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> Origins Of The Universe.
-Fairy-
Posted: Feb 9 2012, 11:04 AM


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Hi there, and thank you for the input Sir!!!!



Well i think this is worth discussing.

The Eye of the Storm: Light from the Inner Plunging Region of Black Hole Accretion Discs


Yucong Zhu, Shane W. Davis, Ramesh Narayan, Akshay K. Kulkarni, Robert F. Penna, Jeffrey E. McClintock

(Submitted on 7 Feb 2012)



ABSTRACT: please read carefully!

QUOTE
It is generally thought that the light coming from the inner plunging region of black hole accretion discs contributes negligibly to the disc's overall spectrum, i.e. the plunging fluid is swallowed by the black hole before it has time to radiate. In the standard disc model used to fit X-ray observations of accretion discs, the plunging region is assumed to be perfectly dark. However, numerical simulations that include the full physics of the magnetized flow predict that a small fraction of the disc's total luminosity emanates from this plunging region. In this work, we investigate the observational consequences of this neglected inner light. We compute radiative transfer based disc spectra that correspond to 3D general relativistic magnetohydrodynamic simulated discs (which produce light inside their plunging regions). In the context of black hole spin estimation, we find that this neglected inner light only has a modest effect (this bias is less than typical observational systematic errors). For rapidly spinning black holes, we find that the combined emission from the plunging region produces a weak power law tail at high energies. This indicates that infalling matter is the origin for some of the `coronal' emission observed in the thermal dominant and steep power law states of X-ray binaries.






I'm sitting on the fence until someone gives us evidence.
Regardless you can still look at both options and look at the ins and outs.


Gravity it cannot propagate at c - at least not via any particle or wave or density change or curvature change - it is not consistent with observations.




So much inter-esting



Thank you
-Fairy- ( In Memory of Harry Costaz)





PS Not my Sock. Can we have a unban Harry poll?


Harry Costaz If your reading this by Chance, please join and make a new account.


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Utkarsh
Posted: Mar 16 2012, 08:18 AM


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Hello all
if that iz origen of universe from anyone
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Guest
Posted: Mar 16 2012, 08:20 AM


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Hello all
if that iz origen of universe from anyone than from where that organised who do so it wth nd so on..hence universe not organise from anywhere
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qnewera
Posted: Mar 17 2012, 10:04 AM


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Man,,,,,,,,,,,what is your point.


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http://www.photo-to-paintings.com/
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Cwilm
Posted: Mar 22 2012, 12:54 AM


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One of the more popular views pertaining to the origin of our universe is the multiverse theory which states that there are a total of 11 dimensions, with the 11th being the multiverse itself. This theory explains that our universe is one of many that float about in hyperspace. Assuming the multiverse exists, I am now questioning what contains the multiverse itself; or is the multiverse the last level, or a sea of nothing that holds within itself our and infinite other universes? It would be reasonable to conclude that the multiverse must be contained inside something.. Much like planets are contained within galaxies and galaxies are contained within our universe. Furthermore, This leads me to believe That this theory will lead to a never-ending explanation.. Galaxies are contained within the universe, universes are contained within the multiverse, the multiverse is contained within blank.. And so on.


--------------------
Rather than looking for a problem in my reasoning, find a solution and be production.

"A perfection of means, and confusion of aims, seems to be our main problem."
-Albert Einstein
"An idea that is not dangerous is unworthy of being called an idea at all."
-Oscar Wilde
"A question that sometimes drives me hazy: am I or are others crazy?"

"I can press where there needs to be pressed; I can hold hands When there needs to be -- hold hands."
-George w bush. This guy was president?! Wow I guess it is true you can be whatever you wish to be.
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AlexG
Posted: Mar 22 2012, 01:17 AM


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QUOTE
One of the more popular views pertaining to the origin of our universe is the multiverse theory which states that there are a total of 11 dimensions, with the 11th being the multiverse itself.


