======================================================================= SELF INDUCTIVE RELATIVISTIC EFFECTS IN THE ATOM AND IN DECAY PARTICLES. RELATIVISTIC TRANSFORMATIONS CREATE A STEADY STATE ATOM. ======================================================================= Download http://visitastronpomy.com/viewer.com since this page contains a handfull of ascii graphic characters used for equations where no pure typewriter characters will work. Viewer.com is loaded at your Dos prompt by command: dos> Viewer atom.txt Also see http://abstrac1.txt - a brief corollary for atom.txt ---------------------------------------------------------------------- Begin March 14, 1995, two minutes before 3 PM, with an empty blank page. Greydon Moore email: greydon@look.com -------------------------------------------------------- ATOM.TXT --- some elements in the equations in this file could not be presented without the use of a few 'ascii graphic' characters. You need to use Viewer.com or other 'ascii' means to view this file. If necessary, download viewer.com and use it to read this file, at your Dos prompt type: VIEWER ATOM.TXT -------------------------------------------------------- ABSTRACT --- Solution to the existence of steady state fundamental constants in the Hydrogen atom. -------------------------------------------------------- Original's line length = 3862 lines Original's size = 147,035 K -------------------------------------------------------- corollary | An Electron mass energy of .51099906 5 has been used throughout the following. The reason is intuitional. Things seems to co-ordinate in a slightly better way with one more digit added to the Electron's mass, so .00000005 was used (half way between 0 and 9) for the added digit. constants All Physical Contants used are listed on Page 1233 of the Physical Review D Particles and Fields, 1 August, 1994, Part 1, Volume 50, Third Series, Number 3, published by The American Physical Society, through the American Institute of Physics, and Great Britain allies. Particle mass energy datas used in this disclosure are also from the same journal. dedication There are parts to this disclosure which are wordy, for deliberate reasons. Super pros in the business have no difficulty 'capturing' information in the sketchiest of brief mathematics. Others yearn for details and descriptions and reasons thereof. This disclosure is written also for those who do not know how to switch their computers to the A: drive at the Dos prompt. There are many advanced users who know how to do this step in an instant, through several mouse clicks in Windows, or a program, but do not know how to go to the Dos prompt let alone how to switch the drive with a non-mouse command. To these I dedicate the words and verbage of this paper. Painters who were tossed out of the French Academy for incompetence were vilified, discredited, spurned, but didn't quit; Gauguin went to the South Pacific, Van Gogh experimented, Picasso just kept on painting, Monet suggested the Academy finger itself and set up his own studio. Painters who create pictures outside the conditions of an Academy are also thus on the list of dedicatees, as well as of course, those most hard working of all, who compiled the Physical Constants datas upon which this disclosure is based, these are amongst the hardiest of all painters, because they are amongst the most accurate and far seeing. LONG/SHORT ABSTRACT -------------------------------- The velocity of an Electron in the rest state Bohr orbit of a hydrogen atom is a perfect ratio, exactly the speed of light diminished by the Fine Structure Constant. In other words, that velocity is C --- = A V where A is the FSC = 137.0359895 and C is the Speed of light. At that velocity, there will be slight Special Relativistic effects seen upon the Electron, relative to a stationary Proton looking out to the Electron constantly orbiting it, and also to any stationary laboratory observer outside the atom looking inward toward the atom. Even tho the special relativistics effecting the Electron will appear slight, there is no cause to believe they also have no meaning. There are many internal pictures, pursuent for instance to the distance of the Electron from the Proton (the Borh orbit), and to the Electron's Compton wavelength. These comprise parts of a self contained internal picture whose Relativistic views are relativistically within reach of each other, and therefore can be internally coherent one to another. In fact the 'view' effects are fundamental to the creation of, and constant maintainance of, fundamental structures relating to atomic shape, and fundamental particle manifestos. It is not that the velocity of the Electron is the cause, via Relativity. The Electron velocity results from a number of factors which tie together through an interlinking embrace of various Relativistic effects, wherein only those effects which can mututally maintain a 'perfect' balance in a self sustaining way, result. The effects are mainly seen involving the attributes of SPACE and MASS. The scene of SPACE, and its tiny mass distributions within the large area, are keenly defined by their Relativistics. The Electron velocity is an easy entry into the scene comprising the self sustained embracements which result in effects which pull together into a long range 'finding' of great might that is a unique creation, making mutually exclusive energy structures called constants. The reach of this 'finding' is all the way from a photon right up to the highest masses amongst Meson elementary particles. Photons, and certain leptons and mesons, are fundamentally linked. This is not news, the basic tenets of Chromodynaic Theory include this. The news is in describing a backbone structure that links a whole range of phenomena into certain discrete outputs which cannot change, in co-created constancy, resulting from their principles. The following is a description of what occurrences lead to a balanced self-sustained result. These we see in fundamental physics as empirical hard facts such as the atom, photon spectra, the Electron, and certain elementary particle mass energies and Compton wavelength states, all of which are, or effectively act as, contants. In the context of a Special Relativistic view of fundamental causality, it is clear that certain fundamental constants have their unique values because of the balance, and any minor change to any of the constants can cause such 'major' resulting changes in ensuing Relativitic 'power' that the balance simply dissolves when the Relativistic changes resulting are too great, even when an exceedingly minor change is enviegled somewhere into the system. In other words, the system is self locked. It seems invariant at a fundamental level, due to various Relativistic tensions, all seeking a perfect balance, perfect accord. It helps explain a reason why certain fundamental physical constants have the values they do, and can have no other values. A SPECULATION ------------- In the following a Relativitistic EXPANSION in the equations leads to more accurate whole particle results for most every instance of Relativitistic exploration, even though the fact of EXPANSION may be counter intuitive to an assumed Relative CONTRACTION pre-existing, for instance upon a wavelength. It is possible that CONTRACTION is correct. But usually the result is slightly under an anticipated whole particle fact. This may be suggesting thus an external input of very small nature, for instance a photon energy input of variable kind is needed to bring the consequence to whole particle result in which case the system becomes spontaneously unstable and a decay or frequency shift results. This speculation is but an idea of a kind that would be explored here if more about fundamental spectrum issues for atomic and nuclear property were known. But this is not the case, here. What you get in this disclosure, is what you've got, regards my knowledges. Photons can be absorbed by any charged particle, including Protons in the nucleus. In other words, photons inveigled into the system bring the system into total whole particle balances but unbalance the Relativistics, causing a spontaneous ejection, or frequency shift, to bring back a state of Relativistic self sustained tension. The slightly less than whole particle fact is what keeps the system self systained, self feeding, as constants. Perhaps. Speculation finished. =================================================== THE STEADY STATE ATOM INTRO SUMMARY the gears, bells, and ball bearings =================================================== Let's cut straight to some guts! 1. Relativistic EXPANSION of the Electron rest mass, in atomic structure, is the CAUSE of the Electron's binding energy. 2. Relativistic CONTRACTION of the Electron Compton wavelength, is also a cause of the Electron's binding energy. These two mighty proclaims are easily demonstrated, as follows: Let BETA = the Relativistic transformation effect expected by the Electron's velocity in orbit in the Hydrogen atom. Since the Electron's velocity in the rest state orbit is less then the speed of light by the ratio 137.0359895; a ratio also known as the Fine Structure Constant; then BETA is the ratio: BETA = .99997337 39653 . Demonstrating that Relativistic mass expansion has kind in the atom, begins straight in as follows: LET E = Electron rest mass. = .510999065 Mev Ew = Electron Compton wavelength = 3861.59323637 x 10 to -14 cm LET Eo = Electron binding energy = E x 1/ 2(FSC squared) = .00001360569808 Mev LET A = Fine Structure Constant = FSC = 137.0359895 1. Demonstrating that the Electron REST MASS is Relativistically EXPANDED in the atom: -=======================================- relativistic expansion electron | | (E x 1/BETA) - Eo = E = .510999065 5 Mev | binding energy binding energy appears as extra quanta in the E mass EXPANDED. ALSO E x (2 FSC), x 1/BETA = (E + Eo) x (2 FSC) for .510999065 5 + Eo . 2. Demonstrating that the Electron WAVELENGTH is Relativistically CONTRACTED in the atom: -========================================- relativistic binding contraction energy | | (Ew x BETA) = wavelength for (E + Eo) for E = .510999065 5 Mev = Electron binding energy appears as extra quanta in the E wavelength CONTRACTED. -=====================================- ENERGY ............. WAVE expand contract = plus 1 Eo = plus 1 Eo -=====================================- -====================- ATTEMPTED CONFIRMATION -====================- E ------ = .99997337 50281 E + Eo COMPARED TO BETA = .99997337 39653 It is self evident that the two figures are not equal in the ways of being total absolutes, even though, when one ratio is divided into the other, the difference is actually so slight it show up as number .99999999 8937 at the 9th significant digit in the result, when: beta ratio .99997337 39653 --------------- = .99999999 89372 .99997337 50281 Eo ratio Is this deviation due to digital trunkation, or to intrinisic divergences in Relativistic form, which co-incidentally touch but do not precisely equal, the Eo term determined by the Fine Structure Constant. Answers are not easy to come by, regards the discrepency. However, there are many other derivations that all point to hard core Relativistics at work in the atomic/nuclear structure, giving definition to several fundamental physical constants, and to the masses of certain fundamental particles. Details of these matters, plus further description of BETA, continue next below. ==================================================== SELF INDUCED RELATIVITY ==================================================== ---------------------------------------------------- BEGIN a description of the FUNDAMENTAL ACCORD ---------------------------------------------------- PROVISO --------------- The following is a bare bones romp along a bottom line schetching in details of a self sustaining Relativistic embrace. Relativistic effects on magnetism are not addressed, neither are quantum states such as up/down spins, and + - orbital momentums and directions. These are considered results and consequences of the embrace, and magnetism is considered a possible cause for flips in integer or half integer spin qualities as a resolving of tensions from tiny Relativistic imbalances seeking solution in the most harmonious, least energy expending, ways. Relationships to Elementary Charge are also not addressed - no need in the bare bones scope of this disclosure. Someone else who knows some right stuff about charges may have pleasure seeking to jig-saw elementary charge questions into the picture. -------------------------------- START WITH BASIC RELATIVITY -------------------------------- Simple transformations in Special Relativity work upon the shape of space, intrinsic mass, and time; to slow time, contract space, and enhance mass, when Special Relativistics are in effect. The effects are seen by an external observer, seeing the effects from a stationary position, or in motion but at a different rate of velocity than the source of the effects relative to the speed