1417 lines
56 KiB
Groff
1417 lines
56 KiB
Groff
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ A TEST CASE: ³
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ÛÄ´ GOLDEN HARMONIC RATIO IN THE TWO MODES OF RELATIVITY ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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Let's look at the critical limit situation in more detail.
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An apparent mass aggregate Mk contains an original mass, plus
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an augmentation in mass due to gravitational relativity. And
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so let the originating mass be Mo, the augmenting mass be Ko,
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and the resulting mass be Mk. And therefore:
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ For Gravity relativity ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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EQUATION Z-2
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G (Mo) Mo is an original mass
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Eg = ³ 1 Ä ÄÄÄÄÄÄÄ before augmentation
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\³ Cý R
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EQUATION Z-3
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(Mo x 1/Eg) - Mo = Ko Ko is the mass augmentation
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on Mo, due to effect 1/Eg
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EQUATION Z-4
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Mo + Ko = Mk Mk is the measured (apparent)
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mass, consisting of original
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plus augmentive masses
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EQUATION Z-5
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When Mo = Mc = Mk/GH then: Where Mc is a critical mass
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value for original mass Mo
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G Mk
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Eg = ³ 1 Ä ÄÄÄÄÄÄ Mk is black hole mass with
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³ GH horizon radius Rbh, and GH is
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³ ÄÄÄÄÄÄÄÄÄÄÄÄ the Golden Harmonic Ratio equal
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\³ Cý Rbh to the number 1.61803398875
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EQUATION Z-5-1
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Mass Mbh is the same as mass
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³ 2G Mbh aggregate Mk.
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Eg = ³ 1 Ä ÄÄÄÄÄÄ
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³ Ng Ng is ratio Nx when the value
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³ ÄÄÄÄÄÄÄÄÄÄÄÄ of Nx is GH, which is the
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\³ Cý Rbh Golden Harmonic Ratio
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EQUATION Z-6
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With digits substituted for GH, then:
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ 2G Mbh
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Eg = .61803398875 = ³ 1 Ä ÄÄÄÄÄÄ = 1
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³ 1.61803398875 ÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ ÄÄÄÄÄÄÄÄÄÄÄÄÄ 1.61803398875
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\³ Cý Rbh
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EQUATION Z-7
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because:
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ When and only when Nx = GH.
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1 ³ 1 The Golden Ratio contains
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ÄÄÄ = ³ 1 Ä ÄÄÄ this self appreciating
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Nx \³ Nx mathematical property
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and so:
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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1 ³ 1 GH is the Golden Ratio
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ÄÄÄ = ³ 1 Ä ÄÄÄ 1.61803398875
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GH \³ GH
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ For Special relativity ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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EQUATION Z-8
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ ÚÄ Ä¿ý ³ (Vc)ý
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Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ
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³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý
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³ ³ ÚÄÄÄÄ ³
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³ ³ \³ Nx ³
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³ ÀÄ ÄÙ
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³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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\³ Cý
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EQUATION Z-9
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ ÚÄ Ä¿ý ³ (Vc)ý
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Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ
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³ 1 Ä ³ ÄÄÄÄÄÄÄÄ ³ \³ cý
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³ ³ ÚÄÄÄÄ ³
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³ ³ \³ GH ³
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³ ÀÄ ÄÙ
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³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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\³ Cý
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EQUATION Z-9-A And so:
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(Mc x 1/Es) = (Mc x GH) = Mbh, because (Es = 1/GH)
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when 1/Es is the special relativitistic effect on
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mass Mc which is moving at velocity Vc of EQ Z-9
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EQUATION Z-10 As in:
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ ÚÄ Ä¿ý
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.61803398875 = ³ ³ C ³
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³ 1 Ä ³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³
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³ ³ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³
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³ ³ \³ 1.61803398875 ³
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³ ÀÄ ÄÙ
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³ ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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\³ Cý
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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ÛÄ´ FOR SPECIAL RELATIVITY EFFECT ON BOTH MASS AND RADIUS ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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There is yet another factor to consider. In special relativity
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the radius of a mass contracts in reciprocal proportion to the
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enhancement of mass. In this regard, when the radius is contracted,
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less mass will be required to form a black hole in the relativist-
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ically reduced radius.
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How does this effect the status of the critical limit Mc,
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where the original mass Mo is the black hole mass divided
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by the Golden Ratio?
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Specifically, what mass will now form the black hole,
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when the original mass's radius is concomitantly reduced
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by special relativity's effect?
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The new mass is easy to find.
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EQ Z-9 is abruptly rewritten to accommodate both a reduction in
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radius, and expansion in mass, upon original (critical) mass Mc.
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The correct velocity for mass Mc can be labelled as (Vbh), as in
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'Velocity for black hole', and is easy to find. It turns out to be:
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Vbh = (C / GH) Given as:
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EQUATION Z-11
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
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³ ÚÄ Ä¿ý ³ (Vbh)ý
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Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ
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³ 1 Ä ³ ÄÄÄÄ ³ \³ cý
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³ ³ GH ³
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³ ÀÄ ÄÙ
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³ ÄÄÄÄÄÄÄÄÄÄÄ
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\³ Cý
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Es turns out to be the reciprocal of the square root
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of the Golden Harmonic. That is; Es = (1/ûGH).
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It means that when a mass Mc is physically moving at velocity
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Vbh relative to a stationary observer, its radius Rbh contracts
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by (1/ûGH), as its rest mass Mc expands by (ûGH), with the result
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that a new black hole is formed, having a lesser mass equal to
|
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(Mc x ûGH), and a lesser radius equal to (Rbh x 1/ûGH).
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As already said, this occurs when velocity Vbh is equal
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to the speed of light divided by the Golden Harmonic Ratio.
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The new mass can be labelled as Mbh-, which is less than the
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gravitational black hole mass Mbh, by a factor of ûGH. As already
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indicated, Mbh/Mc = GH, but the special relativistic mass result
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Mbh- is not the same as Mbh. There is a series:
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EQUATION Z-12
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Mc x ûGH = Mbh- x ûGH = Mbh
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It means that a visible mass cannot expand to infinity,
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because velocities can approach but can never reach the speed
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of light, due to built in limiting factors. This statement
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is true specifically for visible masses.
