantial relativistic consequences. 3. Further, mass can be removed or added within the same radius, dramatically changing the aggregate's relativistic components. Conversely the same mass can be drawn closer together or spun farther apart, thus changing the radius, thus again dramatically effecting the aggregate's relativistic components. 4. A similar though not identical property can occur in less dynamic realms, for instance in mass aggregates which are the size of the Sun. In this case extra mass in the same radius (the Sun's radius) can for instance produce a relativistic factor E which when imaginarily applied to another mass aggregate, can produce a Kx augmentation which is otherwise gained from a different mass aggregate. In the case of the solar system, the Sun's radius and resident mass aggregate are not the total quantities involved in the aggregate's relativistic components. Planet masses in the bodies of Jupiter, Venus, and Mars, are also involved. It means that the relativistic components include something which is manifesting in an external- ization of the effect, occurring at long distances from the field which is generating the relativistic effect. What these external- izing influences are is not immediately known. Nonetheless the evidence of their existence is unmistakable. The evidence in fact does infer that a mass augmentation is present in a field of gravity. In truth, the evidence does not immediately prove whether the mass augmentation is a relativistic increase, or decrease, on an original mass. The equations herein shown have assumed that the augmentation is an increase. The evidence on its own raises questions which are not answered at all. For instance, how come the particular planet orbits for Jupiter, Venus, Mars, and also the Earth? And what linkages might angular momentum and/or planetary spin have, if any? Etc. The gist of Part 2 is not in the speculation, but in certain understandable exactitudes which do occur. These exactitudes are particularly easy to see in high mass ranges closing in right on black hole masses, and so can be extrapolated back to less easily seen low mass effects in gravitational relativity. What is more important, is that a direct tie-in between gravitational and special relativity becomes obvious. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ³ A UNISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY ³ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ There is a direct connection between the effects of gravitational relativity, and special relativity, to the extent that; given a gravitational mass and its confining radius (so that its mass augmentation effect on original gravitational mass is known), the same quantity in mass augmentation can be determined for special relativity, according to the mass increase gained by the same original mass if traveling at some portion of the speed of light. Specifically, the gravitational relativity equation provides a term which allows that the exact velocity of the mass if moving can be perfectly known, in terms of special relativity. The predictability between the two relativities is, as said, exact. That is, the gravitational relativity effect factor from gravity is related to the proportion by which the speed of light is reduced, so that the same mass travelling at the stated velocity (predictably reduced below the speed of light) will experience a special relativity effect on its mass identical to the effect on its mass experienced by gravitational relativity. (This assumes that gravitational relativity indeed has an effect on a gravitational mass, such that there is for instance an augmentive relativistic gain in the mass itself when the mass is standing still. This mass gain by gravitational relativity, and by the instantly predicted velocity in special relativity, are identical amounts of gain). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ THE GRAVITY - SPECIAL RELATIVITY CONNECTION IN DETAIL ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The connection between gravitational and special relativity is not quite so naive as first suggested above, when it comes to actually working out a connection between a given gravitational mass and its special relativistic equivalent. To begin with, a certain parameter must be determined for the gravitational effect. To wit, the radius involved is a control parameter. Given the radius, the amount of mass needed to have a black hole confined in the radius as an event horizon, is determined. (A black hole silent partner for the given mass, so to speak). The ratio of the partner black hole mass, over the mass in question, supplies an essential term. Let's call this term Nx. Let's call the black hole silent partner mass equivalent Mbh. And let's call the original given mass M. The ratio of Mbh divided by M, is our ratio Nx. The speed of light C is divided by the square root of Nx, to give a velocity that is less than C. Lets call this velocity Vx. If mass M is travelling at velocity (Vx), then mass M will experience the same gain in rest mass enhancement via special relativity, as is otherwise gained when the mass is standing still but is augmented by its own gravitational relativity. In a further comment, in the scenes of gravitational relativity, it turns out that ratio Nx (gained as the ratio of a given mass divided into its black hole silent partner mass) is a different view of the relativistic effect factor Ex, which is gained by calculating the given mass's gravitational relativistic effect. This puzzling statement has an easy explanation. For a fact, when: EQUATION T Mbh ÄÄÄÄÄ = Nx Then relativistic effect Ex is: M EQUATION T-1 Gravitational relativistic ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ effect Ex is calculated from ³ 1 ratio (Mbh/M), when the mass Ex = ³ 1 Ä ÄÄÄÄÄÄÄ of black hole silent partner \³ Nx Mbh is calculated from the radius of M, by: EQUATION T-2 Cý R Mbh = ÄÄÄÄÄÄÄÄÄ As in: 2G EQUATION T-3 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 1 Ex = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ ³ ³ CýR ³ ³ ³ ÄÄÄ ³ ³ ³ 2 G ³ ³ ³ ÄÄÄÄÄÄÄÄÄ ³ ³ ³ M ³ \³ ÀÄ ÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ EXAMPLES OF THE GRAVITY - SPECIAL RELATIVITY CONNECTION ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In Equations U through X which follow: (Eg) is the effect (in gravity) for a mass M in gravitational relativity (Es) is the effect (in special relativity) for mass M in motion at a significant velocity in special relativity (Mbh) is a black hole mass from a given radius Rx, as calculated in EQ V below or EQ T-2 above. Mbh is the silent partner mass for any given mass M (Nx) is the ratio of the black hole mass Mbh, divided by the given mass M EQUATION U ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G M Eg = ³ 1 Ä ÄÄÄÄÄ \³ Cý R EQUATION U-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ Vý Es = ³ 1 Ä ÄÄ \³ Cý EQUATION U-2 Gravity relativity Bare bone version ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 1 ³ 1 Eg = ³ 1 Ä ÄÄÄÄÄÄÄ = ³ 1 Ä ÄÄÄÄÄ ³ Mbh \³ Nx ³ ÄÄÄ \³ M EQUATION U-3 Special relativity Bare bone version ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ 1 Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄÄ ³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ Nx ³ ³ ÚÄÄÄÄ ³ ³ ³ \³ Nx ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý As seen in Equations U-2 and U-3, a fundamental statement for both special and gravitational relativity are indistinguishable when given in a Bare bones manner containing term 1/Nx. This is not false, but misleading, in that term Nx is found from the ratio Mbx/M of EQ U-2. In the Bare bones version of EQ U-3, term Nx cannot reveal what the velocity that mass M is moving at in order to have a relativistic effect factor Es in EQ U-3 that is equal to Eg in EQ U-2. This is by no means a critical shortcoming. Without knowing term Nx, the velocity of a moving M can nevertheless be determined directly, if a substitution is made for term Nx in EQ U-3. This substitution cannot be easily shown in the full equation in a typed manuscript such as this. However, the factor to be substituted in EQ U-3 is easily shown. It is Term 1 shown below in EQ U-4. Term 2 of EQ U-4 is taken straight from EQ U-3. EQUATION U-4 Term 1 Term 2 Term 3 an exact ÚÄ Ä¿ ÚÄ Ä¿ velocity V ³ C ³ ³ C ³ ³ ÄÄÄÄÄÄÄÄÄÄ ³ ³ ÄÄÄÄÄÄÄÄ ³ V Substitute ³ ÚÄÄÄÄÄ ³ For ³ ÚÄÄÄÄ ³ = ÄÄÄ ³ ³ Mbh ³ ³ \³ Nx ³ C ³ ³ ÄÄÄ ³ ÀÄ ÄÙ ³ \³ M ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÀÄ ÄÙ C ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ C Term 1 of EQ U-4 gives the exact velocity V (as used in EQ X below), at which mass M must be moving, in order to have a special relativistic effect (Es) identical to a gravitational relativistic effect (Eg). In this connective equality between relativities, identical augmenting effects on the moving rest mass (Mass)(1/Es) of special relativity, and aggregate mass (Mass)(1/Eg) of gravitational relativity, are gained for an original mass when moving (special relativity) and when standing still (gravitational relativity). Inter-combinant mathematics between the two modes of relativity have so far been shown strictly for the effect of one mode (gravity) on the other mode (motion). There are other potentials. For example, would the motion's effect increment upon the gravity effect. If this is so, than Equations T to X need to be expanded to include modifying terms giving the velocity needed when other effects on mass are considered. Such potential views in the mathematics are not herein pursued. