NEWTONIAN TORSION PHYSICS

Transcription

1 NWTONIAN TOION PHYI William. Alk INTAK, IN., 45 N. Tatum Bld, t -43 UA Phon: (48) mailto:william.alk@intalk.com ABTAT: Th purpos of this book is to plor concpts rlatd to F nrg and th control of Grait/Antigrait that ar basd ntirl within th framwork of tndd classical Nwtonian phsics calld Nwtonian Torsion Phsics. It is shown that th caus of grait is a tp of macroscopic torqu btwn inrtial frams whr th origin of th torqu occurs within imaginar or compl spac. Th ffct manifsts in ral spac as unirsal mass attraction, or grait. A corrlation has bn discord btwn mass, inductors, and capacitors, thrb rlating th imaginar or compl origin of torqu to grait, and how this sam torqu affcts lctromagntism. A simplifid torsional mass rlatiit modl calld Natural latiit (N) Thor is prsntd and dirctl rlatd to grait. This thor is thn corrlatd to instin's pcial latiit () Thor, and as a consqunc, crats a corrctd Principl of quialnc Thorm showing th origin of grait and antigrait coms from imaginar or compl spac. A tmporal rotation oprator is introducd using ulr s Idntit, which shows th imaginar or compl (i.., tim-past and tim-futur) motion of mattr as positi or ngati displacmnt into imaginar spac, which mbodis th fundamntal concpt of tim tral. Th spd of light c, Planck's constant h, prmabilit μ, prmittiit ε, Boltzmann's onstant k, lctric charg q, and th Fin tructur onstant α ar inariant btwn inrtial frams and thrfor, unaffctd b torqu bcaus th fluctuation or curatur of th fundamntal paramtrs that compos ths constants ar shown to aluat to unit gain. In othr words, ths constants rmain constant anwhr within a gin torqu fild or grait wll. Graitomagntic Thor shows that th magntic fild nrg producd b a moing lctron is shown to b a spcial rlatiistic mass fluctuation, and thrfor crats a ral torqu, which coupls to grait as a scondar graitational ffct. This motion can ithr ha a ral locit, or an imaginar or compl (i.., tim-past or tim-futur) locit. If th locit is compl, thn th spcial rlatiistic mass fluctuation or corrsponding graitational or antigraitational ffct, which consquntl producs a compl (i.., tim-past or timfutur) magntic fild. This is th origin of th ffct calld grait or antigrait. In addition, th olum of th total fild nrg of a compl magntic fild can ithr b positi or ngati, which can add or subtract from th nrg producd b a ral magntic fild. In th Bohr modl of th Hdrogn atom, an Amprian urrnt is dscribd as an lctron circulating around a nuclus at a rlatiistic spd. This crats a magntic induction mrging from th cntr of th nuclus. Fluctuating this fild b appling an trnal magntic induction causs th locit of th lctron to bcom compl. Th prsnc of NGATIV ITAN, th production of NGATIV NGY, and th control of GAVITY/ANTIGAVITY occur b fluctuating th mass of an objct in compl spac. Th thor prsnts a concptual brakthrough for th dlopmnt of nrg and high-spd fild propulsion tchnologis. ± of an lctron can b ithr positi or ngati, and hibits a INTODUTION Puthoff (99) coind th phras, mtric nginring, and Puthoff, ittl and Ibison () considr th acuum to b a polarizabl mdium, and that it can b prssd in trms of tnsor formulations of curd spac-tim. Th bnding of light passing nar a massi objct is causd b inducd spatial ariation in th rfracti ind of th acuum nar th objct. This is corrlatd to changs in prmabilit μ and prmittiit ε of th acuum. hangs occurring in th acuum also affct th mass of objcts, th lngth and bnding of rulrs, th frqunc of clocks, th nrg of light, tc. This book both simplifis and links grait with lctromagntism b prsnting formulations of curd spac-tim in trms of tndd classical Nwtonian phsics, which ar causd b rlatiistic fluctuations of mass, inductanc, and capacitanc of an objct. For ampl, whn an objct

2 Nwtonian Torsion Phsics INTAK, IN. 3.9 with mass naturall falls downward in a gin grait wll, its natural rlatiistic mass + incrass du to Nwtonian Graitation, or unirsal mass attraction. Th nw mass of an objct + is displacd to a nw position within this wll, thn mass-nrg rmains consrd b rturning th mass to its plac of origin, or +. In othr words, b conrting this incras in rlatiistic mass + to nrg +, a forc acts upon th objct, and th nw mass is now displacd back to its original position that was highr rticall in th wll. Th objct hibits an antigraitational ffct b rmoing or subtracting from. Th rat of chang of this fluctuation could caus th spd of th objct to asil cd th spd of light. This is bcaus th rlatiistic graitational mass of th objct, which is shown to b conrgnt, is moing at right angls to a rlatiistic inrtial mass, which is shown to b dirgnt. inc th spd of th objct with rlatiistic graitational mass has no known uppr limit, th rsulting spd through dp spac could b normous and ncssitats th us of th warp factor quation. VYTHING IN THI UNIV I UVD! TWO PHIA OBJT WITH IDNTIA A AND VOU WH r r PH r g PH r g Y OBV ON ATH WOUD TWO IDNTIA PH UFA OF ATH FIGU. Two idntical sphrs as sn b an obsrr on th arth. ass and olum of mattr ar undr th influnc of diffrnt grait. hown in Fig. abo ar two idntical sphrs, PH and PH, with qual mass and olum as sn b an obsrr on th arth. PH is now mod to th oon as shown in Fig. blow. UVATU DU TO GAVITY OBV ON OON WOUD PH ON ATH A BING O AIV AND A IN IZ r g OON r g Y PH UFA OF OON PH UFA OF ATH Y OBV ON ATH WOUD PH ON OON A BING AIV AND AG IN IZ FIGU. Two idntical sphrs chang in mass and olum rlati to position of th obsrr. William Alk Pag 5/4/8

3 Nwtonian Torsion Phsics INTAK, IN. 3.9 PH on th lft is undr th influnc of grait of th oon and PH on th right rmains undr th influnc of grait of th arth. inc th grait of th oon g OON is approimatl th grait of th arth g, an obsrr on th oon would masur th sphr on th arth as haing slightl mor mass + and bing slightl smallr in olum V than th sam sphr on th oon. ikw an obsrr on th arth would masur th sphr on th oon as haing slightl lss mass, and slightl largr in olum + V. This is du to th ffct of curatur of spac and tim upon mattr causd b torsion originating from imaginar or compl spac and obsrd in ral spac as unirsal mass attraction, or grait. APPYING TH PODUT U armt () considrs sparatl th influnc of a graitational potntial upon mattr, and assums for th momnt that kintic nrg is zro. Th kintic nrg and graitational nrg ar aluatd indpndntl and thrfor ar considrd mutuall clusi. For Kintic nrg sstms, and gin a fram of rfrnc, th following inrtial-basd paramtrs mass, inductor, and capacitor, ar considrd inariant. Howr, for Graitational nrg sstms, and gin an quipotntial surfac of grait rfrnc, th following torsionalbasd paramtrs rlatiistic mass ±Δ, rlatiistic inductor ±Δ, and rlatiistic capacitor ±Δ, fluctuat or cur btwn inrtial frams. o, b appling th product rul, this principl is mathmaticall prssd as, Whr, th Inrtial Trm is gin as, And th Torsional Trm is gin as, o, d da db Δ a Δ b n() t ( ab) b + a ba + ab b + a dt dt dt Δt Δt ba ab db Δb nt () ab a a dt Δt Th first trm is rgardd as inrtial, and thrfor is considrd kintic or flus, and is Nwtonian-basd. Th scond trm is rgardd as torsional, and thrfor, causs grait. Whn aluating Graitational nrg sstms, th Inrtial Trm must b qual to zro, laing onl th Torsional Trm to b dtrmind. Th Torsional Trm ma rsult in a positi or ngati numbr maning that th chang in Graitational nrg ma b ithr positi or ngati. This principl tnds Nwtonian-basd phsics to includ Nwtonian Torsion Phsics, and is formulatd and analzd in th dirction of grait, or towards a cntr of mass. A positi chang in Graitational nrg indicats displacmnt towards a cntr of mass and a ngati chang in Graitational nrg indicats displacmnt awa from a cntr of mass. William Alk Pag 3 5/4/8

4 Nwtonian Torsion Phsics INTAK, IN. 3.9 TOIONA A FUTUATION FUTUATING A ± + r r g FIGU 3. Th fluctuating mass of an objct du to grait. Appling th product rul, th complt idal momntum modl is composd of two trms, dpy d( Y) dy d f () t + Y Y + Y () dt dt dt dt Whr, th Inrtial Trm is Y, and mass is inariant within an quipotntial surfac of grait g Y. Th Torsional Trm is Y, and changing mass fluctuats btwn quipotntial surfacs of grait. For a mass fluctuating sstm, th Torsional Trm is NOT zro Nwtons. o, gin an objct haing mass moing at constant locit Y, or Y m s, th Inrtial Trm This rmos th Inrtial Trm, laing onl th Torsional Trm, f () t N () Y f () t N (3) Y inc has units of rsistanc in mns m, its dirction of chang could ithr b POITIV or NGATIV. If is ngati, it has units of ngati rsistanc or, < mns m (4) Now, th instantanous graitationall inducd powr P of a fluctuating mass P () t f () t (5) Y Y o, for crtain alus of, th total instantanous powr P can b NGATIV or, P () t < Watts () Thn, intgrating P with rspct to tim whn th total powr is lss than zro watts rsults in NGATIV nrg of mass or, (7) t P t dt dt t Jouls () () Y Y () < William Alk Pag 4 5/4/8

5 Nwtonian Torsion Phsics INTAK, IN. 3.9 If is positi, it has units of positi rsistanc or, > mns m (8) Now, th instantanous graitationall inducd powr P of a fluctuating mass P () t f () t (9) Y Y o, for crtain alus of, th total instantanous powr P can b POITIV or, P () t > Watts () Thn, intgrating P with rspct to tim rsults in css POITIV nrg of mass or, () t P t dt dt t Jouls () () Y Y () > o, th nrg quialnt of mass (graitational nrg) () t () t () Y B rarranging trms, th mass quialnt of nrg () () t t (3) Y Th fluctuating mass quialnt of nrg (4) Y o, th graitational momntum modl f t (5) () Y Y Y Y tting d dt, th Torsional Forc Trm Y B rarranging trms, th fluctuating nrg quialnt of mass f () t () () f t (7) Th total nrg containd within mattr () t () t c (8) William Alk Pag 5 5/4/8

6 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th chang in this total nrg c (9) B rarranging trms, th chang in total mass c () o, th tim driati form of th Torsional ass Trm f () t c () Th driati form d f d () c Th diffrnc form Δ Δ f (3) c William Alk Pag 5/4/8

7 Nwtonian Torsion Phsics INTAK, IN. 3.9 TOIONA INDUTIV A FUTUATION + I FUTUATING INDUTAN ± g + - FIGU 4. Th fluctuating inductanc of an objct du to grait. Appling th product rul, th complt idal inductor modl is composd of two trms, d di d ν () t ( I) + I I + I (4) dt dt dt Whr, th Inrtial Trm is I, and inductanc is inariant within an quipotntial surfac of grait g Y. Th Torsional Trm is I, changing inductanc fluctuats btwn quipotntial surfacs of grait. For an inducti fluctuating sstm, th Torsional Trm is NOT zro olts. B appling a constant currnt I through inductor, or I Amps s, th Inrtial Trm This rmos th Inrtial Trm, laing onl th Torsional Trm, ν () t I Volts (5) ν () t I Volts () inc has units of rsistanc in ohms, Ω, its dirction of chang could ithr b POITIV or NGATIV. If is ngati, it has units of ngati rsistanc or, < Ω (7) Now, th instantanous graitationall inducd powr P of a fluctuating inductor P () t I ν () t I (8) o, for crtain alus of, th total instantanous powr P can b NGATIV or, P () t < Watts (9) William Alk Pag 7 5/4/8

8 Nwtonian Torsion Phsics INTAK, IN. 3.9 Thn, intgrating P with rspct to tim whn th total powr is lss than zro watts rsults in NGATIV nrg of inductor or, If is positi, it has units of positi rsistanc or, (3) () () < t P dt I dt I t Jouls > Ω (3) Now, th instantanous graitationall inducd powr P of a fluctuating inductor P () t I ν () t I (3) o, for crtain alus of, th total instantanous powr P can b POITIV or, P () t > Watts (33) Thn, intgrating P with rspct to tim rsults in css POITIV nrg of inductor or, quat this to th nrg quialnt of mass (34) () () > t P dt I dt I t Jouls, Thn, th nrg quialnt of mass (graitational nrg) () t () t (35) () Y () () t t I t (3) B rarranging trms, th mass quialnt of nrg () t I () t () t Y Y (37) I t () Y () t (38) Th fluctuating mass quialnt of nrg I (39) Y Y o, th graitational inductor modl I f (4) () t Y Y Y Y Y William Alk Pag 8 5/4/8

9 Nwtonian Torsion Phsics INTAK, IN. 3.9 tting d dt, th Torsional Inducti Forc Trm Y B rarranging trms, th fluctuating nrg quialnt of mass () () t f t (4) () f t (4) Th total nrg containd within mattr () t () t c (43) Th chang in this total nrg c (44) B rarranging trms, th chang in total mass () t I I () t f c c I () t t () () t (45) o, th tim driati form of th Torsional Inducti Trm () t () t f () t c (4) Th driati form d d f (47) c Th diffrnc form Δ Δ f (48) c William Alk Pag 9 5/4/8

10 Nwtonian Torsion Phsics INTAK, IN. 3.9 TOIONA APAITIV A FUTUATION + FUTUATING APAITAN ± + - g i V + V - FIGU 5. Th fluctuating capacitanc of an objct du to grait. Appling th product rul, th complt idal capacitor modl is composd of two trms, d dv d i() t ( V) + V V + V (49) dt dt dt Whr, th Inrtial Trm is V, and capacitor is inariant within an quipotntial surfac of grait g Y. Th Torsional Trm is V, and changing capacitanc fluctuats btwn quipotntial surfacs of grait. For a capaciti fluctuating sstm, th Torsional Trm is NOT zro amps. B appling a constant oltag across capacitor, or V Volts s, th Inrtial Trm This rmos Inrtial Trm, laing onl th Torsional Trm, i () t V Amps (5) i () t V Amps (5) inc has units of conductanc in mhos,, its dirction of chang could ithr b POITIV or NGATIV. If is ngati, it has units of ngati conductanc or, < (5) Now, th instantanous graitationall inducd powr P of a fluctuating capacitor is P () t i () t V V (53) o, for crtain alus of, th total instantanous powr P can b NGATIV or, P () t < Watts (54) William Alk Pag 5/4/8

