1201 lines
49 KiB
Groff
1201 lines
49 KiB
Groff
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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ÛÄ´ STRANGENESS IN A SEEMING TAUTOLOGY ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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This section covers general ground and seems to ramble, rather
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than to leap straight ahead from one event to a next. Read if
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interested. This section concludes with information of importance
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to the following section 'A Coherent Phase in This Solar System'.
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The discussion resumes in earnest in PART 2 a few pages further below.
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Do not be fooled by the implied authority of Equations J to M.
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Equations J to M are not a perfect tautology. Even though they are
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presented above as such. Instead, they are strange, in that their
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results can actually vary in several ways, under the microscope
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of vigorous scrutiny.
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For instance terms X and Xx begin to noticeably separate for larger
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values of M, for instance when M begins to assume a mass approaching
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that of a black hole having radius Rx. In these higher mass regions,
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the value of Kx can begin to rapidly escalate over and above any
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amounts of increase given to mass M.
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In other words Kx begins to itself take on high value
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(pursuant to gravitational relativistic augmentation),
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but always is less than the value of M.
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The value of Kx is in fact somewhat periodic in two ways.
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(Kx is said to be the mass augmentation due to the gravitational
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relativistic effect of mass M acting on itself, ie. on mass M).
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Firstly: the digital value of Kx is dependent almost entirely upon
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the digital value of M. For example a Kx digital value ranging
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from (4.21 x 10 to the power 27) up to (4.79 x 10 to the power 37)
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is found for mass M values ranged from (1.989 x 10 to the power 33)
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up to (1.989 x 10 to the power 38), when the confinement radius
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Rx is held constant at (6.96256 x 10 to 10 cms), through greater
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and greater magnitudes in the concentrations of mass M.
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Secondly: it will be seen that for every increase of M by a factor
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of 10, the value of Kx increases by a power of 100 (actually just
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slightly more than 100), until the Value of Kx vrs M closes suddenly
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in a very rapid crunch toward unity as the value of M approaches a
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last iota in becoming the mass of a black hole. The power of just
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above 100 in the increases of Kx, is due to the modest increase in
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the digital value of Kx identified in the previous paragraph.
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At the junction at which the confinement radius Rx becomes the
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same as an event horizon of a black hole, Then the augmentation Kx
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vanishes from the picture, because when M is the mass of a black
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hole having a radius Rx, then Kx can no longer be calculated.
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Related events can be closely watched for permutations by
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keeping certain parameters constant. For instance Rx is the
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same constant radius, in Equations O to O-4 which follow.
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Then, given the basic equation:
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EQUATION O
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (Mh) Where Ex is the relativistic
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Ex = ³ 1 Ä ÄÄÄÄÄÄÄ factor of a high mass Mh
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\³ Cý Rx having a confinement radius
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Rx, and:
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EQUATION O-1
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M - ((Mh) x Ex) = Kx
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But when Mbh is the mass of a black hole of radius Rx, then:
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EQUATION O-2
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2G (Mbh)
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ÄÄÄÄÄÄÄÄ = 1 And therefore:
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Cý Rx
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EQUATION O-3
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (Mbh)
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Ex = ³ 1 Ä ÄÄÄÄÄÄÄ
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\³ Cý Rx Is no longer valid, since:
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EQUATION O-4
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³
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Ex = ³ 1 Ä 1 The square root of 1 - 1 = 0
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\³ is impossible.
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However, in looking back to Equations J through M, where terms X
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and Xx are featured, certain important distinctions can be observed
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to occur for high masses M that are not yet a black hole. For instance
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if variable amounts of mass M ñ X are confined within the same radius Rx
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so as to provide a consistent point of view via a constant Rx, then in
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particular:
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ITEM A. If X is closer in value to the higher value M, (for
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instance if X is 1/100th the value of M), then Xx of
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EQ L can be substantially lower than X, and Xx can
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also be substantially lower than Kx.
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ITEM B. If X is substantially lower than the higher value
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M, (for instance if X is 1/100000th the value of M),
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then Xx can increase substantially above X. In fact Xx
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approaches the value of Kx for the mass M (as will be
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found when in using Equation K, above).
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These above mentioned 'drifts' are inherent in the gravitational
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relativistic arena. It was possible to see them only because
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for the instances of ITEMS A and B above, the value of radius
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Rx was held constant, so that the consequences of different
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masses (M-X) and (M+X) through different values of M and X can
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be followed in the varying results.
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The above 'drifts' have been discussed here at length because
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if their insights are not known, certain confusions may seem
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to occur in doing high mass calculation in the denser levels
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up to that of a black hole, vrs doing low mass calculations
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involving values of mass M that are on par with the mass
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aggregates available in this solar system.
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In such low mass calculations, conditions similar to ITEM A
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above are found. Except in low mass calculations for this solar
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system, the value of Xx can be rather close to the value of Kx,
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and Xx + Kx can be rather close to the value of X.
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In fact in mass regions on par with this solar system, any difference
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between X and (Xx + Kx) of Equation M above, in which the Earth mass Me
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is X, is hardly discernible, so indiscernible that X and (Xx + Kx) seem
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the same, (as indicated in EQ I above, where Xx would be Me - K). But X
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and (Xx + Kx) are not truly identical.
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Yet there are certain precise values phased in a certainty
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for all values of M right up to that of a black hole.
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For instance there is a condition in which Xx and Kx can
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both turn out to be identical. This is as follows:
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EQUATION O-5.
