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5SPACE: A Theory that Mass is geometrically descrete based on the five dimensional function: (N/2)^5.

The DISCOVERY: 5SPACE: a 5th power mathematical distribution that maps to Elementary Particle Mass !

Abstract: The simple function (N/2)^5 for N=1 to 24, maps the Mass range of ALL known Major Particles;
eg the Proton Mass is given by N = 9 as (9/2)^5 [1845.3 'e' masses or 943Mev ]; a half a percent fit based on
N = 2, being the Electron REFERENCE mass.

This model's prediction that its fifth power Nodes are exact,
coupled with its internal table of six and twelve used in the pion/muon derivations;
independently validates the 5SPACE Model for the LHC at N=24!

5SPACE explicitly validates the Higgs as the upper limit of particle mass without requiring mass to be Higgs generated.

This model's N = 3 node is the foundation for an "Aether Theory",
based on 3.7 Mev Inverse Cherenkov radiation data.

All in all, a Geo-packing of energy as mass, from a Simple Fifth Power Law!    QED.

 Table of Contents

1. Established fifth power relations in Physics

2. Scale and Volume Considerations

3. First six Indicies

4. Second six Indicies

5. Mapping the Muon and Pion

6. (N/2)^5 Mass table and conclusions

7. Discussion and Speculations

8. PMF Appendix


What is Mass and why does it have such an almost random range?

It seems that as modern physics acquires more knowledge and scope,
the nature of Mass and Energy appears more disjointed and contradictory.

Little fundamental insight has been added to Einstein's famous "E=mc^2" all these years later.

Now consider a few unresolved problems like Neutrino mass, dark matter, Charge, and Strangeness;
then factor in long-standing concerns about decay life-time scales and observed Parity violations.

What remains cannot even be labeled as a "Zoo" since that implies a set of common conditions;
particle mass is more like a group of scattered free roaming clans with limited commonality.

When the masses of the most stable particles are compared, a common Particle Mass Factor of 17.5 MeV's emerges.

Another particle mass factor of ~4 MeV is seen as steps in the Pi and Sigma families;
note its (3/2)^5 = 3.88 MeV nearness.

Matter, Energy and the Fifth Dimension

There are four major proven relations in Physics concerning a Fifth power law.

The First Fifth power Relationship

The first from Classical Physics is the fundamental law of energy radiation known as Wien's law.
It is based on wavelengths to the fifth power.

This means energy as photons is based on wavelengths to the fifth power!
Atomic and nuclear-emitted energy have a proven fifth power basis; just as the 5SPACE formula has.

However when Wein's law form was used for the Rayleigh-Jeans spectral distribution of radiation;
it suffered from a false prediction of larger energy at ever smaller wavelengths.

Planck avoided this by showing that if energy was emitted in quanta, the observed data matched at all scales.
This formed the basis of Quantum Mechanics.

The Second Fifth power Relationship

Thermal radiation per time per area and its "Black Body" character
had been measured by Stefan (1879) to be directly proportional to the fourth power of Temperature.
Integration of the total indicates that energy has a Fifth power density.

The Third Fifth power Relationship

After Einstein failed in his attempt to unify Gravity with Electromagnetism,
Kaluza & Klein [K&K] proved that if space-time had a fifth dimension,
Gravity and Electromagnetism could indeed be unified with General Relativity.

They found that "Charge was angular momentum" in that fifth dimension.

So a Grand Unified Theory [ GUT] of Everything already exists;
even though it seemed then to be an un-insightful answer.

The Fourth Fifth power Relationship

Just as Wiens law established a fifth power relation at atomic scales,
astronomy uses a fifth power relation for stellar magnitudes.

The fifth root of one hundred is used as a stellar magnitude scale step of 2.512.

The above Four relations clearly establish that ALL spatial volumes have a fifth power nature!

This paper's new Fifth power Relationship: (N/2)^5

This text describes a new fifth power discovery that complements the first four,
and offers new insights into the K&K GUT [Grand Unified Theory].

The name "5SPACE" best captures the essence of this new fifth power relation,
and is based on the assumption that nuclear volume is Unique and Digital as Planck's Constant implies.

This discreteness is seen in the fifth power mass node index,
representing how many "Electron masses" that index volume can hold.

eg. The Proton is the N=9 index node with "(9/2)^5 = 1845~" Electron masses!

Table of Contents

Volume and Scale Considerations

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?

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 for a moment to consider how a planetary orbital volume makes any human scale volume
seem insignificant; whether it's a cc or a cubic mile.

