**CHAPTER 6: LATTICE-LENGTH OF THE EPOLA-CELL**

**“‘Son, if I could remember the names of all these particles, then I would have been a BOTANIST'” —– Enrico Fermi, to a physics grad student**

In his “Electron-Positron Lattice Model of Space” **[Refs. #2, 2a, 2b, 2c],** **Dr. Menahem Simhony **says that there is an aether-like substance everywhere in our universe, which carries all the different kinds of **electromagnetic radiations** which travel thru space, and which is also responsible for the existence of **gravity.** He would prefer that we call this stuff **“EPOLA”** —(short for **“electron-positron lattice”)—** rather than “aether” or “ether”. Why?? because, unlike the “aether” of 19th century scientists, Simhony’s “epola” is not thin, and not wispy, or “aetheric”, or “aethereal”: info on one of Dr. Simhony’s web-sites says that it’s “stiffer than a diamond.” More re this later.

**{ Please note that there is no contradiction between the words “stiff” and “elastic”: i.e., a substance can be both “stiff” and “elastic”: e.g., billiard-balls }**

Simhony says that the “epola” consists of nothing but electrons + positrons, and that its structure is perfectly cubical, [“face-centered cubic”], like ordinary table salt. He says that its **lattice length (LL),** (the distance between an epola-element and its nearest neighbor), is approximately 4.42 x 10^(-13) cm [4.42 x 10^(-15) meter]. In modifying Simhony’s model, I’ve calculated a (LL) of approx. 7.615 x 10^(-13) cm —– almost twice as large … Why?? Because I’ve borrowed some ideas from **Dr. Ernest Sternglass [Refs.#1, 1a],** whose **“electron-positron pair model of matter”** is, in my opinion, a major advance in our understanding of nature, as is Simhony’s model, the **“electron-positron lattice model of space.”**

Inspired by Paul Dirac’s so called **large numbers hypothesis** {one can go to http://www.GOOGLE.com for details}, Sternglass hypothesizes that the ratio of **the strength of the electrical attraction between an electron and a positron to the strength of the gravitational attraction between** **the same two little rascals** might be equal to the square root of the ratio [(Mu) / (Me)], where “Mu” is the mass of our universe, and “Me” is the mass of an electron (or positron) [p.265, **Ref.#1** — be careful: there’s a typographical error in the book].

How does he presume to know the mass of our universe ?? Well, in his book he explains how he derived an elegant way to calculate this huge numeric value, theoretically, based on a slight variation of Dirac’s “large numbers hypothesis” — mentioned above … **[Refs. #18 + #19]. ** **{[ more details in APPENDIX3 ]}**

It’s well known that the strength of the electrical attractions between electrically charged tiny objects in our universe is much much greater than the strength of their gravitational attractions. Some book writers, when they mention this, use the electron and the proton to illustrate the idea, using the simple math formulas from Physics-101 to calculate the ratio between electrical and gravitational attraction. But Sternglass uses the electron and the positron —(not the proton)— to illustrate this idea, and to calculate the mass of our universe. **“I decided to see what [Dirac’s] numbers would give for the mass of the universe if the basic particles were the electron and positron rather than the proton and anti-proton” [p.210, Ref.#1].**

In this way he calculates a ratio of 4.167 x 10^(42) as the ratio mentioned above, re the electrical attraction –vs– the gravitational attraction between an electron and a positron. That’s a very large number: 4,176, with 39 zeros after it. Following Dirac, he squares this very large number, and gets 1.736 x 10^(85), (obviously a much much larger number), and hypothesizes that this might represent the ratio (mass of our universe) / (mass of one electron): this allows him to calculate a theoretical numeric value for the mass of our universe: approximately 1.58 x 10^58 grams.