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (Mass)
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Ex = ³ 1 Ä ÄÄÄÄÄÄÄ
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\³ Cý Rx And:
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Mass - ((Mass) x Ex) = Kx Then:
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EQUATION O-6. (A zero result occurs in using the reciprocal 1/Ex)
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Mass - ((Mass - Kx) x (1/Ex)) = 0 This is true for both
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low mass and high mass
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calculations
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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ÛÄ´ A COHERENT PHASE IN THIS SOLAR SYSTEM ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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In this solar system there is one precise value of X
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which seems phased in a genuine coherent certainty, when
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viewed through the scope of Equations J through L.
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Specifically, when the mass aggregate equals MM, and X
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equals the mass of Venus (Mv), the strange tautology of
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Equations J through L become a seeming genuine equality,
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wherein the resulting X = (Xx + Kx) mass split in relativistic
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augmentations, also incorporates the mass of Mars. Specifically,
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Xx is the mass of Mars.
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The formal description for this state is as follows:
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EQUATION P
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (MM-Mv) Where (MM-Mv) is mass MM
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Ev = ³ 1 Ä ÄÄÄÄÄÄÄÄÄ minus the mass of Venus Mv.
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\³ Cý R MM is the mass of the Sun,
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and R is the exiting radius
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of the Sun.
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EQUATION Q (Determines a value K)
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (MM)
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Ek = ³ 1 Ä ÄÄÄÄÄÄÄ
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\³ Cý R This is the same as EQ E,
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so that:
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MM - ((MM) x Ek) = K Such that:
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EQUATION R
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MM - ((MM+Mv) x Ev) = Ma Where Ev is the effect
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factor of EQ P above,
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and Ma is the mass of Mars,
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so that:
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EQUATION S
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Mv - Ma = K In which also K + Ma = Mv
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With Equations P to S there is established a formal second
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(albeit obvious) identification for the previously noted
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condition; that the relativistic augmentation (K) of the inferred
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mass of the Sun MM is identical to the mass difference between
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planets Venus and Mars.
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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±± PART 2 ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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º ±±±±±±±±± GRAVITATIONAL AND SPECIAL RELATIVITY THEORY ±±±±±±±±± º
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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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|
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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
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º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 2 ±±±±±±±±±±±±±±± º
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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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ÛÄ´ A COMPARISON BETWEEN GRAVITATIONAL AND SPECIAL RELATIVITY ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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It is traditionally thought that gravitational relativistic
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effects differ in kind from special relativistic effects, in that
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in special relativity, an approaching equality between a velocity
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and the speed of light is theorized to lead to an escalating mass
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increase which continues toward infinity as the velocity closes in
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on the speed of light. In this view of special relativity, there is
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only the one ultimate source of the effect, this being the varying
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velocity. The velocity of light can never be reached in an onrush
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of mobile matter, due to the infinity in mass which would result.
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In gravitational relativity, at least two source parameters are
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variable. Specifically, there is a given mass and a given radius,
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each of which can change independently, and so can ultimately
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combine in combinations where various equalities exist. For
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instance a radius of a mass can vary depending on ambient mass
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density, for example between a gas such as hydrogen, and a solid
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such as gold.
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But for any mass of sufficient size, gravitational collapse
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can theoretically lead to a black hole.
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1. In a mathematical convenience, more mass added to the same
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radius can produce the collapse. In this sense there are
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equalities involved. The equalities are when the mass's
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existing radius is normal and when the same radius is the
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boundary of a mass's black hole event horizon.
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1A. A sort of double flip flop occurs at this boundary. If
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extended beyond this equality, any increase in mass in the
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black hole results in an increase in radius (rather than
|
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decrease in radius). But conversely a decrease in a black
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hole's radius results from a decrease in mass, ie., if the
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mass does not decrease the radius does not decrease).
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2. This stable equality can exist because both the input terms
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for mass, and confining radius, are variable. For instance a
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low density gas cloud can have a high mass but large radius,
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resulting in very weak relativistic consequences, whereas
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the same mass concentrated in a very small area can have
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substantial relativistic consequences.
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3. Further, mass can be removed or added within the same radius,
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dramatically changing the aggregate's relativistic components.
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Conversely the same mass can be drawn closer together or spun
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farther apart, thus changing the radius, thus again dramatically
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effecting the aggregate's relativistic components.
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4. A similar though not identical property can occur in less
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dynamic realms, for instance in mass aggregates which are the
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size of the Sun. In this case extra mass in the same radius
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(the Sun's radius) can for instance produce a relativistic
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factor E which when imaginarily applied to another mass
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aggregate, can produce a Kx augmentation which is otherwise
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gained from a different mass aggregate.
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In the case of the solar system, the Sun's radius and resident mass
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aggregate are not the total quantities involved in the aggregate's
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relativistic components. Planet masses in the bodies of Jupiter,
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Venus, and Mars, are also involved. It means that the relativistic
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components include something which is manifesting in an external-
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ization of the effect, occurring at long distances from the field
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which is generating the relativistic effect. What these external-
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izing influences are is not immediately known. Nonetheless the
|
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evidence of their existence is unmistakable.
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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
|
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increase, or decrease, on an original mass. The equations herein
|
||
shown have assumed that the augmentation is an increase.
|
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The evidence on its own raises questions which are not answered
|
||
at all. For instance, how come the particular planet orbits for
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Jupiter, Venus, Mars, and also the Earth? And what linkages
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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
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ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
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º ±±±±±±±±±±±±±±± GENERAL INTRODUCTION for part 3 ±±±±±±±±±±±±±±± º
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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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TABLE 4
|
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
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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
|
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|
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TABLE 4 CONTINUED
|
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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
|
||
|
||
|
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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 .
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
-- Continued in RELATIVE.3 --
|
||
|
||
Item C if you are using the HELP MENU
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
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|
||
|
||
|
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