Can any basis of linearity be possible or even imaginable over these vast scale 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.
for example, static electricity dominates for most surfaces and materials at small scales.

5space: Mass nodes at (N/2)^5

This theory asserts Particle MASS exists in unique near-nuclear fifth-dimensional regions/volumes,
labeled "5space; where the MASS of Elementary Particles resides/exists"; a Geometrical node of mass!

5space theory has four assumptions:
  1. Electron Mass of 0.511 MeV as the reference mass.
  2. Volume is obviously discrete as Planck's Constant implies!
  3. ~2860 MeV is the upper limit for the range of nucleon scale observed particle mass;
  4. The Z & W particles are the upper limits for mass.
     Official Mass values.

Predictions; If the "5space" theory/model is correct, then
Particle Mass mapped by (N/2)^5 function should be self-evident [QED],
and provide some new insights into mass.
Since particle mass is already considered "compacted",
any relationships that encompass the entire range of mass should be self-evident .

Table of Contents

First six examples of the (N/2)^5 function

1: Electron at (2/2)^5 is one standard mass at 0.511 MeV

2: (8/2)^5 maps both to the Kaon's 493.7 MeV at -6% and Eta's 547.5 MeV at 4.4%
Note here from a volume perspective, that the minus six percent of the kaon,
signals its strong missing mass-energy potential that would account for its long lifetime.
Just as the plus 4.4% of the Eta signals its very short excited lifetime.

If (K + ETA)/2 mass is used , then it's a -0.4% match.
noted in this text as K' for the pairing half value at 523 MeV.

3: Proton at (9/2)^5 = 943 MeV; a -0.5% fit to the 938.3 MeV measured mass.

4: Omega at (10/2)^5 = 1597 MeV; maps to its 1673 MeV with a 4.6% fit.
Again, note here how Omega's in an excited state, some 76 MeV excess.
Also, the Tau Lepton has a mass similar to the Omega, making for another 10 family member.

5: Nucleon Max at (11/2)^5 = 2600 MeV; a 10% fit to ~2860 MeV
  An upper limit of nuclear geometry is seen in the 2600 to 2860 MeV range.

6: W = (22/2)^5 at -2.3% and Z = (22.5/2)^5 at -1.1% .
  For the largest recorded masses , the upper limit was the 'Z & W' at 92 & 82 Gev.
--------4th assumption satisfied as Particle mass maximum

First six (N/2)^5 zones

N____ 2___ 8___ 9___ 10__ 11__ 22__
ID e K' P Om MAX W
err% 0 -0.4 -0.5 4.6 10 -2.3

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The remaining six 5SPACE nodes

The remaining six 'N' values were separated into two groups;
a 5/2, 6/2 & 7/2 family group and 4/2, 3/2 & 1/2 singlet group.

PMF at (4/2)^5

After re-studying all the Elementary Particle masses,
It was noted that node 4 is +1% near the common Particle Mass Factor of 17.5 MeV.
suggesting an internal mass grouping; ie a mass UNIT of 32 'e'-masses; see the Appendix.

Two basic values taken from the "Aether Theory", of 17.5 MeV and 15 MeV average to 16.25 MeV for ~1% error.

Since 5SPACE is a geometrically based theory,
it follows that the PMF is merely a local packing factor or geo-unit of volume.

Here are figures for the CMQ's

Mass Node at (3/2)^5 matches the ICA limit.

The paper "Laser Acceleration of Relativistic Electrons
Using the Inverse Cherenkov Acceleration (ICA)"
1995 ICA at BNL illustrates how the 3.7 MeV ICA experiment's limit was reached.

Given that Cherenkov radiation results when light speed slows due to changes in medium,
it seems natural to attribute this to an Aether effect such as node disturbances.

The Inverse Cherenkov Acceleration experiment could not go beyond the 3.7 MeV limit
even though their model predicted it should have gone higher.

This 3.88 MeV mass/energy zone is also the same scale as the energy difference in the Pion and Sigma families.

It is also labeled CMP in the mass table for "Composite Monopole Pair",
from the "Aether model" .

ATOM ( 1/2 )^5

This 16 Kev value can be interpreted as a volume quantum.

It can also be seen as the building unit of the electron; thirty-two of them equal the electron mass of 511 Kev.

This is also close to the 17 Kev smallest energy of the electron neutrino in Tritium decay.

"See the Aether model", for more details.

What is below this (1/2) as 16 Kev minimum?

