Change. Flamenco Chuck Keyser. Updates 11/26/2017, 11/28/2017, 11/29/2017, 12/05/2017. Most Recent Update 12/22/2017

Transcription

1 Change Flamenco Chuck Keyser Updates /6/7, /8/7, /9/7, /5/7 Most Recent Update //7 The Relatvstc Unt Crcle (ncludng proof of Fermat s Theorem) Relatvty Page (n progress, much more to be sad, and revsons to be made) (Ths page wll be fleshed out wth dagrams, explanatons, etc, but the bascs are here) v v, v v,,,, v v v In the lnear case, the assumpton s that there s no nteracton between the ntal condton and the perturbaton feld v va complex conjugaton, where v v c v c v c * s then equated to the fnal result so that * If * * then the tme dlaton equaton obtans, where one has elmnated the nteracton product v the Bnomal Expanson for n=: v c v c v c v c v c whch arses from

2 Then v v and w v c are countable wdgets that don t nclude the nteracton, so that w v c ;.e. The metrc for such a system s then a Pressburger arthmetc, whch doesn t nclude scalar multplcaton (.e., scalar nteracton ). For physcs, s nterpreted as spn s where h s Planck s constant and h h s, s v s v, so that s. Note that h depends on the set v,,, n the case where nteracton s ncluded n the analyss. In partcular, for c, the relatvstc unt crcle n terms of sne and cosne (no nteracton) s generated, and the perturbed system s represented by hyperbolc sne and cosne. The confuson les n that for both the ntal state (where there s no feld) and the fnal state when v (the perturbaton has stopped.e., the system has fnally absorbed the feld (, ), correspondng to a postve rotaton from sn n the non-nteractng case, and from tan n the nteractng case. These angles are the same n the relatvstc unt crcle, but n the nteractng case, the unt radus has changed from n the nteractng case. Note that absorpton corresponds to a postve rotaton and radaton corresponds to a negatve rotaton ; for a sngle partcle v Radaton nvolves the reverse product, so that, If n the rotaton, there s no nteracton (sn and cos are orthogonal ); otherwse, the nteracton term s sn cos, but snce ths s at,, nothng has changed n a complete rotaton, snce t represents a fnal state = ntal state. For n, each n wdgets are non-nteractng, where v both for the ntal case and the fnal case, and can thus be counted as ntegers. For the Bnomal Expanson for ntegers, ths means that n n n c a b rem ( a, b, n) for,,, a b c n postve ntegers; snce rem ( a, b, n) represents nteger

3 n n multplcaton, the factors n w w w cannot be counted, snce the wdgets are not n ether n an ntal state or a fnal state v. For v, w, so n n w w, a tautology. Ths proves Fermat s Theorem. In order to elmnate nteractons where each wdget s a dmenson, complex conjugaton must be mplemented for each par of products n the Multnomal Expanson or the nteracton s elmnated by settng v for all nteractons. The states are then ether fnal states ( affne vectors wth no connecton) or ntal states ( affne vectors wth no connecton), where the connecton mples that there s a local nteracton. Ths result also proves Euler s conjecture, and valdates Gödel s theorem, where propostons that are NOT represented by sequences of prme numbers must also be ncluded for arthmetc completeness (.e., such propostons can be ambguous, or nteract, and thus can t be counted). can only be an nteger f v so that n n n n, v for,, v for c,,, v. That s, n s an nteger only for the ntal or fnal state, but cannot be an nteger for v v unless v s a countable object by charge conjugaton, so that ct c v c v c v * * * ( ) ( ) Where c v c v c v Although t s clear that complex conjugaton must be appled to acheve Fermats expresson, so that t doesnt conform to propertes of real numbers (whch nclude multplcaton), and that the Bnomal Theorem s vald even for n=, t stll doesnt show that the expresson cannot be ntegers. Ths s accomplshed by analyss from the Theory of Relatvty, where the Tme Dlaton equaton s a lnearzaton of the general Bnomal expresson for real numbers, snce t doesnt nclude the area of the ncluded trangle (and hence the nteracton energy, whch s also mssng n the outer product). The Relatvstc Unt Crcle shows that ph can be an nteger only at ponts such that beta= as the hyperbolc expanson s extended, wth the "states" mergng to a "contnuum" as n > nfnty (physcsts already know ths, I thnk, anyway..:), the pont s that for ths model there s no contnuum; each nteger for whch v=c s a fnal state, where ct/ct = so nct/nct=, beta==v /c, c = ct wth each rotaton from theta = to theta = p/ of the RUC (all elements are postve for v ncreasng). It s easy to see ths f my dagram s flpped so the vertcal sdes correspond to the gamma= axs, wth ntegers ncreasng vertcally (but the space between them dmnshng as n -> nfnty) Ths result s then extended obvously to n>, and fnally to proof of Eulers conjecture for multnomals

