**APPENDIX9: SIZE OF THE EPOLA-ELEMENTs (refers to the discussion in CHAPTER 2)**

In my re-visualization of Sternglass’s and Simhony’s models, there is a numeric value re the epo-lattice which I need to explain: the SIZE of the elements which compose the epola; i.e., the size of the epola-elementss … In **CHAPTER 2,** I mention that epola-elements are much smaller than proton-elements, and more dense: here are some details re why I say this …

Using only easy maths, (i.e., “high-school algebra”), one can derive the size and mass and mass density of an epola-element from Dr. Sternglass’s **“Table 1” **— which appears on **p.234** of his book **[Ref.#1] **… **In my opinion, “Table 1” might be one of Sternglass’s most important and significant contributions to our knowledge + understanding re how our universe works: this is because in Table 1 Sternglass details mass and size data of a kind of substance which other theorists only HINT at …**

For example, many years ago, the creative + far ranging imagination of Dr. JOHN ARCHIBALD WHEELER enabled him to come up with the concept of a kind of object which contains **“matter without matter”** as he stated it … He called these rascals **“GEONs”** — and described them as follows: “in the geon paper [published during 1955] … I concluded that the smallest ‘purely classical’ geon (a geon for which quantum effects could be ignored) was a donut the size of the sun with a mass of about a million suns … the equivalent mass of the electromagnetic energy coursing around the donut racetrack … ‘matter without matter’ in the sense that it relies on no material particles … larger geons were in principle possible, I found, up to the size of the universe” **[p.237, Ref.#24] **…

Similarly, in his “Table 1”, Sternglass lists masses and sizes, (and rotational periods, too), of “cosmological-systems” [“cosmo.systs”] which contain no protons or neutrons, i.e. “no material particles” … Instead, each consists of nothing but the electromagnetic field energy of a single electron-positron pair, which can be of ANY size, and ANY mass, up to that of our universe [“the primeval-atom”] **[p.175, Ref.#1] **…

**One of my first (!!AHA!!)-moments after I started studying Sternglass’s book came to me when I noticed that, if one extend “Table 1” a bit farther than it appears in the book, down into the part which Sternglass would call “stage 28”, then one finds there a place for a cosmo.syst whose mass is that of a single electron, and whose radius would be approx. 5.6 x 10^(-13) cm, that “special” numeric value, already mentioned near the end of CHAPTER 6 … Except that Sternglass says that the tiny systems in this part of Table 1 experience a “relativistic shrinkage” (by a factor of approx. 137; i.e., “the inverse of the fine-structure constant”), which reduces the theoretical size of the radius to the very tiny size of only approx. 4.11 x 10^(-15) cm (i.e., to approx. 4.11 x 10^(-17) meter) … This is MUCH smaller than a proton …**

But the **“!!AHA!!” **did not come immediately: in fact, for several years I puzzled re what might be the significance of this, during which time I “discovered” the work of Dr.Simhony **[Refs.#2, 2a, 2b, 2c] **… The **“AHA” **came when I realized that this particular (pun intended) “cosmo.syst” in Sternglass’s model, and the individual “epola-element” in Simhony’s model, might be one and the same … **I.e., that these 2 gentlemen, who never collaborated with each other, might have independently identified the most common kind of object in our universe: because, as already mentioned, epola-elements are everywhere in our universe, while “ordinary” objects (mainly protons + neutrons) are, by comparison, very few and far between … **

**So, if I’m correct in my interpretation of Sternglass + Simhony, the EPOLA-ELEMENT is, by far, the MOST COMMON kind of object in our universe …**

**DETAILS OF THE CALCULATION**

From data in Sternglass’s “Table 1” **[p.234, Ref.#1]** one can derive a math-formula for the radius of a small “cosmological system” (cosmo.syst) in terms of the system’s mass:

**R = {2 x G x [Ms x Mu]^(1/2)} / {c^2 x 137.036}, **where “R” is the system’s radius, “G” is Newton’s gravitational constant, “Ms” is the mass of the system, “Mu” is the mass of our universe, and “c” is the speed of light.