of light. The faster the source moves, approaching the speed of light, the more the Special Relativistic effects on SPACE, TIME, and MASS, are noticed by an observer. The effects are not lineal. That is, there is not a smooth rising rate of effects in keeping with a smooth rising accelaration toward the speed of light. Most of the effects become apparent within the last 25 % of the speed of light's velocity, and the main effects do not occur until within speeds aproaching the last 3.7 % of the speed of light. The standard transformation equation (originally introduced by Albert Einstein at the turn of the century 89 years ago), is an abstract set of factors which produces a single term, commonly known as the Beta factor (after the Greek Alphabet letter beta that is used as the mathematical symbol for the term). The beta factor is a decimal number, a ratio, of value 0 to 1; 1 when no effects are present; and 0 when the source object is travelling at the speed of light. In geometry the same ratio terms for the sine of one of the angles that is not the 90 degree angle in a right angle triangle, is identical to the ratio produced in Special Relativity as the term named BETA. Here is how the term is derived, according to Einstein's original equations: EQUATION 1 ________________________ | | Ú V ¿ 2 BETA = b = | 1 - ³ --- ³ \| À C Ù which interprets as: BETA equals the square root of the ratio of the following: (the source velocity divided by speed of light) all squared, and subtracted from 1. V In some reference works, BETA is cited as the ratio itself, of --- . C In this documentation, that ratio will be cited as 1/A (as will be shown further on), and BETA will be cited as the ratio for the possible factored variables, as derived in EQUATION 1 above. In some reference works, a slightly simplified form of EQUATION 1 is cited, this being: EQUATION 2 ________________________ | | 2 | V BETA = b = | 1 - --- | 2 \| C where, also, the greek letter gamma (like a 'y') is used instead of beta (like a 'b'). The choice of gamma or beta is the choice of the author writing the works. The fact is, the factoring statements of EQUATIONS 1 and 2 produce the same BETA ratio. In the following, BETA is used throughout for the symbol of the ratio of resulting Relativistic effect, as defined by EQUATION 1. ------------------------- RATIO INTERPRETATION ------------------------- It is easy to be fooled by the value of BETA. A value less than but nearly equal to 1 seems like nothing much is happening, but there is. The BETA value that is nearly, but not quite, 1 comes into Relativistic effects for a source that is barely moving, almost standing still. Whereas, as the source approaches the velocity of the speed of light, its BETA value shrinks, until many 0's appear after the decimal point of BETA as the velocity approaches toward the final iotas to becoming the speed of light. For example, a source travelling at .99999 percent of the speed of light will have a BETA effect of .004472124 such that, for instance, the source's apparent mass will be increased by a magnetude of 223.697356769 times, because 223.697356769 is the reciprocal of .004472124 . See what I mean, a low BETA ratio represents a high Relativistic effect. At the speed at which the Electron permits around in the Borh orbit the expansion of mass upon the rest state mass of the Electron is only .00001360569808 Mev, compared to the Electron rest state mass itself of .510999065 Mev. Thus the resulting apparent mass is increased Relativistically to become merely .511012671 Mev. This is hardly a noticable change at all, except the tiny extra change happens to be identical to the binding energy which hold the Electron in orbit in the atom. And so, that minute Relativistic transformation (expansion) upon the Electron's rest state mass is highly significant, to say the least. ----------------- SINE RELATION ----------------- Because of the intrinsic relationship between BETA and the sine of a particular angle in right angle triangles, the BETA term is not random or meaningless in terms of anything else other than its report on the status of a Relativisitic situation. In fact the BETA term has many internal 'jump points' that link to other numbers and values that arise as constants, for instance in many forms of plane geometry. It serves to proove that whole piece factors are a fact of Reality in Relativistic situations of certain kinds. Here are three examples of that internal jumping, to be found in BETA terms. A fourth example is a demonstration, shown in APPENDIX 3. -============- 1. For instance, if the velocity of the source object is travelling at 57.7350269 percent of the speed of light, the BETA effects seen for that object by a stationary observer will be conducive to the ratio .816496580 which also happens to be the reciprocal of the square root of 1.5 in fact, as determined by EQUATION 1. In digits 57.7350269 percent is actually the reciprocal of the square Root of 3, and is also an absolute value inherent in Cube and Sphere geometry which is six sided with a perimeter of equal sides all equal to the radius of the hexagram. When a six sided Star of David is enscribed within the bounds of the hexagram; the points of the Star touching the points of connection of the six sides of the hexagram; the inner points at which the arms of the Star crisscross within the picture, is at a radius of .577350269 when the radius of the hexagram is equal to 1. And so, two sources of an integer value of 577350269 have just been pointed out. So it is obvious that the BETA term in Special Relativity is not unique to objects that are just hurtling through space entirely on their own at relativistic velocities. -============- 2. The 5 sided star, and five sided Pentagram. The 5 sided star is characterised by a pure number for the ratio of the base to the hight of an arm of the star. The same ratio characterizes a Golden Rectangle, whose short side to long side measure is in the same ratio. The ratio is classically known as the Golden Ratio, or Golden Section number. It has a value mathematically manufactured as follows: 1/2 of root 5, plus .5, = 1.6180339887470 = A When this ratio is 'A' in Relativistic terms, then via EQUATION 1 its BETA ratio is; BETA = .7861513777579 and 1/BETA = 1.2720196495130 which is the square Root of 1.6180339887470 The Golden Ratio turns up almost everywhere, when any BETA ratio for a velocity has a value related it seems, in any way to the Golden Ratio digits. FOR INSTANCE If a velocity is the square Root of A = 1.6180339887470 which is 1.2720196495150 then BETA = .6180339887470 which happens to be Golden Ratio - 1 which happens to be the reciprocal of 1.6180339887470 whose square happens to be 2.6180339887470 and so on. ALSO If a velocity is the SQUARE of A = 2.6180339887470 then BETA = .9241763718316 which is not a recognizable digits, until it is learned that it is the square of the number = .8541019662530 which happens to contain the same digits as the 4th power of the Golden Ratio = 6.8541019662530 Etc. Try the same for a velocity which is the square of the Fine Structure Constant. None of the digits which result in Relativistic transformation are recognizable as digits coming from any other sources beyond the Relativity itself. This does not mean to say there are no recurring digits, just that none have been seen poking around with the FSC and Relativity BETA ratios looking for some fast find. -============- 3. The square Root of 2 is also relativistically aware. Root two has geometric source as the hypotenuse of a square whose sides equal 1. Relativistics for Root 2 are: Root 2 = 1.4142135623710 = A When this ratio is A, in Relativistic terms, then via EQUATION 1 its BETA ratio is; BETA = .7071067811876 which is the reciprocal of Root 2 = 1.4142135623710 so that 1/BETA = 1.4142135623710 A source travelling at 70.71067811876 percent of the speed of light, will experience Special Relativitistis transformations at a rate of: BETA = 1/(Root 2) CONTRACTION 1/BETA = Root 2 EXPANSION where 1/(Root 2) is identical to its proportionate velocity. This is where Relativity meets and greets its own terms. In terms of a spread, suppose a system has both a contraction, and expansion, embodied for instance in a piece of space, the total space CONTRACTED .... > .... EXPANDED has digital meaning beyond the Relativistics of Root 2. For example, if the original space length is 3 then: 1/BETA x 3 = 4.24264068712 BETA x 3 = 2.12132034355 ------------- the GAP is 2.12132034355 , ie., twice 4.24264068712 which is the square Root of 18 and 2.12132034355 is the square Root of 5 where square Root of 5 is a source generator for the GOLDEN RATIO, as shown immediately above in the example for 1.618033989. As you can see, geometrics and Relativity LOVE each other. -=============================- BETA IN FUNDAMENTAL PHYSICS -=============================- In fundamental physics, the BETA term in Special Relativity has a well know ratio value that is derived from the real value of one of the most well known fundamental constants in physics, this being the Fine Structure Constant, an absolute ratio (no properties) having the digital value of 137.0359895 whose reciprocal is .007297350796 . This small number is the ratio between the speed of light, and the velocity of an Electron in the rest state orbit of a hydrogen atom. V In this actual instance, the ratio --- = 1/A C for the Electron's velocity in orbit, is actually the fundamental constant known otherwise as the Fine Structure Constant, a constant which turns up throughout the foundations of fundamental atomic and subatomic constructs, as found in nature without tamporing by humans. It is there, all over the place in the realms of the atom and nucleus. C And so, this fundamental principle is a ratio A = --- V where A is the Fine Structure Constant, and V is the rest state velocity of an Electron in the Borh orbit. The value of A transforms into a Relativistic value when transformed through the factoring of EQUATION 1 to become: EQUATION 3 _______________ | | 2 BETA = | 1 - 1/A = .999973373965 \| V in which 1/A = --- = 1/137.0359895 = .007297350796 C in which BETA now describes assumed effects of Special Relativistic transformation upon an electron in the Borh orbit, as seen or experienced by a Proton at the center of the atom, or by a external stationary laboratory observer. In either case, the Electron itself, the source of the velocity, will itself be impressed to Relativistically transform due to its own velocity with respect to the speed of light. The question is, how much effect will there be, concidering that the power in the BETA ratio is very small, seeing that the value of the Electron BETA itself is very small, approaching 1, when 1 represents a 0 velocity for the source. The true question is, can an object's own Relativistic effects, effect itself. The answer is that yes it can, in the case of the Electron, since the Electron is also locked into a solid constant embrace with the stationary Proton through the virtue of Electron Charge, whose positive charge unit (in the Proton) binds the negative charge unit of the Electron to the Proton. Both objects thus read each other directly through the carrier medium of the two opposed charges conjoined as one. However, since the Proton sees the Relativistic effects transforming the Electron even though the Proton itself seems not to be able to be effected by the Relativity it sees (just like you cannot be empirically effected by the Relativity you see in a fast receeding galaxy), none the less those effects are in there, in the atomic structure, effecting the system, and have to be availed somewhere since both parts of the system: that which sees the effects: and that which generates the effects: are mutually bound within the same single system, the atom. What ARE those Relativistic effects (being generated by the Electron), doing, if anything. Obviously they are paramount, since the Proton sees them, and they are inside the system. But what about them, are they vapor? do they vanish in the 'ahem' ether. What? An external search shows that the Relativistic effects of the Electron actually externalize, they separate from their source, and become other entities, being generated and maintained by the constancy of the source of the effects, ie. the Electron's Borh orbit velocity. For instance the Electron's own binding energy, generated as a precipitation by Relativistic event, is such an externalization, since it (the binding energy) is not found inside the naked Electron but in the naked atom which includes the naked Electron. Even though the effects are very small, relativitically, due to the very small power represented in the effect's BETA ratio due to the Electron's rather slow velocity in comparison to the speed of light, the effects are still very precise. (If you wonder what is meant by slow, concider a car travelling at 137 kilometers an hour, and another travelling at 1 kilometer an hour, the faster travelling car representing the speed of light). In fact, the