旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 俳� STRANGENESS IN A SEEMING TAUTOLOGY � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 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 旼컴컴컴컴컴컴컴컴컴컴 � 2G (Mh) Where Ex is the relativistic Ex = � 1 � 컴컴컴� factor of a high mass Mh \� C� 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) 컴컴컴컴 = 1 And therefore: C� Rx EQUATION O-3 旼컴컴컴컴컴컴컴컴컴컴 � 2G (Mbh) Ex = � 1 � 컴컴컴� \� C� Rx Is no longer valid, since: EQUATION O-4 旼컴컴컴컴컴컴컴컴 � Ex = � 1 � 1 The square root of 1 - 1 = 0 \� 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 � 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. 旼컴컴컴컴컴컴컴컴컴컴 � 2G (Mass) Ex = � 1 � 컴컴컴� \� C� 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 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 俳� A COHERENT PHASE IN THIS SOLAR SYSTEM � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 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 旼컴컴컴컴컴컴컴컴컴컴 � 2G (MM-Mv) Where (MM-Mv) is mass MM Ev = � 1 � 컴컴컴컴� minus the mass of Venus Mv. \� C� R MM is the mass of the Sun, and R is the exiting radius of the Sun. EQUATION Q (Determines a value K) 旼컴컴컴컴컴컴컴컴컴컴 � 2G (MM) Ek = � 1 � 컴컴컴� \� C� 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. �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 � 굇굇굇굇굇굇굇굇굇굇굇굇굇굇� PART 2 굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇 � � 굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇� � � 굇굇굇굇� GRAVITATIONAL AND SPECIAL RELATIVITY THEORY 굇굇굇굇� � 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 � 굇굇굇굇굇굇굇� GENERAL INTRODUCTION for part 2 굇굇굇굇굇굇굇� � 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 俳� A COMPARISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 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. �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 � 굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇� � 勁袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴箇袴袴袴袴袴袴袴� � A UNISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY � 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� 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). 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� � THE GRAVITY - SPECIAL RELATIVITY CONNECTION IN DETAIL � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 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 컴컴� = Nx Then relativistic effect Ex is: M EQUATION T-1 Gravitational relativistic 旼컴컴컴컴컴컴컴컴컴컴� effect Ex is calculated from � 1 ratio (Mbh/M), when the mass Ex = � 1 � 컴컴컴� of black hole silent partner \� Nx Mbh is calculated from the radius of M, by: EQUATION T-2 C� R Mbh = 컴컴컴컴� As in: 2G EQUATION T-3 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴 � 1 Ex = � 1 � 컴컴컴컴컴컴컴컴컴 � 旼 커 � � C�R � � � 컴� � � � 2 G � � � 컴컴컴컴� � � � M � \� 읕 켸 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 俳� EXAMPLES OF THE GRAVITY - SPECIAL RELATIVITY CONNECTION � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 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 旼컴컴컴컴컴컴컴컴컴컴 � 2G M Eg = � 1 � 컴컴� \� C� R EQUATION U-1 旼컴컴컴컴컴컴컴컴컴컴 � V� Es = � 1 � 컴 \� C� EQUATION U-2 Gravity relativity Bare bone version 旼컴컴컴컴컴컴컴컴컴컴 旼컴컴컴컴컴컴컴컴컴� � 1 � 1 Eg = � 1 � 컴컴컴� = � 1 � 컴컴� � Mbh \� Nx � 컴� \� M EQUATION U-3 Special relativity Bare bone version 旼컴컴컴컴컴컴컴컴컴컴컴컴 旼컴컴컴컴컴컴컴컴컴컴� � 旼 커� � 1 Es = � � C � = � 1 � 컴컴컴� � 1 � � 컴컴컴컴 � \� Nx � � 旼컴� � � � \� Nx � � 읕 켸 � 컴컴컴컴컴컴컴 \� C� 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 旼 커 旼 커 velocity V � C � � C � � 컴컴컴컴컴 � � 컴컴컴컴 � V Substitute � 旼컴컴 � For � 旼컴� � = 컴� � � Mbh � � \� Nx � C � � 컴� � 읕 켸 � \� M � 컴컴컴컴컴컴컴 읕 켸 C 컴컴컴컴컴컴컴 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. 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 俳� A Support equation for gravitational relativity follows next � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 EQUATION V (Mbh) can be determined from the gravitational relativistic effect (Eg). Given a calculated effect (Eg), as determined in EQ U above, then: 旼� 컴커 � 1 � Mbh = M x � 컴컴컴컴컴컴컴컴 � � (1 � (Eg)�) � � � 읕� 컴� EQUATION V-1 However: 旼컴컴컴컴컴컴컴컴� 1 � 1 컴컴컴컴컴컴컴컴 also equals � 1 � 컴컴� (1 � (Eg)�) \� Nx EQUATION V-2 So that EQ V simplifies to: M x Mbh = M x Nx So that: Nx = Mbh 컴� 컴� 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. 