You've managed to confuse string theory, which calls for 11 dimensions, and the multiverse conjecture. The two really have nothing to do with each other.


--------------------
Its the way nature is!
If you dont like it, go somewhere else....
To another universe, where the rules are simpler
Philosophically more pleasing, more psychologically easy
Prof Richard Fyenman (1979) .....

God does not roll dice with the Universe" - A. Einstein

"God not only plays dice with the Universe, He rolls them where you can't see" - N. Bohr


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Cwilm
Posted: Mar 23 2012, 03:06 AM


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The string theory actually lead to the idea of the m theory, also known as the multiverse. String theory was developed in an attempt to explain the origin of the universe, but of course the string theory failed to do so.. Thus the m theory was proposed as a more revised edition.

On another note, my previous question still is a ponderous one in my opinion..

AlexG, I noticed your signature stating "fear of death is the root of all religion". Very interesting quote.. I was thinking that the faith in religion may be attributed to the unknown origin of everything.. Sorry for going of track; just caught my attention.

This post has been edited by Cwilm on Mar 23 2012, 03:43 AM


--------------------
Rather than looking for a problem in my reasoning, find a solution and be production.

"A perfection of means, and confusion of aims, seems to be our main problem."
-Albert Einstein
"An idea that is not dangerous is unworthy of being called an idea at all."
-Oscar Wilde
"A question that sometimes drives me hazy: am I or are others crazy?"

"I can press where there needs to be pressed; I can hold hands When there needs to be -- hold hands."
-George w bush. This guy was president?! Wow I guess it is true you can be whatever you wish to be.
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Guest
Posted: Mar 23 2012, 04:27 AM


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QUOTE
The string theory actually lead to the idea of the m theory, also known as the multiverse. String theory was developed in an attempt to explain the origin of the universe, but of course the string theory failed to do so.. Thus the m theory was proposed as a more revised edition


Incorrect.

M theory is an attempt to combine the 5 different types of string theory. It is not related to the multiverse hypothesis. Multiverse comes out of the Eternal Inflation theory by Andre Lind and Alan Guth.
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Cwilm
Posted: Mar 24 2012, 01:14 AM


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QUOTE (Cwilm @ Mar 22 2012, 12:54 AM)
One of the more popular views pertaining to the origin of our universe is the multiverse theory which states that there are a total of 11 dimensions, with the 11ThE being the multiverse itself. This theory explains that our universe is one of many that float about in hyperspace. Assuming the multiverse exists, I am now questioning what contains the multiverse itself; or is the multiverse the last level, or a sea of nothing that holds within itself our and infinite other universes? It would be reasonable to conclude that the multiverse must be contained inside something.. Much like planets are contained within galaxies and galaxies are contained within our universe. Furthermore, This leads me to believe That this theory will lead to a never-ending explanation.. Galaxies are contained within the universe, universes are contained within the multiverse, the multiverse is contained within blank.. And so on.

Disregarding the fact that I stated 11 dimensions, I still find the reasoning of the origin of the universe to be flawed when considering the multiverse; after all this is the primary idea of this discussion: the origin of the universe.


--------------------
Rather than looking for a problem in my reasoning, find a solution and be production.

"A perfection of means, and confusion of aims, seems to be our main problem."
-Albert Einstein
"An idea that is not dangerous is unworthy of being called an idea at all."
-Oscar Wilde
"A question that sometimes drives me hazy: am I or are others crazy?"

"I can press where there needs to be pressed; I can hold hands When there needs to be -- hold hands."
-George w bush. This guy was president?! Wow I guess it is true you can be whatever you wish to be.
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norgeboy
Posted: Apr 18 2012, 02:40 AM


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Here is what I think about space.
I think it is one of two universal parts... space and energy.
I fully trust I have proved this theory mathematically.
This attachment derives Planck's constant and the Schwarzschild radius.
The attachment proves a new and correct view of space and time.