Note1: this is a modified “Schwarzschild formula”, in which one uses the “local gravity” which prevails inside of a cosmo.syst, which is much stronger than Newton’s gravity. A full discussion and explanation of this idea appears in **Ref. #1. **

Note2: the **“^(1.2)” **in the formula means that one calculates the square-root of [Ms x Mu].

Note3: Sternglass says that the tiny cosmo.systs experience a “relativistic shrinkage” by a factor of approx. 137, (the so called “inverse of the fine-structure constant”), which accounts for the presence of that number in the formula.

{[ In his book [**Ref.#1]** Sternglass describes how he derived an elegant way to calculate a theoretical numeric value for the mass of our universe. According to this, he calculates that our universe weighs in at approximately 1.58 x 10^(58) grams, which is approximately 100 times the numeric value which appears in some of the books and papers which address this subject, reflecting the idea that approximately 99% of our universe’s mass might be in the form of so called “dark matter” ]}

Using that numeric value for “Mu”, and the mass of the electron [9.11 x 10^(-28) gram] for “Ms”, and 6.7 x 10^(-8) cm.cm.cm/gram.sec for “G”, and 3 x 10^(10) cm/sec for “c”, the formula gives, ** 4.1 x 10^(-15) cm** [i.e., 4.1 x 10^(-17) meter] as the radius of the cosmo.syst in Sternglass’s model whose mass is the rest-mass of an electron. This is how I calculated a theoretical numeric value for the size of the epola-elements in Simhony’s model, on the assumptions (1) that epola-elements are in fact tiny Sternglass cosmo.systs, and (2) that their mass is that of an electron, as Simhony says.

**$$$$$$$$$$$ << END OF APPENDIX9 >> $$$$$$$$$$$**

**~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~**

**APPENDIX10: IF PHOTONs ARE WAVEs, THEN WHY DO THEY NOT SPREAD OUT ??**

This discussion, the very last in this series of essays, refers back to two little details, one in the **INTRODUCTIONs** section, and one in the** AFTER-WORDs **section …

IN the **INTRODUCTIONs **section I suggest that photons are waves, (i.e., vibrations of the elements which compose the epo-lattice), but waves of a very special kind, because (as is already known, yet still considered a MYSTERY) they travel from place to place without spreading out, like little bullets … In the **AFTER-WORDs **section I say that one can visualize the epo-lattice as if it be composed of very very long and very very narrow, BAR MAGNETs, each of which represents a line of magnetic force, and that these align in three [3] mutually-perpendicular orientations … PLUS: I say that, if this is true, then one would expect perpendicular lines of magnetic force to IGNORE each other, like 2 bar magnets ignore each other when one holds them perpendicular to each other …

{ Actually, perpendicular bar magnets experience a TORQUE force, which makes them try to rotate 90 degrees (i.e., 1/4 of a full circle) to align with each other, but they do not experience any attraction TOWARD each other … One can verify this by playing with little toy bar magnets } …

Visualizing the EPOLA in Dr.Simhony’s model as a collection of very long + very narrow mutually-perpendicular bar magnets, I have a feeling that this interesting set of mag’ical [magnetical] circumstances might be the source of an explanation for why the energy content of a photon does not spread out as it travels thru space; but, alas, this is ONLY A FEELING … I’m almost ashamed to include it in this essay, but feel, intuitively, that it might be true … So I include it here as ONLY A SUGGESTION, and admit that it’s a VERY SPECULATIVE suggestion, and might be not true …

However, it it turns out to be true, then I hope to receive a nomination for a Nobel prize in physics … If I live long-enough, that is … As one can say: “OY-VEH: I SHOULD LIVE SO LONG” …..

Sincere-ly, Mark Creek-water Dorazio, ApE (amateur physics enthusiast), age-67, 12-APRIL-2015, Briarcliff Manor, NY, USA, email: MARK.CREEKWATER@gmail.com …..

**$$$$$$$$$$$$$$$$$ << END OF BOOK >> $$$$$$$$$$$$$$$$$**

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