Optional – MISC. DETAILS – OFFSET SECTION (for article: What We See and What We Don’t See)

Scope:  This section has been off-set from the article’s main text because it dives into details not immediately essential to the already long main text.  And some parts below may be not as interesting as other parts; and some speculation is also involved where slightly varied approaches are presented.

Part III, Optional; Protons, Electrons, other details:  (Note, this part, on protons, electrons, and etc., is important and interesting, but nearly two pages long!  So readers may first go to my Illustration and see if that treatment satisfies the reader sufficiently ‘at a glance’, and thus avoid reading further.)

If that is sufficient for the readers, they may just skim or skip Part III, below.  And if after that, or for any other reason, readers still wish a more detailed treatment (somewhat mathematical); they may scroll down from Part III to Part IV or just click: “Go to Part IV, ‘Discussion’.” ) 

Optional Part III, continued:  We know from experiments that two different major elementary particles actually exist, (the electron and the proton), not just one.  So in the next few optional paragraphs, I will try to suggest why both the electron and proton arise.  A few of these paragraphs may be somewhat speculative regarding details, and there may be developed, in the future, better ways of further clarify some details. 

The reader may find my thoughts presented in more detail, by going to my Homepage, and using the link to my article, Mass Ratios and Similar Geometric Volume Ratios.  (A similar article of mine, but shorter and without speculation, was published in a major journal.) 

The basic ideas are these:  In basic geometry, we can imagine that 3 equal touching big spheres can surround and touch 1 small sphere.  And we can also imagine that 3 still bigger equal touching spheres can surround 3 equal touching small spheres, and efficiently so - if packed so that each big sphere touches 2 neighboring small spheres.  And 3 even bigger equal touching spheres can surround 3 small touching spheres using a very non-efficient packing - where each of those very large sphere touches only 1 neighborly small sphere instead of 2. 

These concepts are somewhat similar to those that chemists use when they inquire how large atoms, with net negative charge, (‘anions’) might nicely fit around a centrally located smaller atom, which is positively charged, (say one ‘cation’).  (And some of their phraseology, used in developing that methodology, is:  ‘Radius Ratio’, ‘Ligancy’, and ‘close packing of spheres’.  And they do find some actual atoms that group together that way to form molecules.)

Important:  Anyway, we return to our discussion of geometric patterns; volume ratios that arise; and basic ‘particles’.  We consider the most basic geometric sphere patterns, and the volumes of the large and small spheres that would fit so neatly together to form those different basic patterns.  We then consider the volume ratios (or the average of two volume ratios) by comparing the big and small spheres in those patterns; and we calculate those ratios in each case.  And then we consider the most important real particle mass ratios that exist in nature, such as the proton-to-electron mass ratio; and we note that it rather well corresponds to certain (abstract) volumetric ratios among spheres in basic geometric patterns, as mentioned above.  And so does the Kaon-to-electron mass ratio, and the Pion-to-electron mass ratio – as well! 

((Optional:  incidentally, the ‘muon-to-proton’ mass ratio is comparable to an average ratio involving the volumes of large spheres and spheres inside those spheres:  one large sphere containing 2 smaller spheres, and the other with 3 smaller spheres inside of it.  Note again, that that case involves large spheres with spheres packed inside of them - instead of between them.))

The above two paragraphs are so important, and have so many important implications, that I have written a separate article based on all that, and related issues!

Note -Very Optional:  The next 4 paragraphs involve additional speculation, including some merits of a ‘bottoms-up’ approach vs. ‘top-down’; and even discusses a somewhat ‘circular’ approach.  Readers may skip them or just scan over them, at least temporarily.

First, -- some words about the origin or existence of the ‘Electron’: 

Let us imagine, among many small aether particles near a small region, that there is an average aether ‘particle’ with an average energy; and that it ‘hits’ a small glob of matter.  The amount of mass which separates from the glob—or eventually stabilizes--is the smallest amount that can move at nearly the speed of light and yet its energy is equal to the energy of that ‘average’ aether particle that hits it. 

