Title: The Mathematics of Particle Mass

{ABSTRACT: The DATA Range of a Fifth Dimensional power law.

The simple equation "( n/2 )^5 . n= 1 to 11"
has 11 values that map in a simple mathematical fashion
to the entire range of Elementary Particle mass QED.

-----The upper five region 11 to 7' from ( n/2 )^5
n Name e mass error% Energy

------------------------------------------------------------------------------------------
11 MAX 5033 1 2.6 Bev ; Observation set limit table maximum
10 Om 3124 4.6 1.6 Bev as Tau and Omega range
9 Proton 1845.3 -0.5 943 Mev Proton
8 K' 1024 -0.4 523 Mev ---- K' as Half of Kaon and Eta sum.
7' Pion 275 -0.7 (243+32 ) as 7'=6 plus UNIT /CMF
upper half
----- 6 Empty mid zone at n=(6*2)/2
lower half
5' Muon 211 -2.1 (243-32 ) as 5'=6 minus UNIT/CMF
4 CMF 32 7 Common Mass Factor at ~16Mev to 18Mev ; a 3D UNIT.
3 ? 7.6 ? 3.88Mev ; an unknown zone; perhaps Dark matters?
2 e 1 0 NEGATIVE electron; reference mass; 0.511 Mev !
1 eN 1/32 0.1 Smallest Neutrino in Tritium Beta decay at 16 Kev; a MIN
----- the lower five region 5' to 1 from ( n/2 )^5

-------------------------------------------------------------------------------------

Hello Everyone,

I often wondered why the Klauza-Klein Five Dimensional insights
have not yielded anything interesting or significant;
neither advocates nor theorems.

-------------------------------

--------- Consider a volume of one cubic centimeter; cc = cm^3

Imagine trying to compare Mercury's orbital volume at 32 million miles across or
17,140 million cubic miles or 8e23 cubic KM to a cc.

Compare it with whatever precision you can imagine.

It's equivalent to the nuclear scale volume within that same cc.

Using the scale value of 1e-13 cm as a reference;
it is the same ratio as Mercury's orbital volume is to a cm^3.

A cm^3 was midway between the orbital volume of Mercury
and the volume of the nuclear scale.


================= The subSPACE Theory

Ever ask yourself "What is MASS and where is it?"

This theory asserts MASS exists in a tiny volume,
a near-nuclear scaled region that has its own laws.

I have loosely titled the theory :

"subSPACE ; The fifth dimensional domain of 3D volume
where the MASS of a Particle resides/exists".

--------------------------------------

subSPACE theory assumptions:

1. 2.6 Bev is the upper limit for the range of particle mass.

2. subSPACE is a mathematically generated distribution from
the power function "( n/2 )^5 , n = 1 to 11", Q.E.D.!

This distribution matches very well with measured Particle MASS
distribution.

Since mass is already considered "compacted",
ANY valid mass relation/equation of a fifth power nature that
encompasses most forms and range of mass
would be a self evident proof and Klauza-Klein compatible.

3. Normal spatial concepts of our macro scale do not apply to
this real "subSPACE" scale where mass resides; it's too distant.



--------------------

Predictions; If this "subSPACE" thesis/model is correct, then

Particle Mass mapped by subSPACE would be self-evident [QED]

A new way to measure/see Dark Matter is possible, based on a revealed resonance at
3.88 Mev.


---------------------------------------------


========== Entire particle MASS/Energy range mapped

Here are the first three 5D examples for the electron, proton and upper limit.

e = (1)^5 was one standard e mass at 0.511 Mev

Proton = (4.5)^5 at 1845.3 e masses or 943 Mev; a -0.5% fit.

Max = (5.5)^5 at 5033 e masses or 2.6Bev ; the measured limit of MASS; a 1% fit.

Two more 5th power points emerge upon simple inspection
of Kaon and Omega ranges.

(4)^5 maps to the Kaon at 6%
If (K + ETdA)/2 mass is used , then its a 0.4% match.
------ noted in this text as K' for the pairing half value at 523 Mev.

(5)^5 maps to the Omega at 4.8%

Now there are five fits to a simple 5th power curve!

e = (1)^5 was one standard e mass at 0.511 Mev

K' as (Kaon+eta)/2 was 1024 e masses or 523 Mev at a -0.4% fit.
Proton = (4.5)^5 at 1845.3 e masses or 943 Mev; a -0.5% fit.
Omega at 5^5 was 3124 e masses or 1.6 Bev; at a 4.6% fit

Max = (5.5)^5 or 5033 e masses at 2.6Bev, at a 1 % fit.

----( 11/2 )^5 ----This was the actual observed upper limit at the Particle scale.
-------- 1st assumption satisfied as maximum


-----------------------------

Next, the form of the function is changed to
make a table of (n/2)^5 values from 1 to 11.

The five points are now:

(2/2)^5 (8/2)^5 (9/2)^5 (10/2)^5 (11/2)^5
e--------------K'------------P--------------Om----------Max
0 -0.4 -0.5 4.8 1 %
match


---------------------------------------------

After re-studying all the Elementary Particle masses, It was noted that
(4/2)^5 at 16.4 Mev is 7% near the particle Common Mass Factor-
CMF of 17.5 Mev; suggesting an internal mass grouping; a UNIT mass

eg. Muon is ~6 UNITs , Pion is ~8 UNITs and Proton is ~54 UNITs

Now there are six points, with five remaining unknowns.