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For instance, the maximum velocity possible for mass Mc is Vbh
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which is C/GH, but this is only when the original mass Mo is at
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the critical mass limit Mc which is a black hole mass Mbh divided
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by GH. Whereupon the mass becomes a new black hole of mass Mbh-
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and disappears from view, relative to a stationary observer.
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The ratio C/GH is (C / 1.61803398875)
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(The preceding does not take into account any effect that
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gravity might have to relativistically reduce the radius of the
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mass causing the gravity's relativistic effect. It is realized
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that if a reduction in gravitational radius is also needed as a
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key term, than the parameters of the critical mass limit Mc regards
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the black hole final limit Mbh, will adjust accordingly, as will
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the exact factors related to the Golden Harmonic Ratio).
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(The question of such possible adjusting is not addressed in
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this disclosure, whose prime intention is to simply show that
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certain critical limits and equalities do synonymously exist
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in the domains of gravitational and special relativity. And
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that the Golden Harmonic Ratio is a fundamental primary term).
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ A REMARK ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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The Golden Ratio was not a term pulled with a sleazy wink from
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a magician's hat to fit an idea. The Golden Ratio turned out
|
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to be a resulting term that provided a theory; whose gist is
|
||
as follows:
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How can a limiting velocity (thus a universal barrier to infinite
|
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expansion of visible mass relative to a stationary observer), be
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determined for any visible mass, in special relativity?
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The answer to this is straight forward and demonstrates that
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a visible mass can never expand to infinity. A discussion
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regards this answer begins further below under:
|
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'Special Relativistic Effects on any Mass and Radius'.
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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ÛÄ´ SUPPLEMENTAL REMARKS ³
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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The following remarks are included to complete the discussion
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regards relativity theories and the Golden Harmonic Ratio. These
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supplemental remarks cover the subject of how the Golden Ratio
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was found to be a constant in critical limit situations.
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The remarks discuss the issue from firstly; effects on the critical
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mass only; and secondly for effects on the critical mass and radius.
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ Golden Harmonic Relativistic Effects on Mass Only ³
|
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
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How was the Golden Harmonic found to be the critical
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ratio factor Ng for Nx in Equations Z-5 and Z-5-1 ?
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A value of (square root of 2) was first tried for Nx, yielding
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a mass augmentation result (1/Eg x Mo), which was greater
|
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than mass Mbh, when root 2 for Nx was ratio (Mbh/Mo = Nx).
|
||
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In intuitional trial and error, an Nx value arbitrarily
|
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selected as 1.8 was next tried. It yielded an (1/Eg x Mo)
|
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value which was slightly less than mass Mbh.
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So the two Nx values were averaged as in 1/2(û2 + 1.8)
|
||
to yield a value of 1.608. Since this number was close to a
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known number (1.61803398875), this known number was tried to
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see how close the Es result (1/Es x Mo) came to Mbh, using
|
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this familiar number as Nx for a point of reference.
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It turned out that 1.61803398875 happened to be the very
|
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term wanted, because the result was perfect. This fast
|
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found number was given the label GH.
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When GH was Nx, then (1/Es x Mo) = Mbh.
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And so this particular Nx was
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labelled Ng (for Golden Ratio).
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And Mo was understood to be
|
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the same value as mass Mc.
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Equations Z-6 and Z-7 show why Ng is a constant. The
|
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set of Equations Z to Z-10 followed as a consequence
|
||
of knowing this.
|
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
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³ Golden Harmonic Relativistic Effects on Mass and Radius ³
|
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ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
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But Equations Z to Z-10 consider only the special relativistic
|
||
effect on mass, and left unanswered another question which was:
|
||
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'What modifications would occur in the parameters of
|
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mass when the radius of the mass is also conjointly
|
||
changed by special relativity effects'.
|
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The answer to this was also quickly forthcoming, but
|
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in hindsight seems to reflect a very fortuitous guess.
|
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Trial and error was started again. A velocity was needed,
|
||
to determine at what rate mass Mc would be travelling to
|
||
relativistically increase to mass Mbh-, when radius Rbh
|
||
of mass Mc was conjointly contracted to radius Rbh-.
|
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In this thought balloon, Mbh- and Rbh- would be the
|
||
parameters forming a new black hole when mass Mo was
|
||
travelling at sufficient high velocity.
|
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At this point the rate of joint contraction on mass Mbh
|
||
and radius Rbh was not known. And neither was the velocity.
|
||
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The intention was to find what term Nx is
|
||
divided into C to yield the significant velocity.
|
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In a remarkably lucky guess, the first Nx
|
||
term tried was GH itself, (in EQ Z-11).
|
||
|
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To begin, radius Rbh was modified by (Es x Rbh) as gained
|
||
from (EQ Z-11) with Nx equal to GH in the ratio C/GH, to give
|
||
contracted radius Rbh-. Then, using EQ 5 of APPENDIX B below
|
||
to find the mass of a black hole formed in radius (Es x Rbh-),
|
||
a new mass Mbh- was the result. It turned out that the ratios
|
||
of masses (Mbh/Mbh-) and (Mbh-/Mc) both equaled the square
|
||
root of ratio GH.
|
||
|
||
It had thus been found that when (C/GH = Vbh), then
|
||
EQ Z-11 yielded the square root of GH as the Es value.
|
||
|
||
The result is that with Es equaling the reciprocal of the
|
||
square root of the Golden Ratio, when Rbh is multiplied by
|
||
Es to yield radius Rbh-, and mass Mc is multiplied by the
|
||
reciprocal of Es to yield mass Mbh-, then radius Rbh- and
|
||
mass Mbh- are the correct parameters to form a new black
|
||
hole from the special relativity effects on both mass Mc
|
||
and radius Rbh, when Mc is travelling at a (C/GH) velocity.