11 Nwtonian Torsion Phsics INTAK, IN. 3.9 Thn, intgrating P with rspct to tim whn th total powr is lss than zro watts rsults in NGATIV nrg of capacitor or, (55) () () < t P dt V dt V t Jouls If is positi, it has units of positi conductanc or, > (5) Now, th instantanous graitationall inducd powr P of a fluctuating capacitor P () t i () t V V (57) o, for crtain alus of, th total instantanous powr P can b POITIV or P () t > Watts (58) Thn, intgrating P with rspct to tim rsults in css POITIV nrg of capacitor or, quat this to th nrg quialnt of mass (59) () () > t P dt V dt V t Jouls, Thn, th nrg quialnt of mass (graitational nrg) () t () t () () Y () () t t V t () B rarranging trms, th mass quialnt of nrg () t () t V () t () Y Y V () t Y () t (3) Th fluctuating mass quialnt of nrg V (4) Y Y o, th graitational capacitor modl V f (5) () t Y Y Y Y Y William Alk Pag 5/4/8

12 Nwtonian Torsion Phsics INTAK, IN. 3.9 tting d dt, th Torsional apaciti Forc Trm Y B rarranging trms, th fluctuating nrg quialnt of mass f () t () () f t (7) Th total nrg containd within mattr () t () t c (8) Th chang in this total nrg (9) c B rarranging trms, th chang in total mass f() t V V () t c c V () t t () () t (7) o, th tim driati form of th Torsional apaciti Trm () t () t f () t c (7) Th driati form d f (7) d c Th diffrnc form Δ Δ f (73) c William Alk Pag 5/4/8

13 Nwtonian Torsion Phsics INTAK, IN. 3.9 TH GAVITATIONA OUPING OF A FUTUATING A, INDUTO O APAITO,5. 9,9 GAVITATIONA FN OBJT with A (BFO) ADIU g n G NATUA A n FUTUATION DU TO F FA Δ 7,59 INAD GAVITY OBJT with A + (AFT),378.. g g 7. g 9.8 AATION DU TO GAVITY m sc g n FIGU. Th natural mass fluctuation of an objct du to graitational fr fall. Natural unirsal mass attraction or classic Nwtonian grait is a forc f that acts through a cntr of mass of th arth with mass and a tst mass sparatd b a distanc, G f g (74) o, gin, Graitational constant ass of th arth adius of arth G.759 Nm kg kg.378 m Th surfac grait g of th arth g 4 (.759 N m kg )( kg ) (.378 m) G 9.85m sc (75) William Alk Pag 3 5/4/8

14 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th grait g at GAVITATIONA FN position g 4 (.759 N m kg )( kg ) ( 9.9 m) G.537 m sc (7) Th grait g at position g 4 (.759 N m kg )( kg ) ( 7.59 m) G m sc (77) armt () quats forc f producd b a fluctuating tst mass d to th graitational forc f, Th driati form of a fluctuating tst mass d f () t f () t (78) d f d g d c c (79) Th driati form of th graitational D HIFT (or BU HIFT) of tst mass d and th nrg quialnt of tst mass d displacd d within a gin grait wll g d d g d c (8) armt stats th quation abo shows a calculatd chang of nrg lls as a function of graitational potntial is in prfct agrmnt with th Pound and bka and also th Pound and nidr primnts. Thrfor, nrg incrass as a function of downward or positi displacmnt within a gin grait wll. t dy g g d, th ponntial solutions of th driati form of mass and nrg quialnt of mass ar, d c g dyg (8) g ln (8) c g Y g g ln ln ln c ( ) ( ) ( g g ) (83) g g c (84) g g c (85) William Alk Pag 4 5/4/8

15 Nwtonian Torsion Phsics INTAK, IN. 3.9 g g c (8) o, th Pound, bka and nidr primnt usd ossbaur spctroscop to masur th lctromagntic 57 graitational D HIFT (or BU HIFT) of 4.4kV gamma ras mittd from F through a rtical distanc of.m. With th gamma ras mittd upward, th showd th D HIFT was within on prcnt (%) of this rsult, G g g Δ Δ HIFT (87) c c HIFT 8 ( m sc) 4 (.759 N m kg )( kg ) (.378 m) (.378 m) (88) HIFT With th gamma ras mittd downward, th showd th BU HIFT was, (89) HIFT 8 ( m sc) 4 (.759 N m kg )( kg ) (.378 m) (.378 m) (9) HIFT (9) Now, th forc f producd b a fluctuating inductor d is quatd to th graitational forc f, Th driati form of a fluctuating inductor d f () t f () t (9) d f d g d c c (93) Th driati form of th graitational D HIFT (or BU HIFT) of inductor d displacd d within a gin grait wll g d g d (94) c t dy g g d, th ponntial solution of th driati form of an inductor d c g dyg (95) g William Alk Pag 5 5/4/8

16 Nwtonian Torsion Phsics INTAK, IN. 3.9 ln (9) c g Y g g ln ln ln c ( ) ( ) ( g g ) (97) g g c (98) g g c (99) o, th graitational D HIFT (or BU HIFT) of an inductor G g g Δ HIFT () c c Now, th forc f producd b a fluctuating capacitor d is quatd to th graitational forc f, Th driati form of a fluctuating inductor d f () t f () t () f d g d d c c () Th driati form of th graitational D HIFT (or BU HIFT) of capacitor d displacd d within a gin grait wll g d d g d c (3) t dy g g d, th ponntial solution of th driati form of a capacitor d c g dyg (4) g ln (5) c g Y g g ln ln ln c ( ) ( ) ( g g ) () William Alk Pag 5/4/8

17 Nwtonian Torsion Phsics INTAK, IN. 3.9 g g c (7) g g c (8) o, th graitational D HIFT (or BU HIFT) of a capacitor G g g Δ HIFT (9) c c William Alk Pag 7 5/4/8

18 Nwtonian Torsion Phsics INTAK, IN. 3.9 NATUA ATIVITY THOY DAD GAVITY GAVITATIONA FN INAD GAVITY Δ DAING A INAING A + Δ UVATU DU TO GAVITY A AT T TOWAD NT OF GAVITY Δ +Δ g FIGU 7. A chang of rlatiistic mass du to grait. Th stablishmnt of a GAVITATIONA FN is dfind as a fid plan of rfrnc within a gin grait wll g. This plan is dscribd as an quipotntial surfac of grait, and is usd throughout this book. Natural rlatiistic changs of mass, olum, frqunc, nrg, tc. fluctuat or cur as a function of displacmnt ±Δ from this plan of rfrnc. This displacmnt dfins a nw plan of quipotntial surfac of grait, and th grait at that point ma b incrasd or dcrasd basd upon th sign of th displacmnt. armt () inoks th principl of mass-nrg consration rgarding th displacmnt of mattr btwn plans. For ampl, an objct of mass displacd a distanc Δ changs back to its original mass whn rturnd to its original position within th sam grait wll. Thrfor, a nw and simplifid rlatiit modl is introducd. For graitational nrg sstms, and gin an quipotntial surfac of grait rfrnc, th following paramtrs including rlatiistic mass ±Δ, rlatiistic inductanc ±Δ, and rlatiistic capacitanc ±Δ, fluctuat or cur btwn quipotntial surfacs of grait b displacmnt ±Δ. Again, th kintic nrg of graitational nrg sstms is assumd to b zro. o, gin a common quipotntial surfac of grait rfrnc g, an incras in grait causs a natural rlatiistic incras in mass, nrg quialnt of mass (graitational nrg), inductanc, and capacitanc. ikw a dcras in grait causs a natural rlatiistic dcras in th sam mtrics. Gin an objct with a rst mass capacitanc, th nw rst mass and th nw capacitanc ar,, an quialnt nrg of th rst mass, th nw quialnt nrg of th rst mass, an inductanc, and a, th nw inductanc, γ ±Δ () N γ ±Δ () N γ ±Δ () N γ ±Δ (3) N William Alk Pag 8 5/4/8

19 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th natural rlatiistic gamma γ N g g c γ N (4) Th diffrnc forms and th ponntial forms of th natural rlatiistic mass mass modl, inductor modl, and capacitor modl, nrg quialnt of modl at position ±Δ within a gin grait wll g ar, g g g g c ±Δ ± c g g g g c +Δ ± c g g g g c +Δ ± c g g g g c ±Δ ± c (5) () (7) (8) In summar, Natural latiit (N) Thor dscribs th natur of th primar graitational ffct. William Alk Pag 9 5/4/8

20 Nwtonian Torsion Phsics INTAK, IN. 3.9 PIA ATIVITY THOY OBV B IN OTION B d dt B ds c dt ds c dt A TATIONAY OBV A FIGU 8. Th dfinition of a spac-tim intral rlati to a stationar Obsrr A. instin (95) formulatd his thor of spcial rlatiit and is dscribd as Obsrr B, moing at locit rlati to a stationar Obsrr A, undrgos a rlatiistic ffct. This ffct changs arious proprtis of Obsrr B such as mass, lngths, tim intrals, frqunc and nrg with rspct to stationar Obsrr A. It s prssd as a Pthagoran-tp quantit calld a spac-tim intral, and aluats as a orntz tmporal corrction shown blow. ds ds + d (9) ds ds d () ds c dt d () inc th locit of Obsrr B d () dt d dt (3) o, ds c dt dt (4) Thn, cdt dt ds c dt c dt cdt c (5) William Alk Pag 5/4/8

21 Nwtonian Torsion Phsics INTAK, IN. 3.9 inc th spd of light c ds c dt s () ds c dt (7) o, th orntz tmporal corrction rlati to Obsrr B cdt cdt (8) c dt dt (9) c dt dt c (3) Thrfor, rlati to stationar Obsrr A with a tim intral ticking slowr or D HIFTD, and ha th following orntz tmporal corrction, dt A, Obsrr B s clock at tim intral dt B will b dt B B dta (3) c For >, B dt A > dt (3) B Δ t >Δ t A B ikw rlati to Obsrr B in motion with a tim intral dt B, stationar Obsrr A s clock with a tim intral dt will b ticking fastr or BU HIFTD, and ha th following orntz tmporal corrction, A dt A dt B c B (33) For >, B dt B < dt (34) A Δ t <Δ t B A William Alk Pag 5/4/8

22 Nwtonian Torsion Phsics INTAK, IN. 3.9 TI FUTU t TI PAT DAD GAVITY + j Δ Δ GAVITATIONA FN INITIA A, AT T AND t sc UVATU DU TO VOITY +Δ g INAD GAVITY j t + Δ FIGU 9. A chang of rlatiistic mass du to imaginar or compl locit. Gin th rst mass of an objct, th spcial rlatiistic mass objct moing at locit modl prsntd b instin (95) shows an γ + d c (35) Th gamma γ γ c (3) Implmnting th binomial pansion of th abo quation, Using th st ordr trm of th pansion shown abo whr γ (37) 4 8 c 8 c c 8 c c, th nw spcial rlatiistic gamma γ γ + (38) c Th driati form of th spcial rlatiistic mass modl moing at locit γ ± d ± c (39) William Alk Pag 5/4/8

23 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th driati form of a fluctuating mass d d (4) c An objct can mo at a ral (i.., tim-forward) locit, at an imaginar (i.., tim-futur) locit j, or at a locit that is a combination of th two. Th ral and imaginar componnts ar rotatd about th tmporal ais and thrfor, can b dscribd as compl motion. Th rotation is gin as θ 9, whr th ral ais is j θ and th imaginar tim-futur ais is θ 9. Th compl numbr uss th ulr s idntit θ, which functions as a tmporal rotation oprator. jθ cosθ + jsinθ (4) o, th driati form of th inrtial D HIFT (or BU HIFT) of mass d, nrg quialnt of mass d, inductor d, or capacitor d of an objct moing at a ral locit or a compl locit j d d d d HIFT (4) c Th ponntial solution of th driati form of mass d (43) c ln ( ) (44) c ln ( ) ln ( ) ln c (45) c (4) c (47) c (48) c (49) c (5) William Alk Pag 3 5/4/8

24 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, th inrtial D HIFT (or BU HIFT) of a mass, an nrg quialnt of mass a capacitor, an inductor, and Δ Δ Δ Δ HIFT (5) c Th spcial rlatiistic gamma γ c γ (5) Th diffrnc forms and th ponntial forms of th spcial rlatiistic mass modl, nrg quialnt of mass modl, inductor modl, and capacitor modl of an objct moing at a ral locit or a compl locit j ar, c ±Δ ± c c ±Δ ± c c ±Δ ± c c +Δ ± c (53) (54) (55) (5) William Alk Pag 4 5/4/8

25 Nwtonian Torsion Phsics INTAK, IN. 3.9 DID INTIN GT IT IGHT, O NOT? instin s Gnral latiit Thor (9) quats Nwton s scond law of motion, f ma i, whr m i is th inrtial mass to Nwton s graitational forc, f mg g, whr m g is th graitational mass. Is this concpt corrct? instin usd this to formulat his quialnc principl and statd, Thr is no primnt a prson could conduct in a small olum of spac that would distinguish btwn a graitational fild and an quialnt uniform acclration. Is this statmnt corrct? ts tst instin s principl in th following thought primnt: AT T AATING d d> g i fg fi ON TH ATH IN PA FIGU. An lator at rst on th arth is NOT quialnt to an lator acclrating in spac. As shown abo, th natural rlatiistic mass fluctuation of an lator at rst on th surfac of th arth is zro, or d. Howr, th scond ordr spcial rlatiistic mass fluctuation of th sam lator acclrating in spac is non-zro or d >, and as a consqunc, radiats lctromagntic was. According to Woodward (998), radiation raction is obsrd in bodis bing acclratd basd upon Nwton s scond law of motion, f ma. Thrfor, gin this scnario, th graitational mass can t b quialnt to its inrtial mass du to thir diffrncs in mass fluctuations. William Alk Pag 5 5/4/8