Electron's own Binding Energy within the Borh orbit in the hydrogen atom turns out to be exactly THERE, calculated to full amount, (or near full amount), by the terms of the Electron's own Relativity behavior. In this case a tiny unit of energy is externalized from the Relativity ingredients of the moving Electron, to be used to permanently bind the Electron itself in place in the atom within which it is generating the constant Relativistic effect that creates the binding force in the first place. In this sense, a Relativistic 'yearn', a form of 'glue', is the binding energy that holds the Electron in place. The glue is extra energy, equaling the Relativistic increase in mass over and above the Electron's inherent rest state mass in the universe. And the 'yearn' is a form of an incompatable Relativistic generation which cannot transform the Electron itself (its source) and so has to succor itself somewhere else, to 'isolate' as the extra mass generated by the Electron's velocity in the atom, and since that extra mass does not really exist in terms of the atomic mass parts themselves, the extra mass reaches out long distance from its Relativistic source, (is 'expunged' or externalized from its source since it is incompatable with the source's own rest mass) and works to become the little extra energy needed to hold the Electron permanently in place at a permanent velocity in the atom. Concider that extra energy, in the amount of the binding energy is needed 'inputted' from outside the system (from the universe at large), in order to knock the Electron loose from the system. At least that is how an unschooled self-taught might rant about the situation, such as me. The point is, that the Relativistic effect is there, and is obviously externalized from the source of the mass generating the effect, and so is somehow operating as a purged agent (or expunge) involving the Relativity itself, while still inherent and bound within the system generating it. --------------------------------------- EXTERNALIZED RELATIVITY IN THE SUN --------------------------------------- That a long distance manifestation of a Relativistic effect occurs outside of the source causing the effect is easily seen in the case of the Sun in the solar system. The Sun's gravitational amount, housed within an area known to be of finite size described as the Sun's radius, has General Relativistic effects that are known to effect the so called 'bending of space' for light passing from behind the Sun. It can also be presumed that the 'light' is passing through space contracted around the Sun, hence the apparent bend; as the light is being doppler shifted to a higher frequency as it approaches the Sun, then doppler reduced again as the light pulls away from the Sun. If it is assumed that the gravity of the Sun also causes effect on Mass, then the question is raised: how much increase in mass occurs upon the Sun due to its own gravitational General Relativity. The amount of gravitational mass held by the Sun is actually very small, compared to, for instance, super high densities of mass found within a supposed black hole. Nevertheless, the amount of mass increased by General Relativity in the Sun can be easily calculated, and turns out to be in no way just some mass randomly occurring as some Relativistic extra in the universe. It turns out that the amount of mass generated by the Sun is equal to the mass of VENUS, minus the mass of MARS. Subtract the mass of the one planet from the other, and that which remains, is exactly how much mass the Sun produces Relativistically in General Relativity, due to its gravitational density, by the Sun's rest state mass confined within its radius, when assuming that a mass increase is a General Relativistic effect of gravity. In fact that little bit of mass constancy (Venus mass minus Mars mass = Sun's gravitational psuedo mass) is proof that General Relativitistic effects include augmentation of MASS by the Relativistic power of an object's gravity. What is seen at once, is that the extra mass generated is not within the Sun, but psuedo connected to 'hard copy' particles (two physical small planets) precipitated well outside of the Sun's radius. In some way the two small mass particles are in an induction, since they are stable and very hard, very dense. Since the Sun's actual mass cannot be determined to great accuracy beyond 2 to 3 significant digits, due to the fact that it is not possible to put the Sun on a scale and weigh it - the Sun's mass is inferred by behavior amongst all of the orbiting planets, and whatever happens to be the latest estimate of the Universal Gravitational Constant, a constant also not well known beyond 3 significant digits. The VENUS - MARS masses can nonetheless be determined to within .1 percent of error using the Sun's known mass, using gravitational Relativistic equations. By using the known masses of MARS and VENUS, the Sun mass can be determined in reverse engineering to much more, in digits and percent of accuracy, in which the full value of these known planet masses are used, and the determined Sun mass lands right in the middle of the error range astronomers assign for their current Sun mass estimates, except it is now readable as a value of up to 6 significant digits or more, via the reverse engineering method, an improvement of a full 3 orders of magnetude at least. The significance is, that a known manner of an externalized Relativistic state of action, has been identified and proven, by the demonstration of the handshake calculations of two planet masses, from the Sun mass, via General Relativity. See APPENDIX 2 at the end, for mathematical details. ----------------------------------------- SPECIAL VRS GRAVITATIONAL RELATIVITY ----------------------------------------- Be aware that the Einstein equations for General Relativity are not the same as those for Special Relativity. The BETA effect of Special Relativity transmutes at a different rate, there is a marked difference in the rates at which things transform via the ratios involving the two forms of Relativity. However it has just been disclosed that the General Relativity form transforms rest state mass (the Sun) to an expunged external place, split into two permanent condensed states (VENUS and MARS), the mass expunged from the incompatables of Relativity transforming itself into exactly the amount of mass comprising VENUS minus MARS. Two planets that exist, related to a third planetary mass quantity that does not exist, reaching through the none-existent form being the amount of mass the Sun Relativistically generates by its own Relativity. Summing the states the other way; the sum of the Sun's Relativitistic mass increase, plus MARS, equals the mass of VENUS. A question: can the non-existent mass (Venus - Mars) be like a binding energy equivalent, the amount of energy it would take to knock the two planets out of the system, or something like that. In other words, is that 'missing' mass actually being expressed somewhere else, unrecognized at the moment in the gravitational dynamics of the Solar system? (Speculation). Without question there is nonetheless a quantal effect in gravity, relating to the materialization of at least 2 empirically precise planet masses. -------------------------------------------- IF FOR INSTANCE ALSO SPECIAL RELATIVITY -------------------------------------------- In the case of the atom, a similar situation is seen to occur, only in this case it is not gravitational Relativity (General and stationary) but the Special Relativity form (due to motion). If, for instance, the Sun also happened to be bound in a two part system, for instance around a black hole whose mass was roughly 1,836 times more than the Sun mass so that the Black Hole stayed essentially stationary (a slight wobble) with the Sun trafficing around it at a velocity approaching 137.0359895 times less than the speed of light, we would also have in place a similar situation as found between the Electron and Proton, and further, that the Sun's Velocity would also be producing an effect from its motion due to Special Relativity. The analogy cannot continue because the analogy simply cannot say if or if not the Sun's increase in mass is local (apparent only to an external observer) or internal (due to the direct gravity link to the Black Hole), in which case, if internal, the Sun's increase in mass due to the Special Relativity would have to appear somewhere in a self sustained way. But what that appearance might be is not made self evident by the analogy. It is self evident, however, in the atomic analogy counterpart, that externatized Special Relatavistic effect occurs, to wit, involving the Proton, and Electron orbiting around it comprising a hydrogen atom. In the case of the atom, the expunged mass re-appears in the form of and is put to work as, the Electron's binding energy. How come? There might be a rule in this, that can be stated something like: A rest state mass in the presence of a Relativistic influence tends to stay at the rest state value, and the extra mass due to the Relativistic influence must be externalized but still remain within a thermodynamic system to stablize the externalization of the extra mass. In the case of the orbiting Electron, it seems that the Electron binding energy is one of the means of stablization. How come it is energy is simply a quality of the mass/energy equality inherent in all material through E = M (C squared) For instance a photon of the right energy will move the Electron out to another orbit, when absorbed. And when emitted, a photon of the right energy will cause the Electron to loose its bind and leave the atom. An Electron can absorb photons until enough energy has been absorbed to be released all at once as a photon (in the high ultra-violet range), in an amount quantally equal to the unit of force called the Electron's binding energy. The release can all be in a single photon of that precise amount of energy. Mathematics that road map how some of this occurs are very easy to produce, as follows: EQUATION 4 ________________________ | | Ú V ¿ 2 B = BETA = | 1 - ³ --- ³ Special Relativitity \| À C Ù effects Ratio (BETA) ------------------- TERMS AND CONSTANTS ------------------- B = .9999733739653 BETA ratio for contraction 1/B = 1.000026626744 BETA ratio for expansion C A = --- = FSC = Fine Structure Constant V = 137.0359895 A* = (A squared) = the FSC squared E = .51099906 5 = Electron mass energy (Mev) Eo = .000013605698088 = Electron binding energy (Rydber energy) (Mev) Eo = E x 1/A* = E x 1/ (2 (A squared)) Ew = 3861.5932363790 = Electron Compton wavelength x 10 to -14 cm = h^/E Bo = 529177.25019370 = Borh orbit (rest state) x 10 to -14 cm = Ew x A -------------------------- h^ = (1973.2705332 MeV -14cm) = Plank's Converter Constant PLANK'S CONSTANT CONVERTER used to convert mass energy to -------------------------- Compton Wavelength, and visa versa using full floating decimal system rather than scientific notion. Plank's Constant value of (6.5821220 x 10 -22MeV s) speed of light times (2.99792458 x 10 to the power 10 cm s-1) equals (1.9732705332 MeV -11cm) times 1000 equals (1973.2705332 MeV -14cm) equals h^ The above data summary is all that is needed for the code to show full mass in-house self sustained Relativistics at work. -------------------------------------- BEGIN CODES March 16, 1995. -------------------------------------- Assume the Electron in Borh orbit will experience slight Relativistic effects due to velocity. The effect on Electron rest state MASS will be: EQUATION 5 An expansion; (E x 1/BETA) - E = .00001360 62413 Mev Note that this Eo is slightly larger than the Eo derived from the FSC (Fine Structure Constant), as shown in the above table of TERMS AND CONSTANTS. -------------- OTHER DYNAMICS -------------- Two other dynamical infrastructures within the Hydrogen atomic system may also be assumed to experience Relativistics, due to the Electron's velocity. These are: Electron Compton Wavelength The Electron Bohr Orbit (rest state orbit). These two dynamics, with assumed in-house self systained Relativistics, lead directly to elementary particle states known as the PION meson particle, and UPSILON meson, as well as the Electron Radius (classical). How this is so is shown as this discussion continues below. ASSUMPTIONS ----------- In keeping with general tenets of the Theory of Special Relativity, an assumed increase in rest state mass, and decrease in rest state space (size) presumes that the rest mass of the Electron is larger, and the Compton wavelength of the Electron and also the Borh orbit are contracted. In Relativistics which can be shown for a simple Hydrogen atom, both contraction and increase of SPACE seems to be in the picture. Therefore no limitation has been placed on what kind of derivation should, or should not, produce results. Derivations that produce results are shown in the TABLE OF DERIVATIONS below. The derivations are shown in two forms, as simplified abstracts using symbols to denote terms comprising steps in