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ How was this verified ? ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
The 'dual effect' event was easily
|
||
verified by the following:
|
||
|
||
|
||
|
||
A. Radius Rbh- was found from radius Rbh,
|
||
by using the Es effect of EQ Z-11 in:
|
||
|
||
Rbh x Es = Rbh-
|
||
|
||
B. Using radius Rbh- to find mass Mbh- in:
|
||
|
||
Cý Rbh- Finding mass Mbh- needed for a
|
||
Mbh- = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild
|
||
2G radius is given as Rbh-
|
||
|
||
|
||
C. Mbh- turned out to be mass Mbh / (1/ûGH)
|
||
when effect Es (of EQ Z-11) was 1/GH.
|
||
|
||
D. It meant mass Mbh- and radius Rbh- form a new black hole,
|
||
which is less than a black hole of mass Mbh and radius Rbh,
|
||
by a factor of the square root of the Golden Ratio for
|
||
both Mbh- and Rbh-.
|
||
|
||
E. This is true when mass Mc is travelling in special
|
||
relativity, at a reduced velocity Vbh, as gained
|
||
from EQ Z-11.
|
||
|
||
F. The synonymous special relativistic 'dual effect' event
|
||
for a gravitational relativistic event at the critical
|
||
mass limit Mc, is gained by using term Nb = GH (as used
|
||
in EQ Z-5-1), to find velocity Vbh in EQ Z-11.
|
||
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
|
||
ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
º SPECIAL RELATIVISTIC EFFECTS ON ANY MASS AND RADIUS º
|
||
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
|
||
Only certain critical limit cases
|
||
(for masses Mo and Mc = black hole mass Mbh/GH)
|
||
have so far been considered.
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ QUESTIONS ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
What if instead of Mc there is given any general mass Mo,
|
||
having a radius said to be Ro. Would there still be critical
|
||
limits involving Golden Harmonic factors that would limit a
|
||
general test case to a state that is less than infinite mass,
|
||
at a velocity which can never tightly approach the speed of light?
|
||
|
||
For that matter are other, more general, limits possible,
|
||
besides those already shown to be related to the Golden Ratio?
|
||
|
||
And if general limits are in the fabrics of physics, how to
|
||
determine them, given a general mass quantity that to begin
|
||
with is not known to be related to anything else, especially
|
||
when it is NOT RELATED to the Golden Ratio ?
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ ANSWER ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
This questioning also came to a quick answer, although
|
||
the finding of the answer was not all that straightforward.
|
||
|
||
The answer demonstrates that any visible mass travelling at a
|
||
relativistic velocity in special relativity, reaches a limiting
|
||
barrier, beyond which the mass does not visibly increase any further
|
||
toward infinity, and its velocity closes no further toward equaling
|
||
the speed of light.
|
||
|
||
|
||
The first insight is that any entity (in its most general
|
||
sense) comprises a mass and a radius. With mass is some
|
||
gravity. For instance a typical Sun sized star is an
|
||
ideal test case entity.
|
||
|
||
For example, the ratio of the Sun's existing mass M over
|
||
the Sun's existing radius R is its (mass/radius) ratio,
|
||
ie., M/R
|
||
|
||
(Note that Mo would be the Sun's original mass before any
|
||
mass augmentation effect due to gravitational relativity.
|
||
The Sun's original mass Mo is less than its existing
|
||
mass M, since the existing mass as physically measured
|
||
is assumed to include a mass augmentation upon mass Mo).
|
||
|
||
|
||
|
||
The Sun's black hole Mbh mass (silent partner mass)
|
||
is easily found by:
|
||
|
||
|
||
|
||
|
||
|
||
EQUATION Z-13
|
||
|
||
|
||
|
||
Cý R Finding mass Mbh needed for a
|
||
Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild
|
||
2G radius is given as R when
|
||
R is the radius of the Sun
|
||
|
||
so that another ratio is found, this being (Mbh/R)
|
||
which is the Sun's (black hole mass/radius) ratio.
|
||
|
||
But actually, term Mbh of EQ Z-13 is worthless. What
|
||
we really want to find is what (Mbh-/R-) ratio forms a
|
||
black hole out of the original Mo/R parameters, when Mo is
|
||
travelling at increasingly faster velocities approaching the
|
||
speed of light.
|
||
|
||
We need a comparative term, to study any differences between
|
||
the Sun when standing still, and when moving at a relativistic
|
||
velocity. The comparative term we want to know is found as:
|
||
|
||
|
||
|
||
EQUATION Z-14
|
||
|
||
|
||
Mbh Cý Where ratio Cý/2G is a constant,
|
||
ÄÄÄ = ÄÄÄÄ when C is the speed of light, and
|
||
R 2G G is the universal gravitational
|
||
constant.
|
||
|
||
R is the original radius of original mass Mo
|
||
|
||
Mass Mbh is instantly found from EQ Z-13.
|
||
|
||
The logical argument formed in advance, was that
|
||
any mass result M+, and radius result R-, ensuing
|
||
from special relativistic effects on original states
|
||
Mo and Ro, should also equal the black hole constant
|
||
ratio Cý/2G, if mass M+ and R- were relativistically
|
||
altered sufficiently to form a new black hole.
|
||
|
||
Ratio Cý/2G can be labeled ratio CR (for 'constant ratio') and
|
||
has the value of (6.735275620 x 10 to 27 grs/cm), given a speed
|
||
of light whose digital value is 2.99792458, and a gravitational
|
||
constant whose digital value is 6.6720 x 10 to -8.
|
||
|
||
|
||
Ratio Cý/2G is known as a constant
|
||
for the given values of C and G.
|
||
|
||
|
||
What we can do is follow special relativistic changes upon
|
||
both Mo and Ro through successively greater velocities, until
|
||
the combined ratios (1/Es x Mo) / (Es x Ro) equals the ratio
|
||
Cý/2G, as in:
|
||
|
||
|
||
|
||
EQUATION Z-14A
|
||
|
||
|
||
|
||
((1/Es x Mo) / (Es x Ro)) = (M+/R-) = (Cý/2G)
|
||
|
||
where Es is the special relativistic effect.
|
||
|
||
|
||
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ Finding a significant Velocity value, which results in ratio CR ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
It was useful that a good test model was available in the
|
||
solar system's Sun, where given the Sun's existing mass as M,
|
||
and existing radius as R. The Sun has to be accelerated to such
|
||
an extent that through the parameters of special relativity, the
|
||
Sun's modified mass M+ and radius R- reach a point where they
|
||
transfigure into conditions which form a new black hole.