_____________________________
The Natural Theory of Space Quantum t=cB


Table of Contents in reverse order:

XII. Appendix M: Frequencies (Hz)
XI. Appendix L: Mass and Dimensional Geometry
X. Appendix K: Spatial Curvature
IX. Appendix H: Definition of the Event-Horizon for Black Holes
VIII. Appendix G: Boundary Conditions Regarding Black Holes and Range of Density
VII. Appendix E: Energy Relationship Regarding Quantum Mechanics and Black Holes
VI. Appendix D: Definition of Planck’s Constant
V. Appendix C: General Calculations
IV. Appendix B: Alternate Calculations
III. Appendix A: Time vs. Space Calculations
II. Manuscript and Main Text
I. Abstract


I. Manuscript Abstract:

A variable transformation for time t is supported by wave mechanics and relativity theory and shows that time and space can be related and connected by the concept of physical events per unit space. The transformation confirms our daily macroscopic experience as unchanged from classical physics while still suggests new physics regarding small energies and large spaces. Perceived time can be altered relative to Earth-bound clocks in regions of lower or higher gravitational force. A series of calculation-verifications proves the theory, derives Planck’s constant and defines quantum mechanics. Black holes and their mass-radius relationship are defined. The Schwarzschild radius is defined. Minimum and maximum energies are defined.

II. Manuscript:

A Mathematical Transformation of Variables Defining Space – Time and the Constant h

Marc E. King
Silicon Valley, California
January, 2012

Abstract

A variable transformation for time t is supported by wave mechanics and relativity theory and shows that time and space can be related and connected by the concept of physical events per unit space. The transformation confirms our daily macroscopic experience as unchanged from classical physics while still suggests new physics regarding small energies and large spaces. Perceived time can be altered relative to Earth-bound clocks in regions of lower or higher gravitational force. A series of calculation-verifications proves the theory, derives Planck’s constant and defines quantum mechanics. Black holes and their mass-radius relationship are defined. The Schwarzschild Radius is Defined. Minimum and maximum energies are defined.

Introduction

In this model, it is shown that continuous time t and a contiguous view of spatial frames are mathematically the same in the macroscopic sense. A suggested transformation of variables presents interesting differences in concept for small and large energies and spaces.

Concept

We postulate that continuous time as experienced can also be represented, with the same physical result, as a directional spatial sequence or frames of events.

We consider a new unit system using the transformation t = cB with c = speed of light,
where one spatial frame (size B ) is related to one physical event B by

b (meter) = 1 (event) / B (events meter^-1)

The transformation t = cB implies the units t (sec) = c (met/sec) x B (sec^2 met^-1)

Then B events per meter = B sec^2 per meter,
and one physical event = one square second = sec^2.

Derivation

From wave mechanics, we have the Schrödinger equationi
dψ/dt = +/- 2πi/h x Eψ as a partial derivative

and the related approximation

ΔxΔk ≥ O(1).

This defines the uncertainty in measurements

Δx Δp ≥ h/2π.

Implying Δp = m Δx / Δt and using a transformation for Δt, then

Δp = m Δx / Δ(cB)

This leads to

m (Δx)^2 ≥ (h/2π J-s) (ΔcB) = (h/2π J) (cB) (ΔcB)

Per unit mass, then

(Δx)^2 ≥ (h/2π)(ΔcB)(cB) from transformation.

For a single B (events-meter^-1) the corresponding Δx = b meters and Δ(cB) = 1/(cB)

Then b ≥ (h-bar)^1/2.
Further defining b-minimum as the minimum Δx and using the positive root in this analysis, then

b(min) =1.027E-17 meters.

Subject to the further justification below, we assert:

E = F-sub-B x b

Where F-sub-B = F-sub-G = the gravitational force at the spatial location of event B.

And on the planet surface, F-sub-B = ma = m x 9.8 meters-sec^-2.