Since 1/2 is the table's lowest index value,
5SPACE theory posits nothing of a singular nature.

However, the Chemistry of molecular bonds seems to be a good fit based on local volume scales.

Again, a geometrical energy match to this theory's conclusion that
volume is proportional to Energy in a fifth power mathematical proof; QED!

Entire particle MASS/Energy range mapped , for N = 1 to 24

N____ 1___ 2___ 3___ 4___ 8___ 9___ 10__ 11__ 22__ 22.5 24
ID Monopole e ICA PMF K' P Om MAX W Z LHC
err% ??? 0 -4.8 1 -0.4 -0.5 4.6 10 -2.3 -1.1 ???

The (1/2)^5 to (24/2)^5 span maps the complete range of Particle mass/energy,
from a minimum of 16 Kev to maximum of 127 Gev.

5SPACE treats both the (1/2)^5 and (24/2)^5 nodes, as absolute limits and therefore exact!

Therefore, the LHC value would represent the limit below which, mass would be possible.

N____ 1___ 2___ 3___ 4___ 8___ 9___ 10__ 11__ 22__ 22.5 24
ID Monopole e ICA PMF K' P Om MAX W Z LHC
err% 0 0 -4.8 1 -0.4 -0.5 4.6 10 -2.3 -1.1 0

Table of Contents

Mapping the Muon and Pion

The three 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 with the Node=6 emerges; with (6/2)^5 as 243 'e' masses, .

Think of Particle mass having an upper and a lower region with little in common.

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

An ad-hoc rule for the "6" slot at 243 'e' masses was used 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 PMF as a UNIT of 32 'e' masses

The Muon then is 211; 243 minus the UNIT of 32.

And the Pion is 275; 243 plus a UNIT of 32, both in 'e' masses.

-------the new table mid range

5' Muon is 211 Electron masses; (Mu = 243 - 32); -2.1% from 206.77

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

7' Pion is 275 Electron masses (Pi = 243 + 32); -0.7% from 273.2

Table of Contents

---------------Putting all of them together in a Table

Particle Mass Table from (N/2)^5

INDEX N Name ____ Electron masses * .511 MeV error % Value______ Notes__________
24 H 248832 127.1~ Gev -1.6% 125.~ Gev LHC Higgs as the upper limit.
22.5 Z 180203 92.08 Gev -1.1% 91.18 Gev Neutral Weak Force Boson
22 W 161051 82.3 Gev -2.4% 80.4 Gev Charged Weak Force Boson
12+ Exotic Matter Zones
11 MAX 5033 2600 MeV +10% ~2860 MeV Baryon Scale volume Limit
10 Omega 3124 1597 MeV +4.6% 1673 MeV Strange = -3
9 Proton 1845.3 943 MeV -0.5% 938.3 MeV Hydrogen
8 K' 1024 523 MeV -0.4% 520.6 MeV K'=(Kaon+Eta)/2
7' Pion 275 140.52 MeV -0.7% 139.6 MeV 243+32=275
6 Empty 243 124 MeV _ Table mid-zone
5' Muon 211 107.82 MeV -2.1% 105.66 MeV 243-32=211
4 PMF 32 16.4 MeV +1% 16.25 MeV Nuclear Particle Mass Factor
3 CMP | ICA 7.6 3.88 MeV -4.8% 3.7 MeV Composit Monopole Pair | Inverse Chrenkov limit
2 Electron 1 .511 MeV 0 .511 MeV Table reference Mass
1 ATOM 1/32 16 Kev -0.122% 15.82~ Smallest monopole Quantum = 67Kev/P^3 .


The Fifth Dimensional nature of MASS and Energy is conclusively revealed by this "N over two to the fifth power" law;
it maps the entire range of Mass from 16 Kev to 127 Gev.

This seems to be to be a QED example of "Dimensional Analysis" in a literal sense!

Each interior node maps a significant stable particle family identity; QED.

When the Electron mass is used as a standard density for MASS,
this fifth power law proves that each of the N/2 nodes approximates that same density
as evidenced by the stable particle mass family therein.

This theory answers the question of the Proton to Electron mass ratio quite elegantly
and provides insight into particle families over their entire range.

Noted also, is the negative sign of most table error values, suggesting "a missing mass" factor,
not unlike that found in nuclear mass deficits to reflect a binding energy component.
Since the nodes mark volumetric sizes/capacities; the negative error sign signals no overflow.