Because of the large average angular momentums of various aether flows around that initially compact electron, and because of fluctuations and tendencies to vibrate—that electron spreads out like a solid spinning gold ring.  Then it has a greater angular momentum, which more nearly matches its surroundings.  And, actually, it probably forms a hollow ring style, like refrigeration tubing or bellowed sail, to pick up sufficient net stabilizing amounts of aether pressure pulses from various directions, including from its own partly self-shielded directions.

The following may seem unusual; but I think it is a sort of ‘expansion’ on concepts developed earlier, i.e., for example, Tait’s ‘dynosphere’ bubble concept; and/or Reynolds’ concept of ‘ethereal spheres constituting the substructure of the universe’; and/or an expansion of Heisenberg’s ‘granular concept of space’: 

Let us think of our very small ethereal ‘aether grain’ as a sort of average sponge ball.  But let us try to apply my previously mentioned concept of ‘big sphere patterns surrounding smaller ones’.  Correspondingly, we imagine that a big aether pattern or ethereal structure also hits a bigger glob of matter.  A big glob of mass separates, and eventually stabilizes with its ‘vibrational’ plus spin energy nearly matching the ‘average’ energy hit of those larger aether structures or patterns.  Unlike the lesser mass electron, the larger (proton) easily develops the angular momentum of its surroundings without spinning quite as fast or spreading out.  Thus, its greater inertia and other factors allow it to remain as a much more localized concentration of matter than the electron.  (Probably more like a very compact spinning large ball, instead of a more spread-out thin spinning hollow ring.)

I am not totally sure exactly why almost all ethereal regions of ‘space’, fundamentally, seem to have very appreciable angular momentums, like they are strong vortex-like regions.  That may be due to ‘just the way the ethereal swirls have always been’ and ‘it tends to conserve that angular momentum’.  Or it might be due to the great compact spinning actions of the protons in space, ordering or helping the very small ethereal vortices to group into bigger vortices.  And perhaps the spinning electron rings also contribute something to forming those aether vortices, too.  (Although not directly related to that -- maybe the rather constant energy of each electron encourages ethereal balls, equal to it in energy, to gather around itself.  And these, in turn, add a further stability to similar ethereal quantum energy balls scattered all over space.  And larger, higher energy quantum balls form, of such size and energy, as to fit neatly around them). 

That is about all I want to say about the proton vs. electron in this article.  And I might not bother to distinguish in this article, again, between an aether particle and a ‘pattern of aether particles’!

IV.  DISCUSSION; Some details, the ‘Background Mass’ and ‘Broader Picture’: (Reminder, the non-specialist may wish to just click my Illustration and my Summary, and skip the below, if those links prove sufficiently satisfying.)

The below is a somewhat detailed presentation of a ‘bottoms up’ approach to the subject of aether and elementary particles (instead of a perhaps simpler ‘top-down’ approach that is outlined elsewhere in my article).

As implied, the discourse below contains a lot of nomenclature, equations, and tedious  juggling.  Although the reader is invited to follow all details, we will try to repeat the main points after some related groups of paragraphs, and also in my Summary.  In the below, we will continue to use some ‘order of magnitude’ estimations, approximations and over-simplifications that should not alter the conclusions.

(Some of my discourse is somewhat similar to treatments found in textbooks discussing ‘Ideal Gas Theory’.)  The ‘aether particle’ that we imagine is likely an over simplification, (the actual ones may be bigger and with a hollow interior).  Yet our initial simplification is easier to handle mathematically.  And thus progresses to conclusions that are fairly consistent with reality and with many aspects that are conceptually useful.

Let us consider a ‘background’ consisting of many hard to detect, neutral aether ‘particles’. Each significant aether particle has an average ultra small mass, ‘m_ae ‘.  (Note, the subscript,  ‘ae’, as in ‘aether’)  All of my subscripts are intended to help readers remember what each term denotes.  Each m_ae has an ultra fast ‘translational’ ‘mean’ velocity, ‘v_ae’, in ‘this or that’ direction.  Each m_ae initially has an average distance or spacing, ‘s_ae’ between it and its nearest m_ae significant neighbor.  Thus, each m_ae has a rather vacant small volume surrounding it of about (s_ae )³ volume. 

