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. {Most of these have given a numeric value of approx. 8.7 x 10^(-14) cm for proton-radius [e.g., **Ref. 20**].}

Plus, 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.

Sternglass **[Ref. #1]** has developed a model which accounts for the origin of protons and neutrons in our universe, and describes their structure. Starting with the “primeval atom” hypothesis of Georges Lemaitre **[Refs.#18, #19]** he describes a scenario in which the rotating electromagnetic field of this hypothetical “primeval atom” —(whose electromagnetic field initially contained all the mass and 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 divide-in-half process, there would be 2^270 tiny pieces, each with the mass of approximately 5 neutrons.

{ Note: 2^(270) is a very very large number: more than a trillion trillion trillion trillion trillion trillion !! }

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 of the primeval atom re-configured, in a way which led to the production of many zillions of protons and neutrons 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 high-energy photons [“gamma rays”]; enough energy to power a “big bang”.

Sternglass compares this phase transition to the phase transition which happens when water freezes, a process which releases energy (binding energy), the same amount of energy which is needed to melt the ice. Likewise the phase transition which happened at the start of the big bang released a very very large amount of energy, as zillions of sub-atomic sized objects re-configured, forming neutrons, most of which quickly “decayed” — producing protons.

Thus Sternglass’s model explains both the Big Bang and the formation of all the protons + neutrons which now exist.

Using data from Sternglass’s “Table 1″ **[p.234, Ref. 1],** one can derive a math formula (below) for the radius of each of the many differently-sized “cosmological systems” which participate in the divide-in-half scenario. Sternglass calls these objects “cosmological systems”, regardless of their size **[p.234, Ref. 1],** and says that **“For every system, the mass is proportional to the square of the radius” [p.225, Ref. 1].**

Here is the math formula:

where *“Rs”* is the radius of the system’s torus-[donut]-shaped, rotating, electromagnetic field, which I will call the **“system-radius”; ** *“G” *is Newton’s gravitational constant; *“c”* is speed-of-light; *“Mu”* is the mass of our universe; * “Ms”* is the mass of the system; [1/137.036] is the so called “fine-structure constant”, and “^(1/2)” means that one calculates the square root of [*(Mu)* (Ms)].

Please note that this is a modified “Schwarzschild formula”, in which the “local gravity” is greatly increased, according to Sternglass’s theory. (More details in **CHAPTER 10.**) Note also that 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.

Note: after I “discovered” Simhony’s model **[Ref.#2], **I realized that the reason **why **the little rascals shrink is because they “want” to go inside an epola-cell. This idea coincides with Sternglass’s idea that the cosmo.syst at the place in Table 1 which he calls “stage 27” is very special. With a mass of approx. 8.33 x 10^(-24) gram, (almost exactly that of 5 protons), it’s mid-way between the mass of a **J/psi meson** and that of an **upsilon meson,** which physicists discovered during 1974 and 1977, respectively, as Sternglass details in **Ref.#1. **Please **google** these mesons if you want or need to.

Table 1 gives the radius of the cosmo.syst at “stage 27” as approx. 5.4 x 10^(-11) cm: if one shrinks this by a factor of 137.036 [the inverse of the fine-structure constant], then one finds that its radius is approx. 3.94 x 10^(-13) cm, just right to fit inside an epola-cell.

Inspired by Paul Dirac’s so called “large numbers hypothesis”** [p.224, Ref. 18; pp.73-76, Ref. 19], **Sternglass derived an ingenious way to calculate the mass of our universe, theoretically. More regarding this, below.

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:

where *“h”* is Planck’s constant, *“c”* is the speed-of-light, and *“M”* is the object’s mass.

Likewise, the Compton radius is just simply the Compton wave-length divided by [2(pi)]:

where *“Rc”* is Compton-radius and *“h-BAR” * is (Planck’s constant) / (2(pi)).

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, {which I call “the count-down to the Big Bang”}, the masses of the systems, and the sizes of their electromagnetic fields, decrease, while their Compton-radii increase: after 270 divide-in-half generations, there are many trillions of tiny systems, and the length of the *COMPTON-radius* *[Rc]** * of each tiny system is almost equal to that of its **SYSTEM-radius [Rc].**

At some point during this “count-down”, the size of the Compton-radius must equal that of the system-radius — the *“Rs”* in Eqn. 1. One can use easy maths to calculate both the mass *(Ms)* and radius *(Rs)* of the system whose system-radius *(Rs)* equals its compton-radius *(Rc).*

By definition, one has:

** ***Rc = [h-BAR] / [(c) (Ms)], * (Eqn. 2b),

where *“Rc”* is Compton-radius and *“Ms”* is mass-of-system.

Equating this *(Rc)* to the *(Rs)* in Eqn. 1, one has:

Solving this equation for (Ms):

Sternglass’s formula for the mass of our universe, (using the identity **e^2) = **

where *“K”* is Coulomb’s famous electrostatic constant; *“Qe” *is the electrical charge of an electron;* **“G”* is Newton’s famous gravitational constant; and *“Me” *is the gravitational mass of an electron.

Re-arrangeing this, to make it more beautiful and “elegant”:

{NOTE: this expression 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 and papers and essays which address this subject. This is **“consistent with the evidence that only about one percent of the mass of the universe is in visible form” [p.210, Ref.1]**}

Inserting this expression for *(Mu)* into Eqn. 3, one has: *(Ms) * =

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 Qe Qe] = 2.3071 x 10^(-19) (gram.cm^3)/sec^2 ; one calculates that

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., the system’s so-called “Compton-radius” *[Rc]*.

One can now use Eqn. 2b to calculate this radius:

Note #1: this is very close to the **measured** “radius of the proton”, which many teams of experimental physicists 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 [Ref. 3].

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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

As for 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] 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 *[Rs]* ??

PERHAPs THIS IS WHY PROTONs ARE SO STABLE ???

Using only Sternglass’s model, and some of his numbers, one can solve two easy algebraic equations [Eqns. #1 and #2b, above] simultaneously, to calculate theoretical values for the mass and the radius of one of the four [4] electron-positron pairs which constitute most of the proton’s mass in Sternglass’s proton model. The calculated numeric value for radius given by this method is very near to that of the “proton-radius” —– as measured by many teams of experimental physicists during the past 50 years. One suspects the possibility that the experimenters might have been measuring the radius of one of the four ep-pairs assumed by Sternglass to be inside protons, rather than that of the entire proton.

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

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