26 Nwtonian Torsion Phsics INTAK, IN. 3.9 F FA A GIVN DITAN ONTANT VOITY d > d > g i fg f i NA ATH IN PA FIGU. An lator in fr fall abo th arth is quialnt to an lator moing at constant locit in spac. As shown abo, an lator traling a distanc + d in fr fall and th sam lator moing at a constant locit at right angls to fr fall produc irtuall no radiation raction. o, gin this scond scnario, ths mass fluctuations ar considrd quialnt, hnc, stablishing a nw Principl of quialnc Thorm. A NW PINIP OF QUIVAN THO. INTIA A (kg) TI-PAT -TI-FUTU INTIA FN INAING INTIA A (D HIFT) DAING INTIA A (BU HIFT) TI -FOWAD c.9 ±. j 8 7 ± 7.5 j 7 ± 5. j 7 ±.5 j. VOITY (m/sc) FIGU. Vlocit profil of a kg inrtial mass. William Alk Pag 5/4/8

27 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th inrtial D HIFT of an objct du to locit Δ HIFT (57) c. GAVITATIONA A (kg) DAING GAVITY GAVITATIONA FN g DAING GAVITATIONA A (BU HIFT) g g c INAING GAVITATIONA A (D HIFT) DIPANT FO NT OF ATH (m) FIGU 3. Displacmnt profil of a kg graitational mass du to arth s grait wll. And sinc th graitational D HIFT of th sam objct du to grait g G g g Δ HIFT (58) c c B quating an inrtial D HIFT to a graitational D HIFT, a nw Principl of quialnc Thorm is dtrmind as, G g g (59) c c c William Alk Pag 7 5/4/8

28 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, an objct displacd locit, ±Δ within th arth s grait wll g is quialnt to th sam objct moing at compl ( ) g g G () Δ 7.. DAING INTIA A (BU HIFT) DIPANT (m) Δ + G DAING GAVITATIONA A (BU HIFT).. INAING GAVITATIONA A (D HIFT) 8 4 INTIA - GAVITATIONA FN j. ATH UFA.378 m 4 j j 8j j VOITY (m/sc). INAING INTIA A (D HIFT) FIGU 4. quating an inrtial D (BU) HIFT to a graitational D (BU) HIFT. As shown abo, if th displacmnt Δ of an objct is POITIV, thn th objct is moing at a ral locit. Howr, if th displacmnt tim-futur) locit Δ is NGATIV, thn th sam objct is moing at a compl (i..,, or locit j, whr j. Th ral and imaginar componnts ar rotatd William Alk Pag 8 5/4/8

29 Nwtonian Torsion Phsics INTAK, IN. 3.9 about th tmporal ais as a compl locit. Th rotation is gin as θ 9, whr th ral ais is θ j and th imaginar tim-futur ais is θ 9. Th compl numbr uss th ulr s idntit θ, which functions as a tmporal rotation oprator. jθ cosθ + jsinθ () o, gin an objct moing at a compl locit, th quialnt displacmnt to position within th arth s grait wll g, whr < or G g + G + g () Thrfor, th quialnt displacmnt Δ within th arth s grait wll g Δ + G + G (3) Th quialnt maimum compl locit ma at is + (4) G ma G (5) o, gin th quialnt maimum compl locit ma, th minimum mass min at G min + c c G c () In summar, this nw Principl of quialnc Thorm dscribs an objct moing at on-half th squar of a ral locit is quialnt to th sam objct haing falln down a displacmnt + d within a gin grait wll g. This objct naturall acquirs mor rlatiistic mass, inductanc and capacitanc as it mos at a ral locit, and augmnts its own graitation with othr objcts. On th othr hand, th sam objct moing at on-half th squar of a compl locit j is quialnt to th sam objct haing falln up a displacmnt d in th sam grait wll. This objct naturall loss mor rlatiistic mass, inductanc and capacitanc as it mos at a compl locit j, and diminishs its own graitation with othr objcts. Thrfor, spcial rlatiit is considrd to b a scondar graitational ffct. William Alk Pag 9 5/4/8

30 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl. Gin th locit profil abo of an objct haing a mass moing at a spcial rlatiistic timforward locit, comput th nw spcial rlatiistic inrtial mass o, gin, Dirction of tim θ ass of objct.kg 8 Vlocit of objct. m sc Th tim-forward locit of an objct. m m jθ 8 j 8. sc. sc (7) Th nw spcial rlatiistic inrtial mass 8 (. m sc) 8 c ( m sc) (. kg) (8) Th inrtial mass of th objct was incrasd b,.57kg (9).57kg. kg.57kg (7) ampl. Gin th locit profil abo of an objct haing a mass moing at a spcial rlatiistic locit tim-futur j, comput th nw spcial rlatiistic inrtial mass. o, gin, Dirction of tim θ 9 ass of objct.kg 8 Vlocit of objct. m sc Th tim-futur locit of an objct m j m jθ 8 j9 8. sc. sc (7) Th nw spcial rlatiistic inrtial mass 8 (. j m sc) 8 c ( m sc) (. kg) (7) Th inrtial mass of th objct was rduc b, kg (73) kg. kg.54kg (74) William Alk Pag 3 5/4/8

31 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl 3. Gin th graitational profil abo of an objct haing a mass within arth s grait wll o, gin, ass of objct g, comput th nw natural rlatiistic graitational mass.kg Objct on arth s surfac.378 m 8 Objct displacd to. m 8 pd of light c m sc Graitational constant G.7 Nm kg 4 ass of th arth kg Th acclration du to grait at surfac of arth displacd to a position Δ. g 4 (.7 N m kg )( kg ) (.378 m) G 9.85m sc (75) Th acclration du to grait at altitud. 8 m abo th arth g 4 (.7 Nm kg )( kg) 8 (. m) G m sc (7) Gin th ponntial solution of th natural rlatiistic mass modl, th nw graitational mass 8 (.39894m sc )(. m) ( 9.85m sc )(.378 m) g g 8 c ( m sc) kg (77) (. ) kg (78) Th graitational mass of th objct was rducd b, kg kg kg (79) ampl 4. Assuming thr ar no othr graitational influncs bsids th arth, comput th nw minimum natural rlatiistic graitational mass min of an objct at. o, gin, ass of objct.kg Objct on arth s surfac.378 m 8 pd of light c m sc Graitational constant G.7 Nm kg 4 ass of th arth kg William Alk Pag 3 5/4/8

32 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th minimum graitational mass min at 4 (.7 N m kg )( kg ) G 8 (.378 m)( m sc) c kg (8) min. Th graitational mass of th objct was rducd b, min kg (8) kg kg kg (8) HOW GAVITY AFFT TH VOU OF OBJT An objct of olum V (lngth, width W, and hight grait wll g. ikw th sam th olum V dilats as a function of position H ) contracts as a function of position +Δ within Δ in th sam grait wll. o, th diffrnc form of th graitational D HIFT (or BU HIFT) of an objct of olum ΔV V displacd Δ within a gin grait wll g Δ ΔW ΔH g g W H c (83) Th diffrnc forms and ponntial forms of th natural rlatiistic objct of olum V at position ±Δ g g g g c Δ (84) c g g g g c Δ W W W W W (85) c g g g g c Δ H H H H H (8) c An objct of olum V (lngth th sam objct of olum HOW VOITY AFFT TH VOU OF OBJT, width W, and hight V dilats moing at a compl locit H ) contracts moing at a ral locit. ikw o, th diffrnc form of th inrtial D HIFT (or BU HIFT) of an objct of olum ΔV V moing at a ral locit or a compl locit j j. Δ ΔW ΔH W H c (87) William Alk Pag 3 5/4/8

33 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th diffrnc forms and ponntial forms of th spcial rlatiistic objct of olum V moing at a ral locit or a compl locit j c Δ (88) c c W W Δ W W W (89) c c H H Δ H H H (9) c within grait wll as a function of position HOW GAVITY AFFT TH FQUNY OF TI A mchanical oscillator ibrating at a frqunc f contracts (i.., slows down) as a function of position +Δ g. ikw th sam mchanical oscillator ibrating at a frqunc f dilats (i.., spds up) Δ in th sam grait wll. o, th diffrnc form of th graitational D HIFT (or BU HIFT) of an oscillator ibrating at a frqunc Δ f f displacd Δ within a gin grait wll g Δ f g g (9) f c Th diffrnc form and ponntial form of th natural rlatiistic frqunc f of an oscillator at position ±Δ g g g g c Δ f f f f f (9) c HOW VOITY AFFT TH FQUNY OF TI A mchanical oscillator ibrating at a frqunc f contracts (i.., slows down) whil moing at a ral locit. ikw th sam mchanical oscillator ibrating at a frqunc f dilats (i.., spds up) whil moing at a compl locit j. o, th diffrnc form of th inrtial D HIFT (or BU HIFT) of an oscillator ibrating at a frqunc Δ f f whil moing at a ral locit or a compl locit j Δ f (93) f c William Alk Pag 33 5/4/8

34 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th diffrnc form and ponntial form of th spcial rlatiistic frqunc f of an oscillator moing at a ral locit or a compl locit j c f f Δ f f f (94) c HOW GAVITY AFFT AN INTVA OF TI A mchanical oscillator ibrating for an intral of tim t contracts (i.., slows down) as a function of position +Δ within grait wll g. ikw th sam mchanical oscillator ibrating for an intral of tim t dilats (i.., spds up) as a function of position Δ in th sam grait wll. o, th diffrnc form of th graitational D HIFT (or BU HIFT) of an oscillator ibrating for an intral of tim Δ ttdisplacd Δ within a gin grait wll g Δ t g g (95) t c Th diffrnc form and ponntial form of th natural rlatiistic tim intral t of an oscillator at position ±Δ g g g g c Δ t t t t t (9) c HOW VOITY AFFT AN INTVA OF TI A mchanical oscillator ibrating for an intral of tim t contracts (i.., slows down) whil moing at a ral locit. ikw th sam mchanical oscillator ibrating for an intral of tim t dilats (i.., spds up) whil moing at a compl locit j. o, th diffrnc form of th inrtial D HIFT (or BU HIFT) of an oscillator ibrating for an intral of tim Δ ttwhil moing at a ral locit or a compl locit j Δ t (97) t c Th diffrnc form and ponntial form of th spcial rlatiistic tim intral t of an oscillator moing at a ral locit or a compl locit j c t t Δ t t t (98) c William Alk Pag 34 5/4/8

35 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th momntum grait wll sam grait wll, HOW GAVITY AFFT INA ONTU p of an objct of mass g. ikw th momntum moing at locit incrass as a function of position p of th sam objct dcrass as a function of position p +Δ within Δ in th (99) o, th diffrnc form of th graitational D HIFT (or BU HIFT) of momntum displacd Δ within a gin grait wll g Δ p p of an objct Δ p g g () p c Th diffrnc form and ponntial form of th natural rlatiistic momntum p at position ±Δ g g g g c ±Δ ± p p p p p c () HOW VOITY AFFT INA ONTU Th momntum th sam objct dcrass moing at a compl locit p of an objct of mass incrass moing at a ral locit. ikw th momntum p j, p of () o, th diffrnc form of th inrtial D HIFT (or BU HIFT) of momntum ral locit or a compl locit j Δ p p of an objct moing at a Δ p (3) p c Th diffrnc form and ponntial form of th spcial rlatiistic momntum locit or a compl locit j p of an objct moing at a ral c p p ±Δ p p ± p c (4) Th angular momntum function of position inariant as a function of position HOW GAVITY AFFT ANGUA ONTU of an objct of mass moing at locit with a radius r is inariant as a +Δ within grait wll g. ikw th angular momntum Δ in th sam grait wll, of th sam objct is r (5) William Alk Pag 35 5/4/8

36 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, th diffrnc form of th graitational D HIFT (or BU HIFT) of angular momntum objct displacd Δ within a gin grait wll g Δ of an Δ () Th diffrnc form and ponntial form of th natural rlatiistic angular momntum at position ±Δ (7) HOW VOITY AFFT ANGUA ONTU Th angular momntum of an objct of mass is inariant moing at a ral locit with a radius r. ikw th angular momntum of th sam objct is inariant moing at a compl locit j, r (8) o, th diffrnc form of th inrtial D HIFT (or BU HIFT) of angular momntum moing at a ral locit or a compl locit j Δ of an objct Δ (9) Th diffrnc form and ponntial form of th spcial rlatiistic angular momntum of an objct moing at a ral locit or a compl locit j () William Alk Pag 3 5/4/8

37 Nwtonian Torsion Phsics INTAK, IN. 3.9 TH PA-TI DIA O TH ATH Z ε TI t Z G Z μ B FIGU 4. Th spac-tim mdia or athr. According to Puthoff (99) and Puthoff, ittl and Ibison (), th acuum is dscribd as haing magntic prmabilit μ and dilctric prmittiit ε, and acts to impd th propagation of light and th motion of mattr. Dirct modification of ths componnts changs th natur of light and mattr. g +Δ g ' +Δ ' UVATU DU TO GAVITY r r Δr AFYING OF r Δr r PA-TI DIA + Δ +Δ GAVITATIONA FN FIGU 5. Two similar objcts undrgoing natural unirsal mass attraction. Th acti acuum of spac, or spac-tim mdia (i.., th athr) is composd of uncondnsd rlatiistic mass. An objct mad of mattr (i.., atoms) and gin a GAVITATIONA FN point undrgos unirsal mass attraction (i.., graitational fr fall) with anothr objct. Both objcts acquir rlatiistic mass b a natural mans from th surrounding spac-tim mdia as a function of displacmnt +Δ btwn th two objcts. This mdia condnss onto both objcts as mor rlatiistic mass, thrb incrasing thir total mass n +Δ n, inductanc n +Δ n, and capacitanc n + Δ n. This action changs th rlatiistic momntum of both objcts rsulting with incrasing forc of attraction. Th spac-tim mdia btwn ths objcts rarf or rlatiistic mass condnss out of th mdia thrb affcting both th magntic prmabilit μ and th dilctric prmittiit ε of fr spac. This rarfaction of mdia is rfrrd to as a grait wll, and as a consqunc, causs th olum of spac occupid b both objcts and th spac btwn thm to b rducd. Th spac-tim mdia in a rarfing stat mans grait btwn ths objcts is incrasing, which causs light passing nar ths objcts to amplif in nrg λ and incras in frqunc f λ as pron b th Pound and bka primnt (94). This bhaior of spac-tim mdia acts as an impdanc upon th natural motion of mattr and th propagation of light. William Alk Pag 37 5/4/8