The aether particle mass, m_ae, consists of ultra high density material, which is the highest density possible in our universe, and therefore the density is incompressible (or nearly incompressible and non-porous).  Thus, we consider m_ae to have a high density, ‘p_{k max}’.  But since each m_ae particle has an empty (s_ae )³ space surrounding it, it helps constitute a rarefied ethereal ‘spacial density’, equal to (m_ae ) / (s_ae )³ , which is a very low average ethereal density, indeed.  And we denote that ethereal density as, ‘p_{ae includes space} ’, in case needed in any calculation later on.  (Reader, note, we have used an italicized ‘p’, instead of using the Greek letter ‘rho’, to denote ‘density’, but we hope it resembles the commonly-used ‘rho’, often used in textbooks when discussing density.)

Thus, the kinetic energy ‘E_ae’, of each m_ae aether particle, is (1/2) m_ae (v_ae)².  The kinetic energy per volume, i.e. per (s_ae)³ , is approximately (1/2) m_ae (v_ae)² / (s_ae )³ , and that entire expression has ‘equivalent dimensions’ of pressure.  In fact, let us suppose, that this aether particle, together with all the others somewhat like it, create a real ethereal background pressure, ‘P_ae’, given approximately by:

P_ae = (1/3) [m_ae (v_ae)²] / [s_ae]³ or by rearranging terms, P_ae = (1/3) [m_ae / (s_ae)³] [v_ae]²

Now, let us turn our attention to a durable, larger ‘detectable’ mass, such as a proton or other ‘elementary’ particle, (instead of the ‘too-small-to-detect’ aether particle).  That comparatively ‘large’ glob of mass will be denoted, ‘M_glob’; and we will think of it as a proton, for simplicity.  (We will hope that our developing discussion establishes good reason to believe that our comparatively large glob mass, M_glob, will develop into a stable proton, or other stable particle, and remain stable, even though our treatment will not be very rigorous.)

Let us also assume, for simplicity, that our likely proton, M_glob, and our typical aether particle, m_ae, both exist with equal amounts of kinetic energy.  That concept is known as the ‘equipartition of energy principle’; and it is often applied to gas mixtures, made up of large and small atoms, such as argon and helium atoms.  In fact, there are some limitations in applying the principle to complicated gases, such as gases made up of hydrogen molecules.  So when we apply it to our glob (proton) and aether particles, which constitute a sort of gas mixture; we will keep in mind that it is only a rough approximation, at best.

Applying the ‘equipartition of energy principle’; let us write that the kinetic energy of the (proton) glob is equal to the ‘mean’ energy of an aether particle:

Using appropriate subscript notation, we have:  ‘E _{ke of  M glob}’ = ‘E_ae’.

Important:  To understand why there arises, in this universe, small discrete elementary particles, such as ‘protons’, but not just any infinitesimally small stable particles, consider the following:  Let us imagine that a rather large glob of mass has been scraped by an average aether particle, and therefore begins to spin with about the same energy as the aether particle that hit it.  (Another words, ‘E_{spin of  M glob}’ = ‘E_ae’.  In fact--it may take quite a few ‘scrapes’ before the coerced glob and its vicinity approach a near balance with each “aether particle’s punch”.)  Because of, initially, the rather large glob’s mass, that glob can spin at a rather slow speed and still manifest or contain that average E_ae amount of energy.  (Since E_{spin of  M glob} = E_ae, approximately; we will say that each has “a ‘quantum’ amount of energy”, and that “that ‘quantum’ amount” is the energy of an ‘average’ aether particle.) 

The rather large glob’s centrifugal-related pressure is very small because of its slow spinning speed and its large surface, which is exposed to the high-pressure aether.  So, here at least, we don’t have the type of instability that arises when a body spins too fast! 

