**A SEMI-CLASSICAL CALCULATION RE PROTON-RADIUS**

by Mark Creek-water Dorazio, Amateur-Physics-Enthusiast; MARK.CREEKWATER@gmail.com

**SUMMARY: **Following DR. ERNEST STERNGLASS **[Refs. 1 + 2]**, one can visualize the PROTON as composed of four ELECTRON-POSITRON PAIRs [ep-pairs] and an UNPAIR’D POSITRON AT THE CENTER … using this model, and Sternglass’s “semi-classical” math approach, one can calculate a THEORETICAL numeric value which agrees close ly with the results of experiments which have been done to determine the proton’s radius; {Most of these have given a numeric value of approx. 8.7 x 10^(-14) cm for proton-radius **[e.g., Ref. 3]**} …

ADDITIONALLY, one can propose that this numeric value is **NOT** a measure of the entire proton’s radius, but of the radius of one of the four [4] ep-pairs in Sternglass’s proton-model …

**TEXT: **Sternglass **[Ref. 1]** has developed a model which accounts for the origin of PROTONs + NEUTRONs in our universe, and describes their structure …

Using the “PRIMEVAL ATOM” hypothesis of GEORGES LeMAITRE **[Refs. 4 + 5]** he describes a scenario in which the rotating electromagnetic field of this hypothetical “primeval atom” —(WHOSE EM FIELD INITIALLY CONTAINED ALL THE MASS/ENERGY IN OUR UNIVERSE)— divided in half, and each of the pieces divided in half, and so on and so forth …

AFTER ONLY 270 GENERATIONs of such a process, there would be 2^270 tiny pieces, each with the mass of APPROX. 5 NEUTRONs … At this point, or soon after, there was a “PHASE TRANSITION” [Sternglass’s words, P.11, **Ref. 1**] in which many zillions of the tiny pieces re-configured, in a way which led to the production of zilions of NEUTRONs, SOME of which quickly “DECAYED” —producing PROTONs … Many zillions of protons + neutrons emerged from this process, during the last “stage” [Sternglass’s word] of the long divide-in-half scenario, with the release of very large amounts of ENERGY, in the form of hi-energy PHOTONs [“gamma rays”]; enough energy to power a “BIG BANG”, if in fact such a “big bang” ever happened …

… THUS STERNGLASS EXPLAINs both the “BIG BANG” and the formation of all the PROTONs + NEUTRONs which now exist …

**Here is the math formula: (Rs) = [ 2G / c^2 ] x [ ( Mu x Ms )^(1/2) ] x [ 1 / 137.036 ] … [EQN. #1], **where

Please note that this is a modified “Schwarzschild-formula”, in which the “local gravity” is greatly increased, according to Sternglass’s theory, which he details in his BOOK **[Ref.#1] **…

{ Sternglass says that the tiny systems near the last stage of the long divide-in-half scenario experience a “RELATIVISTIC SHRINKAGE” by a factor of approx. (137.036), which explains the presence of that number in the formula } …

Re the mass of our universe, Sternglass uses PAUL DIRAC’s so called “LARGE NUMBERs HYPOTHESIS” [p.224, **Ref. 4**; pp.73-76, **Ref. 5**] to derive an ingenious way to calculate it … More regarding this, below …

**COMPTON WAVE-LENGTH AND COMPTON-RADIUS**

The physicist ARTHUR COMPTON, during the first half of the 20th century, popularized the idea that there is a so called “COMPTON WAVE-LENGTH” associated with every object which a physicist might want to study; defined as the wave-length of a PHOTON whose ENERGY CONTENT is equivalent to that of the object, and given by a simple math formula:

**(***WL-compton)*** = (***h***) / ( ***c ***x ***M ***)**,

where **“ h”** IS Planck’s-constant,

Likewise, the COMPTON-RADIUS is just simply the Compton wave-length divided by [2x(

where “

In Sternglass’s model there is initially only ONE “cosmological system” — the “PRIMEVAL-ATOM” … Because its mass/energy content so large —(BEING THAT OF OUR ENTIRE UNIVERSE !!)— its **Rc ** is ridiculously small: because smaller photons contain more energy … As the divide-in-half scenario proceeds, the masses of the systems, and the sizes of their em-fields, DECREASE, while their Compton-radii INCREASE: after 270 divide-in-half generations, there are many trillions of tiny systems, and the SYSTEM-radius

AT SOME POINT, the size of the Compton-radius must equal that of the system-radius — the **“ Rs”** in