4 x x j j j * x x j x x j x x j x x j x x j x x j j j x x j x x j x x j x x j x x j * j j * * * x x x j j j x x x x x, x ~ j j j j

5 (An magnary number s complex only f you thnk t s real). That s, an magnary number (negatve axs) results from magnng a connecton at the center of the relatvstc unt crcle for a sngle partcle n a sngle dmenson or magnatvely removng the nteracton between two partcles connected at the center by complex conjugaton so that c, v for all, j Ths result can then extended to the multnomal expanson, where removal of nteractons (tensor contracton ) removes dmensons untl n, at whch pont the conjugate elements commute, so gve the appearance that the result s real. However, the nteracton s real only for two partcles, n whch case negatve values only apply to sn, representng absorpton and radaton respectvely, where the velocty s a resultant feld from all partcles relatve to the dmenson servng as a bass (whch must be the smallest to avod magnary values where, c, v for the total system (galaxy, unverse, photon,,,, myself Newton s laws of momentum and energy (/9/7) Note that v v c,, for both negatve and postve values. For a unt mass, v Vm m ( m) ( ) m mv, m, c, v Ths s the knetc energy of a sngle c element (dmenson) of the S-Matrx for two nteractng partcles. When v, the knetc energy dsappears, but remans as the fnal state, whch s the correspondence to Newton s law of energy, and n frst order represents the equal and opposte forces of two dentcal partcles. h v, h h( c,, v, ) ntal fnal h h s v c s v c ntal fnal h vpmv, m whch s Newton s Law of Momentum v Snce the momentum s equal and opposte, the polartes of can be represented by. c

6 The Paul Matrces /5/7 (In progress) Note to self (needs to be mplemented) The square of an magnary number s not a negatve real number. That s, the product of two magnary numbers s an magnary area, not a real area. 4 Much more to be sad (I m pedalng as fast as I can).,, 3 3 (To be revsed and re-wrtten). Addng the dentty matrx for two dmensons yelds 3 3 Where Tr 3 and Det 3 ( ) Note that Tr and Det (To be contnued) (In progress) Snce ths can then represent charge wth no mass n the Paul Matrx:

7 Note that the trace of ths matrx s, but the cross product s v v v v v That s, the nteracton of the two postve elements s zero f referenced to the center of the crcle, where cos, sn, snce sn cos so thatsn cos. Where the magnary number means the system s vewed from the center of the rest mass, so that ths s equvalent to the matrx S, where the observer of two partcles s at the zero pont mass/energy. The nteracton of each partcle s then s wth the dameter of the crcle equal to., and r. Note that the trace of the spn matrx S. For two partcles S, so that S, v For the nteracton of two postve partcles, v wth the nteracton at the center f the crcle, representng equal and opposte momentum/force,

8 v, S tan Ths nteracton can then be elmnated by the Paul Matrces where, 3 3 * Tr( *) So that the mass nteracton s magnatvely removed n by movng the reference pont to the center of the crcle and modelng charge as complex, and by charge conjugaton n the case of and 3 Note that Tr( 3) Tr So that charge s magnary f referenced from the center of the crcle, whch corresponds to the relaton * where the nteracton term has been removed by charge conjugaton: * v * ( ) cosh snh v, cosh, snh

9 The Mnkowsk matrx I m??? I m * 4 4 * 4 * * *