|
||
|
||
It was assumed that such a transfiguration should
|
||
occur, and that the transfigurating velocity in
|
||
special relativity could be inferred.
|
||
|
||
How could the velocity needed for the transfiguration, be
|
||
determined for an arbitrary general case such as the Sun ?
|
||
|
||
At this point, some intuitively lucky guesswork again prevailed;
|
||
a 'seeing around corners' so to speak. To make a long story short,
|
||
it is easy to predetermine the prerequisite velocity. How, is
|
||
outlined as follows:
|
||
|
||
|
||
1. Given an existing Sun mass M of 1.99099305 x 10 to 33 gms
|
||
(mass MM from Part 1 above)
|
||
|
||
1A. Given a Sun radius R of 6.96265 x 10 to 10 cms
|
||
|
||
1B. Given constant ratio CR = Cý/2G
|
||
= 6.735275620 x 10 to 27 grms/cms
|
||
|
||
2. Given the black hole radius parameter
|
||
of EQ 4 of APPENDIX B, as:
|
||
|
||
|
||
|
||
EQUATION Z-14-1
|
||
|
||
2G M Finding the Schwarzschild
|
||
R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's
|
||
Cý event horizon, when given
|
||
mass M
|
||
|
||
|
||
3. And given Equation 5 of APPENDIX B, rewritten as:
|
||
|
||
|
||
EQUATION Z-14-2
|
||
|
||
|
||
|
||
Cý R Finding mass Mbh needed for a
|
||
Mbh = ÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild
|
||
2G radius is given as R
|
||
|
||
Mass Mbh is the black hole silent
|
||
partner mass for any given mass M.
|
||
|
||
|
||
|
||
4. Given Equation Z-8 above for special relativistic effect
|
||
on both an original rest mass and its original radius, based
|
||
on a term Nx to determine a velocity, so that:
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
EQUATION Z-15
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ÚÄ Ä¿ý ³ (Vx)ý
|
||
Es = ³ ³ C ³ = ³ 1 Ä ÄÄÄÄÄÄ
|
||
³ 1 Ä ³ ÄÄÄÄ ³ \³ Cý
|
||
³ ³ Nx ³
|
||
³ ÀÄ ÄÙ
|
||
³ ÄÄÄÄÄÄÄÄÄÄÄ
|
||
\³ Cý
|
||
|
||
|
||
|
||
5. Given that (1/Es x M) = M+
|
||
|
||
6. Given that (Es x R) = R-
|
||
|
||
7. Given that (1/Es x M+) / (Es x R-) = Cý/2G = M+/R-
|
||
|
||
8. Then it should be possible to find a velocity for EQ Z-15-1
|
||
below such that the resulting (M+/R-) ratio = Cý/2G
|
||
|
||
|
||
9. A first arbitrary value for Nx was tried, being 1.0001, which
|
||
produced results that were too low for the above Item 7 to be
|
||
correct.
|
||
|
||
10. A second arbitrary value for Nx was tried in EQ Z-15, being
|
||
1.00001, which was of the right magnitude for a mass M+, but
|
||
Item 7 was still not correct.
|
||
|
||
11. However, it was noticed that 1/1.00001 by itself was in the
|
||
magnitude range of gravitational relativistic effect Eg from
|
||
the Sun's mass, as determined in EQ C of Part 1 further above.
|
||
(MM in EQ C is the same value as Sun mass Mo given in EQ Z-2,
|
||
and immediately above in Item 1. And Eg of EQ Z-2 is the same
|
||
as Eg used immediately below in Item 12).
|
||
|
||
12. And so Eg was determined for the Sun's mass M = MM = Mo in
|
||
EQ Z-2, and conveniently labelled Egs (for 'effect gravity Sun
|
||
mass'), and was substituted as term 1/Nx in EQ Z-15 immediately
|
||
above, to give:
|
||
|
||
|
||
|
||
|
||
|
||
EQUATION Z-15-1
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ³ C x Egs ³ ³ (Vx)ý
|
||
Ess = ³ À Ù = ³ 1 Ä ÄÄÄÄÄÄ
|
||
³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý
|
||
\³ Cý
|
||
|
||
where velocity Vx is (C x Egs),
|
||
and special effect Ess conveniently
|
||
means an Es effect related to the
|
||
gravitational mass via term Egs.
|
||
|
||
|
||
13. Then; Sun mass M in (M x 1/Ess) = M+
|
||
|
||
14. And; Sun radius R in (R x Ess) = R-
|
||
|
||
15. And; ratio (M+/R-) = 6.73527458 x 10 to 27 grms/cms
|
||
|
||
As found in:
|
||
|
||
|
||
EQUATION Z-15-2
|
||
|
||
(M x 1/Ess) / (R x Ess) = CR = (M+/R-)
|
||
|
||
|
||
16. Which turned out to be an excellent approximation of ratio
|
||
CR (being Cý/2G as created in Item 1B immediately above)
|
||
|
||
Well, this was very good for a first found attempt. How
|
||
about for other masses, and how did the ratio result of
|
||
Item 15 favorably equate in truth to Item 1B above, in
|
||
that the CR result in Item 15 is marginally below the
|
||
CR constant in Item 1B ?
|
||
|
||
17. The mass of the Sun was arbitrarily raised by a factor
|
||
of 1000, so that now M = 1.99099305 x 10 to 36 grms
|
||
|
||
18. A new Egs effect factor was determined using the
|
||
larger mass of Item 17, in EQ Z-2 above
|
||
|
||
19. The new Egs factor was substituted in EQ Z-15-1
|
||
to give a new Ess factor
|
||
|
||
|
||
20. The new Ess factor was substituted in the
|
||
terms of Items 13, 14, and 15
|
||
|
||
21. The result M+/R- = 6.735275620 x 10 to 27 gms/cms = CR,
|
||
which is exactly the constant of Item 1B
|
||
|
||
Two things were instantly made clear.
|
||
|
||
It is clearly evident that Equations Z-15, Z-15-1,
|
||
and Z-15-2, are correct for any mass, to yield (M+/R-)
|
||
ratios equal to Cý/2G.
|
||
|
||
It is clearly evident that ratio (M+/R-) closes
|
||
in on ratio Cý/2G, the closer that given original
|
||
mass M is to the black hole silent partner mass Mbh
|
||
as determined in EQ Z-14-2
|
||
|
||
(It is also clear from preceding explorations, that
|
||
when relativistic effects are to act upon an original
|
||
mass, the original mass M can never approach its black
|
||
hole silent partner equivalent Mbh any closer than by
|
||
Mbh divided by factors of the Golden Ratio).