the equations, but more often with digital detail included. IN PRE-SUMMARY -------------- PION Relativistic change to the BORH ORBIT (rest state orbit) leads directly to the Compton wavelength of a single stable PION charged particle mass. The change incorporates an Electron mass, and 1/2 unit of Electron binding energy, and other whole integer terms effecting the value of Eo. UPSILON Relativistic change to the ELECTRON'S COMPTON WAVELENGTH, leads directly to the Compton wavelengths for a pair of UPSILON meson mass energies, (a high mass particle always produced in 'pairs' in particle experiments). The change can incorporate a PION mass, possibly a unit of the PION particle charge/neutral mass difference (4.5936 Mev), an Electron, and a unit of the Electron binding energy, per Upsilon. ELECTRON RADIUS Relativistic change to the BORH ORBIT DIAMETER (full cross section of the rest state Borh orbit) leads directly to the 'Electron Classical Radius'. ELECTRON BINDING ENERGY Relativistic change to the ELECTRON REST MASS leads directly to the 'Electron binding energy', (already shown in EQUATION 5), and known as the Rydberg Energy Constant. ELECTRON MASS ITSELF Relativistic change to the sum of the Electron rest mass, plus the Electron binding energy, raised in power by 2 times the Fine Structure Constant to allude the PION mass, as a wavelength added to the Bohr Orbit, leads directly to the Electron rest mass itself. It falls out of the powerframe, on its own, as an induced product. ----------------- IN PRE-DISCLOSURE ----------------- There are probably 2,000 or more different ways quantum physical information can be shown or described. After giving some thought to various ways, lineal deterministic derivation step after step; vrs boolean virtual reality abstractions; vrs something made up on the spur of the moment; it has been decided to simply list a table of derivations. The derivations and their results will be self evident and proof of any derivation will be seen at once by anyone who does a derivation exactly as shown. ACCURACY -------- The derivations are done maintaining utmost accuracy available at the time of doing the calculations. This is an accuracy up to 13 significant digits. Since input data (values of the known Physical Constants) is not beyond 7 to 10 digits for the constants at this time, March 1995, there is inherent trunkation (spurious digits) in the results but this 'noise' is always in just the final few digits of a result, at the 7th significant digit or beyond. Spurious 'digitation' is also recognized as occuring in the Relativistic transformations working through the BETA ratio, since 4 zeros are bound in a ratio reciprocated from the 4 digits of number 9 persuent to a BETA ratio value converging toward a value of 1 at zero Relativistic velocity. These inherent 0's and 9's reduce the maximum range of possible intrinsic accuracy to the 13 digit limit, so it is assumed that the results using the BETA ratio are reliable to about the 7th to 9th significant digit of a calculation. ABSOLUTES --------- A test was run on the question of 'exactitudes' vrs 'convergence' in the self-sustained Relativistics of the Hydrogen atom construct, testing the accuracy of certain codes using arbitrary whole integer inputs to follow Relativistic transformations. The test demonstrates that the Relativistic derivations for the Hydron atom construct involve 'convergences', and are not 'exactitudes'. Under APPENDIX 1 is a summary of the test. ============================================ SELF SUSTAINED 'RELATIVITISTICS' IN THE ATOM ============================================ ++++++++++++++++++++ TABLE OF DERIVATIONS ++++++++++++++++++++ ========================================================= DERIVING - ELECTRON BINDING ENERGY Disclosure 1 ========================================================= LET Eo = Electron Binding Energy = .0000136056981(40) Mev LET A* = FSC squared (Fine Structure Constant) THEN: THE ORIGINAL BINDING ENERGY Eo = E x 1/2A* = .000013605698088 Mev EQUATION 6 ________________________ | | Ú 1 ¿ 2 BETA = | 1 - ³ --- ³ = .9999733739653 \| À A Ù E x 1/BETA = .5110126712413 Mev = E + Eo = E+ - Eo (gained from E x 1/2A*) = .510999065 / 543 Mev THE ORIGINAL ELECTRON MASS In another approach; E+ = .5110126712413 Mev from EQUATION 6 - E 1. = Eo = .00001360 624130 Mev THE ELECTRON BINDING ENERGY compared to Eo derived from the FSC as: E x 1/A* = Eo 2. Eo = .00001360 569808 Mev compared to Eo as a published physical constant: 3. Eo = .00001360 56981(40) Mev (the published constant). Regards the Relativistic derivation (.00001360 624130 Mev) compared to the FSC derivation (.00001360 569808 Mev) the figures are close to exact. But exactitude is an illusion. Such seeming exactitude (assuming inherent digital trunkation due to large decimal terms) does not confirm, using random or arbitrary numbers to follow how the digits permutate. See APPENDIX 1 below, for a test case using easy to follow arbitrary numbers to test the digitation in the transformations. The test case of APPENDIX 1 deems that the Eo term determined as a Relativistic transformation on the Electron mass by 1/BETA is co-incidental to an Eo term gained by E x 1/2A* = Eo . Nevertheless, the fact is that the BETA derived Eo, and FSC derived Eo are close indeed. Their departure occurs at the 9th significant digit. Which raises a serious question about the Rydberg Energy Constant = Eo the Electron Binding Energy. Is it E x 1/A*, or is it more accurately E x 1/BETA when ________________________ | | Ú 1 ¿ 2 V BETA = | 1 - ³ --- ³ when A = --- \| À A Ù C and V is the Electron's Borh orbit velocity. 11:05 PM. March 16, 1995. PAUSE DISCUSSION ---------------- Immediately after this point in time (11:05 PM. March 16, 1995), a number of things were factored, both on an exploratory basis, and on fact finding missions. Since many of the exploratory missions proved unproductive they need not be mentioned, although a few did hold surprises in somewhat kinky ways, (for instance exploring Relativitistics in the Borh DIAMETER), and these are shown in an ad hoc way in 'THE FABULOSO PERHAPS COLLECTION' further below. The mainstream stuff, straight to the core of the matter, is shown in the following, beginning next, with Relativistics found in the Borh Orbit. ANOTHER PAUSE DISCUSSION ... PION and UPSILON particles ---------------------------------------------------------- The full mass system is the Electron mass, plus its Binding Energy generated by Special Relativity due to the Electron's orbital velocity in a Hydrogen atom. What other fundamental mass equivalents might be generated by such a self-enhancing dynamic system. Here is what can be shown readily, about two other particle masses. In these two cases, it is the WAVELENGTHS that are the carrier of the Relativitics information, which translate by the Plank's Constant conversion to mass. These WAVELENGTHS are of SPACE, including Compton Wavelengths as a measure of distance, and the Borh orbit, also a measure of distance. ============================================ THE BORH ORBIT Disclosure 2 ============================================ The BORH ORBIT is the orbital distance from a Proton around which an Electron in its rest state level, orbits in a Hydrogen atom at a velocity which is less than the speed of light by a ratio equal to the Fine Structure Constant. When the BORH ORBIT is Relativistically transformed, the following happens; For the naked Electron (.510999065 Mev) ; Bo = h^/(E x A) = 529177.250193 x 10 to -14 cm. If Bo is the contracted state, then the full system state (original) is; expansion Bo x 1/BETA = 529191.340460 x 10 to -14 cm. = Bo* Bo* x 1/A turns out to be the Compton wavelength of E - Eo where 1 unit of Electron Binding Energy is manifested in the relativistic transformation of the Borh orbit, by the transformation of 1/BETA, THAT IS h^/ (Bo* x 1/A) = .5110126712 Mev - Eo = .510999065 5 Mev compared to the original Electron rest mass = .510999065 Mev compared to the published Electron rest mass = .51099906(15) Mev COMMENT ------- See further below under 'KINKY BORH ORBIT FRACTURING' for a derivation which splits Eo into 1/2 Eo and 3/2 Eo units via transformations of the Borh orbit . ================================================================= BORH ORBIT AGAIN Full Mass System - holder of a PION ================================================================= For E + Eo = E+ = the full mass Electron (.5110126706 Mev) ; h^/ (E+ x A) = Bo+ = 529163.160864 x 10 to -14 cm ; where Bo+ is a 'reduced' Borh orbit calculated as E enhanced by the Electron binding energy Eo reduced by the FSC, and converted to a wavelength. Bo+ can be called a 'full mass' Borh orbit, for the sake of convenience, rather than as a definition. Assuming the full mass Borh orbit space state is not yet contracted, then: Bo+ x BETA = CONTRACT to transformed state Bo+ - (Bo+ x BETA) = PION+ state wavelength = 14.089516700 x 10 to -14 cm h^/PION+ = 140.052393223 Mev x 1/A then - Eo, then x 1/2 = .51099907 86 Mev the Electron. PION .... 1 PION, plus 1 Electron, expanded by the FSC from 2 Electrons, PLUS 1 Eo binding energy, is imbedded as a Compton wavelength increment from a Borh+ orbit constractive transformation on the Electron full mass Borh+ orbit state, in comparing the contracted space length, to the original Borh+ state. In converse, if the Borh+ state is assumed ALREADY contracted, THEN Bo+ x 1/BETA = EXPAND to non-transformed state and the sequence points to the embedding of 1 PION, plus 1 Electron, expanded by the FSC from 2 Electrons, MINUS 1 Eo binding energy, for E = .51099907 31 Mev. A switcheroo has occurred; as a PLUS 1/2 Eo entity for a Borh+ already contracted and so has to be expanded back to non-Relativistic rest state space, vrs a MINUS 1/2 Eo entity if the Borh+ space is rest state, and so has to be transformed by Relativistic contraction. PAUSE COMMENT ------------- In concidering that Gluons are the theoretical carrier of the STRONG force in nuclear interractions; gluons knit Quarks together, which is how PIONS are produced, from three different 2 Quark combinations involving 2 Quarks (Postive PION), and a Quark / anti-Quark (Neutral PION), or 2 anti- Quarks (Negative PION), it may seem that a two-Electron atomic (or more) Relativistically resonating system can be involved, since PIONS are often produced in pairs, as well as in just about any quantity, singly or otherwise. (Speciulation). DISCUSSION ---------- In the next derivation, a 'KINKY BORH ORBIT FRACTURING' for a rest state Electron mass derivation, splits Eo into 1/2 Eo and 3/2 Eo units via transformations of the Borh orbit. =============================================== KINKY BORH ORBIT FRACTURING =============================================== The Borh orbit itself, transformed from both an assumed contracted state, and non-contracted state, produces tiny differences in Relativistic results to the Borh orbit measure which are PION Compton wavelengths, that hark back to the Electron, and its binding energy, in an interesting way. The 'interesting way' is the occurrence of 1/2 and 3/2 Eo states accruing. HERE IS HOW: LET Bo = (Electron Compton wavelength x A) equals the Borh orbit, 529177.250193 x 10 to -14 cm (published). Relativistically contracting Bo, then; pion + E wavelength Bo - (Bo x BETA) = 14.089891800 x 10 to -14 cm now contracted which is the Compton wavelength for 140.048664759 Mev which is a PION + E mass derivative incorporating; 1/2 Eo .... 2A x (E - 1/2 Eo), for Eo = .000013 57491500 Mev ------ AND ALSO -------- pion + E wavelength Bo - (Bo x 1/BETA) = 14.090267200 x 10 to -14 cm now un-contracted which is the Compton wavelength for 140.044933512 Mev which is a PION + E mass derivative incorporating; 3/2 Eo .... 