38 Nwtonian Torsion Phsics INTAK, IN. 3.9 TH GAVITATIONA OUPING OF AN TOAGNTI WAV DAD GAVITY g Δ PHOTON A Δ D HIFTING: DAING FQUNY AND NGY GAVITATIONA FN g ONOHOATI IGHT OU +Δ BU HIFTING: INAING FQUNY AND NGY INAD GAVITY TOWAD NT OF GAVITY g +Δ PHOTON B FIGU. lctromagntic was propagating within a gin grait wll. hown abo is th BU HIFTING of an lctromagntic wa du to grait. lati to a GAVITATIONA FN point or quipotntial surfac of grait within a gin grait wll g, PHOTON A dcrass in nrg λ and frqunc f λ as it propagats through dcrasing grait g Δ. ikw PHOTON B incrass in nrg λ and frqunc f λ as it propagats through incrasing grait g +Δ. This ffct was dmonstratd in th Pound, bka and nidr primnt, which usd ossbaur spctroscop to masur th lctromagntic 57 graitational D HIFT (or BU HIFT) of 4.4kV gamma ras mittd from F through a rtical distanc of.m. Using th diffrnc form of fluctuating nrg Δ λ of an lctromagntic wa propagating through grait wll g and th gamma ras mittd upward, th D HIFT was within on prcnt (%) of this rsult, Δ g g λ HIFT c λ (9.858 sc )(.378 ) 9.85 sc.378 HIFT 8 ( m sc) m m m m () () HIFT (3) William Alk Pag 38 5/4/8

39 Nwtonian Torsion Phsics INTAK, IN. 3.9 And with th gamma ras mittd downward, th BU HIFT was, HIFT 9.85 msc.378 m (9.858msc )(.378 m) ( m sc) 8 (4) HIFT (5) Th diffrnc form and ponntial form of th natural rlatiistic lctromagntic nrg λ at position ±Δ g g g g c ±Δ ± λ λ λ λ λ () c inc th nrg λ of a singl photon Thn, th Planck's constant h hf (7) λ λ λ h (8) f Th diffrnc form of th graitational D HIFT (or BU HIFT) of frqunc Δ fλ fλ of an lctromagntic wa propagating Δ within a gin grait wll g λ Δ f g g λ (9) f c λ Th diffrnc form and ponntial form of th natural rlatiistic lctromagntic frqunc f λ at position ±Δ g g g g c ±Δ ± fλ fλ fλ fλ fλ c () o, th natural rlatiistic Planck's constant h ranging from position Δ to +Δ aluats to unit gain or, h g g c λ λ g g fλ c fλ λ h f λ () Thrfor, th natural rlatiistic Planck's constant h is inariant btwn quipotntial surfacs of grait or, 34 h.755 Joul sc () William Alk Pag 39 5/4/8

40 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th spd of light c c λ f λ (3) Th diffrnc form of th graitational D HIFT (or BU HIFT) of th walngth lctromagntic wa displacd Δ within a gin grait wll g Δ λ λ of an Δ λ g g (4) λ c Th natural rlatiistic walngth λ at position ±Δ g g g g c Δ λ λ λ λ λ (5) c o, natural rlatiistic th spd of light c ranging from position Δ to +Δ aluats to unit gain or, g g g g c c λ λ λ λ λ λ c f f f c () Thrfor, th natural rlatiistic spd of light c is inariant btwn quipotntial surfacs of grait or, c m sc (7) HOW GAVITY AFFT TH PABIITY OF PA-TI DIA Th prmabilit μ of spac-tim mdia is gin as, μ π (8) 7 4 H m Th diffrnc form of th graitational D HIFT (or BU HIFT) of inductanc within a gin grait wll g Δ displacd Δ Δ g g (9) c Th inductanc of spac-tim mdia at position ±Δ g g g g c Δ (3) c William Alk Pag 4 5/4/8

41 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th diffrnc form of th graitational D HIFT (or BU HIFT) of lngth Δ displacd Δ within a gin grait wll g Δ g g c (3) Th lngth of spac-tim mdia at position ±Δ g g g g c Δ (3) c o, th natural rlatiistic prmabilit unit gain or, μ of spac-tim mdia ranging from position Δ to +Δ aluats to g g c g g c μ μ (33) Thrfor, th natural rlatiistic prmabilit surfacs of grait or, μ of spac-tim mdia is inariant btwn quipotntial μ 7 4π H m (34) HOW GAVITY AFFT TH PITTIVITY OF PA-TI DIA Th prmittiit ε of spac-tim mdia is gin as, ε F m (35) Th diffrnc form of th graitational D HIFT (or BU HIFT) of capacitanc Δ within a gin grait wll g Δ displacd Δ g g (3) c Th capacitanc of spac-tim mdia at position ±Δ g g g g c Δ (37) c William Alk Pag 4 5/4/8

42 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th diffrnc form of th graitational D HIFT (or BU HIFT) of lngth Δ displacd Δ within a gin grait wll g Δ g g c (38) Th lngth of spac-tim mdia at position ±Δ g g g g c Δ (39) c o, th natural rlatiistic prmittiit ε of spac-tim mdia ranging from position unit gain or, Δ to +Δ aluats to g g c g g c ε ε (4) Thrfor, th natural rlatiistic prmittiit ε of spac-tim mdia is inariant btwn quipotntial surfacs of grait or, ε F m (4) HOW GAVITY AFFT TH VITUA ITAN OF PA-TI DIA Th spac-tim mdia has irtual rsistanc or impdanc Z, and thrfor, isn't capabl of absorbing or dissipating lctromagntic nrg. Its A rsistanc is infinit or,. This mdia srs to impd th propagation of light and th motion of mattr and is calculatd as, Z μ (4) ε inc it has bn shown th prmabilit quipotntial surfacs of grait, it follows th natural rlatiistic impdanc position Δ to +Δ aluats to unit gain or, μ and prmittiit ε of spac-tim mdia ar inariant btwn Z of spac-tim mdia ranging from Z μ Z (43) ε Thrfor, th natural rlatiistic impdanc of grait or, Z of spac-tim mdia is inariant btwn quipotntial surfacs Z 37.73Ω (44) William Alk Pag 4 5/4/8

43 Nwtonian Torsion Phsics INTAK, IN. 3.9 HOW GAVITY AFFT TH PD OF IGHT Th spd of light c btwn spac-tim mdia c (45) μ ε inc it has bn shown th prmabilit μ and prmittiit ε of spac-tim mdia ar inariant btwn quipotntial surfacs of grait, it follows th natural rlatiistic spd of light c through spac-tim mdia ranging from position Δ to +Δ aluats to unit gain or, c c (4) μ ε Thrfor, th natural rlatiistic spd of light c through spac-tim mdia is inariant btwn quipotntial surfacs of grait or, c m sc (47) HOW GAVITY AFFT BOTZANN' ONTANT Th Boltzmann's onstant k is gin as, k (48) N inc th Idal Gas onstant and Aogadro's Numbr it follows th natural rlatiistic Boltzmann's onstant k ranging from position gain or, N ar inariant btwn quipotntial surfacs of grait, Δ to +Δ aluats to unit k k (49) N Thrfor, th natural rlatiistic Boltzmann's onstant k is inariant btwn quipotntial surfacs of grait or, 3 k.3858 Jouls K (5) HOW GAVITY AFFT AN TI HAG A fundamntal lctric charg q is gin as, q f (5) Th lctric forc f incrass with th squar of a dcrasing distanc, and th lctric fild also incrass with th squar of a dcrasing distanc at position + d. ikw th lctric forc f dcrass with th squar of a William Alk Pag 43 5/4/8

44 Nwtonian Torsion Phsics INTAK, IN. 3.9 incrasing distanc, and th lctric fild it follows th natural rlatiistic lctric charg q ranging from position also dcrass with th squar of a incrasing distanc at position Δ to d, +Δ aluats to unit gain or, q f q (5) Thrfor, th natural rlatiistic lctric charg q is inariant btwn quipotntial surfacs of grait or, q oul (53) HOW GAVITY AFFT TH FIN TUTU ONTANT Th Fin tructur onstant α q α (54) ε hc inc an lctric charg q, th spd of light c, th prmittiit ε, and Planck's constant h ar inariant btwn quipotntial surfacs of grait, it follows th natural rlatiistic Fin tructur onstant α ranging from position Δ to +Δ aluats to unit gain or, α q α (55) ε h c Thrfor, th natural rlatiistic Fin tructur onstant grait or, α α is inariant btwn quipotntial surfacs of (5) William Alk Pag 44 5/4/8

45 Nwtonian Torsion Phsics INTAK, IN. 3.9 A TYPIA TOAGNTI WAV B FAT PA-TI DIA t FIGU 7. Propagation of lctromagntic wa in flat spac-tim. B t t FIGU 8. Tpical B and Filds. William Alk Pag 45 5/4/8

46 Nwtonian Torsion Phsics INTAK, IN. 3.9 GAVITATIONA BU HIFTING OF AN TOAGNTI WAV NOT: PA-TI DIA I ODD A UNONDND ATIVITI A, INDUTAN AND APAITAN THAT AN B OPD O AFID. B AFYING PA-TI DIA t FIGU 9. Propagation of lctromagntic wa in rarfid spac-tim. B t t FIGU. Incrasing magnitud and frqunc of B and Filds b graitational function. William Alk Pag 4 5/4/8

47 Nwtonian Torsion Phsics INTAK, IN. 3.9 GAVITATIONA D HIFTING OF AN TOAGNTI WAV NOT: PA-TI DIA I ODD A UNONDND ATIVITI A, INDUTAN AND APAITAN THAT AN B OPD O AFID. B OPING PA-TI DIA t FIGU. Propagation of lctromagntic wa in comprssing spac-tim. B t t FIGU. Dcrasing magnitud and frqunc of B and Filds b graitational function. William Alk Pag 47 5/4/8

48 Nwtonian Torsion Phsics INTAK, IN. 3.9 FIGU 3. A Global Positioning atllit. ampl 5. A Global Positioning atllit (GP) transmits an lctromagntic signal at a frqunc f λ AT of ~.3Hz down to th arth from an altitud of,8.8km, and has an orbital locit of km sc. Th natural rlatiistic BU HIFT du to grait and th spcial rlatiistic D HIFT du to locit changs th frqunc of this transmittd signal. o, gin th corrctd transmittd frqunc f λ AT, comput th BU HIFT and D HIFT such that a ground-basd rcir will rad a signal f λ X that is prcisl 3. Hz. Th signal frqunc of th satllit is adjustabl down to μ Hz. o, gin, Altitud of satllit Δ.88 m 3 Orbital locit m sc orrctd frqunc of satllit f Hz λ AT cir locatd on surfac of arth.378 m 8 pd of light c m sc Graitational constant G.7 Nm kg 4 ass of th arth kg Th initial radius of th satllit abo th arth m m m +Δ (57) William Alk Pag 48 5/4/8

49 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th acclration du to grait at altitud.549 m abo th arth g 4 (.7 N m kg )( kg ) (.549 m) G.553m sc (58) Th acclration du to grait at altitud 7.59 m abo th arth g 4 (.7 N m kg )( kg ) (.378 m) G 9.85m sc (59) Gin th ponntial solution of th natural rlatiistic frqunc modl, th graitational BU HIFTD frqunc ( 9.85m sc )(.378 m) (.553m sc )(.549 m) g g 8 c ( m sc) f f Hz () λ λ ( ) f Hz f () λ λ Gin th ponntial solution of th spcial rlatiistic frqunc modl, th D HIFTD frqunc of th BU HIFTD frqunc computd abo 3 ( m sc) 8 c ( m sc) f f Hz () λ λ ( ) f 3. Hz f (3) λ o, a ground-basd rcir will rad a signal that is prcisl 3. Hz with a satllit frqunc f λ AT gin abo. λx FIGU 4. A constllation of 4 Global Positioning atllits (GP) orbiting th arth. William Alk Pag 49 5/4/8

50 Nwtonian Torsion Phsics INTAK, IN. 3.9 GAVITOAGNTI THOY P db r UNT NT θ AGNTI INDUTION I d FIGU 5. Th magntic induction producd b a positi currnt lmnt. A constant positi lctric currnt I must crat a stabl magntic fild B around a wir. This stabl fild is du to th flow of lctric currnt shown abo. Th chang of magntic induction db at a fid point P producd b a currnt lmnt d is calculatd using th Biot-aart s aw, db μ I d r 4π r (4) 3 Or, μ I sin ( θ ) d db (5) 4π r inc charg q is quantizd in a singl lctron passing a fid point pr chang of tim dt or, thn, lctric currnt I is dfind as quantit N of chargs dq d N I q () dt dt And locit of an lctron passing a fid point is dfind as chang of distanc d pr chang of tim dt or, d (7) dt William Alk Pag 5 5/4/8

51 Nwtonian Torsion Phsics INTAK, IN. 3.9 Thn, th lctric currnt I is rdfind as, d( N ) I (8) d o, th chang of magntic induction db at a fid point P producd b quantit N of chargs locit moing at db μ sin ( θ ) d( N ) (9) 4π r To find th magntic induction B producd b a singl lctron at point P whn θ 9 intgrat, and N, thn μ B 4π r db (7) Th total nrg dnsit u B of magntic fild B containd within olum V u B U B B V μ (7) Thrfor, th total fild nrg Th chang of magntic fild nrg Th total nrg U B of magntic fild B containd within olum V U containd within mattr B B μ V V (7) 4 μ 3π r du B containd within a chang of olum d V B μ du B d V d V (73) 4 μ 3π r c (74) quat total magntic fild nrg U B to th total nrg U B containd within mattr, (75) o, th chang of magntic fild nrg du B du B d B c (7) William Alk Pag 5 5/4/8

52 Nwtonian Torsion Phsics INTAK, IN. 3.9 Thrfor, th fluctuating magntic mass d B containd within a chang of olum d V d B ( ) du μ B d V (77) 4 c 3π r c ω r ma r min FIGU. Th olum V of an lctron is modld as a hollow sphroid. inc th nrg of an lctron is finit, no fild componnt can b prsnt at its cntr. o, th olum of an lctron is modld as a hollow sphroid, Th fluctuating magntic mass π rma rmin ma V π sin ω d ω r dr 4π r dr (78) r rmin d B containd within a chang of olum d V of a hollow sphroid ( ) μ ( ) r ma (79) rma ( 4π r ) 4 min rmin μ d B d r dr d dr 3π r c 8π c r Gin th radius of a fluctuating magntic mass r, th driati form of a moing lctron r d ranging from a classic lctron radius r to infinit, or Th fluctuating magntic mass d B d B ( ) μ dr 8π c (8) r r d B ( ) μ (8) 8π r c William Alk Pag 5 5/4/8

