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

PAUL DIRAC was one of the 20th century’s greatest physics+math geniuses … He lived until 1984, and was still quite active during Sternglass’s career … In his book **[Ref.#1], **Sternglass tells about exactly 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+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 …**

**[ (sq.rt. 10) x (10^(39)) ]^2 = [10^(79)]; **

WHY WAS DIRAC LOOKING at these particular 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; ie, [(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.#25],** in section 7-7, titled **“What Is Gravity ?” **Feynman gives a LARGE NUMBER which is also in Sternglass’s book:

**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 book, 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” — in honor of 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 comes out …

Perhaps Feynman was not aware of this aspect of Sternglass’s work, tho 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 (google it) 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, a **KNOWN** quantity **[approx. 1.022 x 10^(6) eV, **which is equivalent to the energy content of an electron + 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” becomes “matter” 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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