2A x (E - 3/2 Eo), for Eo = .000013 60104733 Mev ------ =============================================== UPSILONS with a pair of PIONS =============================================== The Compton wavelength of the Electron, Relativistically transformed, holds a space incremental which happens to be exactly the mass energy equivalent of 2 UPSILONS, 2 PIONS, 2 ELECTRONS, and units of Eo the Electron binding energy. The neutral PION mass is precipitated. Here is how: Assume the 'full mass' Electron Compton Wavelength is already CONTRACTED, in keeping with an atomic Electron that is Relativistically expanded. Therefore E+ = E + Eo AND SO E+w = h ^/ (E+ x BETA) = 3861.49042156 x 10 to -14 cm E+w x 1/BETA - E+w = .10281 89170 x 10 to -14 cm h^/ (.1028189170) = 19191.7070396 Mev 1/2 (19191.7070396) = 9595.85351983 Mev - UPSILON mass 1 S state being 9460.37(21) Mev = 135.483519835 Mev - Electron (.510999065 Mev) = 134.97 2520770 Mev close enough to PION Neutral 134.97 64(6) Mev not to quibble at all. Working back to basic atomic Electron Relativistics; 19191.7070396 Mev x 1/2A* = .5109922691 Mev - Electron (.510999065 Mev) = 1/2 Eo (.000013 59162700 Mev) OR ALSO Electron (.5109922691 Mev) - 1/2 Eo (.000013 60569808 Mev) from E x 1/A* = Electron (.5109990 720 Mev) SECOND VERSION for UPSILONS ----------------------------- Assume the 'full mass' Electron Compton Wavelength is currently EXPANDED, (not yet contracted), then the contracted version has as Relativistic products: E+w = h ^/ (E+ x BETA) = 3861.49042156 x 10 to -14 cm E+w - (E+w x BETA) = .10281 61780 x 10 to -14 cm h^/ (.1028161780) = 19192.2183024 Mev 1/2 (19192.2183024) = 9596.10915122 Mev - UPSILON mass 1 S state being 9460.37(21) Mev = 135.739151225 Mev - Electron (.510999065 Mev) = 135.228152160 Mev - 1/2 Electron (.2554995325 Mev) = 134.97 2652627 Mev close enough to PION Neutral 134.97 64(6) Mev not to quibble at all. Working back to basic atomic Electron Relativistics; 19192.2183024 Mev x 1/2A* = .5110058819 Mev - Electron (.510999065 Mev) = 1/2 Eo (.0000136 3381200 Mev) OR ALSO Electron (.510999065 Mev) - 1/2 Eo (.000013 60569808 Mev) from E x 1/A* = Electron (.5109990 790 Mev) =============================================== ONE UPSILON from bracketed Relativistics =============================================== UPSILONS are typically precipitated in pairs in the above collection of Relativistic derivations. Single Upsilons can be had, but from a different kind of regime, which may, or may not, be valid. It is shown as follows, in case there is validity. Here is an example of a spread arrising from a CONTRACTION, and EXPANSION, creating a gap in space, and the gap having a precise precipitation in terms of certain mass energies. In particular, a single UPSILON 1 S state mass, and a neutral PION are fundamnental in the bracket in space. --------- BRACKET 1 --------- LET h^/ (E + Eo) = Br expansion contraction (Br x 1/BETA) - (Br x BETA) = bracketed SPACE. AND SO h^/ (E + Eo) x 1/BETA minus h^/ (E + Eo) x BETA = bracketted SPACE = .2056350940 x 10 to -14 cm AND h^/ (.2056350940) = 9595.981389 Mev Upsilon + Pion x 1/A* = .5109990 779 Mev Electron . NOTE THAT: 9595.981389 - 134.9764(6) Mev = 9461.00498049 Mev pion neutral Upsilon 1 S + small extra 9460.37(21) Mev --------- BRACKET 2 --------- For a basic rest state Electron, the bracketing yields; h^/ E x 1/BETA minus h^/ E x BETA = .2056405710 x 10 to -14 cm h^/ (.2056350940) = 9595.725802 Mev Upsilon + Pion x 1/A* = .5109854680 Mev + Eo = .00001360569 Mev E binding energy = .5109990737 Mev Electron NOTE THAT: 9595.981389 - 134.9764(6) Mev = 9460.749402 Mev pion neutral - E Electron = 9460.23840350 Mev Upsilon 1 S + small extra 9460.37(21) Mev AND 9460.749402 Mev + 1/2 E Electron = 9461.004902 Mev which is the same mass determined in BRACKET 1 The two 'BRACKET' Upsilon variants, appear to differ by 1/2 Electron mass equivalent. =============================================== CLASSICAL ELECTRON RADIUS =============================================== QUICK SUMMARY ------------- So far, Relativistic harmonics of the atom have upchucked incorporate parts including the Electron binding energy, a single charged PION, two UPSILONS (1 S states), and 2 neutral PIONS. These have come from Relativistic glue for the Electron mass, and Electron wavelength, and the Borh orbit. The Borh diameter (atomic cross section) holds the blueprint for the 'classical' Electron Radius, as follows: -------- RADIUS 1 -------- LET Bo = E wavelength x A = 529177.2501 x 10 to -14 cm x 2 = 2Bo = 1058354.50038 x 10 to -14 cm contraction 2Bo - (2Bo x BETA) = 28.17978400 x 10 to -14 cm = Classical Electron Radius variation h^/ (28.17978400) = 70.024331385 Mev x 1/A = .5109922702 Mev - E x 2 = .0000135 8942160 Mev Electron binding energy variant -------- RADIUS 2 -------- LET Bo = E wavelength x A = 529177.2501 x 10 to -14 cm x 2 = 2Bo = 1058354.50038 x 10 to -14 cm expansion 2Bo - (2Bo x 1/BETA) = 28.18053400 x 10 to -14 cm = Classical Electron Radius variant h^/ (28.17978400) = 70.022467750 Mev x 1/A = .5109786706 Mev - E = .00002039431830 Mev x 2/3 = .0000135 9621220 Mev Electron binding energy variant -------- RADIUS 3 -------- LET Bo+ = (E + Eo) wavelength x A = 529163.160864 x 10 to -14 cm x 2 = 2Bo+ = 1058326.32172 x 10 to -14 cm contraction 2Bo+ - (2Bo+ x BETA) = 28.17903300 x 10 to -14 cm = Classical Electron Radius variation h^/ (28.17903300) = 70.026197605 Mev x 1/A = .5110058887 Mev - E x 2 = .0000136 4750980 Mev Electron binding energy variation -------- RADIUS 4 -------- LET Bo+ = (E + Eo) wavelength x A = 529163.160864 x 10 to -14 cm x 2 = 2Bo+ = 1058326.32172 x 10 to -14 cm expansion 2Bo+ - (2Bo+ x 1/BETA) = 28.17978400 x 10 to -14 cm = Classical Electron Radius variation h^/ (28.17978400) = 70.0243313893 Mev x 1/A = .51099227202 Mev - E x 2 change sign = .0000135 8942160 Mev Electron binding energy variation ------------ SPECIAL NOTE ------------ Of main interest, is that the Eo variation precipitated from RADIUS 1, is identical to the Eo variation precipitated from RADIUS 4. RADIUS 1 Eo precipitated variation = .00001358942160 Mev RADIUS 4 Eo precipitated variation = .00001358942160 Mev =============================================== RECURRSIVE 'RELATIVISTIC HARMONICS' =============================================== There are strong hints that a 'recursive' nature is incorporated within the Relativistic harmonics of the atomic/nuclear structure. The recursive nature can be seen in the following, in which certain variant terms show up over and over again, as if trying to state that the terms are self-locked ad infinitum. Unfortunately, problems of inherent trunkation in the digits make it all but impossible to determine if strange attractors are involved (whereby certain terms become closed and re-appear as constants ad infinitum) or if the system is open and certain terms re-appear a few times, gradually morphing, until suddenly resulting terms morph beyond coherent value and fall out of the recursive system, which ends at that point. No matter whether 'closed' or 'open', the recursive system is intriguing to look at, as follows: To see an example of the 'recursive' nature, the PION's wavelength is added to the Electron's wavelength, to form a base entity, and Relativistics are followed upon the combined wave structure, yeilding recursive datas which are not seen elsewhere until the combinant wave form of the Electron plus PION Compton wavelengths are mutually transformed as one wave. For example: --------------------------- HIDDEN DEEP 1 no Relativistics --------------------------- For full mass Electron, and for Pion = E + Eo, times 2, times FSC, - E THEN electron wavelength h^/ (((E + Eo) x 2A) - E) + Ew = 3875.73416017 x 10 to -14 cm pion wavelength h^/ (3875.73416017) = Electron variant = .5091481509 Mev - E = -.001850914064 Mev x A x 2 = .5072836804 Mev recursor 1 - E = -.00371538452 Mev change sign x A x 1 = .5091413941 Mev recursor 2 - E = -.001857670846 Mev change sign x A x 2 = .5091355252 Mev recursor 3 - E = -.001863539741 Mev change sign x A x 2 = .5107440249 Mev recursor 4 - E = .0002550400198 Mev abruptly ends here x 2 = .5100800396 Mev - E = .0009190254 Mev nothing recognizable A moisy thought can almost lead one into thinking about resonances, but ones which actually re-cycle through the same states for a few times, then quit. T H E S E would be 'resonances' in the full sense of the word. --------------------------- HIDDEN DEEP 2 Relativitics --------------------------- For full mass electron, and for Pion = E + Eo, times 2, times FSC, - E THEN electron wavelength h^/ (((E + Eo) x 2A) - E) + Ew = 3875.73416017 x 10 to -14 cm pion wavelength contraction x BETA = 3875.63096474 x 10 to -14 cm h^/ (3875.63096474) = .509148200 Mev - E = .001850864 Mev x A = .253634988 Mev x 2 = .507269976 Mev recursive 1 - E = -.003729088 Mev change sign * for Borh orbit x A = .511019385 Mev recursive 2 - E = .000020320 Mev recursive 3 = 3/2 Eo = .000013547 Mev ends here * This Mev value is an energy equivalent to an equivalent Wavelength space, known otherwise as dynamic space called the Borh Orbit. --------------------------- HIDDEN DEEP 3 --------------------------- The Pion term Subtracted from the Electron wavelength (rather than Added), does not seem to be Relativistically recursive. Nothing noteworthy is seen when following the Subtracted form through the derivation technique of HIDDEN DEEP 2. --------------------------- HIDDEN DEEP 4 no Relatistics --------------------------- For an ordinary rest state Electron (no Relatistics), the Pion wavelength is added to the Borh orbit, and the result converted to mass energy. The result plays a 'strange attractor' game with the Electron, through 5 solidly recurred instances. borh orbit Bo - h^/ (((E x 2A)) - E) = 527239.382924 x 10 to -14 cm pion wavelength h^/ (527239.382924) = .003742646314 Mev x A E approx. = .512 8772410 Mev recursor 1 - E = .001878176013 Mev x A = .2573777085 Mev x 2 E approx. = .51475541 70 Mev recursor 2 - E = .003756352012 Mev Borh orbit energy x A E approx. = .51475541 49 Mev recursor 3 - E = .003756349929 Mev x A E approx. = .514755 1295 Mev recursor 4 - E = .003756064511 Mev x A E approx. = .5147 160168 Mev recursor 5 - E = .003716951890 Mev x A E approx. = .5093561802 Mev jumps out here -------- - E = .001642884734 Mev unravelled x A x 2 = .4502686703 Mev - E = .06073039468 Mev x A = 8.322249728 Mev dissolved This demonstration went through a sequence of 5 recursive approximations of the Electron, then dissolved when the digits walked out of synch. Uncovered unexpectedly March 20, 1995 late afternoon, while double checking datas for other HIDDEN DEEP recurrances. It is not easy to reproduce such a sequence by mere factoring of the physical constants, go ahead and try. have fun. For instance; LET E = Electron rest mass LET A = Fine Structure Constant E + (E x 1/A) - E = R (recursor term) x A = E. The sequence ends abtruptly after 1 recursor. So what? is a 'recursor' term that will stay locked through many recurrances of ((((((R x A) - E), x A) - E), x A) - E),.... n Here is one secret: The energy equivalent of; the Bohr orbit - the Electron wavelength; contains a recursor element for the Electron, as follows: Bo - E wavelength = 525315.656957 x 10 to -14 cm h^/ (525315.656957) = .003756352027 Mev x A = .5147554170 Mev 1 2 3 4 5 - E, x A, - E, x A, - E, x A, - E, x A, - E, x A = .5093914357 Mev dumps out here after 5 recurrances the repeater resonance suddenly dumps out. The 'secret' unexpectedly uncovered March 21, 1995, 2 am. while double checking datas for DOUBLE RELATIVISTICS ON THE BORH ORBIT. --------------------------- HIDDEN DEEP 5 no Relatistics --------------------------- Reduced Electron mass wavelength = h^/ (E - Eo) = Ew- no relativistics. Then h^/ ((E x 2A) - E) + Ew- = 3875.837358349 x 10 to -14 cm pion wavelength reduced electron wavelength h^/ (3875.837358349) = .5091210881048 Mev Recursing begins: - E = .001877976895 Mev x A x 2 = .5147008441 Mev recursive 1 - E = .003701779183 Mev x A = .5072769733 Mev recursive 2 - E = .003722091637 Mev x A = .5100605105 Mev recursive 3 - E = .0000938554 Mev recursive 4 is spurious, the recursiveness has passed into a fade-out. --------------------------- HIDDEN DEEP 6 Relatistics --------------------------- With relativitistics, pre-contracted state assumed. h^/ (((E + Eo) x 2A)) - E)) + Ew = 3875.734160172 x 10 to -14 cm pion wavelength electron wavelength x 1/BETA = 3875.837358353 x 10 to -14 cm expanded to non relativistic state h^/ (3875.837358353) = .5091210881048 Mev The datas are hereafter identical to the 'recursing begins' datas of HIDDEN DEEP 5. The difference is that the ((E + Eo) x 2A), and E (for Electron wavelength) terms of HIDDEN DEEP 6, are lock-stepped with the non-relativitistic derivation terms (E x 2A), and (E - Eo) (reduced Electron wavelength) terms of HIDDEN DEEP 5. --------------------------- HIDDEN DEEP 7 Relatistics --------------------------- With the initial condition for HIDDEN DEEP 2 = h^/ (((E + Eo) x 2A)) - E)) + Ew = 3875.734160172 x 10 to -14 cm pion wavelength electron wavelength An assumed rest state therefore needs to be Relativistically contracted. Then the following recursive sequence occurs; x BETA = 3875.63096474 x 10 to -14 cm expanded to non relativistic state h^/ (3875.63096474) = .509148200938 Mev Recursing begins: - E = .001850864061 mev x A x 2 = .5072699761 mev recursive 1 - E = -.003729088887 mev change sign x A = .511019385563 mev recursive 2 - E = .000020320563 mev x 2/3 = .00001354704 mev recursiveness fades out approximating Eo. --------------------------- HIDDEN DEEP 8 no Relativistics, ends --------------------------- at Eo binding energy Rest state whole form recursing. This demonstration includes the Electron binding energy, in full measure, without relativistics. There are no 'resonances' in this example. assumed untransformed h^/ (((E + Eo) x 2A)) - E)) + Ew = 3875.734160172 x 10 to -14 cm pion wavelength electron wavelength THEN h^/ (3875.734160172) = .5091346443411 Mev - E change sign = .001864420658 Mev x A = .2554927298366 Mev x 2 = .510985459673 Mev recursor 1 - E = .000013605 32680 Mev recursing abruptly ends! at exactly Eo. Electron binding energy for comparison is = .000013605 6981(40) Mev --------------------------- HIDDEN DEEP 9 no Relativistics, ends --------------------------- at