53 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, gin th rst mass of an lctron moing at locit is, th diffrnc form of th spcial rlatiistic mass of an lctron γ ± d ± c (8) B quating th fluctuating magntic mass d B to th spcial rlatiistic mass d, Th quation rducs to, ( ) μ (83) 8π r c c ( ) o, gin, 7 Prmabilit of fr spac μ 4π H m Fundamntal charg of an lctron.77 5 lassic lctron radius r.8794 m st mass of an lctron μ (84) 8π r 3 kg 9 ( π ) 5 8π (.8794 m) H m kg (85) This shows th fluctuating magntic mass of a moing lctron is idntical to th spcial rlatiistic mass at an locit, Thrfor, th fluctuating magntic mass (8) d B is th fluctuating mass d B d of an lctron, d (87) o, th magntic mass B and th mass of th lctron B ( ) μ (88) 4π r And th fluctuating magntic mass Δ B and th fluctuating mass Δ ( ) μ ( ) μ B 8π r c 4π r c c Δ Δ (89) William Alk Pag 53 5/4/8

54 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, th locit of an lctron π r Δ Δ c c (9) μ ( ) Thrfor, if th fluctuating mass is positi, thn th locit of th lctron is ral. Howr, if th fluctuating mass is ngati, thn th locit is imaginar. IF TH AGNTI FID NGY Δ U B <, AND Δ <, TH VOITY I IAGINAY A I B μ H + - N IF TH AGNTI FID NGY Δ U B >, AND Δ >, TH VOITY I A PANNT AGNT ODD A A ONOID FIGU 7. Th magntic fluctuating mass. Now, th diffrnc form of th inrtial D HIFT (or BU HIFT) of th magntic mass Δ B B and th mass Δ of a particl moing at a locit Δ B Δ (9) c B A particl can mo at a ral (i.., tim-forward) locit, at an imaginar (i.., tim-futur) locit j, or at a locit that is a combination of th two. Th ral and imaginar componnts ar rotatd about th tmporal ais and thrfor, can b dscribd as compl motion. Th rotation is gin as θ 9, whr th ral ais is j θ and th imaginar tim-futur ais is θ 9. Th compl numbr uss th ulr s idntit θ, which functions as a tmporal rotation oprator. Th compl locit Gin th rst mass of an lctron rlatiistic magntic mass jθ cosθ + jsinθ (9) or th classic lctron radius r, th diffrnc forms of th spcial, whr θ 9 ar, modl of a particl moing at a compl locit c ±Δ ± c ( ) μ ( ) c 4π r c 4π r μ ±Δ ± (93) (94) William Alk Pag 54 5/4/8

55 Nwtonian Torsion Phsics INTAK, IN. 3.9 Now, appl th nw Principl of quialnc Thorm whr th fluctuating magntic mass of a moing lctron is quialnt to natural rlatiistic mass du to th arth s grait wll, μ ( ) ( g g ) Δ G (95) 8π r c c c c ( ) g g G (9) Th position of an lctron moing at a locit within arth s grait wll g Y whr < or G Δ c g g + + g g (97) c Δ + + G G (98) Th quialnt maimum compl locit ma at ma G (99) Gin th quialnt maimum compl locit ma, th minimum graitational mass min at G min + c c G c (3) Th quialnt maimum fluctuating graitational mass of th lctron ma min c Δ at G Δ (3) o, th diffrnc form of th graitational D HIFT (or BU HIFT) of th magntic mass Δ B B and th mass Δ of a particl displacd a distanc Δ within a gin grait wll g Y ( g g ) Δ Δ c B (3) B William Alk Pag 55 5/4/8

56 Nwtonian Torsion Phsics INTAK, IN. 3.9 Gin th rst mass of an lctron or th classic lctron radius r, th diffrnc forms of th natural rlatiistic mass modl of a particl displacd a distanc Δ within a gin grait wll g Y ar, g g ( g g ) c c ±Δ ± g g ( ) ( g g ) μ ( ) μ ±Δ ± c 4π r c 4π r (33) (34) In summar, Graitomagntic Thor shows that a moing lctron producs an incras in rlatiistic mass that tnds from its classic radius r to infinit, and coupls to grait. This motion can ithr ha a locit or a compl (i.., tim-futur) locit j. If th locit is compl, thn th lctron will hibit an antigraitational ffct, and produc a compl (i.., tim-futur) magntic fild jb. In addition, th total fild nrg U B of a compl magntic fild jb containd within a olum V is NGATIV. ampl. An lctron moing through a wir at a tim-forward locit whr θ producs a timforward magntic induction B at a distanc r. Gin, Dirction of tim is forward θ Vlocit of lctron through a wir. m sc 7 Prmabilit of fr spac μ 4π H m 9 Fundamntal charg of an lctron.77 3 st mass of an lctron kg adius r.m Graitational constant G.7 Nm kg adius of surfac of arth.378 m ass of th arth Th tim-forward locit, whr θ 4 kg m m Th tim-forward magntic induction B at distanc r B jθ j. sc. sc (35) 7 9 ( 4π H m)(.77 )(. m sc) μ 4π r 4π. (3) ( m) B 8.77 T (37) William Alk Pag 5 5/4/8

57 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th POITIV fluctuating mass Δ of th lctron (. m sc) 8 ( m ) Δ kg c sc 3 ( ) (38) 5 Δ kg (39) Appling th nw Principl of quialnc Thorm, (.378 m) (.378 )(. sc) 4 ( Nm kg )( kg) + m m G (3) o, th quialnt POITIV displacmnt m (3) Δ is graitational within th arth s grait wll Δ m (3) 5.98 ampl 7. An lctron moing through a wir at a tim-adancd locit whr < θ < 9 producs a tim-adancd magntic induction B at a distanc r. Gin, Dirction of tim is adancd θ 45 Vlocit of lctron through a wir. m sc 7 Prmabilit of fr spac μ 4π H m 9 Fundamntal charg of an lctron.77 3 st mass of an lctron kg adius r.m Graitational constant G.7 Nm kg adius of surfac of arth.378 m 4 ass of th arth kg Th tim-adancd locit, whr θ 45 m j m jθ j sc sc (33) Th tim-adancd magntic induction B at distanc r B ( 4π H m)(.77 )( j m sc) μ + 4π r 4π. (34) ( m) 8 8 B j T + (35) William Alk Pag 57 5/4/8

58 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th IAGINAY fluctuating mass Δ of th lctron ( j m sc ) ( m ) Δ kg c sc (3) Δ (37) j kg Appling th nw Principl of quialnc Thorm, (.378 m) ( )( sc) (.7 Nm 4 kg )( kg) + m j m G + (38) o, th quialnt IAGINAY displacmnt Th maimum tim-futur locit m j m (39) Δ is shown to b non-graitational within th arth s grait wll Δ j m (3) 5.98 ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (3) j m (3) 4 ma.84 sc ampl 8. An lctron moing through a wir at a tim-futur locit whr θ 9 producs a timfutur magntic induction B at a distanc r. Gin, Dirction of tim is futur θ 9 Vlocit of lctron through a wir. m sc 7 Prmabilit of fr spac μ 4π H m 9 Fundamntal charg of an lctron.77 3 st mass of an lctron kg adius r.m Graitational constant G.7 Nm kg adius of surfac of arth.378 m ass of th arth Th tim-futur locit, whr θ 9 4 kg m j m jθ j9. sc. sc (33) William Alk Pag 58 5/4/8

59 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th tim-futur magntic induction B at distanc r B 7 9 ( 4π H m)(.77 )(. j m sc) μ (34) ( m) 4π r 4π. 8 B.77 j T (35) Th NGATIV fluctuating mass Δ of th lctron (. j m sc) 8 ( m ) Δ kg c sc 3 ( ) (3) 5 Δ kg (37) Appling th nw Principl of quialnc Thorm, (.378 m) (.378 )(. sc) 4 ( Nm kg )( kg) + m j m G (38) o, th quialnt NGATIV displacmnt.3785 m (39) Δ is antigraitational within th arth s grait wll Th maimum tim-futur locit Δ m (33) 5.98 ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (33) j m (33) 4 ma.84 sc William Alk Pag 59 5/4/8

60 Nwtonian Torsion Phsics INTAK, IN. 3.9 TH ATIVITY OF OBITA PIN z ω r P r P A linar spac-tim intral is dfind as, FIGU 8. Th dfinition of a rotating spac-tim intral. ds + dr c dt (333) inc z, r + + z + (334) dr d + d + dz d + d (335) According to Fock (94), a rotating spac-tim intral is dfind as, This rducs to, cosω t+ sinω t (33) sinω t+ cosω t (337) ( ω ) ω ds c + dt d d dt d + d + dz (338) ( ω ) ω ds c r dt d d dt dr (339) William Alk Pag 5/4/8

61 Nwtonian Torsion Phsics INTAK, IN. 3.9 OPX APIAN UNT TON IN OTION F j θ NUU r z j B θ TPOA OTATION θ 9 AGNTI INDUTION IUA TON OBIT FIGU 9. Th complt compl Bohr modl of th Hdrogn atom. In th Bohr modl of th Hdrogn atom, lctrons mo at rlatiistic spds in discrt circular orbits around a nuclus. It has bn dtrmind th incras in rlatiistic mass of th lctron is in th form of total magntic fild nrg producd b th circulating lctron. o, as a consqunc of this motion, a magntic induction B is producd at th cntr of th orbit. If an trnal magntic fild is applid to this induction, th locit of th lctron bcoms compl b partiall rotating into th imaginar ais. Th locit of th lctron ma incras or dcras as a function of th applid trnal fild. If th fild opposs th induction B, th ral locit will appar to dcras as it rotats into th imaginar ais. If th lctron s locit is full rotatd into th imaginar ais and thrfor moing at a tim-futur locit j, a tim-futur magntic fild jb will mrg from th cntr. Th complt compl Bohr modl includs th following charactristic quations shown blow. Ths quations contain th ral and imaginar componnts of a moing lctron that is rotatd about th tmporal ais as compl motion. Th rotation is gin as θ 9, whr th ral ais is θ and th imaginar tim-futur ais is θ 9. Th compl numbr uss th ulr s idntit o, gin, Dirction of tim θ Frqunc of orbit f Prmabilit of fr spac μ Fundamntal charg of an lctron lassic st Bohr orbital radius r st mass of an lctron pd of light c Graitational constant G an radius of surfac of arth ass of th arth an radius of surfac of un ass of th un UN j θ, which functions as a tmporal rotation oprator. William Alk Pag 5/4/8

62 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th compl frqunc of orbit f, whr θ 9 Th compl Amprian urrnt i of th lctron Th compl agntic Dipol omnt μ of th lctron jθ f f f cosθ + j f sinθ (34) i f (34) μ π π (34) r i r f Th compl angular locit ω of th lctron ω π f (343) Th compl locit of th lctron rω π r f (344) Th compl magntic fild B at th cntr ais of th orbit z μ r i μ μ μ r f μ r ω μ r B ( r + z ) π ( r + z ) ( r + z ) π ( r + z ) π ( r + z ) (345) μi μ μ μ f μ ω μ B (34) 3 r π r r 4π r 4π r Th magntic forc F of th lctron dirctd upon th nuclus F B (347) μ μ μ ω μ i μ 4 π ( ) f F μ π (348) π r 4π 4π r Th dirction of lctron motion is such that th magntic forc F is an attracti forc btwn th lctron and th nuclus. Th spcial rlatiistic mass of th circulating lctron c ±Δ ± c (349) William Alk Pag 5/4/8

63 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th chang in rlatiistic mass of th lctron producd b th circulating lctron. Δ is in th form of th chang in magntic fild nrg Δ U B Δ UB Δ Δ c (35) Th diffrnc form of th inrtial D HIFT (or BU HIFT) of th mass Δ of an lctron moing at a locit o, th compl locit of th lctron Δ π r i μ π r f r ω (35) c c c r c c r π F Δ c (35) μ Th compl Amprian urrnt i of th lctron i F c Δ μ π π r (353) Th compl agntic Dipol omnt μ of th lctron μ π F Δ r cr (354) μ Th compl frqunc of orbit f of th lctron f F c Δ (355) μ π π r Th compl angular locit ω of th lctron π F c Δ ω (35) μ r o, th compl magntic forc F of th lctron F dirctd upon th nuclus ( ) c ( ) ( ) Δ Δ ΔU B π r π r π r μ μ μ (357) And th diffrnc form of th inrtial D HIFT (or BU HIFT) of th mass Δ of an lctron Δ π r F (358) μ c William Alk Pag 3 5/4/8

64 Nwtonian Torsion Phsics INTAK, IN. 3.9 Appling th nw Principl of quialnc Thorm, r ω π r f π r i μ π r F Δ c c c (359) c c r c o, th compl locit of th lctron ( ) ( ) μ ( ) ( g ) g Δ G (3) c c ( ) g g G (3) Th compl angular locit ω of th lctron ω ( g ) g G r r (3) Th compl frqunc of orbit f of th lctron f g g G π r π r (33) Th compl Amprian urrnt i of th lctron g g G i π r π r (34) Th compl agntic Dipol omnt μ of th lctron g g G μ r r (35) Th compl magntic forc F of th lctron dirctd upon th nuclus μ μ g g G F π r π r (3) William Alk Pag 4 5/4/8

65 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th quialnt displacmnt to position of an lctron moing at a locit within arth s grait wll g Y whr < or G g + G + g (37) r ω g + G + g r ω ( π ) g + r f + g π r f π r i g ( ) G + g ( ) π r i + μ g ( ) G + g ( ) r μ + g π r F ( ) r G + g μ ( ) π + μ r F G (38) (39) (37) (37) (37) Th diffrnc form of th graitational D HIFT (or BU HIFT) of th mass Δ of a particl displacd a distanc Δ within arth s grait wll g Y ( g g ) Δ G c c (373) Gin th rst mass of an lctron displacd a distanc, th diffrnc forms of th natural rlatiistic mass Δ within arth s grait wll g Y ar, modl of a particl g g ( g g ) c c ±Δ ± (374) William Alk Pag 5 5/4/8

66 Nwtonian Torsion Phsics INTAK, IN. 3.9 G ±Δ ± c G c (375) In summar, if th ral componnt of th magntic fild is canclld, or B, du to an trnall applid magntic fild B XT, th locit of th circulating lctron is compl, or j and a compl magntic fild jb mrgs. This compl magntic fild is blid to b prsnt in th Aharono-Bohm primnt, which affctd j th flow of lctrons. Th compl Amprian urrnt uss th tmporal rotation oprator or ulr s idntit θ, whr θ 9. As th motion of an lctron rotats from ral to imaginar, or θ 9, th lctrons spcial rlatiistic mass Δ in th form of magntic fild nrg Δ U B dcrass. In addition, th lctrons rst mass as wll as its charg is inariant during acclration or dclration. TON IN OTION F NUU r B z TPOA OTATION θ AGNTI INDUTION IUA TON OBIT FIGU 3. Th tim-forward Bohr modl of th Hdrogn atom. ampl 9. In th tim-forward Bohr modl of th Hdrogn atom th lctron circulats around th nuclus at a rlatiistic locit as shown abo. This crats a magntic induction B mrging from th cntr of th nuclus. o, gin, Dirction of tim is forward θ 5 Frqunc of orbit f.8 Hz 7 Prmabilit of fr spac μ 4π H m Fundamntal charg of an lctron.77 lassic st Bohr orbital radius r m 3 st mass of an lctron kg 8 pd of light c m sc Graitational constant G.7 Nm kg an radius of surfac of arth.378 m 9 William Alk Pag 5/4/8