Then E / m = a x b = 9.8b meters / (cB)^2 or

E / m = 9.8b / (c/b)^2 and

E / m = 9.8 / 9 (10^-16) b^3 J-kg^-1,

Or we can write the expression:

E / m / b^3 = 1.089E-16 J kg^-1 or

E-sub-B / m = 680 eV / kg for one cubic spatial boundary.

Justification for Spatial Dimension b

Using uncertainty and similar to the derivation above, one estimation using neurological sensory communication as an upper bound on Δx = b (in one dimension) for spatial boundary (frame) size is suggested by:

(Spatial Frame Width)^2 ≤ (h – bar ) x © x (Time Required for Sensory Continuity)

Using orders of magnitude 10^-34 J-sec (and adjusting for units) from wave mechanics and estimating the time required for sensory communication in the range 10^-3 sec – 10^-6 sec from synapse switching (potential change) rate, we would then estimate the magnitude:

Δx = b ~ 10^-14 to 10^-16 meters (for example as an upper spatial bound) in order to perceive continuity from actual contiguity of frames.


The neurological bound approximates the largest frame or spatial size that could be perceived as the continuity of time and accommodates the calculated boundary dimension Δx = b ~ 10^-17 meters.

b(min) = 1.027E-17 meters was derived assuming t = cB so that c is assumed to be the maximum achievable velocityiii and as such defines a maximum sequential rate and a minimum allowable b.

Justification for Spatial Barrier Energy

Using a one dimensional example,

E = F x distance.

We are using the transformation t = cB where B = 1 / b and b has the spatial dimension of meters.

The energy associated with the distance b is a function of a force F acting upon a mass m at a particular set of spatial coordinates.

It follows, the innate force acting on the mass m in space is the gravitational force.

There are no external forces to be considered for the mass m for our purpose regarding the transformation associating time and space.

Verification of Calculations

E-sub-B is then a function of gravitational force.

Using the calculations above and for a single event B = 1,
we can also write, for the planet surface as an example:

E / m = a x b = b x 9.8 (c / b )^-2 = 9.8 / c^2 / b.

Then 1.089E-16 = 9.8 / c^2 / b.

And for the planet surface E-sub-B, we verify our unit of measure calculations:

b meters = (1 event / B events meter^-1) = 1.000 as a confirmation of the energy calculation 680 eV / kg.

Independently, we can re-calculate the value of b using F-sub-G on the planet surface:

b = E-sub-B / m x (a)^-1 = 1.089E-16 / 9.8 = 1.111E-17 meters.

This should be the universal value of b and is independent of F-sub-G since the accelerations “g” cancel for any spatial position.

This value is larger than the allowed minimum calculated b(min) = 1.027E-17 by the difference 8.4E-19 meters
and we find the calculated surface value to be approximately 8% larger than the minimum allowed value b(min) using the Earth gravitational acceleration a = g = 9.8 m-s^-2 and using no transformations in this calculation. We do not pursue further calculations in the present scope. (See Appendices for calculations.)

Energy Change as a Function of F-sub-G = F-sub-B

Assuming mass m and boundary b are unchanged, then E-sub-B changes as a function of F-sub-G = F-sub-B the gravitational force at the location of physical event B.

This follows directly from

E-sub-B = F x b.

A smaller gravitational force leads to a smaller E-sub-B relative to the planet surface.

With different E-sub-B, clocks should appear to run at different rates in regions of higher or lower F-sub-G relative to the planet surface.

A fictitious force, like the Coriolis force or the weightlessness of orbit, should not affect the real force F-sub-G = F-sub-B.

Conclusions

Continuous time can be represented by a contiguous spatial sequence of frames, or boundaries Δx = b, while conforming to existing physics in the macroscopic sense and with our sensory perceptions.

The transformation t = cB leads to the spatial frame dimension b(min) = 1.027E-17 meters and corresponds to
3 x 10^8 physical events in one second of time t.

