**APPENDIX 3: DIRAC’s “LARGE-NUMBERs HYPOTHESIS”**

Paul Dirac was one of the 20th century’s greatest physics and math geniuses. He lived until 1984, and was still quite active during Sternglass’s career. In his book **[Ref.#1], **Sternglass tells about how he used a slight modification of Dirac’s **“large-numbers hypothesis”,** which enabled him to calculate, very elegantly, a theoretical numeric value for the mass of our universe.

Richard Feynman, who lived until 1988, was also one of the 20th century’s greatest physics and math geniuses, and in fact was one of Sternglass’s professors at Cornell University, where Sternglass earned his PhD. In his famous lecture notes from 1962-1963, now published in a “definitive edition” for our reading pleasure **[Ref.#25]**, Feynman also tried to use Dirac’s large-numbers hypothesis, but without much success.

It might be interesting, and illuminating, to analyse their different approaches, and why I say that Feynman’s use of this idea was not very successful.

One can go to **http://www.GOOGLE.com **for details re Dirac’s famous idea, but a quick description is as follows: Dirac called attention to two [2] very large numbers: 10^(39) and 10^(79): i.e., a one with 39 zeros after it and a one with 79 zeros after it. One immediately notices that 39 + 39 = 78, i.e., almost 79: i.e., that 10^39 x 10^39 = almost 10^79 … In fact, one can get a better understanding regarding what Dirac’s idea is about, if one makes a slight adjustment to one of the numbers, to make the square of the smaller number exactly equal the larger number. This is very easy, because [**(sq.rt. 10) x 10^(39)], squared, equals exactly 10^79.**

**I.e.: [ 3.162 x (10^(39)) ]^2 = [10^(79)]; **

Why was Dirac looking at these particular large numbers ?? Because the ratio (mass of our universe) / (mass of proton) is approx. 10^(79): i.e., (**Mu) / (Mproton) = approx. 10^(79) …**

**“Dirac argued that these and other simple relationships involving cosmological quantities were unlikely to be pure coincidences, and that somehow these relations had to be explained in terms of a model for the evolution of an expanding universe” [Sternglass, p.210, Ref.#1].**

The mass of the proton is known to be approx. 1.67 x 10^(-24) gram. Multiplying this by 10^(79) gives 1.67 x 10^(55) grams, which is a good estimate for the total mass of our universe, based on what astronomers can see.

Other interesting ratios involve the square root of this large number; i.e., [(sq.rt. 10) x 10^(39)], which equals approx. 3.16 x 10^(39). One can calculate the ratio **(strength of electrical attraction) / (strength of gravitational attraction) **between a proton and an electron: **[ K x Qe x Qpr ] / [ G x Me x Mpr ], ** where “K” is Coulombs electrostatic constant, “Qe” is the electric charge of an electron, “Qpr” is the electric charge of a proton, “G” is Newton’s gravitational constant, “Me” is the mass of an electron, and “Mpr” is the mass of a proton. Looking up the numeric values of all this stuff, and then doing the math, reveals that this ratio is approx. 2.23 x 10^(39) — very close !!

In volume 1 of the lecture notes from 1962-1963 **[Ref.#25a],** in section 7-7, titled **“What Is Gravity ?” **Feynman gives a large number which is also in Sternglass’s book. Plus, he gives the same number on page 25 of his book **The Character of Physical Law **(1965, 1967).

**4.17 x 10^(42) is the ratio [(electric attraction) / (gravitational attraction)] for an electron-positron pair, which is different from the previously calculated ratio, which applies to electrons –vs– protons, not electrons –vs– positrons. Sternglass notes, in his book, that this ratio is very close to the square root of the ratio (mass of universe) / (mass of electron), which is, of course, also the ratio (mass of universe) / (mass of positron), because the 2 little rascals (electron and positron) carry equivalent masses.**

In HIS books, Feynman mentions that that large number represents a ratio between forces (electrical vs gravitational), without mentioning the ( Mu / Me )-connection. Perhaps he didn’t notice it ??

**After noticing that (Mu / Me) = approximately [ (electrical force) / (gravitional force) ]^2, Sternglass takes this idea and runs with it, to develop an elegant way to calculate, theoretically, the mass of our universe. This idea appears on p.265, Ref.#1. Plus: he uses a more accurate version of this number [4.167 x 10^(42)] in several of his published papers, calling it “the Dirac number”. [He calls its square, 1.736 x 10^(85), “the Eddington number” — to honor Sir Arthur Eddington (a colleague of Einstein), who loved to play with large numbers]. Feynman does nothing similar with these numbers, which is why I say that he did not find a very good way to use Dirac’s large-numbers hypothesis.**

In the following link:

one can hear Feynman give “black holes” as the possible explanation for “quasars”, with no mention of Sternglass’s model, which features objects which are more like white holes: nothing gets sucked in, and large amounts of stuff come out.

Perhaps Feynman was not aware of this aspect of Sternglass’s work, though he had been Sternglass’s professor at Cornell.

**$$$$$$$$$$$ << END OF APPENDIX3 >> $$$$$$$$$$$**

Simhony and Sternglass have different explanations for the phenomenon of “pair production”.

Simhony says that pair production does not really involve anything being produced; instead, he says that a photon which contains a certain amount of energy** **will knock an electron-positron pair loose from the pair’s location in the epo-lattice. He mentions Carl Anderson’s 1932 experimental discovery re this. He says that the energy content of the photon must be at least as much as the “binding energy” of the ep-pair to the lattice, approx. 1.022 x 10^(6) eV, which is equivalent to the energy content of an electron and a positron, “at rest”.

Sternglass, by contrast, explains “pair production” as follows: **“It happens all the time, when energetic gamma-rays coming from outer space strike the particles in our atmosphere … the photons produce electrons and positrons with high energy, in a process called pair production” [p.182 Ref.#1]. **According to this way of thinking, “energy” (photons) becomes “matter” (ep-pairs) by some unexplained process.

However, there is a **hint** of an explanation elsewhere in his book, where he talks about how protons behave: ** ****“the proton … can absorb energy from its environment, and turn this energy into other forms such as massive electron[-positron] pairs emerging as mesons, returning to its normal state in the process. And when given enough internal excitation energy, it can reproduce itself, giving birth to a proton / anti-proton pair” [p.253, Ref.#1].**

Perhaps epola-elements are similar: perhaps, being ep-pairs, the little rascals might have the capability to produce an electron-positron pair as a response to being hit by a large jolt of photon energy, i.e., a “gamma-ray”. Perhaps an epola-element can somehow condense the energy content of a photon to produce “particles” of ordinary matter.

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