Also noted was that Quarks, Gluons, or Strings were not evident or needed
to explain this fifth powered Colorless order of particle masses!

The LHC Higgs candidate

In July 2012, CERN announced it had a Higgs final candidate near 125 GeV; this value is also index 24 of 5SPACE.

In the 5SPACE muon and pion derivation,
the concept of table 'N' having a range of 12 with a midpoint at 6,
was used successfully to calculate their actual mass.

This LHC Higgs data supports this significantly when one sees 24/2 as 12;
making for a solid 'N' series of 6, 12 and 24 at ratios of ( 1/2, 1, 2 )!

5SPACE explicitly validates the Higgs as the upper limit of particle mass without requiring mass to be Higgs generated.

-------- All assumptions are satisfied! --------Mass's Fifth power identity is firmly established.

The model's data proves that space is indeed Five Dimensional at the particle scale,
just as K&K proved it for GR!

Table of Contents


Particle Mass is still complex, but seeing it geometrically as fifth power nodes,
seems like the place to start unraveling its structures!

Giving every main particle a fifth power index in the N/2 form reveals mass steps and zone families.
eg. the 10/2 zone had Omega and Tau, the 8/2 zone has the Eta and Kaon.

What does it all mean? Aside from it being an extremely improbable coincidence,
this N/2 formula indicates that the fifth dimension is fundamental to Mass;
just as the Klauza-Klein's work did with Einstein's GR Physics.

One way to think of the indices is that they represent volume zones where energy can condense to a solid Mass.

The 16 Kev minimum value would represent the smallest zone or ATOM,
and a monopole that was half of a 32 Kev pair of opposite poles.

The PMF represents energy in a common geometrical packing factor of some form;
which is much simpler than other mass theories such as Quark or String theory.


Can it all be so simple ?
D5 as Mass and Energy,
D4 as TIME,
D3 as Volume,
D2 as Area
and Dimension 1 as Length or Width!

Why not; the simplest answer usually proves best over time?

These "(N/2)^5" insights should allow many other theories like Dark Matter to be fine-tuned by their authors.

Another interesting area is the Cherenkov radiation's 3.88 MeV spectrum; which is quite close to the (3/2)^5 node.

Analyses of the (3/2)^5 node revealed resonances at 121 KeV and 134 KeV;
which match the values found from the decay of Cobalt-57 to Iron-57
in the original experiments of Mossbauer spectroscopy.

Given these resonances, The (3/2)^5 mass node became the foundation for an
"Aether Theory";
that is based on the 3.7 MeV Cherenkov radiation being the value for an Aether node mass.

Another insight of 134 KeV comes from PHOTO-NUCLEAR data

Comments are welcome.
Table of Contents


Appendix PMF ; "The Particle Mass Factor".
The Statistics of Particle Mass; its common denominator is 17.5 MeV

Particle Muon Pion Kaon Rho  Proton Sigma Lamda Chi Omega
MeV 105.66 139.57 493.7 770 938.27 1189.4 1115 1314.8 1673
/17.5MeV 6~ 8~ 28~ 44~ 54~ 68~ 64~ 76~ 96~
PMF / 2 3 4 14 22 27 34 32 38 48

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LINKS & References

Observation of inverse Cherenkov acceleration at the BNL accelerator test facility
W. D. Kimura, G. H. Kim, R. D. Romea, L. C. Steinhauer, I. Pogorelsky, K. P. Kusche, R. C. Fernow, Xijie Wang, and Y. Liu,
AIP Conf. Proc. 335, 131 (1995), DOI:10.1063/1.48236

Official Mass values.

1995 ICA paper at BNL

134 Kev from PHOTO-NUCLEAR data

author: RD O'Meara Oak Park, IL.

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

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

Primes3D: A Construction Proof of Prime Numbers having a cubic Nature.

JID's SLOPE: The Universal Slope of Volume,
both Mathematically and Physically   AKA, the Rydberg constant of 1.0973~!

Short proof of Fermat's FLT: A proof based on power sequences infinite transcendental Logs.

Monopole Aether Theory: A Classical model of the Aether based on paired monopoles.


My Real interests are in computer science.
I have spent my career as a cybernetic engineer/designer
who is concerned about the future of our digital data.

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especially in the areas of forgery and security, for data and their time stamps.

In that vein, I am seeking venture capital for my NEW multi-Computer
Distributed Kernel SECURITY Architecture or 'DSA' ; based on
Posopip: a 3CPU template that inherently guarantees Trust & Fidelity.

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