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ Finding that terms M+ and R- are properties of a black hole ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
At this point we are still not finished. The final question is;
|
||
are terms M+ and R- (as determined by Equations Z-15-1 and Z-15-2),
|
||
in fact the terms of a new black hole whose mass is M+ and whose
|
||
radius is R- ?
|
||
|
||
This final question was very easy to test by a double check:
|
||
|
||
22. The value of M+ from Equation Z-15-1 and Item 13 for the
|
||
Sun mass arbitrarily increased by a factor of 1000, as in
|
||
Item 17, yielded an Ess value in Item 19, which as applied
|
||
to Item 13, was:
|
||
3.055623494 x 10 to 27 grms
|
||
|
||
23. The value of R- from the same Ess in Item 19, applied
|
||
to Item 14, was:
|
||
4.536746031 x 10 to 9 cms
|
||
|
||
24. Looking to Equations Z-14-1 and Z-14-2, it was found in
|
||
EQ Z-14-2 (given mass M+ of Item 22), and found in EQ Z-14-1
|
||
(given radius R- of Item 23), that (M+/R-) = CR. This is shown
|
||
in the following three equations:
|
||
|
||
|
||
EQUATION Z-15-3
|
||
|
||
2G M+ Finding the Schwarzschild
|
||
R' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄ radius R' of a black hole's
|
||
Cý event horizon, when given
|
||
mass M+
|
||
|
||
R' was 4.536746031 x 10 to 9 cms,
|
||
exactly the same as R- in Item 23
|
||
|
||
|
||
|
||
EQUATION Z-15-4
|
||
|
||
Cý R- Finding mass M' needed for a
|
||
M' = ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ black hole whose Schwarzschild
|
||
2G radius is given as R-
|
||
|
||
M' was 3.055623493 x 10 to 27 grms,
|
||
exactly the same as M+ in Item 22
|
||
|
||
|
||
EQUATION Z-15-5
|
||
|
||
|
||
And so: M' of EQ Z-15-4, divided by R' of EQ Z-15-3, = CR
|
||
as in: (M'/R') = CR
|
||
where: CR is the constant of Item 1B
|
||
proving: that M+ of Item 22 and R- of Item 23 are the
|
||
correct parameters of a new black hole created
|
||
by relativistic effect Ess of Item 19, on higher
|
||
mass M of Item 17, using EQ Z-15-1 to determine
|
||
Ess, after using EQ Z-16 to determine Egs.
|
||
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
ÛÄ´ SUMMARY EQUATIONS ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
The delineations of Items 1 to 23, and Equations Z-14 to Z-15-5,
|
||
once understood, resolve into a quick series of steps, used to
|
||
determine a relativistic barrier for any given mass M and its
|
||
radius R, as in:
|
||
|
||
|
||
EQUATION Z-16
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ 2G M M is any mass, R is its
|
||
Egs = ³ 1 Ä ÄÄÄÄÄÄ radius, and Egs is the
|
||
\³ Cý R gravitational relativistic
|
||
effect of mass M
|
||
|
||
|
||
EQUATION Z-16-1
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ÚÄ Ä¿ý ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ³ C x Egs ³ ³ (Vx)ý
|
||
Ess = ³ ÀÄ ÄÙ = ³ 1 Ä ÄÄÄÄÄÄ
|
||
³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ \³ Cý
|
||
\³ Cý
|
||
|
||
Ess is the special relativistic effect ensuing from
|
||
velocity Vx, determined as the direct consequence of
|
||
the speed of light reduced by the mass's gravitational
|
||
relativistic effect Egs.
|
||
|
||
|
||
EQUATION Z-16-2
|
||
|
||
(M x 1/Ess) = M+
|
||
|
||
|
||
EQUATION Z-16-3
|
||
|
||
(R x Ess) = R-
|
||
|
||
|
||
EQUATION Z-16-4
|
||
|
||
(M+/R-) = Cý = CR
|
||
ÄÄÄÄ
|
||
2G
|
||
|
||
and mass M+ and radius R- are a relativistic transfiguration of
|
||
M and R into the parameters of a black hole, when ratio (M+/R-) = CR.
|
||
|
||
CR is a physical constant in black holes,
|
||
whose value is given as the speed of light squared
|
||
divided by twice the gravitational constant, and
|
||
whose value is 6.735275620 x 10 to 27 gms/cms.
|
||
|
||
EQUATION Z-16-5
|
||
|
||
And ultimately, Ess can be determined directly
|
||
from Egs, by:
|
||
|
||
Essý = 1 - (Egs)ý
|
||
|
||
|
||
Ess is not the same value as Egs. Ess can be higher
|
||
or lower than Egs. The exact relationship between the
|
||
value of Egs and Ess is known by:
|
||
|
||
|
||
|
||
EQUATION Z-16-6
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
Ess = \³ 1 - (Egs)ý
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
Egs = \³ 1 - (Ess)ý
|
||
|
||
|
||
|
||
|
||
Why this relationship occurs is explained
|
||
further below, beginning with EQ Z-17),
|
||
and explicitly in EQ Z-19.
|
||
|
||
|
||
In a nutshell, Equations Z-16 to Z-16-6 fully show that
|
||
fundamental terms in both gravitational (stationary) and
|
||
special (moving) modes of relativity are synonymous.