Electron rest mass And finally, here is one which comes right back to an Electron after only 3 recursive resonances. this resonance starts out the same as HIDDEN DEEP 1 except E+ rather than E is the Electron mass equivalent in conjunction with the Pion variant. For full mass Electron, and for Pion = E + Eo, times 2, times FSC, - E+ THEN electron wavelength h^/ (((E + Eo) x 2A) - E+) + Ew = 3875.63134673 x 10 to -14 cm pion wavelength h^/ (3875.63134673) = Electron variant = .5091481507 Mev - E = -.001850914245 Mev x A x 2 = .5072837301 Mev recursor 1 - E = -.003715334886 Mev change sign x A x 1 = .5091345924 Mev recursor 2 - E = -.001864472545 Mev x A x 2 = .510999 6803 Mev recursor 3 = Electron abruptly ends! at close to E. SPECULATION ----------- There could be other 'recursives' in atomic/nuclear inner scene structures. The examples (shown above) are the only recursors that has been explored for this disclosure, because they are so self evident, and so far none else have turned up. No diligent search has been conducted through the realm of possibilites checking other variables that may harbor more recursive 'resonances'. The recursive nature of the examples appeared as a consequence of doing the derivations. Prior, there was no insight that any such 'recursive' nature was hidden, to be exposed by mathematics, until the sequence in HIDDEN DEEP 2 was first factored. The other HIDDEN DEEP examples were turned up by poking around like an explorer, without a theory up front to point the way. Those HIDDEN DEEP examples incorporate re-combinant wavelengths added together to comprise the SPACE being examined, to reveal lengthy sequences of recursoring involving more than one inner manifestation of the Fine Structure Constant ratio, per each recursive sequence. In fact a 're-combinant' wave factor; comprising the Bohr orbit, plus the Electron Compton wavelength; holds within its pictures the naked Electron itself, as demonstrated in 'DIRECT HIT ! - the Electron itself', immediately below. This 'Direct Hit' example is entirely closed, with no self locking 'strange attractor' self re-generating Relativistic dynamics at work. As follows: =============================================== DIRECT HIT ! - the Electron itself =============================================== The Self-Sustained Electron: There are 8 steps that lead to popping the Electron mass out of its own works in the infrastructure of atomic Relativitistics. The Relativitistic harmonics have a self contained image of the Electron itself wrapped within the dynamic images of the innerscene of the atom, seen by a particular derivation, as follows: The self-sustained Electron: -------- DIRECT 1 -------- LET Bo = Borh orbit = E wavelength x A Borh orbit [h^/ ((E + Eo) x 2A)] + Bo = 529191.339523 x 10 to -14 cm Pion + Electron wavelength 1 2 3 4 5 number of steps Relativitistically CONTRACT it: 6 529191.339523 x BETA = 529177.249256 x 10 to -14 cm 7 h^/ (529177.249256) = .003728940607 Mev 8 x A = .510999065 9 Mev Direct hit! This is where the Electron bombs right into the open, whole sound and perfect, as a direct result of relativistic contraction of atomic dynamic space. A pre-existing nuclii resonant ability called the PION (in augmented state), holds part of the blueprint for the complete picture. 1:45 pm, March 18, 1995. -------- DIRECT 2 -------- Here is what happens when the space is pre-contracted, so that EXPANSION is used to see the Relativistic inner space matter: Relativitistically EXPAND it: 529191.339523 x 1/BETA = 529205.430165 x 10 to -14 cm h^/ (529177.249256) = .0037287420361 Mev x A = .5109718545098 Mev - E = .0000272104902 Mev = 2 Eo x 1/2 = Eo = .000013605 24510 Mev compared to Eo = .000013605 69808 Mev Direct hit! This time (expansion from pre-contracted state) reveals 2 units of the Electron Binding Energy inbound within the harmonics of the atom/nuclear interface. Discussion ---------- If the Relativistic BETA transformation was not a part of this derivation, then the emergence of the Electron could simply be due to a tautological re-factoring of the fundamental constants. However, this is not the case. The Relativistic transformation on a precise and re-combinant segment of space has produced the Electron mass in toto, plus two units of the Electron binding energy, as shown immediately above by DIRECT 1 and DIRECT 2. This product could be the Electron mass, or an equivalent unit of momentum energy. At this point what that unit is, is not the point. The point is that this unit appears in direct consequence to inner Relativistic harmonics that are self-built, self-contained, and self-inducted in the dynamics of the atomic/nuclear structure. If momentum energy is assumed for the Electron mass unit, then it could be nuclear related, which takes the scene directly back into inner nuclear resonant harmonics, since the PION particle is a fact of nuclear, not atomic, interactions. In the equations of KINKY BORH are hinted a tight together coherency which ties together inner nuclear properties (PION particle wavelength) directly to the outer fringes of atomic structure (borh orbit). See in 'KINKY BORH ORBIT FRACTURING' The single field of a combined Positive and Negative charge, which pervades the whole structure, may be a carrier of the Relativistics revealed by DIRECT 1 - 2; (something akin to a gravitational field surrounding the source that generates General Relativistic effects); the combined charge field being the carrier or containment vehicle for the Relativistic effects induced by the motion of the Electron in the atom. THEORY - DISCUSSION --------------------- Since both the Electron, and Proton, are independent existent; (both can exist independent of an embodiment in an atom); the essence seems to be that the Electron (and Proton) hold the blueprints by which the shape and structure of the atom is created, by the internalized Relativistics in the combined dynamic system. It may be (due to the PION connection) that the PROTON holds part of the blueprint for atomic construction, a blueprint which does not appear until an Electron arrives to bind with the Proton and activate the full blueprint, the resulting system contrived by mutually agreed dependence upon the limited possibilities the Relativistic harmonics can allow. In this scene, the Electron, Borh orbit, Pion mass, and other fundamental entities, do not appear simply because God made them to have such appearance. Something more fundamental in the nature of God has made the whole system by which the appearance of atomic parts manifest in toto. The parts cannot change in any large scale variance, or else the Relativistic harmonics will simply fall apart, loose its glue, de-converge, and presto! the atom as we know it would vanish from the empirical dimension. The atom's Relativistic signatures define its existence. Here is a statement: The atom cannot exist without its self induced Relativistic Harmonics. SPECULATION ----------- If two opposite charges sang together in a straight line rather than in a saturating field, the link between Electron and Proton swinging around through space could provide a 'manner' by which Relativistics are propigated against a stationary backdrop of the universe, in terms of 'compare' to the constancy of the speed of light. Like a magnet swinging around through an electrical field generating another force, the swinging Electron and charge-polarized link are swinging through a universe in which velocity is deemed generative because of a speed of light maximum, in this case the velocity is generating another force, known as 'Relativity', which transforms the source of the in-motion generating entities. Or else a mathematical point source hurtling through the stationary field of its own backdrop linked to the Proton is the means by which another force is generated. However the theory will unfold, there is no question that one thing (motion) is generating another thing, Relativistic harmonics - self induced. MOIRE PATTERN VRS WAVE HARMONICS -------------------------------- Actually, since wave harmonics dominate the field of Electron occupancy around the orbital shell of an atom, it is possible to think of a moire pattern cycling around the field, through the charge density medium of the wave harmonics, the velocity of the Electron the speed at which the moire pattern moves in cyclical motion through the wave harmonics. ==================================================== SCHEMATICS ==================================================== -===========- INNER SCENE 1 Rest state -===========- Here is a schematic showing in a model linear form a broad band of inner scene SPACE/MASS harmonics. ============= ========= .00000001 Mev 19192 Mev .000013606 Mev .51099906 Mev 140.045 Mev 9596.10 Mev 1 electron upsilon binding 1 mev 2 energy ELECTRON pion | upsilon photon | E mev | mev spectra | | | | .==========.=========.=========>==========.=========.==========.=======. x 4Pi A x 2A x A | x A x 2 x A x 2 .----------.--------.----------|----------.---------.----------.-------. 1/4Pi A 1/2A 1/A | 1/A 1/2 1/A 1/2 .==========.=========.=========<==========.=========.==========.=======. | electron | | | | wavelength electron | | 10 to -6 cm | radius | 2 upsilon =========== borh | wavelength orbit | pion wavelength 10 to -15 cm ============ -===========- INNER SCENE 2 Harmonic inner-scene particles -===========- electron binding 1 of 2 of energy ELECTRON pion upsilon mev mev | | Eo E + Eo P + 1E | 2A x (E + Eo) | | | 2 U + 2 P + 2 E - 1 Eo photon | | 2A* x (E + Eo) | | | | | | | .==========.========.=======>==========.=========.=========.==========. x 4Pi A x 2A x A x A x 2 x A x 2 .==========.========.=======<==========.=========.=========.==========. .==========.========.=======<==========.=========.=========.==========. | electron | | | spectra | wavelength electron | | | radius | 2 upsilon borh | wavelength orbit | pion wavelength ===================================================================== THE FABULOSO PERHAPS COLLECTION ===================================================================== Here are several strings involving Relativitistic harmonics, that either have not made it into one of the catagory demonstrations, or did, but also is within a set having different prioritization. These equations are set forth as if run lineally through a calculator, so there are changes of sign (a larger value subtracted from a lower value) which are self evident yet not noted, due to ideals of keeping the equation strings simplistic, so that several comparisons can be seen at a glance, all together. These strings were turned up during a self imposed crash seminar into the nature of Relativitistic atomic/nuclear harmonics, and are copied as follows more or less in the same form as originally written in notes by hand done in fast mode, working on the calculator, checking out every idea that came to mind, during a two day purge of ideas. Much of the information uncovered in the crash course is already detailed in one or another of the demonstrations, but in other ways with other themes. THE FABULOSO COLLECTION has a whole bunch of themes together, including leftovers that didn't fit elsewhere. -------------------------------------- DOUBLE RELATIVISTICS ON THE BORH ORBIT -------------------------------------- LET Bo = Electron wavelength x FSC = Borh orbit. twice contracted Bo - (Bo x 2 BETA) = Electron RADIUS for (E x A) for E = .5109990 739 Mev LET Bo+ = Electron wavelength x FSC, (for (E + Eo)) twice contracted Bo+ - (Bo+ x 2 BETA) = Electron RADIUS for ((E + Eo) x A) for E = .5109990 744 Mev ----------------------------------------------- DOUBLE RELATIVISTICS ON THE ELECTRON WAVELENGTH ----------------------------------------------- LET U* = E x 2(A squared) = Upsilon region twice contracted E wavelength - (E wavelength x 2 BETA) = U* for E = .5109990 729 twice expanded ((E wavelength x (2 (1/BETA)) - E wavelength = U* for E = .5109990 722 - 2 Eo twice contracted E + Eo wavelength - (E + Eo wavelength x 2 BETA) = U* for E = .5109990 728 - 1 Eo twice expanded ((E + Eo wavelength x (2 (1/BETA)) - E + Eo wavelength = U* for E = .5109990 712 - 1 Eo ----------------------------------------------- SINGLE RELATIVISTICS ON THE ELECTRON WAVELENGTH ----------------------------------------------- contracted E + Eo wavelength - (E + Eo wavelength x BETA) = U* for E = .5109990 740 + 1/1 Eo expanded ((E + Eo wavelength x (1/BETA)) - E + Eo wavelength = U* for E = .5109990 720 - 1/2 Eo -------------------------------------- SINGLE RELATIVISTICS ON THE BORH ORBIT -------------------------------------- LET Bo = Electron wavelength x FSC, for E LET Bo+ = Electron wavelength x FSC, for (E + Eo)) LET P* = Pion status = E x 2A augmented contract Bo+ - (Bo+ x BETA) = Pion status for (E + 1/2 Eo) for E = .5109990 786 Mev augmented expand Bo+ - (Bo+ x 1/BETA) = Pion status for (E - 1/2 Eo) for E = .5109990 731 Mev To find E, E was multiplied by 2 and Eo (.00001360569808 Mev) was subtracted. ------------- LITTLE GOODIE ------------- LET Bo+ = Electron wavelength x FSC, for (E + Eo)) LET Bo = Electron wavelength x FSC = 529177.250 193 x 10 to -14 cm Identical augmented expand Bo+ x 1/BETA = 529177.250 756 x 10 to -14 cm Identical Both values are the same to the 9th significant digit. It suggests that the native state for the Relativistic Borh orbit is the augmented orbit, contracted, since when expanded (Relativistic transformation is removed) the augmented Borh orbit state becomes equal to the naked Borh orbit. ===================================================================== MORE FROM THE FABULOSO PERHAPS COLLECTION ===================================================================== --------------------------------------------------- SOME SINGLE UPSILON YIN-YANG RELATIVISTIC HARMONICS --------------------------------------------------- LET U* = E x A* = 9595.98113748 Mev expand U* x 1/BETA - U* = 1/2 (E + 3/2 Eo) for Eo = .00001360 06666 MeV contract U* x BETA - U* = 1/2 (E + 1 Eo) for E = .5109990571 MeV to find E, E was multiplied by 2 and Eo (.00001360569808 Mev) was subtracted. contract h^/U* x BETA wavelength = h^/(E + Eo) for E = .5109990655 Mev --------------------------------------------------- SOME PION YIN-YANG RELATIVISTIC HARMONICS --------------------------------------------------- LET P* = E x 2A = 140.05052501 Mev expand P* x 1/BETA - P* x A = E - (E + 1/A Eo) for E + .00002040456660 MeV = 3/2 Eo for Eo = .00001360304440 MeV contract P* x BETA - P* change sign x A = E + 1/2 Eo for E = .510999059 MeV to find E, E was multiplied by 2 and Eo (.00001360569808 Mev) was subtracted. 