Knowing all this from my reading of Sternglass’s book **[Ref.#1]** inspired me to try something similar for the epo-lattice in Simhony’s model: ** “What if”, I asked myself, “the EPOLA (“electron-positron lattice”) in Simhony’s model [Ref.#2] is real, and what if the ratio [(amount of “EPOLA” stuff) / (amount of “ORDINARY” stuff)] in our universe is related to the ratio [(Mu) / (Me)] ??”**

Epola stuff is everywhere in our universe, while bits of ordinary stuff, (composed mostly of protons and neutrons, by weight), are, by comparison, few and far between. So the total amount of epola stuff is much much greater than the total amount of ordinary stuff. Sternglass’s theoretical calculation for mass of our universe, already mentioned, gives Mu = 1.581 x 10^(58) grams [p.210, **Ref.#1**]: the mass of one electron is well known to be approx. 9.1094 x 10(-28) gram: the ratio of these two numbers is approx. 1.736 x 10^(85): the square-root of this is approx. 4.167 x 10^(42). If the total mass of epola stuff is 4.167 x 10^(42) times the total mass of ordinary stuff in our universe, then one can calculate a (**NEW!!**) theoretical lattice-length for the epola. And the maths are easy: no calculus needed !!

First one calculates the hypothethcal **total mass of epola stuff** as [4.167 x 10^(42)] x [1.581 x 10^(58) grams] = [6.588×10^(100) grams]. ** {The mass in this calculation is Sternglass’s theoretical mass of ordinary stuff in our universe, as already mentioned }.** If each of the elements which compose the epola (i.e., the epo-lattice) has exactly the mass of one electron (or positron), as Simhony says, then the number of epola-cells in our universe must be approx. [6.588 x 10^(100)grams] / [9.1094 x 10(-28) gram] = 7.232 x 10^(127), a very very large number**.**

**{[ NOTE that a similar very large number comes up in a calculation which Dr. Leonard Susskind details in his book THE BLACK HOLE WAR (2008), pages 150-155, where he describes a calculation re “Bekenstein-Hawking entropy”, if one does that calculation for the entire universe ]}**

Using Sternglass’s numbers **[Table 1, p.234, Ref.#1]**, and my visualization of the ultimate boundary *******(see **NOTE1** below) of our universe as of a torus [donut] shape, one has: (total volume of our universe) = {* [ (pi) x (pi) x (Ru)^3 ] / 4 }* = [ 9.870 x (2.348 x 10^30)^3 ] / 4 = 3.194 x 10^(91) cc, where *“(pi)”* = 3.1416, and *“Ru”* is the radius of our universe, which Sternglass gives as approximately (2.348 x 10^30 cm) **[p.234, Ref.#1]**; this means that the volume of each epola-cell is approximate-ly [ 3.194 x 10^(91) cc ] / [ 7.232 x 10^(127) = 4.417 x 10(-37) cc *******(see **NOTE2 **below). One notes that the cube-root of this volume gives the lattice-length of the [cube-shaped] epola-cell as ** (LL) = ( 7.615 x 10^(-13) cm ).**

That is how I calculated a new** lattice-length** for the epo-lattice in Dr. Simhony’s model.

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

**{ ***NOTE1:** in Sternglass’s model, our universe is the largest “cosmological system” [p.234, **Ref.#1**]: so, to be consistent, one needs to view our universe as being of the same shape as the other cosmological systems. The volume of a torus is approx. [*(pi) x (pi) x (RADIUS)^3] / 4 (see* **NOTE3** below)* ***}**

**{ ***NOTE2:** interestingly, and perhaps significantly, 4.417 x 10^(-37) cc is also the volume of a torus-[donut]-shaped object whose radius is 5.636 x 10^(-13) cm, a numeric value which plays an important part in Sternglass’s model {see Figure 14.3 (b), p.215, **Ref.#1**},** **as well as in quantum field theory: **Sternglass says that “This radius is analogous to the mean radius of the volume in which the electron’s field energy is concentrated according to quantum field theory” [p.222, Ref.#1] }.**

**{ NOTE3: the “radius” of a torus [donut] shaped “cosmological system” is the distance between the centers of the electric charges (1 positive and 1 negative) which compose it }**

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

Newark, Delaware, USA, 17 December 2014; mark.creekwater@gmail.com

**$$$$$$$$$$$$$$ << END OF CHAPTER 6 >> $$$$$$$$$$$$$$**

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