|
||
|
||
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
|
||
º UNIFIED EFFECTS IN FIELD BEHAVIOR º
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
|
||
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±± GENERAL INTRODUCTION for part 4 Unified Fields ±±±±±±± º
|
||
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
|
||
|
||
'The best information seems to come after you think you
|
||
have it wrapped up and have stopped thinking about it'.
|
||
|
||
'For example, the following floated into
|
||
consciousness as an afterthought'.
|
||
|
||
In a broad sense, relativity synonymy evokes innuendoes
|
||
of unified behavior between the fields of gravity and
|
||
electromagnetism (a unified field theory).
|
||
|
||
But wait, this is not a fully fledged unified field theory. What
|
||
is under review here are only parts of what appear to be a unified
|
||
field theory environment. What is shown are exactitudes whereby
|
||
gravitational effects of an assumed mass changing character on a
|
||
body, result explicitly in equivalent special relativistic effects
|
||
synonymous to the body moving at characteristic velocities.
|
||
|
||
Certain rules of behavior define these two modes of relativity in
|
||
their unified behavior. These rules are easy to understand, once
|
||
clearly seen, but can be very confusing until their characteristics
|
||
are shown in an obvious way. This next section (Part 4) explores
|
||
the rules.
|
||
|
||
|
||
To do the job, a particular environment is arbitrarily created. Exact
|
||
test cases are followed to the nth degree. The created environment is
|
||
in violation of certain conditions already outlined in Part 2 above;
|
||
to wit: that certain critical limits exist in the rate of mass
|
||
expansion, where the maximum expansion oscillates between a black hole
|
||
mass equivalent Mbh, and plateaus below this, articulated as functions
|
||
of the Golden Harmonic Ratio 1.61803398875.
|
||
|
||
For the test cases, it is desirable to see what happens
|
||
mathematically for events which are right at the brink of
|
||
a black hole mass, compared to masses well below the brink.
|
||
The phenomenology is thus most easily watched in detail.
|
||
|
||
For this, such masses are arbitrarily created, and assumed to exist
|
||
in violation of the statements in Part 2 above (which delineate that
|
||
a mass of black hole equivalent includes an original mass Mo, a mass
|
||
augmentation unit Ko, and resultant mass aggregate which is that of a
|
||
black hole or less. If the mass is that of a black hole, the original
|
||
mass is at a critical mass limit Mc, and the ratio Mbh/Mc = Ng is a
|
||
function of the Golden Ratio. For masses other than than Mc, ratio Ng
|
||
is given the general label Nx).
|
||
|
||
|
||
|
||
In the following, the cases for Mc and Ng parameters are ignored by
|
||
conveniently looking the other way. In the test cases which follow,
|
||
the existence of discrete portions denoted by terms such as Mo, Mc,
|
||
and Ng, are expeditiously put aside, and a mass value is assumed which
|
||
can be anything less than Mbh, even if less than Mbh by a few parts in
|
||
a thousand. This is called a HIGH mass, for convenience.
|
||
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
|
||
ÌÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
º TEST CASE º
|
||
ÈÍÍÍÍÍÍÍÍÍÍͼ
|
||
|
||
In a test case, a HIGH mass value is studied which hangs right
|
||
below the mass of a black hole Mbh. This is in a deliberately
|
||
selected HIGH mass range which as already said ignores properties
|
||
such as a critical mass factor (Mc) outlined in Part 2 above.
|
||
|
||
The intention this time is to follow test case examples in
|
||
excruciating digital detail, so that the effects and their
|
||
changes are unmistakable.
|
||
|
||
|
||
The sole intention of the following, is to observe how certain
|
||
properties are universally united in a general way through various
|
||
transformations between gravity and electromagnetic field behaviors.
|
||
|
||
And so a new study model is created, based on the arbitrary
|
||
criteria that any job needed to do a certain job is good enough
|
||
for the purpose intended.
|
||
|
||
A HIGH mass gravitational event and a LOW mass event are thus
|
||
arbitrarily created from the same Mbh term, which is the mass
|
||
of a black hole confined in the Sun's radius. Mbh for the Sun's
|
||
radius is (4.689536679 x 10 to 38 grms).
|
||
|
||
The Sun's radius (6.96265 x 10 to 10 cms) has been chosen as an
|
||
easily recognized radius for use as a constant to investigate
|
||
the effects of different mass densities confined in a fixed
|
||
(unchanged) area. Otherwise, the Sun's radius has no physical
|
||
significance when tied to the following arbitrary mass aggregates.
|
||
|
||
To supply the study, a small ratio Nx has been selected for a
|
||
control in the study. Nx is meaningless other than its value
|
||
is the charge to mass ratio of the hydrogen atom, ie.:
|
||
|
||
|
||
((Proton + electron) / electron) = 1.000544617 = Nx.
|
||
|
||
(The interpretation is that the negative electron charge
|
||
of the lightweight electron influences the heavy proton
|
||
by only 1.000544617 of the effect the proton has on the
|
||
electron, since both particles have the same quantity of
|
||
charge (opposite) despite widely divergent rest masses.
|
||
This is mentioned only to satisfy curious minds. As said,
|
||
the real value for the above ratio Nx has no intrinsic
|
||
significance in the following).
|
||
|
||
|
||
MASS1 In our study model, Mbh is arbitrarily reduced by the
|
||
small ratio Nx to give a HIGH Mass1 term, which is very
|
||
slightly below Mbh.
|
||
|
||
MASS2 Mass1 is then arbitrarily reduced by a factor of 100,000 to
|
||
give a LOW Mass2 term having the same digits but much lower
|
||
magnitude then Mass1.
|
||
|
||
The intention is to be able to follow certain relativistic field
|
||
effects in detail by following the digital results of both the
|
||
HIGH mass term (Mass1), and LOW mass term (Mass2), to more openly
|
||
|
||
follow the unifying effects between the two fields (being gravity
|
||
and electromagnetism).
|
||
|
||
In the study model, as already said, the value of Nx has no
|
||
significance except that it provides a convenient low value
|
||
Nx ratio to arrive at a HIGH mass term for the study model.
