**CHAPTER 4: A SEMI-CLASSICAL CALCULATION REGARDING PROTON-RADIUS**

**by Mark Creek-water Dorazio, ApE (amateur physics enthusiast);**

**email: MARK.CREEKWATER@gmail.com**

**“It seems obvious to me … that having two incompatible theories of nature is intellectually intolerable” —–LEONARD SUSSKIND [book: The Blackhole War (2008)]**

Following Dr. ERNEST STERNGLASS **[Ref.#1]**, one can visualize the PROTON as composed of four ELECTRON-POSITRON PAIRs [ep-pairs] and an UNPAIRED POSITRON-AT-THE-CENTER … Using this model, and Sternglass’s “semi-classical” math approach, one can calculate a theoretical numeric value which agrees closely with the results of experiments which have been done to determine the proton’s radius … [approx. 8.7 x 10^(-14) cm] …

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

Sternglass 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. #18 + #19]** he describes a scenario in which the electromagnetic field of this hypothetical “primeval atom” —(WHOSE EM-FIELD INITIALLY CONTAINED ALL THE MASS/ENERGY IN OUR UNIVERSE !!)— divides in half, and each of the pieces divides in half, and so on and so on …

After only 270 generations of such a process, there would be 2^270 tiny pieces, each with the mass of approximately 5ive [5] neutrons … **Note: 2^(270) is a very very large number: more than a trillion trillion trillion trillion trillion trillion !!**

Shifting to the present tense: at the end of the divide-in-half scenario (which I call “the count-down to the Big Bang”), there is a “PHASE TRANSITION” [Sternglass’s words, P.11, **Ref.#1**] in which many trillions of the tiny pieces of the primeval atom re-configure, in a way which leads to the production of many trillions of neutrons, most of which quickly “decay” —producing protons … Many trillions of protons + neutrons emerge 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” …

Thus Sternglass explains both the “Big Bang” and the formation of all the protons + neutrons which now exist …

**Here is the math-formula, derived from Sternglass’s “Table 1”: **

**( Rs) = [ 2G / c^2 ] x [ ( Mu x Ms )^(1/2) ] x [1/137.036] [EQN.#1],**

where **“ Rs”** is the radius of the system’s torus-[donut]-shaped electromagnetic field, which I will call the “SYSTEM RADIUS”;

**NOTE1: ( Mu x Ms )^(1/2) means “the square-root of ( Mu x Ms )” …**

**NOTE2: this is a modified “Schwarzschild equation” (google it if you need to), in which the “local gravity” inside a system is much stronger than “Newton’s gravity” … More re “local gravity” in CHAPTER 10 …**

**NOTE3: 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: inspired by PAUL DIRAC’s so called **“large numbers hypothesis” [p.224, Ref.#18; pp.73-76, Ref.#19]** Sternglass uses a similar hypothesis to derive an ingenious way to calculate, theoretically, the mass of our universe, and details how he did this in his book **[Ref.#1]** … More regarding this, below …

**COMPTON WAVELENGTH 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 WAVELENGTH” associated with every object which a physicist might want to study; defined as the wavelength 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 wavelength divided by (2x(

where

In Sternglass’s model there is initially only ONE “cosmological system” — the “primeval atom” … Because its mass/energy content is so large —(BEING THAT OF OUR ENTIRE UNIVERSE !!)— its ** Rc ** is ridiculously small: because more energetic photons are smaller … As the divide-in-half scenario proceeds, the masses of the systems, and the sizes of their EM-fields,

At some point in the divide-in-half scenario, the size of the Compton radius must equal that of the system radius — the **“ Rs”** in equation #1 … One can use easy maths to calculate both the mass (

By definition, one has:

*Rc*** = ( ***h-BAR ***) / ( ***c*** x ***Ms*** )**, **[EQN.#2],**

where **“ Rc”** is Compton radius and

Equating this

Solving this equation for

**MASS OF OUR UNIVERSE ??**

Sternglass’s formula for mass of universe appears on p.265 {careful: there’s a TYPO (typographical error) in the book} in **[Ref.#1]** as:

**(***Mu***) = [ [ ***K*** x ***Qe* x Qe ]^2 ] **/ [ ***G^2 ***x (***Me***)^3 ]**, where *“Me”* is the mass of an electron; *“Qe” *is the electric charge of an electron;* **“K” *is Coulomb’s electrostatic constant; and *“G”* is Newton’s gravitational constant …

Rearranging this, to make it look more 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,** which is approx. 100x greater than the mass of our universe which one usually sees in books + papers + essays: this is

Using this expression for ** Mu** in

**NOTE: ** the** “^(2/3)” **at the end means that one **squares **the whole thing, then calculates the **cube-root **of that …

Using numeric values *c *= 2.9979 x 10^(10) cm/sec, *h-BAR* = 1.0546 x 10^(-27) gram.(cm/sec).cm, *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 x 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 pi-mesons and one 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., equal to its so called “Compton radius” [Rc] …**

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

**(***Rc***) = (***Rs***) = (***h-BAR***) / ( (***c***)x(***Ms***) ) =
[1.0546 x 10^(-27) gram.(cm/sec).cm] / [ (2.9979 x 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: the numeric value (8.677 x 10^(-14) cm) was calculated theoretically, in a “semi-classical” way, from Sternglass’s model, using none of the fiendishly difficult maths for which quantum mechanics is famous …

**======================================**

Regarding the calculated mass, (*Ms*) = 4.0543 x 10^(-25) gram: what might this be ?? Well, in Sternglass’s model, the proton consists of four [4] electron-positron pairs, and an unpaired positron-at-the-center **[p.250, Ref.#1**] …

Perhaps each of these 4 [four] ep-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 **[Ref.#20]** } might actually be measurements of the radius of this particular {[pun-intended]} Sternglass cosmological system whose COMPTON radius ** [Rc]** just happens to be equal to its SYSTEM radius

PERHAPs THIS IS WHY PROTONs ARE SO STABLE ???

**$$$$$$$$$$$$$$ << END OF CHAPTER 4 >> $$$$$$$$$$$$$$**

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