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essay: A SEMI-CLASSICAL CALCULATION RE PROTON-RADIUS

essay:  A SEMI-CLASSICAL CALCULATION RE PROTON-RADIUS

by Mark Creek-water Dorazio,  amateur physics enthusiast;  MARK.CREEKWATER@gmail.com

 

SUMMARY [i.e., “ABSTRACT”]

Following  Dr. Ernest Sternglass [Refs. 1 + 2],  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. 3].}

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.

Key words:  Lemaitre, neutron, primeval atom, proton, proton radius, Sternglass;

 

TEXT

Sternglass [Ref. 1] has developed a model which accounts for the origin of protons and neutrons in our universe, and describes their structure.

Using the “primeval atom” hypothesis of Georges Lemaitre [Refs. 4 + 5] 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.  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 re-configured, in a way which led to the production of zillions of neutrons, some of which quickly “decayed” —producing protons.  Many zillions of protons + neutrons emerged from this process, 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”.

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

 

STERNGLASS’s “TABLE 1”:  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:  (Rs) = [ 2G / c^2 ] [ [(Mu)(Ms)]^(1/2) ] [ 1 / 137.036 ]       (Eqn. 1),

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 “the square root of the expression inside the brackets.

Please note that this is a modified “Schwarzschild formula”, in which the “local gravity” is greatly increased, according to Sternglass’s theory, which he details in his book [Ref.#1].

{ 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 }

Inspired by Paul Dirac’s so called “large numbers hypothesis” [p.224, Ref. 4; pp.73-76, Ref. 5], Sternglass derives an ingenious and elegant way to calculate the mass of our universe, theoretically.  More regarding this, below.

 

COMPTON WAVE-LENGTH AND COMPTON RADIUS:  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:

(WL-compton) = (h) / [(c) (M)]

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)]:

(Rc) = [h-BAR] / [(c) (M)],         (Eqn. 2),

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 em-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 SYSTEM-radius  [Rs]  of each tiny system is almost equal to that of its COMPTON-radius  [Rc].

At some point in 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. 2),

where Rc is compton-radius and Ms is mass-of-system.

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

[h-BAR] / [(c) (Ms)]  =  [ 2G / c^2 ] [ (Mu) (Ms) ]^(1/2) ] [1/137.036];

Solving this equation for (Ms):

(Ms) = { [ (c) (h-BAR) / 2G ] [ (137.036) / (Mu)^(1/2) ] }^(2/3)        (Eqn. 3);

MASS OF OUR UNIVERSE ??

Sternglass’s formula for the mass of our universe, (using the identity  (e^2) = (K) (Qe) (Qe), and neglecting a typo in the book), appears on p.265, Ref. 1, as:

(Mu) = [ [ (K) (Qe) (Qe) ]^2 ] / [ (G)^2 (Me)^3 ]              (Eqn. 4),

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

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

(Mu) = [ { ( K Qe Qe ) / ( G Me Me ) }^2 ] [Me]         (Eqn. 4a);

{NOTE: this 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, papers, and essays which address this issue.  As Sternglass says, 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]}

Using this expression for (Mu) In Eqn. 3, one has:

(Ms)  =  { [ (c) (h-BAR) / (2G) ] [ (137.036) / (Me)^(1/2) ] [ ( G Me Me ) / ( K Qe Qe ) ] }^(2/3);

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 (Ms) = 4.0543 x 10^(-25) gram.

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., is equal to the system’s so-called “compton-radius” [Rc].

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

(Rc) = (Rs) =  [ h-BAR ] / [ (c) (Ms) ]  =

[1.0546×10^(-27) gram.cm.cm/sec] / [ (2.9979×10^(10) cm/sec) x (4.0543 x 10^(-25) gram) ] = 8.677 x 10^(-14) cm.

Note #1:  this is very close to the MEASURED “radius of the proton”, which experiments 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. 3] }  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 ???

 

CONCLUSION

Using only Sternglass’s model, and some of his numbers, one can solve two easy algebraic equations [Eqns. # 1 and #2, 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 obtained by this method is so near to that of the “proton-radius” which has been measured by many teams of experimental physicists that one suspects that the experimenters have been measuring the radius of one of the four ep-pairs, rather than that of the entire proton.

Note that this numeric value [8.677 x 10^(-14)] is calculated with no reference to any of the fiendishly difficult mathematics for which quantum field theory is famous.

Plus:  the calculated numeric value for mass obtained by this method is slightly less than one fourth [¼] the mass of a proton, which supports Sternglass’s idea that there are four [4] electron-positron pairs in a proton (or neutron), and that these four ep-pairs constitute most of the mass of the proton or neutron.

 

REFERENCEs

1) Sternglass, Ernest;  Before the Big Bang (1997, 2001), New York, Four Walls Eight Windows;

2) Sternglass, Ernest,  “Relativistic Electron-pair Systems and the Structure of Neutral Mesons”, Phys Rev (v.123) pp. 391-398, (July 1, 1961);

3) Antognini, A., + others,  “The Proton Radius Puzzle”, Journal of Physics: Conference Series, v.312, n.3 (2011);

4) Kragh, Helge,  Dirac: a Scientific Biography (1990), Cambridge, Cambridge University Press;

5) Dirac, Paul;  Directions in Physics (1978), New York, John Wiley & Sons;

 

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