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ A Support equation for gravitational relativity follows next ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION V (Mbh) can be determined from the gravitational relativistic effect (Eg). Given a calculated effect (Eg), as determined in EQ U above, then: ÚÄÄ ÄÄÄ¿ ³ 1 ³ Mbh = M x ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ (1 Ä (Eg)ý) ³ ³ ³ ÀÄÄ ÄÄÙ EQUATION V-1 However: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 1 ³ 1 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ also equals ³ 1 Ä ÄÄÄÄÄ (1 Ä (Eg)ý) \³ Nx EQUATION V-2 So that EQ V simplifies to: M x Mbh = M x Nx So that: Nx = Mbh ÄÄÄ ÄÄÄ M M (The result of Equations V is obvious for very high masses, for instance for masses approaching that of a black hole. However, in lower mass calculations (such as for gravitational effects for masses found in the solar system), there is an intrinsic truncation eroding the accuracy, leading to imprecise seeming solutions for Equations V to V-2). The simplification of EQ V into EQ V-2 has been shown, because soon we want to watch very closely certain effects involving Nx, when Equations T through U-4 are used to explore particular aspects of both gravity and special relativity modes in masses which work backwards starting at the limit of black hole masses. As seen in Equations V to V-2, term Nx can be made to have an overly complex look (EQ T-3), or overly simplistic look (EQ V-2). The general confusing looks vanish when certain exact values are attached to ratio Nx. In an exploration which follows after the next section, a constant number already well known as the Golden Harmonic Ratio, becomes apparent as a term of fundamental importance when things are looked at through a certain point of view. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ Summary equations for the two modes of relativity follow next ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION W Basic Gravitational relativity equation ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mass) EQ W is the Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄ same as EQ C further above \³ Cý R (Gravitational effect Eg is known to slow time in the vicinity of a (Mass) which is generating effect Eg). EQUATION W-1 (Mass) - ((Mass) x Eg) = Kx Where Kx is an augmentation of (Mass) by gravitational relativistic effect Eg EQUATION X Basic special relativity equation ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ Vý Many text books cite Es = ³ 1 Ä ÄÄÄÄÄ a greek letter for effect \³ Cý Es, and for ratio Vý/Cý Effect 1/Es increases the mass. Es decreases the radius, and slows time for an entity moving at velocity V relative to the speed of light C EQUATION X-1 Basic black hole mass calculation (Mbh) of EQ X-1 is the mass of a black hole mass as gained when radius R is the event horizon (Schwarzschild radius) of the black hole, whose mass is calculated as: Cý R Finding the mass (Mbh) needed for Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄ a black hole whose Schwarzschild 2G radius is given as R. EQ X-1 is the same as EQ 5 of APPENDIX B below ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ INTERPRETATIONS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ It is worth noting that Equations T through X are true for an existing mass. Specifically, there is a given (existing) gravitational mass M which has an augmentation (Kx) included. The augmentation (Kx) is easily found in its exact amount (by Equation W-1). How fast does the existing (Mass) have to be in motion to experience the same degree of augmentation as Kx via special relativity? This simple question has been addressed by Equations T to U-4. However otherwise the equations of gravitational relativity theory lead to this, (which is the same as saying the energy equivalent in forward escaping light is pulled backward (or bent) by powerful gravity at the same rate of acceleration as the forward velocity C of the light), from Term 1 of Equation U-4 above it is clear that at the mass limit of a black hole, the ratio 1/Nx of the black hole mass Mbh to aggregate mass M, is equal to 1. And so in Term 2 of Equation U-4 the ratio of the speed of light C divided by the root of Nx (as in C/ûNx) will also be equal to 1. Special relativistics then will no longer have effect, as in: EQUATION X-2 Term 1 Term 2 Term 3 exact ÚÄ Ä¿ ÚÄ Ä¿ velocity ³ C ³ ³ C ³ ³ ÄÄÄÄÄÄÄÄÄÄ ³ ³ ÄÄÄÄÄÄÄÄ ³ C Substitute ³ ÚÄÄÄÄÄ ³ For ³ ÚÄÄÄÄ ³ = ÄÄÄ = 1 ³ ³ Mbh ³ ³ \³ 1 ³ C ³ ³ ÄÄÄ ³ ÀÄ ÄÙ ³ \³ Mbh ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÀÄ ÄÙ C ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ C However, the situation here is actually more deceptive. For instance how can the rest mass of a relativistically moving mass aggregate increase toward infinity as its velocity ratio V/C from (C/Nx divided by C in EQ U-5) approaches 1, to keep in step with a stationary gravitational mass aggregate approaching its black hole mass limit Mbh as defined in EQ X-1 above, according to the aggregate mass's radius R ? This is no question to be sneezed at. It implies an idealized stable situation, where A = B. That is, the ratio of Mbh/M as A, equals the ratio of velocities V/C as B, such that masses approaching infinity should be possible, as ratio Mbh/M approaches 1. However, the wrinkle is that mass M can never exceed mass Mbh. Not via any mass increases gained by higher and higher gravitational relativistic effects on mass M. And therefore extreme mass enhancements in special relativity as velocity V over C approaches 1, are not possible, if velocity V is gained as an Nx factor directly from the ratio of Mbh/M. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ THE CONUNDRUM ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In the real world, the situation is in no way idealized. For instance masses approaching infinity should begin to appear, as the equivalent mass aggregate M begins to home in on the final iotas before becoming a black hole, if the A = B relationship is in all ways exact. But, the contingency of a mass said to approach infinity in the special relativity side is not proof that mass infinities can be achieved by M plus mass augmentation Kx at higher and higher plateaus of gravitational relativistic mass effect. How might this conundrum be explored as an intellectual exercise? If the confining radius of a mass aggregate itself is being relativistically contracted by effects of the mass's gravity, then the real world situation is very different than the idealized version. For instance, increasingly less mass is required to aggregate in a diminishing radius to form a black hole. It would now seem that the mass aggregate could bleed away toward nothing as the gravity increases in tune with a relativistically diminishing (contracted) confining radius. What would prevent this is two things. First, the mass aggregate increases in relativistic proportion to the decrease in radius. Since both terms are found in the same equation, as in: EQUATION Y ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mass)(1/Eg) Mass is increased by 1/Eg, Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Radius is decreased by Eg \³ Cý R(Eg) which results in the ratio portion (Mass)(1/Eg) / R(Eg) being increased by the square of the reciprocal of Eg. In a second prevention, if 2G (twice the gravitational constant) is decreased by Eg while the square of the speed of light is increased by 1/Eg, as in Equation Y-1: EQUATION Y-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G(Eg) (Mass) Gravity is decreased by Eg, Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄ Cý is increased by 1/Eg \³ Cý(1/Eg) R then the ratio portion (2G)(Eg) / Cý(1/Eg) is decreased by the square of Eg. In which case all relativistic augmentations found in Equations Y and Y-1 internally cancel each other, as in Equation Y-2: EQUATION Y-2 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G(Eg) (Mass)(1/Eg) Eg = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý(1/Eg) R(Eg) and the net internal effect is again simply 2G (Mass) / CýR, as in Equation W above. But this type of intellectual exercise does not solve the above posed conundrum. The conundrum's answer is introduced immediately below. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º THE GOLDEN HARMONIC RATIO IN RELATIVITY THEORY. º º A CRITICAL LIMIT IN THE FOUNDATION OF GRAVITATIONAL RELATIVITY º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 3 ±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ TABLE 4 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ KEY TERMS ³ ³ ³ ³ Mbh Mass of a black hole, having radius Rbh ³ ³ ³ ³ Mo An original mass (before mass augmentation ³ ³ due to gravitational relativity) ³ ³ ³ ³ Ko Mass augmented upon mass Mo due to ³ ³ gravitational relativity ³ ³ ³ ³ M An existing mass, which includes: Mo + Ko ³ ³ ³ ³ Mc A Critical Mass Limit, where Mc is an Mo ³ ³ which is less than Mbh by precisely the ³ ³ Golden Harmonic Ratio ³ ³ ³ ³ Rbh An event horizon radius for black hole Mbh, ³ ³ and for other masses such as Mo, M, and Mc ³ ³ which are evaluated with the same Rbh radius ³ ³ but are not yet at the black hole mass limit. ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ TABLE 4 CONTINUED ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ 1/Ng Ratio Mbh/Mc = 1/Ng when Mc = Mo, as when: ³ ³ Mbh/Mo = 1/Nx ³ ³ ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ GH Golden Harmonic Ratio 1.61803399, also called ³ ³ Golden Ratio, having a digital value equal ³ ³ to 1/2 the square root of 5, plus .5, as in: ³ ³ ³ ³ 1.1603398875 + .5 = 1.61803398875 ³ ³ ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Vc A critical limit velocity in special ³ ³ relativity, where the ratio C/Vc is equal ³ ³ to the square root of the Golden Harmonic ³ ³ ratio GH = 1.61803398875 ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ FUNCTIONAL INTERPHASE BETWEEN ³ ³ GRAVITATIONAL AND SPECIAL RELATIVITY ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The thing about speculations is that many words can be used to discuss a point which has no convincing answer. Whereas a simple equation can state it all for a self evident truth. However, the simple equation may be obvious to only the soul who wrote it. For others, the simple equation may need elaborate support such as explanation and interpretation. The following sets forth a question which begs an answer. The answer being self evident is then quickly stated. But the stating is accompanied by explanation and interpretation. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ QUESTION ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ One important question which comes immediately to mind (already asked further above in 'The Conundrum') is how can the rest mass of a relativistically moving mass aggregate increase toward infinity as its velocity ratio V/C from EQ U-4 approaches 1, to keep in step with a stationary gravitational mass aggregate which is approaching its black hole mass limit? ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ANSWER ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The answer is that a gravitational mass can only increase to a certain limit, reached before the black hole mass. At this reached limit, the increase in gravitational relativistic augmentation on the mass, raises the overall mass in a final bump to the black hole limit. The final range closing in on the black hole limit is bypassed by the bump. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ INTERPRETATION ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The problem is that the conundrum is only apparent and not real; that: as a mass aggregate rapidly approaches its black hole limit, the ensuing special relativity mass increase counterpart will rapidly begin to climb toward infinity, and such an infinite mass is not possible in the sense of real events. For instance, assuming the conundrum is real, in the following thoughts let Rbh be a given radius. Let's say a mass aggregate M of radius Rbh is at 99% of the Mbh black hole mass limit for radius Rbh. The gravitational relativistic effect (Eg) is roughly about Eg = .09950, which translates into a special relativistic mass enhancement effect of roughly (10.049 x M) on the mass travelling at roughly (root 99%) of the speed of light). Effect Es = 10.049 is reciprocally equivalent to effect Eg = .09950. The problem here is that the special relativistic enhancement on the mass will be roughly 10 times the black hole limit for the mass in question. The problem here is also that if mass M is increased by a gravitational relativistic effect Eg of 10.049, then the resulting augmented mass will exceed its own black hole limit by a factor of roughly 10 times. How, then, does an aggregate mass M of radius Rbh increase only to a black hole mass Mbh of radius Rbh, in keeping with a committed tie-in to special relativity, without the moving mass M impossibly increasing to infinity as the aggregate mass M closes in on Mbh, and without the stationary mass increasing wildly above its own black hole limit due to its own gravitational relativity? The question is a thought balloon which seems to go in several directions. But actually has a unique answer. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ EXPLANATION ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ In a fundamental point of view, events are explored from the outlook of an original mass, which is augmented to become an apparent mass. Specifically, let an original mass Mo (before mass augmentation) be used in an Mbh/Mo ratio, to give ratio term 1/Ng (instead of 1/Nx). And let velocity (C divided by the root of Ng) be the velocity the original mass is travelling in special relativity, to have the same enhancing effect on Mo as would be found when the gravitational relativity effect augments mass Mo. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ THE GOLDEN HARMONIC RATIO - A CRITICAL LIMIT ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ When ratio Ng is equal to the Golden Harmonic Ratio, then several striking things happen. The Golden Harmonic Ratio is 1.6180339. It is typically given as a number quantity from (1/2 of root 5, plus .5). Let the Golden Harmonic Ratio be GH. And so let Ng = GH. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ THE CRITICAL LIMIT in gravitational relativity ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ When Mbh/Mo is GH, a vital event occurs. The gravitational effect Eg precisely turns out to be 1/GH (the reciprocal of the Golden Harmonic Ratio). And so mass (Mo x 1/Eg) = (Mo x 1/GH), which precisely turns out to be mass Mbh. Effectively, mass Mo leaps uphill to become mass Mbh in one final single bump. This is a box, where one thing specifically yields another. In interpretation, a mass augmentation (Eg) on an original mass Mo, raises the quantity of the original mass Mo to that of a black hole mass Mbh, when ratio Ng = Mbh/Mo is precisely the Golden Harmonic ratio GH. In which case, in special relativity, when the original mass Mo is moving at a velocity V which is root GH less than the speed of light, the special relativistic effect Es increases mass Mo to mass Mbh in a final single bump. In which case mass Mbh becomes a black hole and disappears from sight, relative to a stationary observer watching the mass move. There is a locked in equality here. Explicitly, Mbh/GH is a critical limit preceding mass Mbh, at which an original mass Mo is raised to the black hole limit Mbh by the mass effect of its own gravitational relativity. Let Mc be the critical mass limit. Effectively, it establishes that if gravitational relativity includes a mass augmentation effect, the original mass cannot exceed the critical mass limit Mc. And so the original mass can never be the same as a black hole mass, or even a fraction less than a black hole mass, since the black hole mass includes an original mass Mo at the critical mass limit Mc, raised to Mbh through a quanta bump equal to the Golden Ratio GH. In this locked in state, Mbh - Mc = Ko, where Ko is the actual mass augmentation, the same as is otherwise said to be Kx, except in this instance, Ko is fundamentally related to the Golden Ratio GH. In exactitude, Ko = Mbh - (Mbh/GH). It means that when the critical mass limit Mc is reached prior to a black hole, the original mass Mo is augmented by effect 1/Eg to become a black hole equivalent, and no more mass can confine in the same radius Rbh. (More original mass added would serve to increase the confining radius to greater than Rbh). As already said, the Mc critical mass limit (for radius Rbh) is simply (Mbh/GH), where (GH) is the Golden Harmonic Ratio. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ THE CRITICAL LIMIT in special relativity ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ It also means that in special relativity, when the critical mass Mc is a rest mass in motion at a velocity equal to C divided by the square root of GH, the original rest mass Mc expands via 1/Es in a single bump to a mass value where it also becomes a synonymous black hole of mass Mbh. In consequence there never is a condition where the original mass Mo in special relativity expands toward infinity as mass Mo closes in on mass Mbh in gravitational relativity, because the convergence in gravitational relativity for an original mass Mo closes off completely at the critical mass limit Mc, when Mc is less than mass Mbh by a ratio equal to GH. This is a simple and elegant exclusion clause here in the realms of the two modes of relativity, gravitational and special. EQUATION Z In gravitational relativity, the critical limit is: Mo = Mc = Mbh/GH Where: Eg is the gravitational relativistic effect of Mc Such that: Eg = 1/GH And Mbh = Mc + Ko, where Ko = (Mc x 1/Eg) - Mc And also: Mc x 1/Eg = Mk, and Mk - Mc = Ko And so: Mbh = Mc x 1/Eg = Mk Only when: Mc = Mbh/GH So that: Mbh = Mk Where Mk an apparent mass equals its own black hole silent partner mass equivalent. This physical condition occurs because the Golden Ratio GH constantly defines Mo as Mbh/GH. EQUATION Z-1 In special relativity, there is a companion critical velocity limit Vc for velocity V, where Vc is the speed of light divided by the square root of the Golden Harmonic, such that a critical velocity limit Vc constantly exists for mass Mc, when C is the speed of light, as in: Vc = (C / root GH) ; where Vc is actually: Vc = (C / root (Mbh/Mc)) or also (C / root GH) when: Mc = Mbh/GH or also GH = Mbh/Mc so that when: Mc is travelling at velocity Vc the special relativity effect is: Es and the special relativity effect 1/Es increases rest mass Mc to black hole mass Mbh in a bump because Eg is equivalent to 1/GH . ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ A TEST CASE: ³ ÛÄ´ GOLDEN HARMONIC RATIO IN THE TWO MODES OF RELATIVITY ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ Let's look at the critical limit situation in more detail. An apparent mass aggregate Mk contains an original mass, plus an augmentation in mass due to gravitational relativity. And so let the originating mass be Mo, the augmenting mass be Ko, and the resulting mass be Mk. And therefore: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ For Gravity relativity ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-2 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (Mo) Mo is an original mass Eg = ³ 1 Ä ÄÄÄÄÄÄÄ before augmentation \³ Cý R EQUATION Z-3 (Mo x 1/Eg) - Mo = Ko Ko is the mass augmentation on Mo, due to effect 1/Eg EQUATION Z-4 Mo + Ko = Mk Mk is the measured (apparent) mass, consisting of original plus augmentive masses EQUATION Z-5 When Mo = Mc = Mk/GH then: Where Mc is a critical mass value for original mass Mo ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G Mk Eg = ³ 1 Ä ÄÄÄÄÄÄ Mk is black hole mass with ³ GH horizon radius Rbh, and GH is ³ ÄÄÄÄÄÄÄÄÄÄÄÄ the Golden Harmonic Ratio equal \³ Cý Rbh to the number 1.61803398875 EQUATION Z-5-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Mass Mbh is the same as mass ³ 2G Mbh aggregate Mk. Eg = ³ 1 Ä ÄÄÄÄÄÄ ³ Ng Ng is ratio Nx when the value ³ ÄÄÄÄÄÄÄÄÄÄÄÄ of Nx is GH, which is the \³ Cý Rbh Golden Harmonic Ratio EQUATION Z-6 With digits substituted for GH, then: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G Mbh Eg = .61803398875 = ³ 1 Ä ÄÄÄÄÄÄ = 1 ³ 1.61803398875 ÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄ 1.61803398875 \³ Cý Rbh EQUATION Z-7 because: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ When and only when Nx = GH. 1 ³ 1 The Golden Ratio contains ÄÄÄ = ³ 1 Ä ÄÄÄ this self appreciating Nx \³ Nx mathematical property and so: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ 1 ³ 1 GH is the Golden Ratio ÄÄÄ = ³ 1 Ä ÄÄÄ 1.61803398875 GH \³ GH ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ For Special relativity ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-8 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ (Vc)ý Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý ³ ³ ÚÄÄÄÄ ³ ³ ³ \³ Nx ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý EQUATION Z-9 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ (Vc)ý Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý ³ ³ ÚÄÄÄÄ ³ ³ ³ \³ GH ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý EQUATION Z-9-A And so: (Mc x 1/Es) = (Mc x GH) = Mbh, because (Es = 1/GH) when 1/Es is the special relativitistic effect on mass Mc which is moving at velocity Vc of EQ Z-9 EQUATION Z-10 As in: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý .61803398875 = ³ ³ C ³ ³ 1 Ä ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ ³ \³ 1.61803398875 ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ FOR SPECIAL RELATIVITY EFFECT ON BOTH MASS AND RADIUS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ There is yet another factor to consider. In special relativity the radius of a mass contracts in reciprocal proportion to the enhancement of mass. In this regard, when the radius is contracted, less mass will be required to form a black hole in the relativist- ically reduced radius. How does this effect the status of the critical limit Mc, where the original mass Mo is the black hole mass divided by the Golden Ratio? Specifically, what mass will now form the black hole, when the original mass's radius is concomitantly reduced by special relativity's effect? The new mass is easy to find. EQ Z-9 is abruptly rewritten to accommodate both a reduction in radius, and expansion in mass, upon original (critical) mass Mc. The correct velocity for mass Mc can be labelled as (Vbh), as in 'Velocity for black hole', and is easy to find. It turns out to be: Vbh = (C / GH) Given as: EQUATION Z-11 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ (Vbh)ý Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ³ ÄÄÄÄ ³ \³ cý ³ ³ GH ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄ \³ Cý Es turns out to be the reciprocal of the square root of the Golden Harmonic. That is; Es = (1/ûGH). It means that when a mass Mc is physically moving at velocity Vbh relative to a stationary observer, its radius Rbh contracts by (1/ûGH), as its rest mass Mc expands by (ûGH), with the result that a new black hole is formed, having a lesser mass equal to (Mc x ûGH), and a lesser radius equal to (Rbh x 1/ûGH). As already said, this occurs when velocity Vbh is equal to the speed of light divided by the Golden Harmonic Ratio. The new mass can be labelled as Mbh-, which is less than the gravitational black hole mass Mbh, by a factor of ûGH. As already indicated, Mbh/Mc = GH, but the special relativistic mass result Mbh- is not the same as Mbh. There is a series: EQUATION Z-12 Mc x ûGH = Mbh- x ûGH = Mbh It means that a visible mass cannot expand to infinity, because velocities can approach but can never reach the speed of light, due to built in limiting factors. This statement is true specifically for visible masses. For instance, the maximum velocity possible for mass Mc is Vbh which is C/GH, but this is only when the original mass Mo is at the critical mass limit Mc which is a black hole mass Mbh divided by GH. Whereupon the mass becomes a new black hole of mass Mbh- and disappears from view, relative to a stationary observer. The ratio C/GH is (C / 1.61803398875) (The preceding does not take into account any effect that gravity might have to relativistically reduce the radius of the mass causing the gravity's relativistic effect. It is realized that if a reduction in gravitational radius is also needed as a key term, than the parameters of the critical mass limit Mc regards the black hole final limit Mbh, will adjust accordingly, as will the exact factors related to the Golden Harmonic Ratio). (The question of such possible adjusting is not addressed in this disclosure, whose prime intention is to simply show that certain critical limits and equalities do synonymously exist in the domains of gravitational and special relativity. And that the Golden Harmonic Ratio is a fundamental primary term). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ A REMARK ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The Golden Ratio was not a term pulled with a sleazy wink from a magician's hat to fit an idea. The Golden Ratio turned out to be a resulting term that provided a theory; whose gist is as follows: How can a limiting velocity (thus a universal barrier to infinite expansion of visible mass relative to a stationary observer), be determined for any visible mass, in special relativity? The answer to this is straight forward and demonstrates that a visible mass can never expand to infinity. A discussion regards this answer begins further below under: 'Special Relativistic Effects on any Mass and Radius'. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ SUPPLEMENTAL REMARKS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The following remarks are included to complete the discussion regards relativity theories and the Golden Harmonic Ratio. These supplemental remarks cover the subject of how the Golden Ratio was found to be a constant in critical limit situations. The remarks discuss the issue from firstly; effects on the critical mass only; and secondly for effects on the critical mass and radius. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Golden Harmonic Relativistic Effects on Mass Only ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ How was the Golden Harmonic found to be the critical ratio factor Ng for Nx in Equations Z-5 and Z-5-1 ? A value of (square root of 2) was first tried for Nx, yielding a mass augmentation result (1/Eg x Mo), which was greater than mass Mbh, when root 2 for Nx was ratio (Mbh/Mo = Nx). In intuitional trial and error, an Nx value arbitrarily selected as 1.8 was next tried. It yielded an (1/Eg x Mo) value which was slightly less than mass Mbh. So the two Nx values were averaged as in 1/2(û2 + 1.8) to yield a value of 1.608. Since this number was close to a known number (1.61803398875), this known number was tried to see how close the Es result (1/Es x Mo) came to Mbh, using this familiar number as Nx for a point of reference. It turned out that 1.61803398875 happened to be the very term wanted, because the result was perfect. This fast found number was given the label GH. When GH was Nx, then (1/Es x Mo) = Mbh. And so this particular Nx was labelled Ng (for Golden Ratio). And Mo was understood to be the same value as mass Mc. Equations Z-6 and Z-7 show why Ng is a constant. The set of Equations Z to Z-10 followed as a consequence of knowing this. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Golden Harmonic Relativistic Effects on Mass and Radius ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ But Equations Z to Z-10 consider only the special relativistic effect on mass, and left unanswered another question which was: 'What modifications would occur in the parameters of mass when the radius of the mass is also conjointly changed by special relativity effects'. The answer to this was also quickly forthcoming, but in hindsight seems to reflect a very fortuitous guess. Trial and error was started again. A velocity was needed, to determine at what rate mass Mc would be travelling to relativistically increase to mass Mbh-, when radius Rbh of mass Mc was conjointly contracted to radius Rbh-. In this thought balloon, Mbh- and Rbh- would be the parameters forming a new black hole when mass Mo was travelling at sufficient high velocity. At this point the rate of joint contraction on mass Mbh and radius Rbh was not known. And neither was the velocity. The intention was to find what term Nx is divided into C to yield the significant velocity. In a remarkably lucky guess, the first Nx term tried was GH itself, (in EQ Z-11). To begin, radius Rbh was modified by (Es x Rbh) as gained from (EQ Z-11) with Nx equal to GH in the ratio C/GH, to give contracted radius Rbh-. Then, using EQ 5 of APPENDIX B below to find the mass of a black hole formed in radius (Es x Rbh-), a new mass Mbh- was the result. It turned out that the ratios of masses (Mbh/Mbh-) and (Mbh-/Mc) both equaled the square root of ratio GH. It had thus been found that when (C/GH = Vbh), then EQ Z-11 yielded the square root of GH as the Es value. The result is that with Es equaling the reciprocal of the square root of the Golden Ratio, when Rbh is multiplied by Es to yield radius Rbh-, and mass Mc is multiplied by the reciprocal of Es to yield mass Mbh-, then radius Rbh- and mass Mbh- are the correct parameters to form a new black hole from the special relativity effects on both mass Mc and radius Rbh, when Mc is travelling at a (C/GH) velocity. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ How was this verified ? ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The 'dual effect' event was easily verified by the following: A. Radius Rbh- was found from radius Rbh, by using the Es effect of EQ Z-11 in: Rbh x Es = Rbh- B. Using radius Rbh- to find mass Mbh- in: Cý Rbh- Finding mass Mbh- needed for a Mbh- = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as Rbh- C. Mbh- turned out to be mass Mbh / (1/ûGH) when effect Es (of EQ Z-11) was 1/GH. D. It meant mass Mbh- and radius Rbh- form a new black hole, which is less than a black hole of mass Mbh and radius Rbh, by a factor of the square root of the Golden Ratio for both Mbh- and Rbh-. E. This is true when mass Mc is travelling in special relativity, at a reduced velocity Vbh, as gained from EQ Z-11. F. The synonymous special relativistic 'dual effect' event for a gravitational relativistic event at the critical mass limit Mc, is gained by using term Nb = GH (as used in EQ Z-5-1), to find velocity Vbh in EQ Z-11. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º SPECIAL RELATIVISTIC EFFECTS ON ANY MASS AND RADIUS º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ Only certain critical limit cases (for masses Mo and Mc = black hole mass Mbh/GH) have so far been considered. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ QUESTIONS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ What if instead of Mc there is given any general mass Mo, having a radius said to be Ro. Would there still be critical limits involving Golden Harmonic factors that would limit a general test case to a state that is less than infinite mass, at a velocity which can never tightly approach the speed of light? For that matter are other, more general, limits possible, besides those already shown to be related to the Golden Ratio? And if general limits are in the fabrics of physics, how to determine them, given a general mass quantity that to begin with is not known to be related to anything else, especially when it is NOT RELATED to the Golden Ratio ? ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ANSWER ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ This questioning also came to a quick answer, although the finding of the answer was not all that straightforward. The answer demonstrates that any visible mass travelling at a relativistic velocity in special relativity, reaches a limiting barrier, beyond which the mass does not visibly increase any further toward infinity, and its velocity closes no further toward equaling the speed of light. The first insight is that any entity (in its most general sense) comprises a mass and a radius. With mass is some gravity. For instance a typical Sun sized star is an ideal test case entity. For example, the ratio of the Sun's existing mass M over the Sun's existing radius R is its (mass/radius) ratio, ie., M/R (Note that Mo would be the Sun's original mass before any mass augmentation effect due to gravitational relativity. The Sun's original mass Mo is less than its existing mass M, since the existing mass as physically measured is assumed to include a mass augmentation upon mass Mo). The Sun's black hole Mbh mass (silent partner mass) is easily found by: EQUATION Z-13 Cý R Finding mass Mbh needed for a Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as R when R is the radius of the Sun so that another ratio is found, this being (Mbh/R) which is the Sun's (black hole mass/radius) ratio. But actually, term Mbh of EQ Z-13 is worthless. What we really want to find is what (Mbh-/R-) ratio forms a black hole out of the original Mo/R parameters, when Mo is travelling at increasingly faster velocities approaching the speed of light. We need a comparative term, to study any differences between the Sun when standing still, and when moving at a relativistic velocity. The comparative term we want to know is found as: EQUATION Z-14 Mbh Cý Where ratio Cý/2G is a constant, ÄÄÄ = ÄÄÄÄ when C is the speed of light, and R 2G G is the universal gravitational constant. R is the original radius of original mass Mo Mass Mbh is instantly found from EQ Z-13. The logical argument formed in advance, was that any mass result M+, and radius result R-, ensuing from special relativistic effects on original states Mo and Ro, should also equal the black hole constant ratio Cý/2G, if mass M+ and R- were relativistically altered sufficiently to form a new black hole. Ratio Cý/2G can be labeled ratio CR (for 'constant ratio') and has the value of (6.735275620 x 10 to 27 grs/cm), given a speed of light whose digital value is 2.99792458, and a gravitational constant whose digital value is 6.6720 x 10 to -8. Ratio Cý/2G is known as a constant for the given values of C and G. What we can do is follow special relativistic changes upon both Mo and Ro through successively greater velocities, until the combined ratios (1/Es x Mo) / (Es x Ro) equals the ratio Cý/2G, as in: EQUATION Z-14A ((1/Es x Mo) / (Es x Ro)) = (M+/R-) = (Cý/2G) where Es is the special relativistic effect. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Finding a significant Velocity value, which results in ratio CR ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ It was useful that a good test model was available in the solar system's Sun, where given the Sun's existing mass as M, and existing radius as R. The Sun has to be accelerated to such an extent that through the parameters of special relativity, the Sun's modified mass M+ and radius R- reach a point where they transfigure into conditions which form a new black hole. It was assumed that such a transfiguration should occur, and that the transfigurating velocity in special relativity could be inferred. How could the velocity needed for the transfiguration, be determined for an arbitrary general case such as the Sun ? At this point, some intuitively lucky guesswork again prevailed; a 'seeing around corners' so to speak. To make a long story short, it is easy to predetermine the prerequisite velocity. How, is outlined as follows: 1. Given an existing Sun mass M of 1.99099305 x 10 to 33 gms (mass MM from Part 1 above) 1A. Given a Sun radius R of 6.96265 x 10 to 10 cms 1B. Given constant ratio CR = Cý/2G = 6.735275620 x 10 to 27 grms/cms 2. Given the black hole radius parameter of EQ 4 of APPENDIX B, as: EQUATION Z-14-1 2G M Finding the Schwarzschild R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's Cý event horizon, when given mass M 3. And given Equation 5 of APPENDIX B, rewritten as: EQUATION Z-14-2 Cý R Finding mass Mbh needed for a Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as R Mass Mbh is the black hole silent partner mass for any given mass M. 4. Given Equation Z-8 above for special relativistic effect on both an original rest mass and its original radius, based on a term Nx to determine a velocity, so that: EQUATION Z-15 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ (Vx)ý Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ³ ÄÄÄÄ ³ \³ Cý ³ ³ Nx ³ ³ ÀÄ ÄÙ ³ ÄÄÄÄÄÄÄÄÄÄÄ \³ Cý 5. Given that (1/Es x M) = M+ 6. Given that (Es x R) = R- 7. Given that (1/Es x M+) / (Es x R-) = Cý/2G = M+/R- 8. Then it should be possible to find a velocity for EQ Z-15-1 below such that the resulting (M+/R-) ratio = Cý/2G 9. A first arbitrary value for Nx was tried, being 1.0001, which produced results that were too low for the above Item 7 to be correct. 10. A second arbitrary value for Nx was tried in EQ Z-15, being 1.00001, which was of the right magnitude for a mass M+, but Item 7 was still not correct. 11. However, it was noticed that 1/1.00001 by itself was in the magnitude range of gravitational relativistic effect Eg from the Sun's mass, as determined in EQ C of Part 1 further above. (MM in EQ C is the same value as Sun mass Mo given in EQ Z-2, and immediately above in Item 1. And Eg of EQ Z-2 is the same as Eg used immediately below in Item 12). 12. And so Eg was determined for the Sun's mass M = MM = Mo in EQ Z-2, and conveniently labelled Egs (for 'effect gravity Sun mass'), and was substituted as term 1/Nx in EQ Z-15 immediately above, to give: EQUATION Z-15-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ C x Egs ³ ³ (Vx)ý Ess = ³ À Ù = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý \³ Cý where velocity Vx is (C x Egs), and special effect Ess conveniently means an Es effect related to the gravitational mass via term Egs. 13. Then; Sun mass M in (M x 1/Ess) = M+ 14. And; Sun radius R in (R x Ess) = R- 15. And; ratio (M+/R-) = 6.73527458 x 10 to 27 grms/cms As found in: EQUATION Z-15-2 (M x 1/Ess) / (R x Ess) = CR = (M+/R-) 16. Which turned out to be an excellent approximation of ratio CR (being Cý/2G as created in Item 1B immediately above) Well, this was very good for a first found attempt. How about for other masses, and how did the ratio result of Item 15 favorably equate in truth to Item 1B above, in that the CR result in Item 15 is marginally below the CR constant in Item 1B ? 17. The mass of the Sun was arbitrarily raised by a factor of 1000, so that now M = 1.99099305 x 10 to 36 grms 18. A new Egs effect factor was determined using the larger mass of Item 17, in EQ Z-2 above 19. The new Egs factor was substituted in EQ Z-15-1 to give a new Ess factor 20. The new Ess factor was substituted in the terms of Items 13, 14, and 15 21. The result M+/R- = 6.735275620 x 10 to 27 gms/cms = CR, which is exactly the constant of Item 1B Two things were instantly made clear. It is clearly evident that Equations Z-15, Z-15-1, and Z-15-2, are correct for any mass, to yield (M+/R-) ratios equal to Cý/2G. It is clearly evident that ratio (M+/R-) closes in on ratio Cý/2G, the closer that given original mass M is to the black hole silent partner mass Mbh as determined in EQ Z-14-2 (It is also clear from preceding explorations, that when relativistic effects are to act upon an original mass, the original mass M can never approach its black hole silent partner equivalent Mbh any closer than by Mbh divided by factors of the Golden Ratio). ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ Finding that terms M+ and R- are properties of a black hole ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ At this point we are still not finished. The final question is; are terms M+ and R- (as determined by Equations Z-15-1 and Z-15-2), in fact the terms of a new black hole whose mass is M+ and whose radius is R- ? This final question was very easy to test by a double check: 22. The value of M+ from Equation Z-15-1 and Item 13 for the Sun mass arbitrarily increased by a factor of 1000, as in Item 17, yielded an Ess value in Item 19, which as applied to Item 13, was: 3.055623494 x 10 to 27 grms 23. The value of R- from the same Ess in Item 19, applied to Item 14, was: 4.536746031 x 10 to 9 cms 24. Looking to Equations Z-14-1 and Z-14-2, it was found in EQ Z-14-2 (given mass M+ of Item 22), and found in EQ Z-14-1 (given radius R- of Item 23), that (M+/R-) = CR. This is shown in the following three equations: EQUATION Z-15-3 2G M+ Finding the Schwarzschild R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's Cý event horizon, when given mass M+ R' was 4.536746031 x 10 to 9 cms, exactly the same as R- in Item 23 EQUATION Z-15-4 Cý R- Finding mass M' needed for a M' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild 2G radius is given as R- M' was 3.055623493 x 10 to 27 grms, exactly the same as M+ in Item 22 EQUATION Z-15-5 And so: M' of EQ Z-15-4, divided by R' of EQ Z-15-3, = CR as in: (M'/R') = CR where: CR is the constant of Item 1B proving: that M+ of Item 22 and R- of Item 23 are the correct parameters of a new black hole created by relativistic effect Ess of Item 19, on higher mass M of Item 17, using EQ Z-15-1 to determine Ess, after using EQ Z-16 to determine Egs. ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ SUMMARY EQUATIONS ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ The delineations of Items 1 to 23, and Equations Z-14 to Z-15-5, once understood, resolve into a quick series of steps, used to determine a relativistic barrier for any given mass M and its radius R, as in: EQUATION Z-16 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G M M is any mass, R is its Egs = ³ 1 Ä ÄÄÄÄÄÄ radius, and Egs is the \³ Cý R gravitational relativistic effect of mass M EQUATION Z-16-1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ³ C x Egs ³ ³ (Vx)ý Ess = ³ ÀÄ ÄÙ = ³ 1 Ä ÄÄÄÄÄÄ ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý \³ Cý Ess is the special relativistic effect ensuing from velocity Vx, determined as the direct consequence of the speed of light reduced by the mass's gravitational relativistic effect Egs. EQUATION Z-16-2 (M x 1/Ess) = M+ EQUATION Z-16-3 (R x Ess) = R- EQUATION Z-16-4 (M+/R-) = Cý = CR ÄÄÄÄ 2G and mass M+ and radius R- are a relativistic transfiguration of M and R into the parameters of a black hole, when ratio (M+/R-) = CR. CR is a physical constant in black holes, whose value is given as the speed of light squared divided by twice the gravitational constant, and whose value is 6.735275620 x 10 to 27 gms/cms. EQUATION Z-16-5 And ultimately, Ess can be determined directly from Egs, by: Essý = 1 - (Egs)ý Ess is not the same value as Egs. Ess can be higher or lower than Egs. The exact relationship between the value of Egs and Ess is known by: EQUATION Z-16-6 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Ess = \³ 1 - (Egs)ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Egs = \³ 1 - (Ess)ý Why this relationship occurs is explained further below, beginning with EQ Z-17), and explicitly in EQ Z-19. In a nutshell, Equations Z-16 to Z-16-6 fully show that fundamental terms in both gravitational (stationary) and special (moving) modes of relativity are synonymous. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º º UNIFIED EFFECTS IN FIELD BEHAVIOR º º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±± GENERAL INTRODUCTION for part 4 Unified Fields ±±±±±±± º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ 'The best information seems to come after you think you have it wrapped up and have stopped thinking about it'. 'For example, the following floated into consciousness as an afterthought'. In a broad sense, relativity synonymy evokes innuendoes of unified behavior between the fields of gravity and electromagnetism (a unified field theory). But wait, this is not a fully fledged unified field theory. What is under review here are only parts of what appear to be a unified field theory environment. What is shown are exactitudes whereby gravitational effects of an assumed mass changing character on a body, result explicitly in equivalent special relativistic effects synonymous to the body moving at characteristic velocities. Certain rules of behavior define these two modes of relativity in their unified behavior. These rules are easy to understand, once clearly seen, but can be very confusing until their characteristics are shown in an obvious way. This next section (Part 4) explores the rules. To do the job, a particular environment is arbitrarily created. Exact test cases are followed to the nth degree. The created environment is in violation of certain conditions already outlined in Part 2 above; to wit: that certain critical limits exist in the rate of mass expansion, where the maximum expansion oscillates between a black hole mass equivalent Mbh, and plateaus below this, articulated as functions of the Golden Harmonic Ratio 1.61803398875. For the test cases, it is desirable to see what happens mathematically for events which are right at the brink of a black hole mass, compared to masses well below the brink. The phenomenology is thus most easily watched in detail. For this, such masses are arbitrarily created, and assumed to exist in violation of the statements in Part 2 above (which delineate that a mass of black hole equivalent includes an original mass Mo, a mass augmentation unit Ko, and resultant mass aggregate which is that of a black hole or less. If the mass is that of a black hole, the original mass is at a critical mass limit Mc, and the ratio Mbh/Mc = Ng is a function of the Golden Ratio. For masses other than than Mc, ratio Ng is given the general label Nx). In the following, the cases for Mc and Ng parameters are ignored by conveniently looking the other way. In the test cases which follow, the existence of discrete portions denoted by terms such as Mo, Mc, and Ng, are expeditiously put aside, and a mass value is assumed which can be anything less than Mbh, even if less than Mbh by a few parts in a thousand. This is called a HIGH mass, for convenience. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º TEST CASE º ÈÍÍÍÍÍÍÍÍÍÍͼ In a test case, a HIGH mass value is studied which hangs right below the mass of a black hole Mbh. This is in a deliberately selected HIGH mass range which as already said ignores properties such as a critical mass factor (Mc) outlined in Part 2 above. The intention this time is to follow test case examples in excruciating digital detail, so that the effects and their changes are unmistakable. The sole intention of the following, is to observe how certain properties are universally united in a general way through various transformations between gravity and electromagnetic field behaviors. And so a new study model is created, based on the arbitrary criteria that any job needed to do a certain job is good enough for the purpose intended. A HIGH mass gravitational event and a LOW mass event are thus arbitrarily created from the same Mbh term, which is the mass of a black hole confined in the Sun's radius. Mbh for the Sun's radius is (4.689536679 x 10 to 38 grms). The Sun's radius (6.96265 x 10 to 10 cms) has been chosen as an easily recognized radius for use as a constant to investigate the effects of different mass densities confined in a fixed (unchanged) area. Otherwise, the Sun's radius has no physical significance when tied to the following arbitrary mass aggregates. To supply the study, a small ratio Nx has been selected for a control in the study. Nx is meaningless other than its value is the charge to mass ratio of the hydrogen atom, ie.: ((Proton + electron) / electron) = 1.000544617 = Nx. (The interpretation is that the negative electron charge of the lightweight electron influences the heavy proton by only 1.000544617 of the effect the proton has on the electron, since both particles have the same quantity of charge (opposite) despite widely divergent rest masses. This is mentioned only to satisfy curious minds. As said, the real value for the above ratio Nx has no intrinsic significance in the following). MASS1 In our study model, Mbh is arbitrarily reduced by the small ratio Nx to give a HIGH Mass1 term, which is very slightly below Mbh. MASS2 Mass1 is then arbitrarily reduced by a factor of 100,000 to give a LOW Mass2 term having the same digits but much lower magnitude then Mass1. The intention is to be able to follow certain relativistic field effects in detail by following the digital results of both the HIGH mass term (Mass1), and LOW mass term (Mass2), to more openly follow the unifying effects between the two fields (being gravity and electromagnetism). In the study model, as already said, the value of Nx has no significance except that it provides a convenient low value Nx ratio to arrive at a HIGH mass term for the study model. Nx is given to 13 significant digits as gained from the ratio (P 938.2796 mev + E .5110034 mev) / (P 9382796 mev) = 1.000544617404 TABLE 4-A ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ARBITRARY STUDY MODEL DATA ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Nx = 1.000544617404 = (P + E) / E ³ ³ Mbh = 4.689536679 x 10 to 38 grms ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ HIGH mass1 = Mbh / Nx ³ ³ = 4.686984066 x 10 to 38 grms ³ ³ Nx = 1.000544617404 ³ ³ ³ ³ LOW mass2 = Mass1 / 100,000 ³ ³ = 4.686984066 x 10 to 33 grms ³ ³ Nx = 100054.4617404 ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ In the following, Equations Z-17-1 and Z-17-3 ³ ³ are the same as EQ Z-15-1 above, except, the real ³ ³ digit value of each Egs ratio is substituted for ³ ³ the algebraic term Egs. ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-17 HIGH gravitational Mass1 results: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (4.686984066 x 10 to 38 grms) Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý R Mass1 has been given in terms of a real weight. Radius R is the radius of the Sun. Egs is the gravitational relativistic effect of Mass1 ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ HIGH gravity field effect Egs = ³ .023330687 ³ Egs is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-17-1 Electromagnetic field effect results (Ess is special relativistic effect) ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ ³ C x .023330687 ³ Vý Ess = ³ À Ù = ÄÄÄÄ ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý \³ Cý .023330687 is effect Egs of EQ Z-17 Ess = 1 - (Egs)ý As in: 1 - (.023330687)ý = .999727802 ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ LOW special field effect Ess = ³ .999727802 ³ Ess is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ V velocity is starting to close toward 0 EQUATION Z-17-2 LOW gravitational Mass2 results: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (4.686984066 x 10 to 33 grms) Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý R Mass2 has been given in terms of a real weight. ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ LOW gravity field effect Egs = ³ .999995002 ³ Egs is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ EQUATION Z-17-3 Electromagnetic field effect results (Ess is special relativistic effect) ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ ÚÄ Ä¿ý ³ ³ C x .999995002 ³ Vý Ess = ³ À Ù = ÄÄÄÄ ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý \³ Cý .999995002 is effect Egs of EQ Z-17-2 Ess = 1 - (Egs)ý As in: 1 - (.999995002)ý = .003161416 ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿ HIGH special field effect Ess = ³ .003161416 ³ Ess is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ V velocity is closing toward 1 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ÛÄ´ COMPARING M+ AND R- RESULTS FOR HIGH AND LOW MASSES ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ As delineated in Items 22 to 24 above, and in Equations Z-15-3 to Z-15-5 which immediately follow Items 22 to 24, two terms M+ and R- represent the enhanced mass and reduced radius on an object due to special relativistic results ensuing from the proper ratio of the speed of light divided by the proportionate relativistic effect of the object's gravity. And so the synonymity of related behaviors, (the resulting effects of Ess from Equations Z-17-1, and Z-17-3), when applied to the HIGH mass of EQ Z-17, and LOW mass of EQ Z-17-2, will yield appropriate M+ and R- terms for each of the masses. These are listed in the following: TABLE 5 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ HIGH MASS GRAVITY ³ ³ ³ ³ MASS1 = (4.686984066 x 10 to 38 grms) ³ ³ ³ ³ RADIUS R = 6.96265 x 10 to 10 cms ³ ³ ³ ³ Ess EFFECT = .999727802 ; from EQ Z-17-1 ³ ³ ³ ³ M+ = (Mass1 x 1/Ess) ³ ³ = 4.688260199 x 10 to 38 grms ³ ³ ³ ³ R- = (radius R x Ess) ³ ³ = 6.9607547839 x 10 to 10 cms ³ ³ ³ ³ CR = ratio (M+/R-) ³ ³ = 6.735275620 x 10 to 27 grms/cm ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ TABLE 6 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ ³ ³ LOW MASS GRAVITY ³ ³ ³ ³ MASS2 = (4.686984066 x 10 to 33 grms) ³ ³ ³ ³ RADIUS R = 6.96265 x 10 to 10 cms ³ ³ ³ ³ Ess EFFECT = .003161416 ; from EQ Z-17-3 ³ ³ ³ ³ M+ = (Mass1 x 1/Ess) ³ ³ = 1.482558107 x 10 to 36 grms ³ ³ ³ ³ R- = (radius R x Ess) ³ ³ = 2.201183848 x 10 to 8 cms ³ ³ ³ ³ CR = ratio (M+/R-) ³ ³ = 6.735276152 x 10 to 27 grms/cm ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ It is seen that results M+ , though higher than an ³ ³ originating mass, are lower than the ceiling mass Mbh ³ ³ in LOW mass results, and close in on ceiling mass Mbh ³ ³ in HIGH mass results. (Ceiling mass means a black ³ ³ hole mass equivalent Mbh formed in radius R. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ In HIGH mass situations, M+ can look like the high ³ ³ mass itself, but in low mass situations, M+ is far ³ ³ removed from the low mass itself. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ Also, it is obvious that M+ of LOW mass results can ³ ³ gain substantially over the LOW mass itself, yet still ³ ³ remain substantially below the final mass Mbh, whereas ³ ³ M+ hardly gains over its originating HIGH mass, and ³ ³ can also look very much like final mass Mbh, when ³ ³ the HIGH mass itself looks closely like Mbh. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ In real situations, the HIGH mass will be fixed at a ³ ³ maximum ceiling of critical limit Mc. In this current ³ ³ test case situation M+ looks neither like Mc, or Mbh. ³ ³ Yet M+ will be explicitly Mc x ûGH, and Mbh/ûGH, when ³ ³ GH the Golden Ratio 1.618034 is term Nx. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ (Ratio CR in the LOW mass situation, is seen to be ³ ³ marginally more than CR = Cý/2G . This shift might ³ ³ be due to intrinsic truncations in the digital ³ ³ accuracy of the equations for lower mass densities. ³ ³ It is hard to tell, in the scope of a digital ³ ³ accuracy limited to 13 significant figures). ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º FIRST INTERPRETATION º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ Thus M+ can approach but never equal or exceed Mbh. As the Egs effect approaches 0 (greatest power in gravity field strength), the Ess effect approaches 1 (the least power, no effect), in velocity related relativistics. At the point where the gravity effect has its greatest value; at Egs = 0 ; the special relativistic effect ceases to exist (comes to a standstill), because there is no velocity, as when: EQUATION Z-17-4 (C/0) / C = 0/C = 0 . This closes right in on a clear insight regards the question of how maximum potential relativistic gravity effect can contain light - effectively cancel the velocity of light. The velocity of light is not cancelled. The ability to have a velocity related to any special relativistic effect is cancelled. It appears this amounts to the same thing as a counteracting of the velocity of light. ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ» º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ º DIRECT INTERPRETATION º ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ A first interpretation of the consequences of Equations Z-17 to Z-17-3, is that a HIGH gravitational mass density results in a LOW special relativistic synonymity. And a LOW gravitational mass density results in a HIGH special relativistic synonymity. It has the immediate interpretation that things run faster in LOW gravitational events, and slower in HIGH gravitational events. It adds another picture to the experimentally confirmed property that proximity to gravity, relativistically causes time to slow. Intuitively, it answers a question as to how gravity at its highest can confine light. A see saw (or yin yang) characteristic in the works is summarized in the following: TABLE 7 ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿ ³ HIGH mass gravity Effect Egs approaches 1 ³ ³ Effect Ess approaches 0 ³ ³ ³ ³ LOW mass gravity Effect Egs approaches 0 ³ ³ Effect Ess approaches 1 ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ You can see at a glance how gravity can confine ³ ³ light. As gravity effect Egs closes in on 1, ³ ³ special effect Ess closes down toward 0 velocity. ³ ³ When Egs is right at 1, Ess is closed down right ³ ³ to 0 and the velocity of light C in a V/C ratio ³ ³ is vanished when 0/C = 0 . ³ ³ ³ ³ Conversely, when Egs is low and closing down to 0, ³ ³ effect Ess intensifies with a velocity approaching ³ ³ 1, which is equivalent to approaching the full ³ ³ speed of light. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ In another sense, it is clearly seen that events ³ ³ are free to move more rapidly in activities of a ³ ³ HIGH velocity, in a LOW gravity field density. ³ ³ ³ ³ And in a HIGH gravity field density, events are ³ ³ constrained to low velocity activity approaching ³ ³ 0 velocity, when the gravity field approaches the ³ ³ density of a black hole, re: special relativity. ³ ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´ ³ ³ ³ Notes: ³ ³ ³ ³ In real events, as summarized above in Part 2, ³ ³ if a mass augmentation is assumed for gravity ³ ³ effect Egs, then when a mass's density (without ³ ³ augmentation) reaches a critical mass factor Mc, ³ ³ the mass augmentation amount Ko is sufficient to ³ ³ jump the mass amalgamation in one whole bump to a ³ ³ black hole quantity Mbh, such that effect Egs = 1. ³ ³ And thus effect Ess = 0; which is the equivalent ³ ³ of a 0 velocity for light. ³ ³ ³ ³ The proportionate bump of mass Mc to Mbh is a ³ ³ function of the Golden Ratio 1.61803398875. ³ ³ ³ ³ It means there never is a situation where effects ³ ³ Egs and Ess slowly converge to 1 and 0, as is ³ ³ fictitiously indicated in Equations Z-17 and ³ ³ Z-17-1. As show in Part 2 further above, effects ³ ³ Egs and Ess will jump in a final leap to 1 and 0 ³ ³ in a single bump via Golden Ratio functions, when ³ ³ the gravity mass density reaches Mc before ³ ³ reaching black hole mass Mbh. ³ ³ ³ ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ 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 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 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 with the observer also present, for example, rather than close to a mathematical data point such as the center of the Sun, or relative to a fixed velocity as when watching a Sun sail by at high speed. 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 obvious and 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 the M+/R- ratio, which is calculated through special relativity using the mass's gravitational effect to state the equivalent relativistic 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 PEACE POWER AND PLENTY EVERYONE ALL DONE