For this model,

The surface barrier energy E sub-B per unit mass = 680 eV / kg has been defined.

E-sub-B is suggested to be a function of gravitational force and so a function of spatial location.

Perceptions of Earth-time and clocks are expected to experience different rates in regions of lower or higher gravitational force relative to the planet surface.





III. Appendix A

The difference in value between b(min) derived from the Schrödinger equation and b calculated empirically from Earth-surface F-sub-G is 8.4E-19 meters and proves to be the mean factor 1.079 or 7.9%.

The concept of continuous time t leads to exponential growth-decay:

a = a-sub-0 x e^ (rate x time) where e = lim (n infinity) (1 + 1/n)^n = 2.718.

Applying the expression for time itself, then

T(new) / T(old) = e^(r x t) = e^(0) = 1.

For time t itself, the rate r = 0 and there is no change in continuous time t so that one “second” of “time t” does not change. Time t is absolute.

Differential equations for centuries, e.g. the Schrödinger equation, assume time t is a real and continuous variable.

In the transformation t = cB, we need to treat continuity of time as a slight-contiguity of space.

In that case, we find 3 x 10^8 met/sec to be a large enough frequency (number n) to continue using the calculated value of e = 2.718 = lim as ninfinity of (1+1/n)^n.

But in a directional spatial sequential model, then space itself advances or grows per some rate different from r = 0.

As a one dimensional chalk line curves in a two dimensional blackboard, and as a two-dimensional earth-surface curves in three-dimensional space, then a change in 3-dimensional space needs to take place in a mathematical dimension higher than 3.

Postulating the higher number of dimension (vertices) to be 5 as in the Fibonacciiv infinite sequence, and considering physical events B = 1 / b = sec^2, then we calculate the following for one second of time t:

(V-sub-S / V-sub-0)^1/5 = e^(rV x t)^1/5 = e^(.618^(5-3))^1/5 = 1.079

or a 7.9% decrease in physical events B (increase in one-dimensional size B ) from the continuous-time model used to calculate b(min).


IV. Appendix B


Another Calculation for difference b-empirical - b(min) = 7.9%:

In two dimensional physics,

F = ma = m x met-sec^-2 becomes F-sub-2 = m x a-sub-2 = m x met –sec^-3/2

and one physical event B would no longer have units of sec^2; instead, sec^3/2.

The uncertainty principle then has a transformed h-bar, and now

b(min) = (h-bar)^1/2 x c^1/2 = 1.779E-13 meters.

Similarly, E-sub-B / m = 9.8 / c^3/2 J-kg^-1 per square boundary = 1.886E-12 J-kg^-1 per boundary and

b = E-sub-B / m / 9.8 = 1.924E-13 meters.

Then we again have the mean factor

= 1.079 or 7.9%

between b(min) and b (from F-sub-G) in two-dimensional space exactly the same as in three-dimensional space.


V. Appendix C

A General Fibonacci Calculation:

The Fibonacci infinite sequence was referenced in Appendix A,

F(n) = F(n-1) + F(n-2) with seed values F(0) = 0 and F(1) = 1.

Ratios converge, and

lim(n infinity) F(n+1) / F(n) = φ = (1 + 5^1/2) / 2 = .618 … and

lim(n infinity) F(n-2) / F(n) = γ = .382 … and so on.

Writing an example expression for spatial dimension ≥ 3 per Appendix A

∫∫∫∫∫∫∫∫dV = ∫∫∫∫∫dV(0) x exp(rV x t)

where rV = r-sub-V = φ^(D(n+1) – D(n))

then

dx /dx(0) = exp(φ ^ (D(n+1) – D(n))^1/(n+1).

Except we are now doing math in another dimension, and while e = 2.718 in three dimensions, the base of natural logarithms should change in higher or lower dimensional space.

For example, in the case of 8 dimensions: e  e^(1/γ)^5/2.