One can use easy maths to calculate both the mass

where

Equating this

Solving this equation for (

**MASS-OF-UNIVERSE ??**

Sternglass’s formula for the mass of our universe, (neglecting a TYPO in the the book, and using the identity **e^2 = K x Qe x Qe**), appears on p.265, **Ref. 1,** as:

**(***Mu***) = [ [ ***K*** x ***Qe* x Qe ]^2 ] **/ [ ***G^2 ***x (***Me***)^3 ]**, where ** “Me”** is the mass of an electron;

Re-arrangeing this, to make it more beautiful + “elegant”: **(***Mu***) = [ { ( ***K*** x ***Qe x Qe*** ) / ( ***G*** x ***Me x Me*** ) }^2 ] x [***Me***] … [EQN. #4];**

[NOTE: this gives a numeric value of (*Mu*) = approx. 1.581 x 10^58 grams] …

Using this expression for **( Mu)** In

**NOTE: **the “**^(2/3)**” at the end means that one **squares **the entire expression and then calculates the** cube-root **of the result …

Using numeric values, *c *= 2.9979 x 10^(10) cm/sec, *h-BAR* = 1.0546 x 10^(-27) gram.cm.cm/sec, *G* = 6.673 x 10^(-8) cm^3 / gram.sec^2, (*Me*) = 9.1094 x 10^(-28) gram, and (*K* x *Qe x Qe*) = 2.3071×10^(-19) (gram.cm^3)/sec^2 ;

one calculates that **(***Ms***) = 4.0543 x 10^(-25) gram** …

**NOTE:** this mass is somewhere between that of two [2] pi-mesons and one [1] pi-meson: it’s the theoretical mass of the “COSMOLOGICAL SYSTEM” in Sternglass’s model whose SYSTEM-RADIUS [*Rs*] is equal to the radius of a photon which contains the same amount of energy; i.e., the system’s so called “COMPTON-RADIUS” [*Rc*] …

One can now use **EQN. #2** to calculate this radius:

**(***Rc***) = (***Rs***) = (***h-BAR***) / ( (***c***)x(***Ms***) ) =
[1.0546×10^(-27) gram.cm.cm/sec] / [ (2.9979×10^(10) cm/sec) x (4.0543 x 10^(-25) gram) ] = 8.677 x 10^(-14) cm …
**NOTE #1: this is very close to the MEASURED “radius of the proton”, which experiments have determined, by a variety of methods, to be somewhere in the neighborhood of between approx. 8.42 x 10^(-14) cm AND 8.97 x 10^(-14) cm

NOTE #2: by this method, one calculates the numeric value [8.677 x 10^(-14) cm] in a “SEMI-CLASSICAL” way, FROM STERNGLASS’s MODEL, using none of the fiendishly difficult maths for which quantum mechanics is famous …

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As for the calculated mass, (

Well, in Sternglass’s model, THE PROTON consists of four [4] electron-positron pairs, and an unpaired positron at the center [p.250,

Perhaps each of these 4 [four] pairs has a mass of approx. 4.0543 x 10^(-25) gram, and a radius of approx. 8.677 x 10^(-14) cm ??

CONSIDER: 4 x [4.0543 x 10^(-25) gram] = 16.217 x 10^(-25) gram = 1.6217 x 10^(-24) gram, WHICH IS ALMOST THE KNOWN MASS OF THE PROTON !! Perhaps the positron at the center provides the remaining mass ??

PERHAPs the “PROTON-RADIUS” which experiments determine to be approx. 8.7 x 10^(-14) cm { CODATA VALUE IS GIVEN AS APPROX. 8.768 x 10^(-14) cm

PERHAPs THIS IS WHY PROTONs ARE SO STABLE ???

**REFERENCEs**

1) Sternglass, Ernest; 1997, **Before the Big Bang,** NewYork, Four Walls Eight Windows;

2) Sternglass, Ernest; 1961, “Relativistic Electron-pair Systems and the Structure of Neutral Mesons”, **Phys Rev** (v.123) pp. 391-398, (July 1, 1961);

3) Antognini, A., + others; 2011, “The Proton Radius Puzzle”, **Journal of Physics: Conference Series,** (v.312, n.3);

4) Kragh, Helge; 1990, **Dirac: a Scientific Biography** Cambridge, Cambridge University Press;

5) Dirac, Paul; 1978, **Directions in Physics, **NewYork, John Wiley & Sons;

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