|
||
|
||
|
||
Nx is given to 13 significant digits as gained from the
|
||
ratio (P 938.2796 mev + E .5110034 mev) / (P 9382796 mev)
|
||
= 1.000544617404
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
TABLE 4-A
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ ARBITRARY STUDY MODEL DATA ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ ³
|
||
³ Nx = 1.000544617404 = (P + E) / E ³
|
||
³ Mbh = 4.689536679 x 10 to 38 grms ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ ³
|
||
³ HIGH mass1 = Mbh / Nx ³
|
||
³ = 4.686984066 x 10 to 38 grms ³
|
||
³ Nx = 1.000544617404 ³
|
||
³ ³
|
||
³ LOW mass2 = Mass1 / 100,000 ³
|
||
³ = 4.686984066 x 10 to 33 grms ³
|
||
³ Nx = 100054.4617404 ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ ³
|
||
³ In the following, Equations Z-17-1 and Z-17-3 ³
|
||
³ are the same as EQ Z-15-1 above, except, the real ³
|
||
³ digit value of each Egs ratio is substituted for ³
|
||
³ the algebraic term Egs. ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
EQUATION Z-17 HIGH gravitational Mass1 results:
|
||
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ 2G (4.686984066 x 10 to 38 grms)
|
||
Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
\³ Cý R
|
||
|
||
Mass1 has been given in
|
||
terms of a real weight.
|
||
|
||
Radius R is the radius of the Sun.
|
||
Egs is the gravitational relativistic effect of Mass1
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
HIGH gravity field effect Egs = ³ .023330687 ³
|
||
Egs is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
|
||
|
||
|
||
|
||
EQUATION Z-17-1 Electromagnetic field effect results
|
||
(Ess is special relativistic effect)
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ÚÄ Ä¿ý
|
||
³ ³ C x .023330687 ³ Vý
|
||
Ess = ³ À Ù = ÄÄÄÄ
|
||
³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý
|
||
\³ Cý
|
||
|
||
.023330687 is effect Egs
|
||
of EQ Z-17
|
||
|
||
Ess = 1 - (Egs)ý
|
||
As in: 1 - (.023330687)ý = .999727802
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
LOW special field effect Ess = ³ .999727802 ³
|
||
Ess is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
V velocity is starting to
|
||
close toward 0
|
||
|
||
|
||
EQUATION Z-17-2 LOW gravitational Mass2 results:
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ 2G (4.686984066 x 10 to 33 grms)
|
||
Egs = ³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
\³ Cý R
|
||
|
||
Mass2 has been given in
|
||
terms of a real weight.
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
LOW gravity field effect Egs = ³ .999995002 ³
|
||
Egs is closing toward 1 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
EQUATION Z-17-3 Electromagnetic field effect results
|
||
(Ess is special relativistic effect)
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ
|
||
³ ÚÄ Ä¿ý
|
||
³ ³ C x .999995002 ³ Vý
|
||
Ess = ³ À Ù = ÄÄÄÄ
|
||
³ 1 Ä ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Cý
|
||
\³ Cý
|
||
|
||
.999995002 is effect Egs
|
||
of EQ Z-17-2
|
||
|
||
|
||
Ess = 1 - (Egs)ý
|
||
As in: 1 - (.999995002)ý = .003161416
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
HIGH special field effect Ess = ³ .003161416 ³
|
||
Ess is closing toward 0 ÀÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
V velocity is closing toward 1
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
ÛÄ´ COMPARING M+ AND R- RESULTS FOR HIGH AND LOW MASSES ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
As delineated in Items 22 to 24 above, and in Equations Z-15-3
|
||
to Z-15-5 which immediately follow Items 22 to 24, two terms
|
||
M+ and R- represent the enhanced mass and reduced radius on
|
||
an object due to special relativistic results ensuing from the
|
||
proper ratio of the speed of light divided by the proportionate
|
||
relativistic effect of the object's gravity.
|
||
|
||
And so the synonymity of related behaviors, (the resulting
|
||
effects of Ess from Equations Z-17-1, and Z-17-3), when applied
|
||
to the HIGH mass of EQ Z-17, and LOW mass of EQ Z-17-2, will yield
|
||
appropriate M+ and R- terms for each of the masses. These are
|
||
listed in the following:
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|
||
TABLE 5
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ ³
|
||
³ HIGH MASS GRAVITY ³
|
||
³ ³
|
||
³ MASS1 = (4.686984066 x 10 to 38 grms) ³
|
||
³ ³
|
||
³ RADIUS R = 6.96265 x 10 to 10 cms ³
|
||
³ ³
|
||
³ Ess EFFECT = .999727802 ; from EQ Z-17-1 ³
|
||
³ ³
|
||
³ M+ = (Mass1 x 1/Ess) ³
|
||
³ = 4.688260199 x 10 to 38 grms ³
|
||
³ ³
|
||
³ R- = (radius R x Ess) ³
|
||
³ = 6.9607547839 x 10 to 10 cms ³
|
||
³ ³
|
||
³ CR = ratio (M+/R-) ³
|
||
³ = 6.735275620 x 10 to 27 grms/cm ³
|
||
³ ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
|
||
|
||
TABLE 6
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ ³
|
||
³ LOW MASS GRAVITY ³
|
||
³ ³
|
||
³ MASS2 = (4.686984066 x 10 to 33 grms) ³
|
||
³ ³
|
||
³ RADIUS R = 6.96265 x 10 to 10 cms ³
|
||
³ ³
|
||
³ Ess EFFECT = .003161416 ; from EQ Z-17-3 ³
|
||
³ ³
|
||
³ M+ = (Mass1 x 1/Ess) ³
|
||
³ = 1.482558107 x 10 to 36 grms ³
|
||
³ ³
|
||
³ R- = (radius R x Ess) ³
|
||
³ = 2.201183848 x 10 to 8 cms ³
|
||
³ ³
|
||
³ CR = ratio (M+/R-) ³
|
||
³ = 6.735276152 x 10 to 27 grms/cm ³
|
||
³ ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
|
||
|
||
ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
|
||
³ It is seen that results M+ , though higher than an ³
|
||
³ originating mass, are lower than the ceiling mass Mbh ³
|
||
³ in LOW mass results, and close in on ceiling mass Mbh ³
|
||
³ in HIGH mass results. (Ceiling mass means a black ³
|
||
³ hole mass equivalent Mbh formed in radius R. ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ In HIGH mass situations, M+ can look like the high ³
|
||
³ mass itself, but in low mass situations, M+ is far ³
|
||
³ removed from the low mass itself. ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ Also, it is obvious that M+ of LOW mass results can ³
|
||
³ gain substantially over the LOW mass itself, yet still ³
|
||
³ remain substantially below the final mass Mbh, whereas ³
|
||
³ M+ hardly gains over its originating HIGH mass, and ³
|
||
³ can also look very much like final mass Mbh, when ³
|
||
³ the HIGH mass itself looks closely like Mbh. ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ In real situations, the HIGH mass will be fixed at a ³
|
||
³ maximum ceiling of critical limit Mc. In this current ³
|
||
³ test case situation M+ looks neither like Mc, or Mbh. ³
|
||
³ Yet M+ will be explicitly Mc x ûGH, and Mbh/ûGH, when ³
|
||
³ GH the Golden Ratio 1.618034 is term Nx. ³
|
||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ (Ratio CR in the LOW mass situation, is seen to be ³
|
||
³ marginally more than CR = Cý/2G . This shift might ³
|
||
³ be due to intrinsic truncations in the digital ³
|
||
³ accuracy of the equations for lower mass densities. ³
|
||
³ It is hard to tell, in the scope of a digital ³
|
||
³ accuracy limited to 13 significant figures). ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
|
||
ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
º FIRST INTERPRETATION º
|
||
ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
|
||
|
||
Thus M+ can approach but never equal or exceed Mbh. As the Egs
|
||
effect approaches 0 (greatest power in gravity field strength),
|
||
the Ess effect approaches 1 (the least power, no effect), in
|
||
velocity related relativistics.