4 pm March 17, 1995. Here is another candidate for the zoo. LET Bo = Borh orbit. LET Bo+ = Borh orbit from the wavelength of (E + Eo) x A. THEN Bo - (Bo+ x BETA) = An Electron Classical Radius for E + 3/4 Eo for E = .5106660 737 Mev AND (Bo+ x 1/BETA) = 529177.2507 5630 x 10 to 14 cm = the Borh orbit = 529177.2507 1937 x 10 to 14 cm It seems the Relativistical Bo+ Space should be identical to the original Borh orbit space, Bo. The minute discrepency is hard to guage. Perhaps it is just digital noise in the calculation's accuracy. Perhaps it is real (not noise). It happens that when both Bo and Bo+ Borh orbit spacials are converted to Electron Classical Radius energy equivalents, the difference between the two energies is exceedingly small, and yet is a seeming factor of: 3/4 Eo for .00001360 117105 divided by FSC cubed. But holy smoke how far is reasonable. The guess is toward elegence, that: (Bo+ x 1/BETA) should equal Bo. The fact of whole piece transformations in Relativistics is well established by demonstrations found below under APPENDIX 3. Since whole piece Relativistic transformations do exist, it is possible therefore, that whole piece Relativistic transformations in the atom, is not an unreasonable or impossible conjecture. ================================================================= CLAIMERS AND DISCLAIMERS ================================================================= comment This information points to things going on in self inductive, self systained Relativitisics in a full mass system of the atom and to inner nuclear decay dynamics involving the Pion particle and others. The self systained Relativistic effects are tracked to the high mass range of UPSILON particles, and backwards, through the Borh orbit, to the Electron binding energy. This disclosure is not meant to be definative. No LAWS or RULES are hailed. It does not mean failure by the discloser. Let's face it, the Quantum Theory took 3 decades for facts being pointed out to be condensed into a work model for a Quantum Theory that was stamped in iron, or, theoretically so stamped. These derivations seem to say otherwise. proviso Obviously, there is no mention whatever of 'WHY' the derivations result as they do. There are mechanical questions regards orbital momentums for UPSILONS, for instance, and spontaneous decay mechanisms involving the fundamental PION particle, and other issues simply left as a big blank void in this disclosure. Just the mention of such dynamics as in the above paragraph is second hand information, gained from reading Scientific American and other publications, well away from the mainstream of hard core physics. Any information known by the author that might shed light has been included. Any information missing is because the author does not know it. footnote I am beginning to wonder if a Postive and Negative charge combined has a Relativistic component in it, the component containing Relativistic ingredients that can start to work when the separate parts are knit together. In this view, the combined charges are a carrier through which Relativistics occur in a lock sustained manner. The combined charges are the ever present observer, a carrier field of the combined charges the compare that manifests single system dynamics which includes Relativistic effect, in an analogous manner to the fact that the speed of light is the 'compare' by which normal Special Relativistics effects are made evident against the backdrop of the universe at large. Self induced Relativitistics would not occur with just a single charge present. Something in the + charge, knits together with something else in the - charge, to produce a mechanic that promotes the existence of self sustained, induced Relativistic effects that are observable as inner system parts, when the innerscene is picked and poked, with the sleuth techniques of a pair of tiny hand tweezers and a microscope, via self evident mathematics. It is certain that atomic/nuclear handshaking is involved, since the Relativistic harmonics reach in to excite (or engage) the STRONG force of the nucleus invloving Gluons and Quarks. -==================- THE RYDBERG CONSTANT - A word or two -==================- It is possible that variable decay momentas are bound in certain Relativistic balances, depending on the parts comprising a given energy's Relativistically resonating STRUCTURE. But momentas are not the only candidates for concideration. Precise photon engagement has been hinted in words in more than one place in this disclosure, alluding to the rag-a-tag tail end (last few digits) in Relativitistcally transformed entities, which could by assumption include the energies of photons in Spectra groups. Electron mev x FSC Eo Binding energy ev Upsilon mev | | | PHOTONS x FSC, x FSC, x FSC, x FSC, x FSC | | x 1/FSC Borh borbit E Classical Radius 5 powers of the FSC are involved in total infra-structuring. The limitations of simple to do extrapolations through large ranges of powers (4 pi, x 2, x (FSC to the 5th power) as the range that includes entities concidered in this conjecture, has discouraged any attempt to explore if, or if not, photon spectra can be tied in to the Relativistics, in a direct, self evident way. The conjecture is not unreasonable, already knowing that Relativistic transformations of fundamental atomic parts, closely track the values of the parts otherwise transducted by powers and whole integer ratios of the Fine Structure Constant. The total FSC range is a magnitude spanning 1.664 x 10 to the power 12 between smallest Rydberg Constant energy range, to the largest, Upsilons mesons range, in whole piece parts. In space whole piece parts the range is actually a 10 to -10 magnitude due to the nature of the Rydberg constant itself and included 4 Pi term. Rydberg Constant .... > .... 2 Upsilon Mesons. | | start of photon highest non-boson spectrum mass energy 10 to -6 cm 10 to -16 cm In fact transducted parts carry directly into the Photon spectrum range, through the Borh Orbit, which when expanded by (A x 4 Pi) is the reciprocal of the well known Rydberg Constant (shown in the tables of Physical Constants as an R with an infinity sign), as follows: Borh Orbit = 529177.250193 x 10 to -9 cm x (4 Pi A) = 10973731.5208 x (1/cm) = Rydberg Constant. The same (Rydberg Constant), is gained in whole term transductions by the so-called 'Wavenumber Constant' multiplied by the Electron Binding Energy, as follows: When the 'Wavenumber Constant' = 8065.54095924 Ev (1/cm) then: 'Wavenumber' x Eo = 10973731.5208 (1/cm) = Rydberg Constant - Finis - ====================================================================== THE APPENDIX ====================================================================== ========== APPENDIX 1 'Convergence' vrs 'Exactitudes' in the derivations. ========== .... These are not exactitudes. The Relativistic quantities closely approximate, but do not typically equal the exact quantities gained by just the pure Fine Structure Constant ratios of A, 2A, 2A squared, and their reciprocals. It happens that at the point where the Electron contains a certain mass, pitted with the nature of Compton wavelengths, and velocity of the Electron in Bohr orbit, that the basic Relativistic changes approximate almost, but not exactly, factors of 2A* (2 times the Fine Structure Constant squared). A simple 'means test' will show at once that exactutudes are not found, just close approximations. The closeness increases in the realm the closer a velocity approaches the speed of light. A simple whole integer quantity, transformed by a simple high velocity Relativitistic power, demonstrates the inexactitudes, as follows: MEANS TEST 1 -------------------------------------------- A test of inherent digital accuracy in a non-relativitistic hidden body system of the atom, using available calculating hardware circ. March, 1995. LET E = .5109990 65 Mev LET Eo = .00001360569808 Mev = E x 1/A* h^/E - h^/ (E + Eo) = .10281481100 x 10 to -14 cm h^/ (.10281481100) x 1/2A* = .511012676112 Mev - Eo = .5109990 704 Mev result mass compared to original E = .5109990 65 No Relativistics were involved in this deriviation and the discrepancy at the 8th significant digit in the resulted mass equivalent of the Electron is due to trunkation in both the available calculator equipment, and the known accuracy of the physical constants circ. 1995. ALTERNATIVELY h^/ (.10281481100) x 1/2A* = .511012676112 Mev - E = .0000136 1111250 Mev compared to original Eo = .0000136 0569808 Mev It is clear that some trunkation has occurred in the accuracy of the sequence of equations. The accuracy is maintained to the 7th significant digit with a slight change in value incurring at the 8th digit. in the light of 'comparison' to Eo, original, vrs derived. The changes revealed above have significant impact on resulting values of Eo through any derivations, since Eo is the most flexible factor, thus the most inherently trunkated in spurious ways, in handling by the available calculating power limited to 13 significant digits in the calculating hardware used for this disclosure. In the case of Eo, although digital accuracy is maintained at the 8th significant digit, change has actually occured at the 4th real digit of Eo, drastically reducing its reliability as a 'definative' data fact. The inherent digit clipping on Eo is most apparent when doing equations in 'Scientific Notation' rather than in floating point decimals. In 'Scientific Notation' the first 4 zeros of Eo's value are not displayed, thus the impact of digital trunkation in the value of Eo as seen by eyesight in the calculator's display register can be very confusing. MEANS TEST 2 for A = 123 a slow velocity ------------------------------------------------------ A test of inherent digital accuracy in the 'Relativitistic' hidden body system of the atom, using available calculating hardware circ. March, 1995, and arbitrary whole numbers for imputs. V 1 LET 1/A = --- = ----- and 1/A = .00813008130 C 123 LET A* = 'A' squared LET mass = M = 1234 M x 1/2A* = .040782602 = Mo ________________________ | | Ú 1 ¿ 2 BETA = | 1 - ³ --- ³ = 1/ 1.0000330507490 \| À A Ù M x 1/BETA - Mo = 1234.00000 202 --------------------- How much of this change is due to trunkation in accuracy? Means test 3, shows the answer. MEANS TEST 3 for A = 1.23 (near the speed of light) ------------------------------------------------------------- V 1 LET 1/A = --- = ------ and 1/A = .813008130 C 1.23 LET A* = 'A' squared LET mass = M = 1234 M x 1/2A* = 407.826029479 = Mo ________________________ | | Ú 1 ¿ 2 BETA = | 1 - ³ --- ³ = 1/ 1.717468426 \| À A Ù M x 1/BETA - Mo = 1711.53009113 compared to the rest state value of 1234 . It is clear that 1711.53009113 (result) is nothing the same as 1234 (starting term). The mass is expanding at an increasing rate beyond the ratio of A as the velocity approaches the speed of light. COMMENT ------- It is obvious that the mass has 'Relativistically' increased well beyond its original starting value, in a simple example for a velocity that is 81.300813 percent of the speed of light. In the case of atomic 'Relativistic harmonics' the velocity of the Electron is .7299270 percent of the speed of light, since .007299270 is the reciprocal of the Fine Structure Constant = 137.0359895(61). It is here at this point in Relativistic geometrics that a converge in the fabrics of space occurs. The geometry and relativity LOVE each other. ================================================================= ========== ----------------------------------------------- APPENDIX 