67 Nwtonian Torsion Phsics INTAK, IN. 3.9 ass of th arth kg Th tim-forward frqunc of orbit f, whr θ Th tim-forward Amprian urrnt i jθ 5 j 5 f f Hz Hz.8.8 (37) i f Hz Amps (377) Th tim-forward magntic fild B at th cntr ais of th orbit z r i r f μ 3 3 B μ ( r + z ) ( r + z ) ( Amps ) 7 π ( m) i B μ 4 H m.93594t r (378) (379) Th tim-forward angular locit ω of th lctron Th tim-forward locit of th lctron ω π π (38) 5 f.8 Hz 4.75 Hz rω m Hz m (38) Th tim-forward magntic forc F of th lctron sc dirctd upon th nuclus 9 (.77 )(.945 sc)( ) F B m T (38) F N (383) Th dirction of lctron motion is such that th magntic forc F is alwas an attracti forc btwn th lctron and th nuclus. Th POITIV fluctuating mass Δ of th lctron (.945 m sc) 8 ( m ) 3 35 Δ ( kg) kg c sc (384) Th incrasd spcial rlatiistic mass of th lctron kg kg kg +Δ + (385) William Alk Pag 7 5/4/8

68 Nwtonian Torsion Phsics INTAK, IN. 3.9 Appling th nw Principl of quialnc Thorm, (.378 m) (.378 )(.945 sc) 4 ( Nm kg )( kg) + m m G (38) o, th quialnt POITIV displacmnt m (387) Δ is graitational within th arth s grait wll Δ m (388) j45 TON IN OTION F NUU r XTNA AGNTI INDUTION z B XT TPOA OTATION θ 45 j45 B AGNTI INDUTION IUA TON OBIT FIGU 3. Th tim-adancd Bohr modl of th Hdrogn atom. ampl. In th tim-adancd Bohr modl of th Hdrogn atom, th ral magntic fild cratd b an lctron circulating at rlatiistic spds is partiall canclld b an trnall applid magntic fild B XT. Th lctron racts b rotating its locit into th imaginar ais as shown abo. As a consqunc of this compl locit j 45 j 45, a compl magntic fild B mrgs. o, gin, Dirction of tim θ 45 5 Frqunc of orbit f.8 Hz 7 Prmabilit of fr spac μ 4π H m Fundamntal charg of an lctron.77 lassic st Bohr orbital radius r m 3 st mass of an lctron kg 8 pd of light c m sc Graitational constant G.7 Nm kg 9 William Alk Pag 8 5/4/8

69 Nwtonian Torsion Phsics INTAK, IN. 3.9 an radius of surfac of arth.378 m 4 ass of th arth kg 8 an radius of surfac of un.9 m 3 ass of th un.9889 kg UN Th tim-adancd frqunc of orbit f, whr θ 45 Th tim-adancd Amprian urrnt i jθ 5 j f f Hz j Hz (389) i f j Hz (39) 4-4 i j Amps + (39) Th tim-adancd magntic fild B at th cntr ais of th orbit z m r i r f μ 3 3 B μ ( r + z ) ( r + z ) ( j Amps ) 7 4π H m ( m) i B μ r (39) (393) Th tim-adancd angular locit ω of th lctron B jt (394) 5 5 ω π f π j Hz (395) ω + j Hz (39) Th tim-adancd locit of th lctron rω m j Hz (397) j m sc (398) Th maimum tim-futur locit ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (399) j m (4) 4 ma.84 sc William Alk Pag 9 5/4/8

70 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th tim-adancd locit of th lctron Th maimum tim-futur locit far cds coupling to arth s grait wll! ma within th un s grait wll 3 ( Nm kg )( kg) (.9 m) G (4) UN ma 8 j m (4) 5 ma.754 sc Th tim-adancd locit of th lctron Th tim-adancd magntic forc F of th lctron far cds coupling to un s grait wll! dirctd upon th nuclus F B (43) 9 (.77 )( sc)( ) F + j m + jt F j N (44) Th dirction of lctron motion is tim-adancd or rotatd into th futur such that th magntic forc F is alwas an attracti forc btwn th lctron and th nuclus. Th IAGINAY fluctuating mass Δ of th lctron ( j m sc ) ( m ) Δ kg c sc (45) Δ (4) j kg Th spcial rlatiistic mass of th lctron 3 35 ( ) ( ) +Δ kg + j kg (47) j kg + (48) Appling th nw Principl of quialnc Thorm, (.378 m) (.378 )( sc) (.7 N m 4 kg )( kg ) + m j m G + (49) jm (4) William Alk Pag 7 5/4/8

71 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, th quialnt IAGINAY displacmnt or, Δ is shown to b non-graitational within th arth s grait wll Δ + m (4) j9 TON IN OTION F NUU r XTNA AGNTI INDUTION z B XT TPOA OTATION θ 9 j9 B AGNTI INDUTION IUA TON OBIT FIGU 3. Th tim-futur Bohr modl of th Hdrogn atom. ampl. In th tim-futur Bohr modl of th Hdrogn atom, th ral magntic fild cratd b an lctron circulating at rlatiistic spds is bing canclld b an trnall applid magntic fild B XT. Th lctron racts b rotating its locit into th imaginar ais as shown abo. As a consqunc of this compl locit j, a compl magntic fild jb mrgs. o, gin, Dirction of tim θ 9 5 Frqunc of orbit f.8 Hz 7 Prmabilit of fr spac μ 4π H m Fundamntal charg of an lctron.77 lassic st Bohr orbital radius r m 3 st mass of an lctron kg 8 pd of light c m sc Graitational constant G.7 Nm kg an radius of surfac of arth.378 m 4 ass of th arth kg 8 an radius of surfac of un.9 m 3 ass of th un.9889 kg UN Th tim-futur frqunc of orbit f, whr θ 9 9 William Alk Pag 7 5/4/8

72 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th tim-futur Amprian urrnt i jθ 5 j9 5 f f Hz j Hz.8.8 (4) i f j Hz j Amps (43) Th tim-futur magntic fild B at th cntr ais of th orbit z m r i r f μ 3 3 B μ ( r + z ) ( r + z ) ( j Amps ) 7 π ( m) i B μ 4 H m jt r (44) (45) Th tim-futur angular locit ω of th lctron Th tim-futur locit of th lctron Th maimum tim-futur locit ω π π (4) 5 f.8 j Hz 4.75 j Hz rω m j Hz j m (47) sc ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (48) j m (49) 4 ma.84 sc Th tim-futur locit of th lctron Th maimum tim-futur locit far cds coupling to arth s grait wll. ma within th un s grait wll 3 ( Nm kg )( kg) (.9 m) G (4) UN ma 8 j m (4) 5 ma.754 sc Th tim-adancd locit of th lctron Th magntic forc F of th lctron far cds coupling to un s grait wll! dirctd upon th nuclus William Alk Pag 7 5/4/8

73 Nwtonian Torsion Phsics INTAK, IN (.77 )(.945 sc)( ) F B j m jt (4) F N (43) Th dirction of lctron motion is tim-futur or rotatd into th futur such that th magntic forc F is alwas an attracti forc btwn th lctron and th nuclus. Th NGATIV fluctuating mass Δ of th lctron (.945 j m sc) 8 ( m ) 3 35 Δ ( kg) kg c sc (44) Th dcrasd spcial rlatiistic mass of th lctron kg kg 9.93 kg +Δ + (45) Appling th nw Principl of quialnc Thorm, (.378 m) (.378 )(.945 sc) 4 ( Nm kg )( kg) + m j m G (4) o, th quialnt NGATIV displacmnt 5.8 m (47) Δ is antigraitational within th arth s grait wll Δ m (48).3785 William Alk Pag 73 5/4/8

74 Nwtonian Torsion Phsics INTAK, IN. 3.9 OPX TON DIFT VOITY GNT OF OPP WI TON DIFT j θ r j θ j θ j θ A j I θ A TPOA OTATION θ 9 FIGU 33. Th complt compl lctron drift locit modl in a coppr wir. If a coppr wir is connctd to a battr, an lctric fild will b st up at r point within th wir. This fild will act on lctrons and will gi thm a rsultant motion. An lctric currnt I is stablishd if a nt charg q u passs through an cross sctional ara A of th conductor in tim t. Th lctric fild that acts on th lctrons dosn t produc a nt acclration bcaus th lctrons kp colliding with th atoms that mak up th conductor. Th lctrons, thrfor, mo at an arag drift locit. If th lctron drift locit j is timfutur, th associatd lctric fild j and magntic fild jb ar also tim-futur. Th complt compl lctron drift locit modl includs th following charactristic quations shown blow. Ths quations contain th ral and imaginar componnts of a moing lctron that is rotatd about th tmporal ais as a compl particl. Th rotation is gin as θ 9, whr th ral ais is θ and th imaginar tim-futur ais is θ 9. Th j compl numbr uss th ulr s idntit θ, which functions as a tmporal rotation oprator. o, gin, Dirction of tim θ urrnt flowing through a conductor I Fundamntal charg of an lctron adius of coppr wir r Dnsit of conductor matrial ( ) D atom Numbr of conduction lctrons pr atom of conductor k atom Aogadro s Numbr N Atomic wight of conductor matrial gmnt lngth of conductor pd of light c st mass of an lctron adius of surfac of arth Graitational constant G ass of th arth W atom sistiit of conductor matrial ( ) ρ atom Th compl currnt I flowing through a conductor, whr θ 9 William Alk Pag 74 5/4/8

75 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th compl currnt dnsit J jθ I I Icosθ + jisinθ (49) J I I (43) A π r Th olum V of a sgmnt of a conductor V A π r (43) Th quantit of conduction lctrons n atom in a olum of conductor n D N k atom atom atom (43) Watom Th nt charg q atom in a olum of a conductor q n V (433) atom atom Th compl locit (434) t Th compl currnt I flowing through a conductor q n V t atom atom I π r natom (435) o, th compl drift locit of an lctron moing through a conductor I J π rn n (43) atom atom Th fluctuating mass Δ of th lctron Δ (437) c Appling th nw Principl of quialnc Thorm, ( g ) g Δ G (438) c c c William Alk Pag 75 5/4/8

76 Nwtonian Torsion Phsics INTAK, IN. 3.9 g g G (439) ( ) g g G (44) Th quialnt displacmnt to position of an lctron moing at a locit within arth s grait wll g Y whr < or G g + g (44) + G (44) Th rsistiit ρ Atom of a conductor is gin as, ρ Atom V V (443) J I I A π r Th rsistanc of a sgmnt of conductor V ρ Atom ρatom (444) I A π r GNT OF OPP WI TON DIFT A r I A TPOA OTATION θ FIGU 34. Th tim-forward lctron drift locit in a coppr wir. William Alk Pag 7 5/4/8

77 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl. A tim-forward lctric currnt I is stablishd if a nt charg q u passs through an cross sctional ara A of th conductor in tim-forward t. Th lctrons mo at an arag tim-forward drift locit. o, gin, Dirction of tim θ urrnt through coppr wir I. Amps 9 Fundamntal charg of an lctron.77 3 adius of AWG coppr wir r.94 m 3 Dnsit of coppr conductor ( ) Du 8.9 gm m Numbr of conduction lctrons pr atom of coppr ku lctron atom 3 Aogadro s Numbr N.37 atoms mol Atomic wight of coppr conductor Wu 3.54 gm mol gmnt lngth m 8 pd of light c m sc 3 st mass of an lctron kg Graitational constant G.7 Nm kg an adius of surfac of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of coppr conductor ( ) Th tim-forward currnt I flowing through a conductor, whr θ Th tim-forward currnt dnsit J j jθ I I. Amps. Amps (445) J (. Amps) I I.9 Amps m A π r π m 3 (.94 ) (44) Th olum V of a sgmnt of coppr wir 3 3 V A π r π.94 m m 5. m (447) Th quantit of conduction lctrons n u in a olum of coppr wir n u n D N k u u u (448) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( lctron atom) (449) ( 3.54gm mol) nu lctrons m (45) Th nt charg q u in a olum of coppr wir William Alk Pag 77 5/4/8

78 Nwtonian Torsion Phsics INTAK, IN. 3.9 u u ( )( 5. )(.7733 ) q n V lctrons m m (45) qu 4 7. (45) Th tim-forward locit (453) t Th tim-forward currnt I flowing through a coppr wir qu nu V I π rnu π rnu. Amps t (454) o, th tim-forward drift locit of an lctron moing through a coppr wir (.9 Amps m ) ( )(.7733 ) I J π rn n lctrons m u u (455) 4.43 m sc (45) Th POITIV fluctuating mass Δ of th lctron 4 (.43 m sc) 8 ( m ) Δ kg c sc 3 ( ) (457) 5 Δ 9.98 kg (458) Th POITIV fluctuating mass of an lctron is almost 5 ordrs of magnitud blow its rst mass Appling th nw Principl of quialnc Thorm,. (.378 m) 4 (.378 )(.43 sc) 4 ( Nm kg )( kg) + m m G (459) o, th quialnt POITIV displacmnt.378 m (4) Δ is graitational within th arth s grait wll 9 Δ m (4).87 Gin a tim-forward oltag V and a tim-forward currnt I, th rsistiit ρ u of coppr wir is gin as, William Alk Pag 78 5/4/8

79 Nwtonian Torsion Phsics INTAK, IN. 3.9 ρ u V V J I A I π r 8.8 Ω (4) m Th rsistanc of a sgmnt of coppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (43) GNT OF OPP WI TON DIFT j45 r j45 j45 j45 A j45 I A TPOA OTATION θ 45 FIGU 35. Th tim-adancd lctron drift locit in a coppr wir. ampl 3. A tim-adancd lctric currnt I is stablishd if a nt charg q u passs through an cross sctional ara A of th conductor in tim-adancd t. Th lctrons mo at an arag tim-adancd drift locit. o, gin, Dirction of tim θ 45 urrnt flow through coppr wir I. Amps 9 Fundamntal charg of an lctron.77 3 adius of AWG coppr wir r.94 m 3 Dnsit of coppr conductor ( ) Du 8.9 gm m Numbr of conduction lctrons pr atom of coppr ku lctron atom 3 Aogadro s Numbr N.37 atoms mol Atomic wight of coppr conductor Wu 3.54 gm mol gmnt lngth m 8 pd of light c m sc 3 st mass of an lctron kg Graitational constant G.7 Nm kg an adius of surfac of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of coppr conductor ( ) William Alk Pag 79 5/4/8