We quickly find dx /dx(0) = 1.08.

A different example, for the case of spatial dimension < 3:

The base e must change as a function of the power of B, i.e. in three dimensional space B ~ sec^2 while in two-dimensional space B ~ sec^3/2.

The difference in power of physical events B

2 – 3/2 = 1/2 and the two-dimensional e = 2.718^1/2.

Then we quickly find dx /dx(0) = 1.08 similar to the previous mean calculations for the difference between b(min) and b-empirical.

The (Fibonacci) calculations hold true for any spatial dimension n moving through n+1 with a dimensional adjustment for e.

VI. Appendix D

Planck’s Constant


Planck’s constantv h = 6.626068E-34 met^2 kg sec^-1:

From the Schrödinger equation,

h = 13.6eV / (1^2) / ν = (13.6eV / (1^2) / c) x 91.2nm

Then h = (E-sub-B / c) x (91.2E-9 / 50)

Or h = (E-sub-B / c) x 1.82E-9

And h = (E-sub-B / c) x (b x c / 1.82)

So

h = E-sub-B x b / 1.82 or

h = e^(-3/5) x b x E-sub-B = b EB / e3/5

where

b = b for Earth surface = 1.111E-17 meters

and

EB = E-sub-B = Earth surface barrier energy = 680eV/kg = 1.089E-16 J/kg

And the calculated h = 2.718^-3/5 x 1.111E-17 x 1.089E-16 = 6.6E-34 per event.

More precisely from our 3-decimal calculations and per appendices A through C,

h  h(1-Δh) where Δh = 0.08^5/2 and h = 6.63E-34 per event.

Units for transformed h:

h ~ met J Kg-1 b-3 ~ met-2 J Kg-1 ~ met-2 met2 sec-2 Kg Kg-1 ~ (one B )^-1 = event-1



VII. Appendix E

The Nature and Meaning of Quantum Mechanics

We postulate that any allowed energy quanta has a wavelength λ = nb where n is an integer and b = 1.111… E-17 meters per the main text.

For example, the 13.6eV H ground state transition is λ = 91.2nm

And n = λ / b = 820882088.

Similarly, the H state 1 to state 2 transition is λ = 121.6nm

And n = 109450945.

An H state 3 to state 1 transition is λ = 486.1nm and n = 43753375.

Then 0 ≤ one energy-event ≤ c / b ( = 2.700E25 J)

and quantum energy = hc/λ is defined as an integral operation of 1/b.

Then the base of all quantum mechanics is 1/b = B where t = cB.



VIII. Appendix G

Density of Matter and Black Holes

As the intersection of one dimensional space (a line) with two dimensional space (a surface) is a single point with zero dimension, the intersection of two and three dimensional space is a line with one dimension, and the intersection of three and five dimensional space should be a surface with two dimensions, then the intersection between five and eight dimensional space should be three-dimensional (observable in 3-dimensions) and is suggested by the spherical volume of a black hole.

From Appendix E, the maximum allowed energy-event is 2.700E+25 J.

Then E-sub-B at a black hole surface should be bounded by the maximum allowed c^3 J kg^-1.

For the hole surface:

EBmax = GmHrH / rH^2 or E-sub-Bmax = G x m / r for the hole, and

c^3 = G x m / r relating to the hole, or we can write

mH / rH ≤ c3 / G

or

mH ≤ rH c^3 / G

where G = 6.673E-11 met^3 kg^-1 sec^-2,
r-sub-H has units meters, and
c (3E+8 numerical) has units J^1/3.

Then c^3 / G ≤ 2.700E+25 / 6.673E-11, and

mH / rH ≤ 4.046E+35 kg met^-1

for any black hole.

If we let E-sub-B = Δλ E-sub-Bmax = Δλ c^3 where 0 < Δλ ≤ 1, and

Δλ = nb where 1 ≤ n ≤ 1/b = B, then

mH = rH Δλ c^3 / G or

mH = KG rH where KG = Δλ c^3 / G.