2 Gravitational Relativity creation of two planet ========== masses, (Venus and Mars). ----------------------------------------------- LET solar constants be: R = Existing Sun radius = 6.96265 x 10 to 10 cms -------------------------------------------------- C = Speed of light = 2.99792458 x 10 to 10 cms/sec -------------------------------------------------- SM = Sun mass = 1.989 x 10 to 33 grms -------------------------------------------------- G = Universal gravitational constant = 6.6720 x 10 to -8 cms3/grms secý ============================================================== SOLAR SYSTEM UNIVERSE Text and Paintings by Don dixon DATA ARE FROM: Houghton Mifflin company Boston 1981. ---------------------------------------------- PLANETARY QUANTITIES pages 220-235 ---------------------------------------------- which used refined details from the Jet Propulsion Laboratory released to the author (Dixon) in 1981. =========================================================== To begin; EQUATION A Determining a relativistic effect factor Em for a mass aggregate, in particular the Sun, using the simple transformation equation for gravitational effects in General Relativity: ÚÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ ³ 2G (MS) Where MS is the mass Em = ³ 1 Ä ÄÄÄÄÄÄÄ of the Sun, and R is \³ Cý R the radius of the Sun, G, universal gravity constant, and C the speed of light EQUATION B Determining how much mass augmentation relativistically occurs in the mass aggregate of the Sun: (MS) - ((MS) x Em) = K Where K is the actual mass augmentation increased on the Sun's original mass due to gravity ================================================= VERIFYING A MASS OF MS FOR THE SUN ================================================= An aggregate mass MS (being the mass of the Sun) found to have intrinsic relativistic consequences, can be easily verified. If starting with an estimated Sun mass, for instance; (1.989 x 10 to 33 grms); and assuming that the Sun mass is already relativistically augmented, the gravitational relativistic mass increase of a Sun mass of (1.989 x 10 to 33 grms) is found (using EQUATIONS A and B), to be slightly less than the mass difference between VENUS and MARS. That is: Venus mass is 4.8683 x 10 to 27 grms Mars mass is .64181 x 10 to 27 grms Venus - Mars is 4.226490 x 10 to 27 grms whereas the mass augmentation Km of a Sun mass of (1.989 x 10 to 33 grms) is (4.218033 x 10 to 27 grms), which is low by a slight amount for VENUS - MARS = K. If the Sun's mass is gradually increased, eventually a mass aggregate will be found, in which the relativistic mass augmentation K is precisely VENUS - MARS , that is: K = 4.226490 x 10 to 27 grms. The point of agreement occurs when the mass aggregate for the Sun mass MS is found to be (1.990993 x 10 to 33 gms). .................. .................. .................. There is a little gem of seeming co-incidence which is the kind that can titillate scientists for years and decades, if no explanation is found. The little gem is that the Sun's mass can be determined rather bang on from a ratio which comes from pure fundamental physics, given a known value 4.226490 x 10 to 27 grms, for the mass increase upon the Sun's mass, by the Sun's own gravitational relativity, as follows: Let Pi = 3.141592653589 Sun psuedo mass 4.226490 x 10 to 27 grms, raised in value by 4 Pi x 2 (FSC squared), comes up to 1.994752.35089 x 10 to 33 grms, which is right back into the mass range of the Sun ! The ratio 4 Pi x 2 (FSC squared), is almost, but not quite exactly, how much the Borh rest state orbit is expanded in space to come into the range of photon spectrum wavelengths in an atom, the difference being that one more FSC term is incorporated in the ratio that leads directly from the Electron's Wavelength to the Rydberg Constant. If the little gem was run in reverse, from the Sun mass, reduced not by 4 Pi x 2 (FSC squared), but by 4 Pi x 2 (FSC CUBED), to make the ratio a full fledged micro/macro recurrance, then the starting mass for the ratio is right in the middle of solar bodies comprising the smaller moons and asteroids, Speckled in space could be 'photon' equivalents, existing in direct proportion between the Electron mass and Hydrogen (or Deuterium) spectrum photons, and the Sun mass and the planetoids. In this case, the Sun is a collosal ELECTRON model, rather than the 'Nucleus' model always in vogue in fiction physics. The idea is not unreasonable. In fact a Sun mass 1.994752.35089 x 10 to 33 grms, divided by the ratio 4 Pi x 2 (FSC CUBED), results in a small mass of 3.084219488 x 10 to 25 grms, which is there in the range of Jupiter's moons, and half the mass (roughly) of the Earth moon. For that matter, Venus mass 4.8683 x 10 to 27 grms divided by FSC, is startingly close to the mass of the Moon. The FSC reduces Venus mass to: 3.552570594 x 10 to 25 grms. x 2 = 7.105141188 x 10 to 25 grms. The mass of Earth's Moon is: 7.350 x 10 to 25 grms. For that matter, the Sun mass derived by physical constants above (1.994752 x 10 to 33 grms) minus the actual Sun mass 1.991 x 10 to 33 grms, is pretty tight on twice the mass of Jupiter. That is: derived SUN mass 1.994752 x 10 to 33 grms minus actual SUN mass 1.990990 x 10 to 33 grms equals 3.7620 x 10 to 30 grms one half of which is 1.8810 x 10 to 30 grms compared to the mass of Jupiter JUPITER mass 1.901 x 10 to 30 grms. Only a light change in the mass of Venus, from 4.8683 x 10 to 27 grms, to 4.868 723 x 10 to 27 grms, will bring Jupiter's mass into the picture in full value. For example: 2 x Jupiter mass 3.802 x 10 to 30 grms plus actual SUN mass 1.990990 x 10 to 33 grms = 1.994952 x 10 to 33 grms x 1/ (2A* x 4 Pi) = 4.226913 x 10 to 27 grms + Mars mass .64181 x 10 to 27 grms = Venus mass 4.868723 x 10 to 27 grms These interplanetary values are so close, that the mass difference between Venus and Mars need only be increased by + .000423, in order for the derived Sun mass subtracted from the real Sun mass, to equal precisely twice the mass of Jupiter. Well, here is another little bit of hokey: The Sun's Relativistically precipitated mass, 4.226490 x 10 to 27 grms, times Root 2, is the mass of the EARTH. 4.226490 x 10 to 27 grms x 1.414213562 equals 5.977159 x 10 to 27 grms factored EARTH mass | compared to | 5.976 x 10 to 27 grms real EARTH mass. Put another way, the mass of EARTH, divided by Root 2, is the mass difference between VENUS and MARS, and is also the invisible mass the SUN precipitates due to its own gravitational Relativistic strength. Some pearls from the Supreme Creators are certainly sitting around in space for humans to ponder. It seems. As already said, geometry and relativity LOVE each other. ================================================================= ========== ----------------------------------------------- APPENDIX 3 A demonstration of multi media digital whole ========== piece states of Relativistically transformed simple numbers. ----------------------------------------------- Cont. from SINE RELATION -=========================- -=========================- 4. 1/2 the speed of light is verrrry interesting in its own right. The BETA ratio for 1/2 C is: _________________ | | 2 BETA = | 1 - .5 = .866025403 \| which is 1/2 of Root 3 1 .732050807 and its reciprocal = 1 .154700538 is the square Root of 1 .333333333 As a facination, the expansion of 1/BETA on the number 3 = 3 .464101615 is the square Root of 12. But also the digit PAK .464101615 has cousins, for instance the square Root of 12, + 4 = 7 .464101615 is the square of (Root 3, + 1) 2 .732050807 whose reciprocal is .366025403, which is BETA - .5 and is also 1/2 of .732050807 (which is Root 3, - 1), which is the reciprocal of 1 .366025403, which is BETA + .5 so on. The digit PAK .154700538 is in the reciprocal of 1/2 Root 3 1 .154700538, and is also the reciprocal of Root 12, + 3 = 6 .464101615, and turns up in many digital permutations. For instance the square of 2 .732050887 = (Root 3 + 1) is 7 .464101615 whose reciprocal is .133974596, which is 1 - BETA yet note that the reciprocal of 7.464101615 - 1 = .154700538, and digit PAK .464101615 is the reciprocal of 2 .154700538. All of this, and more, are in the Relativistics of Root 3, and also a velocity of 1/2 the speed of light. Both Relativistic BETAS are digitally synchronized in facinating ways. For example BETA for a velocity that is less than the speed of light by the reciprocal of Root 3 = .816496580 has a relativistic SPREAD, for example upon number 3, of 3.674234614 2.449489742 (3 x 1/BETA) - (3 x BETA) = 1.224744871 which is the reciprocal of BETA for Root 3 = .816496580, and the relativistic SPREAD for a velocity .5 of the speed of light, .866025403 is 3.464101615 2.598076211 (3 x 1/BETA) - (3 x BETA) = .866025403 being BETA itself for velocity .5 .866025403. Now here is some FUN news! The Relativistic expansion of BETA to 1/BETA, for BETA = .816496580, upon the SPREAD of BETA for a velocity of .5 , is Root 2 = 1.414213562 and the Relativistic expansion of BETA to 1/BETA, for BETA = .866025403 upon the SPREAD of BETA for a velocity of 1/Root 3 , is the reciprocal of Root 2 = .707106781 And so, it is plain that the digits of Root 3 permutations, and of .5 permutations, and of Root 2 permutations, are equatable via Relativistically related digital states in full, where A = B = C exactly. But, this, shown above, is barely scratching the surface of a circus. Relativity is a lot more than just streaks of weirdly morphing material hurtling across the sky, or blurred in an orbit around an atom. - Finis - =================================================================== TURN AROUND =================================================================== Regards charge. Lets assume something else about the Electron, besides knowing that it is an 'entity', and not a shapely thing like the Proton. Lets assume that there is no Electron part for mass, there is only one charge unit comprising the whole Electron, the charge force itself effecting attraction and polarization and magnetism, but the charge itself also has property that can effect physics as if by actual mass (as in the Electron's mass energy) but there is no part which has that mass, that appearance of 'mass' is a result of the unit of charge's 'hidden' way of also effecting things around it in mass-like ways. Think of how many ways it would be easier to describe the Electron if there was no mass part, the mass part being the bane of thinkers who have been trying to find it for nearly a hundred years and still cannot point to a shape that sits as a naked Electron. Oops. Meson subatomic particles also, do they have naked 'shapes' defining a mass part? All of the relativistic transformations that result in 'space' artifacts of precise size, and mass energy states of precise size are in fact arrising from transformations of just simple force and momentum events within precise areas. It can be reasonably argued that the structures are in fact all being described without ANY MASS PARTS that sit naked as shaped entities. The whole of the interweaving structure is the design of relativistic transformations of power and distances, but not mass parts that sit naked like statues of stone. Where ARE the mass parts? Are they only more attributes of charge itself? =================================================================== PITHY'S =================================================================== ---------------------------------------------------------- It is a well known side effect of Murphy's Law that needless speculation becomes increasingly reckless in direct proportion to the fewest known facts. -========================================- Scoffer's don't exist, say those who most want to control the thoughts of others. Here are some scoffer 'proofs': -=========================================- ================================================= FROM F.Y.I. THE OTTAWA CITIZEN, MARCH 22, 1995 ================================================= "This telephone has too many shortcomings to be seriously concidered as a means of communication. The device is inherently of no value to us". - Western Union internal memo, 1876. ------------------------------------ "Heavier-than-air flying machines are impossible." - Lord Kelvin, President, Royal Society, 1895. ------------------------------------ 'Who the hell wants to hear actors talk?" - H.M. Warner, Warner Brothers, 1927. ------------------------------------ "We don't like their sound, and guitar music is on the way out." - Decca Recording Co. rejecting the Beatles, 1962. ------------------------------------ "The wireless music box has no imaginable commercial value. Who would pay for a message sent to nobody in particular?" - David Sarnoff's associates in response to his urgings for investment in the radio in 1920. ------------------------------------ ============================================= FINISHED 4:30 PM Sunday, March 26, 1995 ============================================= Greydon Moore Ottawa, Canada. - end of disclosure -