80 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th tim-adancd currnt I flowing through a conductor, whr θ 45 Th tim-adancd currnt dnsit J j45 jθ I I. Amps jamps (44) ( jAmps) I I J A r j Amps m m π π 3 (.94 ) (45) Th olum V of a sgmnt of coppr wir A π r π.94 m m 5. m 3 3 V (4) Th quantit of conduction lctrons n u in a olum of coppr wir n u n D N k u u u (47) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( lctron atom) (48) ( 3.54gm mol) nu lctrons m (49) Th nt charg q u in a olum of a coppr wir u u ( )( 5. )(.7733 ) q n V lctrons m m (47) qu 4 7. (47) Th tim-adancd locit (47) t Th tim-adancd currnt I flowing through a coppr wir qu nu V I π r nu j Amps t (473) o, th tim-adancd drift locit of an lctron moing through a coppr wir ( j Amps m ) ( )(.7733 ) I J π rn n lctrons m u u (474) William Alk Pag 8 5/4/8

81 Nwtonian Torsion Phsics INTAK, IN. 3.9 j m sc (475) Th fluctuating mass Δ of th lctron ( j m sc ) ( m ) Δ kg c sc (47) Δ (477) j kg Th fluctuating mass of an lctron is almost 5 ordrs of magnitud bond its rst mass Appling th nw Principl of quialnc Thorm, and is imaginar. (.378 m) ( )( sc) (.7 N m 4 kg )( kg ) + m j m G + (478) o, th quialnt IAGINAY displacmnt.378 m (479) Δ is shown to b non-graitational within th arth s grait wll 9 Δ j m (48).4 Gin a tim-adancd oltag V and a tim-adancd currnt I, th rsistiit ρ u of coppr wir is gin as, ρ u V V J I A I π r 8.8 Ω (48) m Th rsistanc of a sgmnt of coppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (48) William Alk Pag 8 5/4/8

82 Nwtonian Torsion Phsics INTAK, IN. 3.9 GNT OF OPP WI TON DIFT j j A r j j ji A TPOA OTATION θ 9 FIGU 3. Th tim-futur lctron drift locit in a coppr wir. ampl 4. A tim-futur lctric currnt + ji is stablishd if a nt charg q u passs through an cross sctional ara A of th conductor in tim-futur t. Th lctrons mo at an arag tim-futur drift locit + j. o, gin, Dirction of tim θ 9 urrnt flow through coppr wir I. Amps 9 Fundamntal charg of an lctron.77 3 adius of AWG coppr wir r.94 m 3 Dnsit of coppr conductor ( ) Du 8.9 gm m Numbr of conduction lctrons pr atom of coppr ku lctron atom 3 Aogadro s Numbr N.37 atoms mol Atomic wight of coppr conductor Wu 3.54 gm mol gmnt lngth m 8 pd of light c m sc 3 st mass of an lctron kg Graitational constant G.7 Nm kg an adius of surfac of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of coppr conductor ( ) Th tim-futur currnt I flowing through a conductor, whr θ 9 Th tim-futur currnt dnsit J j9 jθ I I. Amps. j Amps (483) (. jamps) I I J A r.9 j Amps m m π π 3 (.94 ) (484) William Alk Pag 8 5/4/8

83 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th olum V of a sgmnt of coppr wir A π r π.94 m m 5. m 3 3 V (485) Th quantit of conduction lctrons n u in a olum of coppr wir n u n D N k u u u (48) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( lctron atom) (487) ( 3.54gm mol) nu lctrons m (488) Th nt charg q u in a olum of a coppr wir u u ( )( 5. )(.7733 ) q n V lctrons m m (489) qu 4 7. (49) Th tim-futur locit (49) t Th tim-futur currnt I flowing through a coppr wir qu nu V I π r nu π r nu. j Amps t (49) o, th tim-futur drift locit of an lctron moing through a coppr wir (.9 j Amps m ) ( )(.7733 ) I J π rn n lctrons m u u (493) j m 4.43 sc (494) Th NGATIV fluctuating mass Δ of th lctron 4 (.43 j m sc) 8 ( m ) Δ kg c sc 3 ( ) (495) 5 Δ 9.98 kg (49) William Alk Pag 83 5/4/8

84 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th NGATIV fluctuating mass of an lctron is almost 5 ordrs of magnitud blow its rst mass Appling th nw Principl of quialnc Thorm,. (.378 m) 4 (.378 )(.43 sc) 4 ( Nm kg )( kg) + m j m G (497) o, th quialnt NGATIV displacmnt.378 m (498) Δ is antigraitational within th arth s grait wll Δ m (499) 9.33 Gin a tim-futur oltag V and a tim-futur currnt I, th rsistiit ρ u of coppr wir is gin as, ρ u V V J I A I π r 8.8 Ω (5) m Th rsistanc of a sgmnt of coppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (5) William Alk Pag 84 5/4/8

85 Nwtonian Torsion Phsics INTAK, IN. 3.9 OPX ITO I + j V θ - V + - FIGU 37. Th complt compl rsistor. j Gin a compl oltag sourc V with a tmporal rotation oprator θ, whr θ 9 is acting upon th oltag, a compl dirct currnt flows through rsistor. A compl oltag V appars across th rsistor. Th rsulting instantanous powr P is dissipatd or absorbd b th rsistor. o, gin, Dirction of tim θ Voltag suppl V sistor Th compl oltag suppl V Th compl currnt I flowing through rsistor jθ V V V cosθ + jvsinθ (5) Th compl oltag V across rsistor Th rsistanc I V (53) V I V (54) V (55) I Th instantanous powr P dissipatd and/or absorbd b th rsistor V P V I I (5) William Alk Pag 85 5/4/8

86 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl 5. Gin a tim-forward oltag sourc V and a known rsistor alu, comput th tim-forward currnt and powr dissipatd b th rsistor. o, gin, Dirction of tim θ Voltag ourc V.Volts sistor.5ω Th tim-forward oltag V Th tim-forward currnt I j jθ V V.Volts.Volts (57) I (.Volts) (.5Ω) V 4. Amps (58) Th instantanous powr P dissipatd b th rsistor ( Volts) (.5Ω) V. P 4.Watts (59) ampl. Gin a tim-adancd oltag sourc V and a known rsistor alu, comput th tim-adancd currnt and powr bing dissipatd and absorbd b th rsistor. o, gin, Dirction of tim θ 45 Voltag ourc V.Volts sistor.5ω Th tim-adancd oltag V Th tim-adancd currnt I j45 jθ V V.Volts jvolts (5) I ( jvolts) (.5Ω) V jamps (5) Th instantanous powr P dissipatd and absorbd of th rsistor ( + jvolts) (.5Ω) V P 4. jwatts (5) Th rsistor is dissipating and absorbing an qual amount of hat. Th rsistor is thrfor, tmpratur nutral or adiabatic. William Alk Pag 8 5/4/8

87 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl 7. Gin a tim-futur oltag sourc V and a known rsistor alu, comput th tim-futur currnt and instantanous powr absorbd b th rsistor. o, gin, Dirction of tim θ 9 Voltag ourc V.Volts sistor.5ω Th tim-futur oltag V Th tim-futur currnt I j9 jθ V V.Volts. jvolts (53) I (. jvolts) (.5Ω) V 4. jamps (54) Th instantanous powr P absorbd b th rsistor ( jvolts) (.5Ω) V. P 4.Watts (55) OPX INDUTO i t sc + + j V θ FIGU 38. Th complt compl magntizing inductor. j Gin a compl oltag sourc V with a tmporal rotation oprator θ, whr θ 9 is acting upon th oltag, whn switch closs at t sc, a compl dirct currnt i flows through rsistor and magntizs inductor. A compl oltag appars across th rsistor and a compl oltag appars across inductor. Th rsulting instantanous powr P is dissipatd and/or absorbd b th rsistor, th instantanous powr P stord in th inductor, and th nrg stord in th inductor. o, gin, Dirction of tim θ Tim t Voltag suppl V Inductor William Alk Pag 87 5/4/8

88 Nwtonian Torsion Phsics INTAK, IN. 3.9 sistor Th compl oltag suppl V Th compl oltag across th rsistor Th compl oltag across th inductor jθ V V V cosθ + jvsinθ (5) t i t (57) di (58) () t dt tting t sc, th compl currnt i flowing through th rsistor and th inductor di + + (59) () () () V t t i t dt V () t di dt i + (5) V di dt (5) () t i i () t t di dt V t (5) i () t i () t V ln i () t t V i () t V V ln i () t ln ln t t V V t t () t ( tt ) t i V V t V V i () t t (53) (54) (55) (5) William Alk Pag 88 5/4/8

89 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P dissipatd and/or absorbd b th rsistor V P() t () t i() t i () t t (57) Th instantanous powr P stord in th inductor di P() t () t i() t i V i() t i () t (58) dt t t t t t t V V V V P () t (59) tting t sc, th nrg stord in th inductor di t P dt i dt i di i t i t dt t t i() t () () ( ) t t i( t ) (53) V t t t t V V () t V () t t (53) (53) ampl 8. Gin a tim-forward oltag sourc V, a known rsistor alu and inductor alu, comput th tim-forward currnt and powr dissipatd b th rsistor, and th nrg stord in th inductor. o, gin, Dirction of tim θ Tim.sc t.sc Voltag suppl V.Volts Inductor 47mH sistor.5ω Th tim-forward oltag suppl V j jθ V V.Volts.Volts (533) Th tim-forward currnt i flowing through th rsistor and th inductor at t.sc (.Volts) (.5Ω) (.5Ω) t ( 47 mh ) V t i () t (534) i.sc 3.98 Amps (535) William Alk Pag 89 5/4/8

90 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P dissipatd b th rsistor at t.sc (.5Ω) t ( 47 mh ) (.Volts) (.5Ω) V t P () t (53) P.sc 39.9Watts (537) Th instantanous powr P stord in th inductor at t.3sc and at t.sc (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) (.Volts) (.5Ω) V P () t (538) P P.3sc.Watts (539).sc.95Watts (54) Th nrg stord in th inductor from t.sc to t.sc (.5Ω) t t ( 47 mh ) ( 47 mh )(.Volts) ( Ω) V () t.5 (54).sc 3.73 Jouls (54) ampl 9. Gin a tim-adancd oltag sourc V, a known rsistor alu and inductor alu, comput th tim-adancd currnt and powr dissipatd and absorbd b th rsistor, and th nrg stord in th inductor. o, gin, Dirction of tim θ 45 Tim.sc t.sc Voltag suppl V.Volts Inductor 47mH sistor.5ω Th tim-adancd oltag suppl V j45 jθ V V.Volts jvolts (543) Th tim-adancd currnt i flowing through th rsistor and th inductor at t.sc ( jVolts) (.5Ω) (.5Ω) t ( 47 mh ) V t i () t (544) i.sc j Amps (545) William Alk Pag 9 5/4/8

91 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P dissipatd and absorbd b th rsistor at t.sc (.5Ω) t ( 47 mh ) ( jVolts) (.5Ω) V t P () t (54) P.sc 39.9 jwatts (547) Th instantanous powr P stord in th inductor at t.3sc and at t.sc (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) ( jvolts) (.5Ω) V P () t (548) P P.3sc. jwatts (549).sc.95 jwatts (55) Th nrg stord in th inductor from t.sc to t.sc (.5Ω) t t ( 47 mh ) ( 47 mh )( jvolts) ( Ω) V () t.5 (55).sc 3.73 j Jouls (55) ampl. Gin a tim-futur oltag sourc V, a known rsistor alu and inductor alu, comput th tim-futur currnt and powr absorbd b th rsistor, and th ngati nrg stord in th inductor. o, gin, Dirction of tim θ 9 Tim.sc t.sc Voltag suppl V.Volts Inductor 47mH sistor.5ω Th tim-futur oltag suppl V j9 jθ V V.Volts. jvolts (553) Th tim-futur i flowing through th rsistor and th inductor at t.sc (. jvolts) (.5Ω) (.5Ω) t ( 47mH ) V t i () t (554) i.sc 3.98 j Amps (555) William Alk Pag 9 5/4/8

92 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P absorbd b th rsistor at t.sc (.5Ω) t ( 47 mh ) (. jvolts) (.5Ω) V t P () t (55) P.sc 39.9Watts (557) Th instantanous powr P stord in th inductor at t.3sc and at t.sc (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) (. jvolts) (.5Ω) V P () t (558) P P.3sc.Watts (559).sc.95Watts (5) Th nrg stord in th inductor from t.sc to t.sc (.5Ω) t t ( 47 mh ) ( 47mH )(. jvolts) ( Ω) V () t.5 (5).sc 3.73 Jouls (5) i t sc Gin nrg oltag, whn switch closs at FIGU 39. Th complt compl dmagntizing inductor. stord in inductor with a tmporal rotation oprator j θ, whr 9 θ is acting upon th t sc, a compl dirct currnt i flows through rsistor. Th inductor dmagntizs into th rsistor. A compl oltag appars across th rsistor. Th rsulting instantanous powr P and nrg o, gin, Dirction of tim θ Tim t Initial currnt through inductor I Inductor sistor ar dissipatd and/or absorbd b th rsistor. William Alk Pag 9 5/4/8

93 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th compl currnt I through th inductor At t sc, th oltag V across th rsistor jθ I I Icosθ + jisinθ (53) V I (54) Th compl oltag across th rsistor Th compl oltag across th inductor t i t (55) di (5) () t dt tting t sc, th compl currnt i flowing through th rsistor and th inductor it () t t (57) di (58) () i t dt i di (59) dt () t di dt (57) i t () t di dt I i t () t (57) ln ( ()) i () t t i t t (57) I t i t ln ( i ()) ln ln t I tt I (573) i ( t) ( t t ) I (574) () t i t I (575) William Alk Pag 93 5/4/8