(2/2)^5 (4/2)^5 (8/2)^5 (9/2)^5 (10/2)^5 (11/2)^5
e------ CMF ----K'-----------P----------Om---------Max
0 7 -0.4 -0.5 4.8 1 %

-----------------------

For further study, the remaining five 'n' values were separated
into a (6/2, 7/2 & 5/2) group and 3/2 & 1/2 into another.

-------------------------- Neutrino Match found at ( 1/2 )^5

Finally, consider the enigmatic (1/2)^5 value
at e/32 masses or 16 Kev.

It is an excellent fit to the observed minimum Energy
of (eN) the anti-Neutrino measured in Tritium beta decay (0.1%)

-------------Particle Mass's entire range mapped!

Here is current table of seven from ( n/2 )^5:

n 1 2 4 8 9 10 11
ID eN e CMF K' P Om Max
% err 0.1 0 7 -0.4 -0.5 4.8 1


The (1/2)^5 to (11/2)^5 span maps the complete range
of mass/energy, from a min of 16 Kev to max of 2.6 Bev.
-------- QED literal

----------------------------------------

========= Mapping the Muon and Pion.

The three remaining index values of 5,6 & 7
were the most difficult to match; as their 5th power values
bracketed the muon and pion masses but were not close.

If the (n/2)^5 function is thought of in a zero to twelve range,
then six becomes the boundary between the upper and lower halves.
a symmetric parity; n/2=6*2 or (6/2)^5 at 243 e masses

Think of mass having an upper and a lower region
with NOTHING in between.


Recall that the muon and pion are 6 & 8 CMF's and that the
CMF is 32 e masses from (4/2)^5 .

When the CMF is considered a UNIT,
the Muon is ( 6/2 )^5 minus a UNIT at 211,
and the Pion is ( 6/2 )^5 plus a UNIT at 275 ,
both in e masses.

-------the 5,6,& 7 as table mid range

5' Muon is 211 electron masses; (Mu = 243 -32); -2.1%

6 Table empty mid zone at (6/2)^5 at 243 e masses or ~7 CMFs.

7' Pion is 275 electron masses (Pi = 243 + 32); -0.7%

An ad-hoc rule for the "6" slot was devised to split it
into derived (5'=6-1) and (7'=6+1) slots that
replace the values (5/2)^5 & (7/2)^5 ,
using the CMF as a UNIT of 32 e masses

------------------------------------------------------------------------


---------------Putting all ten together in a Table from: ( n/2 )^5, n= 1 to 11


TABLE: Fifth power LAW of MASS as ( n/2 )^5; n=1 to 11. "subSPACE"

-----The upper five region 11 to 7' from ( n/2 )^5

n Name e mass error%

------------------------------------------------------------------------------------------

11 MAX 5033 1 2.6 Bev ; Observation set limit table maximum

10 Om 3124 4.6 1.6 Bev Tau and Omega range

9 Proton 1845.3 -0.5 943 Mev Proton THE Fundamental MASS atom

8 K' 1024 -0.4 523 Mev ---- HALF of Kaon plus an Eta particle!

7' Pion 275 -0.7 (243+32 ) as 7'=6 plus UNIT /CMF
upper half
------ 6 Empty mid zone at n=(6*2)/2
---------------------------------------------------------
lower half
5' Muon 211 -2.1 (243-32 ) as 5'=6 minus UNIT/CMF

4 CMF 32 7 Common Mass Factor at ~16Mev to 18Mev ; a 3D UNIT .

3 ? 7.6 ? 3.88Mev ; an unknown zone; an insight into Dark matters?

2 e 1 0 NEGATIVE electron; reference mass; 0.511 Mev ! at ( 2/2 )^5

1 eN 1/32 0.1 Smallest Neutrino in Tritium Beta decay at 16 Kev; a MIN.

----- the lower five region 5' to 1 from ( n/2 )^5

--------------------------------------------------------------------

--------------------------- Hypothesis for the zone at ( 3/2 )^5

A new 3.88 Mev mass/energy zone is predicted; It might offer insight into Dark
matters!

--------------------------------------------------------

================== The Fifth Dimensional nature of MASS is conclusively revealed.

1 n/2 to the Fifth power law maps the entire range of Elementary Particle Masses!

2 Since "Elementary Particle mass values" are predicted via (n/2)^5
it can not be disputed, given this definitive 5D power law! QED!
-------- 2nd assumption satisfied

3 It's Physics and Mathematics in a one to one identity.
subSPACE is real and the observed domain of Particle Mass!
-------- 3rd assumption satisfied

---------------------------------------------------------------------------------------------------------

Well, that's it; comments are welcome
as well as any ideas about the 3.88 Mev zone ,
as it's the only unknown index in the 1 to 11 range.

If anything is found around 3.88 Mev or its multiples.
it would be an additional validation for this theory.

--------------------------------

-------------I have a Physics Degree from Univ of IL ; Urbana , 1965

-
Yours truly RD ....... Spring 2008 OP IL 60302 nuz post 4/29

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