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JIDSLOPE

Abstract: Nature's mathematical constants form a straight line whose slope is the same as the Rydberg constant.
The Five points are: (-1,-5/4), (pi/2,pi/2), (P^2,e), (3,pi) and (4,P^3).

INTRODUCTION


Atomic spectra studies were the keys to understanding energy quanta and electron orbital interactions. All of modern physics, including Quantum Mechanics and Astronomy came from these fundamental measurements.

The Rydberg constant was the Key to linking these discoveries to QM in general and electron orbits in particular. This 1.0973~ constant value represents the Prime "Volume and Energy" relationship of basic Physics. The Rydberg constant is the slope of space/volume.

Rydberg Constant


The FIVE Cardinal Points



Consider these five 'Y' values in ascending order: -5/4, pi/2, e, pi, P^3 .

Think of pi/2 as the reference X=Y or null/zero point

These points are all fundamental ones! [ remember P^3 = 2 + sqrt5 ; P^2 = P + 1 ; P = (sqrt5 + 1 ) /2 ].

Take -5/4 or is it (5i^2/4) or was it (-5i^4 / 4i^4)

e & pi   The most basic of all Constants! All agree! Yes!

P^3   a 3D volume cross section; a literal 4.23607~ [ P^3 = 4 + P^-3 ] .

Now add the 'X' coordinate values to generate the five Cardinal points.

  (i^2,-5/4), (pi/2,pi/2), (P^2,e), (3,pi), (4,P^3)

Curve fitting these five points results in the following linear equation:

Y = 1.09733 * X - 0.15276 ; a straight line with a correlation of 0.99999974

Additional points near this curve


As compelling as the above five points are, the curve is near four others of significance.

The two most interesting are (-9,-10), and (12,13) representing a separation between X and Y of UNIT significance.

There are two near integer points at (5,16/3) and (8,69/8).

CONCLUSIONS

Having pure mathematical constants generate a linear curve with a slope that matches exactly with a physical constant of Nature; one that can be measured or derived in different ways, seems very significant !


The function "Y = 1.09733 * X - 0.15276" relates Nature's most basic constants [e & pi] to the energy/volume nature of Spacetime.

Speculations


Could this be the origin of the logarithmic spiral; the physical slope of volume seen as the Rydberg constant.
I wonder if in a relative sense, if every frame could have a common via their pi/2?

The point where X=Y or (pi/2,pi/2) seems ready made for this commonality.

APPENDICES

Appendix 1 : Point Table

Points
Y' -10 16/3 69/8 13 near
Y -5/4  pi/2  e  pi  P^3 exact
X  -9  -1  pi/2  P^2  3  4  5  8  12

Appendix 2: Volume and Scale

Let a cubic centimeter [or cc = cm^3] be the standard volume unit. On our human scale, this small sugar cube sized item seems small and ordinary. What does Mercury's orbital volume of 8e23 cubic KM and the nuclear volume have in common with this standard cm^3 ?

Both are equally distant from a standard cubic centimeter;.
Imagine a cc as the mid zone between Nuclear and Planetary Orbit scales.
This means the volume of Mercury's orbit is as distant as the volume of a nucleus when using a cc reference volume.

Compare it at whatever precision imaginable.

Pause to consider how planetary orbital volumes makes any human scale volume seem insignificant;
whether its a cc or a cubic mile.

Can any basis of linearity be possible or even imaginable at these vast ranges?
Surely VOLUME at the Nuclear scale would be a thing onto itself.
Normal spatial concepts of our macro scale would seem not apply over such a scale distance.

Users of Nano technology are familiar with non-linear scale effects that redefine our common macro sense of volume; eg static electricty.

LINKS

author: RD O'Meara Oak Park, IL.

Email of Author: 'RDo.meara@mister-computer.net'

This WEB page address: "http://mister-computer.net/5space/jidslope.htm"

Rydberg Constant

Official Mass values.

Rydberg Molecule Discovery>

Primes3D: Data table detailing 3D nature of the Prime Numbers

5SPACE: "Particle Mass mapped by (N/2)^5, N=1 to 22"

My Real interests are in computer science, I have spent my career as a cybernetic engineer/designer who is concerned about the chaos of our digital data. Our entire cyber infrastructure lacks "Data Sanity"; especially in the areas of forgery and security, for data and time stamps.
In that vein, I have designed a NEW multi-Computer Operating System, aka Posopip - a 3CPU system

HEDRONS : A slide show of 'The new 1-2-3 Digital Method of Counting in Three Dimensions!

5SPACE in MySpace

PS----- I would appreciate help in getting this into "sci.physics.research" or "sci.math.research" .
Their gate keepers have little imagination.

 TOP Page   17 Feb 2010