|
||
|
||
At the point where the gravity effect has its greatest value;
|
||
at Egs = 0 ; the special relativistic effect ceases to exist
|
||
(comes to a standstill), because there is no velocity, as when:
|
||
|
||
|
||
EQUATION Z-17-4
|
||
|
||
(C/0) / C = 0/C = 0 .
|
||
|
||
|
||
This closes right in on a clear insight regards the question
|
||
of how maximum potential relativistic gravity effect can
|
||
contain light - effectively cancel the velocity of light.
|
||
The velocity of light is not cancelled. The ability to have
|
||
a velocity related to any special relativistic effect is
|
||
cancelled. It appears this amounts to the same thing as a
|
||
counteracting of the velocity of light.
|
||
|
||
|
||
|
||
ÉÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍ»
|
||
º ±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± º
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ÌÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍËÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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º DIRECT INTERPRETATION º
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ÈÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍÍͼ
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A first interpretation of the consequences of Equations Z-17 to
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Z-17-3, is that a HIGH gravitational mass density results in a
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LOW special relativistic synonymity. And a LOW gravitational
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mass density results in a HIGH special relativistic synonymity.
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It has the immediate interpretation that things run faster in
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LOW gravitational events, and slower in HIGH gravitational events.
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It adds another picture to the experimentally
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confirmed property that proximity to gravity,
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relativistically causes time to slow.
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Intuitively, it answers a question as to how gravity at
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its highest can confine light. A see saw (or yin yang)
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characteristic in the works is summarized in the following:
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TABLE 7
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ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ¿
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³ HIGH mass gravity Effect Egs approaches 1 ³
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³ Effect Ess approaches 0 ³
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³ ³
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³ LOW mass gravity Effect Egs approaches 0 ³
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³ Effect Ess approaches 1 ³
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ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
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³ You can see at a glance how gravity can confine ³
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³ light. As gravity effect Egs closes in on 1, ³
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³ special effect Ess closes down toward 0 velocity. ³
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³ When Egs is right at 1, Ess is closed down right ³
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³ to 0 and the velocity of light C in a V/C ratio ³
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³ is vanished when 0/C = 0 . ³
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³ ³
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³ Conversely, when Egs is low and closing down to 0, ³
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³ effect Ess intensifies with a velocity approaching ³
|
||
³ 1, which is equivalent to approaching the full ³
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³ speed of light. ³
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ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
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³ In another sense, it is clearly seen that events ³
|
||
³ are free to move more rapidly in activities of a ³
|
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³ HIGH velocity, in a LOW gravity field density. ³
|
||
³ ³
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³ And in a HIGH gravity field density, events are ³
|
||
³ constrained to low velocity activity approaching ³
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³ 0 velocity, when the gravity field approaches the ³
|
||
³ density of a black hole, re: special relativity. ³
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||
ÃÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ´
|
||
³ ³
|
||
³ Notes: ³
|
||
³ ³
|
||
³ In real events, as summarized above in Part 2, ³
|
||
³ if a mass augmentation is assumed for gravity ³
|
||
³ effect Egs, then when a mass's density (without ³
|
||
³ augmentation) reaches a critical mass factor Mc, ³
|
||
³ the mass augmentation amount Ko is sufficient to ³
|
||
³ jump the mass amalgamation in one whole bump to a ³
|
||
³ black hole quantity Mbh, such that effect Egs = 1. ³
|
||
³ And thus effect Ess = 0; which is the equivalent ³
|
||
³ of a 0 velocity for light. ³
|
||
³ ³
|
||
³ The proportionate bump of mass Mc to Mbh is a ³
|
||
³ function of the Golden Ratio 1.61803398875. ³
|
||
³ ³
|
||
³ It means there never is a situation where effects ³
|
||
³ Egs and Ess slowly converge to 1 and 0, as is ³
|
||
³ fictitiously indicated in Equations Z-17 and ³
|
||
³ Z-17-1. As show in Part 2 further above, effects ³
|
||
³ Egs and Ess will jump in a final leap to 1 and 0 ³
|
||
³ in a single bump via Golden Ratio functions, when ³
|
||
³ the gravity mass density reaches Mc before ³
|
||
³ reaching black hole mass Mbh. ³
|
||
³ ³
|
||
ÀÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÙ
|
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-- Continued in RELATIVE.4 --
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Item D if you are using the HELP MENU
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