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� 俳� Summary equations for the two modes of relativity follow next � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� EQUATION W Basic Gravitational relativity equation 旼컴컴컴컴컴컴컴컴컴컴컴 � 2G (Mass) EQ W is the Eg = � 1 � 컴컴컴컴 same as EQ C further above \� C� 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 旼컴컴컴컴컴컴컴컴컴컴� � V� Many text books cite Es = � 1 � 컴컴� a greek letter for effect \� C� Es, and for ratio V�/C� 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: C� R Finding the mass (Mbh) needed for Mbh = 컴컴컴컴컴컴 a black hole whose Schwarzschild 2G radius is given as R. EQ X-1 is the same as EQ 5 of APPENDIX B below 旼컴컴컴컴컴컴컴컴컴컴컴컴커 � INTERPRETATIONS � 읕컴컴컴컴컴컴컴컴컴컴컴컴켸 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/�Nx) 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 旼 커 旼 커 velocity � C � � C � � 컴컴컴컴컴 � � 컴컴컴컴 � C Substitute � 旼컴컴 � For � 旼컴� � = 컴� = 1 � � Mbh � � \� 1 � C � � 컴� � 읕 켸 � \� Mbh � 컴컴컴컴컴컴컴 읕 켸 C 컴컴컴컴컴컴컴 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. 旼컴컴컴컴컴컴컴컴컴컴컴� � THE CONUNDRUM � 읕컴컴컴컴컴컴컴컴컴컴컴� 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 旼컴컴컴컴컴컴컴컴컴컴컴컴컴 � 2G (Mass)(1/Eg) Mass is increased by 1/Eg, Eg = � 1 � 컴컴컴컴컴컴컴 Radius is decreased by Eg \� C� 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 旼컴컴컴컴컴컴컴컴컴컴컴컴� � 2G(Eg) (Mass) Gravity is decreased by Eg, Eg = � 1 � 컴컴컴컴컴컴 C� is increased by 1/Eg \� C�(1/Eg) R then the ratio portion (2G)(Eg) / C�(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 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴� � 2G(Eg) (Mass)(1/Eg) Eg = � 1 � 컴컴컴컴컴컴컴컴컴 \� C�(1/Eg) R(Eg) and the net internal effect is again simply 2G (Mass) / C�R, 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. �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 � THE GOLDEN HARMONIC RATIO IN RELATIVITY THEORY. � � A CRITICAL LIMIT IN THE FOUNDATION OF GRAVITATIONAL RELATIVITY � � 굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇굇� � 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� �袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴敲 � 굇굇굇굇굇굇굇� GENERAL INTRODUCTION for part 3 굇굇굇굇굇굇굇� � 훤袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴袴� TABLE 4 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 � KEY TERMS � � � � Mbh Mass of a black hole, having radius Rbh � � � � Mo An original mass (before mass augmentation � � due to gravitational relativity) � � � � Ko Mass augmented upon mass Mo due to � � gravitational relativity � � � � M An existing mass, which includes: Mo + Ko � � � � Mc A Critical Mass Limit, where Mc is an Mo � � which is less than Mbh by precisely the � � Golden Harmonic Ratio � � � � Rbh An event horizon radius for black hole Mbh, � � and for other masses such as Mo, M, and Mc � � which are evaluated with the same Rbh radius � � but are not yet at the black hole mass limit. � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 TABLE 4 CONTINUED 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 � � � 1/Ng Ratio Mbh/Mc = 1/Ng when Mc = Mo, as when: � � Mbh/Mo = 1/Nx � � � 쳐컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴캑 � � � GH Golden Harmonic Ratio 1.61803399, also called � � Golden Ratio, having a digital value equal � � to 1/2 the square root of 5, plus .5, as in: � � � � 1.1603398875 + .5 = 1.61803398875 � � � 쳐컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴캑 � � � Vc A critical limit velocity in special � � relativity, where the ratio C/Vc is equal � � to the square root of the Golden Harmonic � � ratio GH = 1.61803398875 � � � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 俳� FUNCTIONAL INTERPHASE BETWEEN � � GRAVITATIONAL AND SPECIAL RELATIVITY � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 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. 旼컴컴컴컴컴컴컴컴커 � QUESTION � 읕컴컴컴컴컴컴컴컴켸 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? 旼컴컴컴컴컴컴컴커 � ANSWER � 읕컴컴컴컴컴컴컴켸 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. 旼컴컴컴컴컴컴컴컴컴컴컴커 � INTERPRETATION � 읕컴컴컴컴컴컴컴컴컴컴컴켸 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. 旼컴컴컴컴컴컴컴컴컴컴� � EXPLANATION � 읕컴컴컴컴컴컴컴컴컴컴� 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. 旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커 � THE GOLDEN HARMONIC RATIO - A CRITICAL LIMIT � 읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸 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. 旼컴컴컴컴컴컴컴컴� � THE CRITICAL LIMIT in gravitational relativity 읕컴컴컴컴컴컴컴컴� 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. 旼컴컴컴컴컴컴컴컴� � THE CRITICAL LIMIT in special relativity 읕컴컴컴컴컴컴컴컴� 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 . -- Continued in RELATIVE.3 -- Item C if you are using the HELP MENU