IX. Appendix H

The Spatial Nature of Black Holes

Per Appendix G,

mH / rH = KG or m-sub-H = K-sub-G x r-sub-H

where KG = Δλ c^3 / G.

The following surface density boundary conditions should apply for any black hole:

1. The hole mass m-sub-H / (“surface-area”) of the 3-dimensional 2-D surface = m-sub-H / (“surface-area”) of the 5-dimensional 3-D surface (volume.)
2. Similarly, mH / (4/3 x π x rH^3) = CR x rH^5 where C-sub-R defines the 5-dimensional “surface-area” for 8-dimensional space.

Then boundary conditions require:

4πrH^2 = CR3-8 x rH^5 and 4/3 πrH^3 = CR5-8 x rH^5

where CR n-m = C-sub-R for dimension n curving through dimension m

and r-sub-H = rH = CR5-8 / CR3-8 from boundary conditions.

Then Δλ = C-sub-R3-8 / C-sub-R5-8 or

Δλ = CR3 / CR5

where C-sub-R3 and C-sub-R5 represent the curvature rates of 3 and 5 dimensional space respectively through 8-dimensional space, where the ratio mH / rH is proportional to Δλ, and where we assume C-sub-R3 ≤ C-sub-R5.

Then there is only an effective zero-density “black hole” for CR3 ~ 0 while the highest density black hole occurs where CR3 = CR5,

Then Δλ represents the ratio of curvatures of 3 and 5 dimensional space through 8 dimensions for the spatial intersections known as black holes.

The higher the mass density in a spatial location, the more the effective radius of curvature should change. With dense enough matter, then curvatures among dimensions become more closely equivalent as density becomes large.

To visualize in two dimensions, πr^2 and 4πr^2 are both two dimensional surfaces that curve in 3-dimensions. The curvature (lack of) for a flat circle is 0 while the curvature for the closed spherical surface is 1.
Appendix H (cont.)

If we assume C-sub-R5 is closed (curvature 1) in 8-dimensions, then C-sub-R3 has the possible range 0  1 in 8-dimensions where 0 represents no intersection at all and 1 represents a closure of the five and eight dimensional intersection.

To see/observe the intersection (black hole) it must be at least a 5 and 8 dimensional intersection (3-dimensional) or constitute the five dimensional surface intersection represented by the integral ∫4πr^2dr throughout r for the continual surfaces.

Then the “smallest” black hole is the “least dense mH / rH” black hole having Δλ ~ 0 but still large enough to represent an intersection of 5 and 8 dimensional space.

Then the boundary condition is a single event:

CR3min = 1 / cB where B = 1 and

Δλmin = 1 meter / c meters = 3.333E-9.

Then

c2 / G ≤ mH / rH ≤ c3 / G or

c^2 ≤ mH / rH ≤ c^3 kg met^-1

or we can write the expression in the Schwarzschildvi form,

rH = k(λ) mH G / c^2 meters

where k(λ) = 1 / cΔλ.


X. Appendix K

The Various Sizes of Black Holes and Curvatures of Three-Dimensional Space

Appendix H defines the mass-radius relationship as observed in three-dimensional space:

mH / rH = KG(λ)

where λ = Δλ = CR3 / CR5

and represents the ratio of curvatures from 3-dimensional space and 5-dimensional space through 8-dimensional space respectively.

We assume, for the three dimensional intersections, that CR5 = 1.

The minimum CR3 = 1 / c and the maximum CR3 = c / c = 1.

Allowed quantum are then n / c for n = 1 to c.

The minimum (least dense) intersection is an intersection among 3, 5 and 8 dimensional space where CR5 = 1 and CR3 = CR3(min) = 1 / c.

The next “largest” (more dense) intersection should occur for CR3 = 2 / c and so on.