But now, let us imagine what happens if that spinning glob gets smaller and smaller and the glob must continue to spin at faster and faster speeds so that the ‘Equal Partition of Energy’ continues to exist between that shrinking glob and average aether particle!  ((I.e., In other words, so that ‘E_{spin of  M glob}’ continues to equal ‘E_ae’, or, approximately, that (1/2) [(M_glob) (V_{glob spin})²] continues to equal (1/2) [(m_ae) (v_ae)²].))  Note that when we reduce the mass of the spinning glob, we also reduce its volume correspondingly, because its mass consists of ‘approximately’ incompressible material.

The reader may recall that Pressure has the equivalent ‘dimensions’ of Energy per Volume.  So that when the spinning glob maintain constant energy, ‘E_{spin of glob}’, but we reduce the glob’s volume nearer and nearer to zero, then at some point the shrinking glob’s mass exhibits such increased ‘outward’ pressure – that it will equal the high aether pressure!  That condition necessitates that there arise a very small, but finite, ‘Proton’, the minimum stable, highly-concentrated, spinning mass, or ‘elementary particle’, that can exist in our universe (with the ‘particular’ characteristics of the aether existing in our universe)!

Optional:  The great gyro-like spin of that highly concentrated mass (the proton’s) as well as subtle aether flows arising around it, likely contribute to the unique stability of the proton.  Rene Descartes was quoted as writing, “Give me matter and motion, and I’ll give you a universe!”  I agree with that Descartes conjecture, but my mechanism-path and my resulting details are somewhat different--since Descartes rejected the ‘Atomic concept’. 

Optional – continued:  Descartes believed that aether left no infinitesimally small crevices or voids unfilled, but I disagree with Descartes there, also. (As did the political theorist and chemist, John Locke! And as did the old Greek ‘Atomist’, Democritus, also, of course.)  In fact, if every solid sphere’s equator spun at a constant speed, say ‘c’; the centrifugal-related pressure developed by each sphere (at its surface – near its equation) would be the same, regardless of each sphere’s size.  Thus, my special treatment above is also dependent on my justifying my imposing a sort of ‘equal partition of energy’ principle (side condition) to the above – to establish a ‘unique mass or size’.  And hopefully we have some ‘void or lesser filled space’ between each of my aether particles’ punches, to make that ‘equal partition’ principle applicable!  I.e., And thus make possible ‘elementary particles’ and atoms, in my approach above.

Important (My ‘Point #1’ about the above):  Our particular aether causes protons to arise--as the minimum highly concentrated stable spinning mass that can exist in our universe.  That (along with the ‘equipartition of energy’ and aether pressure) is highly suggestive of the following also:  The proton will tend to exhibit a limited, small, discrete, ‘quantum’ amount of ‘spin angular momentum’ representing a unique, smallest constant value of ‘that’  for any stable particle.

Optional Related Speculation:  One may scroll back to near the end of ‘Part III’ (under the heading, ‘Important’) for a discussion of why two major types of particles actually arise, the Proton and Electron.  And why it is -- that even significant volumes of aether (i.e., space) seem to have high spin angular momentum, too.  (As mentioned, the spin of the proton, and perhaps the spin of the electron, might help ‘stir’ up many small vortices to form a group of vortices with combined strength comparable to the Proton’s spin angular momentum.) 

Important (My ‘Point #2’ about the above): The concept of our rarefied Aether is that it possesses super-high velocity motions, super-high energy per volume, and above all—that it exerts super-high pressure!  That should make very probable -- that high-density material systems, which occupy small to modest volumes, will generally be limited to some maximum travel speed, which turns out to be the ‘textbook’ speed of light, ‘C’, approximately 3.0x10⁸ m/sec.  We should expect that to be the case, if we note various sensible, familiar equations which are often applied to visible phenomena, but which should also extend to the less visible, for example:

Energy ~ ~ = (1/2) (m) (v)² .  Dividing both sides of that equation by ‘volume’, we have: Energy/volume ~ ~ = (1/2) [(m)/(volume)] (v)².  Note, the mark, ~ , denotes ‘approximately’. Since Energy /volume causes pressure, and is pressure; and m/volume is density, we conclude: Pressure ~  = Density x (velocity)² .  Related to that, we have the following:
(The low aether’s Density) times (Velocity of the aether)² = [a pressure of ~ 1.3x10³³ newt/m²] = ~ (the Density of the densest possible concentrated mass in the universe) times (the maximum spinning Speed of that dense spinning mass) ².  That is necessary so that any spinning mass (such as a spinning elementary particle) maintains its stability.  In fact, the universe’s great ethereal pressure probably exceeds the centrifugal-related pressure of such stable spinning dense entity by a ‘comfortable factor’, say, by double or more — so that other motions, vibrations, and factors are also held in check.  The below ‘Optional’ section also develops and interprets other mathematical expressions, which give insights into why a maximum speed limit tends to become applicable for material ‘bodies’ (the ‘latter’ also historically termed: ‘ponderable mass’ or ‘gross mass’):

Optional (Related Point #3): 

The following thoughts, math, and preliminary conclusions are Optional: 
Expressing the above thoughts and words in mathematic terms, we have:
P_{glob spin} = (1/2)  (p_{k max}) (v_{glob spin})² , 

Where P_{glob spin}  is the ‘outward’ pressure of , for example, a proton made up of roughly the highest density of pure, non-porous matter in the universe, "p_{k max} ".  And "p_{k max} " is also equal to the high density of any pure aether particle, of mass, m_ae.
 
We set: P_{glob spin} = [1/2] (P_ae ), and that allows the aether pressure, P_ae, to exceed “P_{glob spin} ” by at least some ‘safe’ factor.  Since, some pages back, we already established that: P_ae = (1/3) [m_ae / (s_ae)³] [v_ae]² ; we can now write:

  P_{glob spin}   =  (1/2) ( p_{k max}) (v_{glob spin} )² =  [1/2] (P_ae ) =  [1/2]  (1/3) [m_ae / (s_ae)³] [v_ae]² ,

or approximately,  (v_{glob spin} )  =  { 1/3 [(v_ae)²] [(m_ae/(s_ae)³] / (p _{k max}) }^1/2  .

We see at once, that since the low rarefied ethereal density, [(m_ae/(s_ae)³] is being divided by the very high ‘non-porous’ density of a solid aether particle, (p _{k max}), that that results in a very small number.  And that results in the ratio, (v_{glob spin} ) / (v_ae), also being extremely low.  Thus, we conclude that: the highest spinning speed, (v_{glob spin} ), that a proton can have (or even the highest velocity that any significant accumulation of mass can have) is many magnitudes less than the typical speed of an aether particle, (v_ae).  And that generally limiting value, for significant mass accumulations, is ‘the speed of light’, designated ‘c’.

(When Aristotle wrote that low-density masses lead to high velocities, and extremely low density masses lead to extremely high velocities, he was rather wise about that, at least.)
 
 [p _{k max}] times [the very small volume required only for typical solid aether particle] = (m_ae). So dividing both sides of that last equation by { [p _{k max}] times (s_ae)³ }; we obtain:

[ultra small Volume required only for solid aether particle] / [(s_ae)³] = [(m_ae/(s_ae)³] / [p _{k max}]. 

But that [(m_ae/(s_ae)³]  term equals our old low rarefied ethereal density, [p_{ae includes space}], so by substitution, we have:

[the ultra-small Volume required only for solid aether particle] / [(s_ae)³]  =  [p_{ae includes space}] / [p _{k max}]; in other words, we have a ratio of volumes equaling a ratio of densities. 

Thus, we conclude that the ultra-small volume occupied by a typical solid aether particle divided by its own empty lot space, (s_ae)³ that it does NOT occupy  =  the very low rarefied ethereal density consisting of the combined aether particle with its ‘empty lot’ divided by the very high solid aether particle density, itself! 

((Note again, that [(m_ae/(s_ae)³]  gives the rarefied ethereal density on the large scale, i.e., a ‘mass vs. volume’ ratio, applicable for the entire universe, generally; And that on the smaller scale, that same [(m_ae/(s_ae)³] also gives the density applicable to an average typical aether particle and its small surrounding lot, i.e., without its generally being encroached upon by another aether particle!))

---- END of this ‘Optional Off-Set Section’ ----

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