The most dense intersection occurs where CR3 = c / c = 1 and represents a closed third dimension in both eight dimensional and five dimensional space.

To visualize curvatures, the diameter of a circle = d is a straight line with curvature
CR1-3 = 0 while the circumference (length πd) closes upon itself (runs into the back of itself) and has the curvature CR1-3 = 1.

The curvature CR2-3 is closed in 3-dimensions visualized as a spherical (or elliptical, not reviewed in this scope) surface area that has closed itself around a center-of-mass cM.

The two dimensional surface does not alter or “grow” in three dimensions, but the one dimensional line, e.g. the straight path of a distant comet or ray of light (CR1-3 = 0) or the line of a planetary satellite CR1-3 = 1) both curve (or bend) around mass in three dimensions to the two extreme degrees of curvature.

Then the ratio mH / rH = KG should represent a curvature of three-dimensional space through eight-dimensional space.

XI. Appendix L

Definition of Mass and Geometry for Black Holes

From the equation EB = aG J kg^-1 bn^-n x bn ( = 1.089E-16 on Earth surface,)

and from the definition of physical events in dimension n = B where B ~ sec^2 in 3-dimensions and sec^(D-1) per appendix C, then bn has the following value:

3-dimensions: b3 = 1.111E-17 meters (per the main text)
5-dimensions: b5 = b3 / c = 3.703E-26 meters
8-dimensions: b8 = b5 / c^2 = 4.114E-43 meters and so on.

Per Appendices G, H and K, the black hole geometry is a function of mass and becomes a series of symmetrically-closed concentric surfaces having internal densities:

8-dimensional volume in 3-dimensions = 4 / 3 π r8^3
5-dimensional volume ( = ∫ (r5-8-to-r5) 4πr^2 ) = 4 / 3 π r5^3 (including the volume of 8)
3-dimensional volume = 4 / 3 π rH^3 where rH = r5 (including volumes of 5 and 8)

and

the boundary condition for the most-dense black hole is then:

mH / (4πrH^2) = mH / (4/3 πrH^3)

where rH = mH / KG, then

mH(max) = 3KG kg and the corresponding

rH = 3 km.

The black hole mass mH for the general case rH = r5:

mH(λ) = ∫ (from r5 – r8 -to- r5) 4πr^2 dr = 3KG(λ)

where

λ = r8 / r5,
rH = r5 and
r8 is the 3-dimensional-radius of zero-mass 8-dimensional space (b = b8) at the center of the hole.

XII. Appendix M

Frequencies of EM Communication

One boundary condition between 3 and 5 dimensional space is that the largest energy-event in 3-dimensions = the smallest energy event in 5-dimensions. Per Appendix E:

E(max) = c / b in 3-dimensions and

E(min) = c / c = 1 in 5-dimenisions,

so that λ = b = 1.111E-17 meters is the only possible wavelength of communication between dimensions per the above boundary condition.

Then the frequency:

ν = c / λ = c^3 events / sec = 2.700E+25 Hz.

Similarly, the corresponding frequency between 2 and 3 dimensional space should have the lowest three-dimensional energy per event possible or the minimum energy-event:

ν = c / λ = c / 1 meter = c events / sec = 3.00E+08 Hz

and where the intersection between 3 and 5 dimensional space is a 2-dimensional intersection.

References:
__________________________

i Erwin Schrödinger, Quantisierung als Eigenwert Problem, 1926.
ii Werner Heisenberg, Über die Grundprinzipien der 'Quantenmechanik, 1927.
iii Albert Einstein, Zur Elektrodynamik bewegter Körper, 1905.
iv Leonardo Fibonacci, Liber Abbaci, 1202.
v Max Planck, The Genesis and Present State of Development of the Quantum Theory, 1920.
vi Karl Schwarzschild, Uber das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie, 1916.


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This post has been edited by rpenner on Apr 27 2012, 03:59 AM
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