94 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P dissipatd and/or absorbd b th rsistor () () () () t P t t i t i t I (57) tting t sc, th nrg dissipatd and/or absorbd b th rsistor () t t t t t (577) t P dt I dt t t t t I () t I I I () t t (578) (579) ampl. Gin a tim-forward oltag V across inductor, a known rsistor alu and inductor alu, comput th tim-forward currnt flowing through th rsistor, and th powr and nrg dissipatd b th rsistor. o, gin, Dirction of tim θ Tim.sc t.sc Initial currnt through inductor I 4. Amps Inductor 47mH sistor.5ω Th tim-forward currnt I through th inductor j jθ I I 4. Amps 4. Amps (58) Th tim-forward currnt i flowing through th rsistor and th inductor at t () (.5Ω) t ( 47 mh ) t.sc and at t.sc i t I 4. Amps (58) i i.sc 4. Amps (58).sc. Amps (583) Th instantanous powr P dissipatd b th rsistor at t.sc and at t.sc t ().5 ( Ω) t ( 47 mh ) P t I.5Ω 4. Amps (584) P P.sc 4.Watts (585) 4 (.sc) 9.59 Watts (58) William Alk Pag 94 5/4/8

95 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th nrg dissipatd b th rsistor at t.sc.5 ( Ω) t ( 47 mh )( 4. Amps) t ( 47 mh ) I () t (587).sc 3.7 Jouls (588) ampl. Gin a tim-adancd oltag V across inductor, a known rsistor alu and inductor alu, comput th tim-adancd currnt flowing through th rsistor, and th powr and nrg dissipatd and absorbd b th rsistor. o, gin, Dirction of tim θ 45 Tim.sc t.sc Initial currnt through inductor I 4. Amps Inductor 47mH sistor.5ω Th tim-adancd currnt I through th inductor j45 jθ I I 4. Amps jamps (589) Th tim-adancd currnt i flowing through th rsistor and th inductor at t () (.5Ω) t ( 47 mh ) t.sc and at t.sc i t I j Amps (59) i i.sc j Amps (59).sc j Amps (59) Th instantanous powr P dissipatd and absorbd b th rsistor at t.sc and at t.sc Th nrg t ().5 ( Ω) t ( 47 mh ) P t I.5Ω j Amps (593) P.sc 4. jwatts (594) 4 (.sc) 9.59 P j Watts (595) dissipatd and absorbd b th rsistor at t.sc and at t.sc.5 ( Ω) t ( 47 mh )( j Amps) t ( 47 mh ) I () t (59).sc 3.7 j Jouls (597) William Alk Pag 95 5/4/8

96 Nwtonian Torsion Phsics INTAK, IN. 3.9 ampl 3. Gin a tim-futur oltag V across inductor, a known rsistor alu and inductor alu, comput th tim-futur currnt flowing through th rsistor, and th powr and nrg absorbd b th rsistor. o, gin, Dirction of tim θ 9 Tim.sc t.sc Initial currnt through inductor I 4. Amps Inductor 47mH sistor.5ω Th tim-futur currnt I through th inductor j9 jθ I I 4. Amps 4. jamps (598) Th tim-futur currnt i flowing through th rsistor and th inductor at t.sc and at t.sc t () (.5Ω) t ( 47 mh ) i t I 4. j Amps (599) i i.sc 4. j Amps ().sc. j Amps () Th instantanous powr P absorbd b th rsistor at t.sc and at t.sc Th nrg t ().5 ( Ω) t ( 47 mh ) P t I.5Ω 4. j Amps () P P.sc 4.Watts (3) 4 (.sc) 9.59 absorbd b th rsistor at t.sc and at t.sc Watts (4).5 ( Ω) t ( 47mH )( 4. j Amps) t ( 47mH ) I () t (5).sc 3.7 Jouls () William Alk Pag 9 5/4/8

97 Nwtonian Torsion Phsics INTAK, IN. 3.9 OPX APAITO i t sc + + j V θ FIGU 4. Th complt compl charging capacitor. j Gin a compl oltag sourc V with a tmporal rotation oprator θ, whr θ 9 is acting upon th oltag, whn switch closs at t sc, a compl dirct currnt flows through rsistor and chargs capacitor. A compl oltag appars across th rsistor and a compl oltag appars across capacitor. Th rsulting powr P is dissipatd and/or absorbd b th rsistor and th nrg o, gin, Dirction of tim θ Tim t Voltag suppl V apacitor sistor Th compl oltag suppl V Th compl oltag across th rsistor Th compl currnt i through a capacitor is stord in th capacitor. jθ V V V cosθ + jvsinθ (7) t i t (8) d (9) () i t dt tting t sc, th compl oltag across th capacitor V t + t i t + t () d () () t V dt d dt t V () () William Alk Pag 97 5/4/8

98 Nwtonian Torsion Phsics INTAK, IN. 3.9 () t t d dt t () t V (3) () t t ln ( () t V) t (4) t t V ln ( () t V) ln ( V) ln tt V ( t t ) t t V V t V V V t t () (5) () (7) Th instantanous powr P dissipatd and/or absorbd b th rsistor Th instantanous powr P stord in th capacitor () ( V ()) t t V t P() t () t i () t (8) () () () d dt ( V t ( t) ) (9) P t t i t t t t t t t V V V V P () t () tting t sc, th nrg stord in th capacitor d t P dt dt d t t dt t t () t () () ( ) t t ( t ) () t t V t t () t V V V () t t () (3) ampl 4. Gin a tim-forward oltag sourc V, a known rsistor alu and capacitor alu, comput th tim-forward currnt and powr dissipatd b th rsistor, and th nrg stord in th inductor. o, gin, Dirction of tim θ William Alk Pag 98 5/4/8

99 Nwtonian Torsion Phsics INTAK, IN. 3.9 Tim.sc t.sc Voltag suppl V.Volts apacitor 47 μf sistor.kω Th tim-forward oltag suppl V j Th tim-forward oltag across th capacitor at t.sc jθ V V.Volts.Volts (4) t t (.kω)( 47 μf) () t V (.Volts) (5).sc 8.89Volts () Th instantanous powr P dissipatd b th rsistor at t.sc and at t.sc (.Volts) (.kω) V t P () t t (. kω)( 47μF) (7) P P.sc.Watts (8) 3 (.sc).49 Th instantanous powr P stord in th capacitor at Watts (9) t.33sc and at t.sc (.Volts) (. kω) V t t t t (. kω)( 47 μf) (. kω)( 47 μf) P () t (3) P P.33sc.45Watts (3).sc.5Watts (3) Th nrg stord in th capacitor from t.sc to t.sc ( 47 μf )(.Volts) (. kω)( 47 μf) V t t () t (33).8 t Jouls (34) ampl 5. Gin a tim-adancd oltag sourc V, a known rsistor alu and capacitor alu, comput th tim-adancd currnt and powr dissipatd and absorbd b th rsistor, and th nrg stord in th inductor. o, gin, William Alk Pag 99 5/4/8

100 Nwtonian Torsion Phsics INTAK, IN. 3.9 Dirction of tim θ 45 Tim.sc t.sc Voltag suppl V.Volts apacitor 47 μf sistor.kω Th tim-adancd oltag suppl V j45 Th tim-adancd oltag across th capacitor at jθ V V.Volts jvolts (35) t.sc t t (. kω)( 47 μf) () t V ( jvolts) (3).sc jvolts (37) Th instantanous powr P dissipatd and absorbd b th rsistor at t.sc and at t.sc ( jVolts) (.kω) V t P () t t (. kω)( 47μF) (38) P.sc. jwatts (39) 3 (.sc).49 Th instantanous powr P stord in th capacitor at P j Watts (4) t.33sc and at t.sc ( jVolts) (.kω) V t t t t (. kω)( 47 μf) (.kω)( 47 μf) P () t (4) P P.33sc.45 jwatts (4).sc.5Watts (43) Th nrg stord in th capacitor from t.sc to t.sc ( 47 μf )( jvolts) (. kω)( 47 μf) V t t () t (44).8 t jjouls (45) ampl. Gin a tim-futur oltag sourc V, a known rsistor alu and capacitor alu, comput th tim-futur currnt and powr absorbd b th rsistor, and th nrg stord in th inductor. William Alk Pag 5/4/8

101 Nwtonian Torsion Phsics INTAK, IN. 3.9 o, gin, Dirction of tim θ 9 Tim.sc t.sc Voltag suppl V.Volts apacitor 47 μf sistor.kω Th tim-futur oltag suppl V Th tim-futur oltag across th capacitor at j9 jθ V V.Volts. jvolts (4) t.sc t t (. kω)( 47 μf) () t V (. jvolts) (47).sc 8.89 jvolts (48) Th instantanous powr P absorbd b th rsistor at t.sc and at t.sc (. jvolts) (.kω) V t P () t t (. kω)( 47μF) (49) P P.sc.Watts (5) 3 (.sc).49 Th instantanous powr P stord in th capacitor at Watts (5) t.33sc and at t.sc (. jvolts) (.kω) V t t t t (.kω)( 47 μf) (. kω)( 47 μf) P () t (5) P P.33sc.45Watts (53).sc.5Watts (54) Th nrg stord in th capacitor from t.sc to t.sc ( 47 μf )(. jvolts) (. kω)( 47 μf) V t t () t (55).8 t Jouls (5) William Alk Pag 5/4/8

102 Nwtonian Torsion Phsics INTAK, IN. 3.9 i t sc Gin nrg th oltag, whn switch closs at FIGU 4. Th complt compl discharging capacitor. stord in capacitor with a tmporal rotation oprator j θ, whr θ 9 is acting upon t sc, a compl dirct currnt i flows through rsistor. Th capacitor dischargs into th rsistor. A compl oltag appars across th rsistor. Th rsulting instantanous powr P and nrg o, gin, Dirction of tim θ Tim t Initial oltag across capacitor V apacitor sistor At ar dissipatd and/or absorbd b th rsistor. t sc, th oltag V across th rsistor V I (57) Th compl oltag across th rsistor Th compl currnt i through a capacitor t i t (58) d (59) () i t dt tting t sc, th compl oltag across th capacitor d () () () () t t i t dt d dt () t () () t t d dt V t () t () William Alk Pag 5/4/8

103 Nwtonian Torsion Phsics INTAK, IN. 3.9 () t t ln ( () t ) t (3) V t ( t) ln ( () t ) ln ( V ) ln tt V (4) ( t) ( t t ) t V (5) () t Th instantanous powr P dissipatd and/or absorbd b th rsistor t V () t t V P() t () t i () t (7) tting t sc, th nrg dissipatd and/or absorbd b th rsistor t t V t () t P t dt dt t (8) V t t t t V () t V () t V t (9) (7) ampl 7. Gin a tim-forward oltag V across capacitor, a known rsistor alu and capacitor alu, comput th tim-forward currnt flowing through th rsistor, and th powr and nrg dissipatd b th rsistor. o, gin, Dirction of tim θ Tim.sc t.sc Initial oltag across capacitor V.Volts apacitor 47 μf sistor.kω Th tim-forward oltag V across th capacitor Th tim-forward oltag across th capacitor j jθ V V.Volts.Volts (7) t () t (. kω)( 47 μf) t V.Volts (7) William Alk Pag 3 5/4/8

104 Nwtonian Torsion Phsics INTAK, IN. 3.9.sc.Volts (73).sc.9Volts (74) Th instantanous powr P dissipatd b th rsistor at t.sc and at t.sc t. ( Volts) (.kω) V P () t t (. kω)( 47μF) (75) Th nrg P dissipatd b th rsistor at P.sc.Watts (7) 3 (.sc).49 Watts (77) t.sc and at t.sc ( μf )( Volts) (. kω)( 47 μf) V t 47. t () t (78).sc.3 Jouls (79) ampl 8. Gin a tim-adancd oltag V across capacitor, a known rsistor alu and capacitor alu, comput th tim-adancd currnt flowing through th rsistor, and th powr and nrg dissipatd and absorbd b th rsistor. o, gin, Dirction of tim θ 45 Tim.sc t.sc Initial oltag across capacitor V.Volts apacitor 47 μf sistor.kω Th tim-adancd oltag V across th capacitor j45 Th tim-adancd oltag across th capacitor jθ V V.Volts jVolts (8) t () t (. kω)( 47 μf) t V jvolts (8).sc jvolts (8).sc jvolts (83) William Alk Pag 4 5/4/8

105 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th instantanous powr P dissipatd and absorbd b th rsistor at t.sc and at t.sc ( + jvolts) (.kω) V P () t t t (. kω)( 47μF) (84) Th nrg P.sc. jwatts (85) 3 (.sc).49 P j Watts (8) dissipatd and absorbd b th rsistor at t.sc and at t.sc ( μf )( + jvolts) (. kω)( 47 μf) V t t () t (87).sc.3 j Jouls (88) ampl 9. Gin a tim-futur oltag V across capacitor, a known rsistor alu and capacitor alu, comput th tim-futur currnt flowing through th rsistor, and th powr and nrg absorbd b th rsistor. o, gin, Dirction of tim θ 9 Tim.sc t.sc Initial oltag across capacitor V.Volts apacitor 47 μf sistor.kω Th tim-futur oltag V across th capacitor Th tim-futur oltag across th capacitor j9 jθ V V.Volts. jvolts (89) t () t (. kω)( 47 μf) t V. jvolts (9).sc. jvolts (9).sc.9 jvolts (9) Th instantanous powr P absorbd b th rsistor at t.sc and at t.sc t. ( jvolts) (.kω) V P () t t (.kω)( 47μF) (93) P.sc.Watts (94) William Alk Pag 5 5/4/8

106 Nwtonian Torsion Phsics INTAK, IN. 3.9 Th nrg P 3 (.sc).49 absorbd b th rsistor at t.sc and at t.sc Watts (95) ( μf)( jvolts) (. kω)( 47 μf) V t 47. t () t (9).sc.3 Jouls (97) OPX FID A FUTUATION THNOOGI inc a thortical link was stablishd btwn grait and lctromagntism, two mass fluctuation tchnologis ar prsntl undr instigation. Both tchnologis ar lctrical dics with th first bing inducti-basd, and th scond bing capaciti-basd. hown blow is a simplifid schmatic diagram that highlights thir opration. OPX TI-FUTU APIAN UNT INDUTO DAD A Δ OPX TI-FUTU APIAN UNT APAITO DAD A Δ j j i OP >. ji i OP >. ji D OAD D - OAD + OAD OAD + - OAD OAD + V - + V - + V - + V - AGNTIZATION PHA DAGNTIZATION PHA HAG PHA DIHAG PHA INDUTIV AGNTIZATION / DAGNTIZATION Y APAITIV HAG / DIHAG Y FIGU 43. Two tps of compl fild mass fluctuating sstms. Ths sstms ar cclic, and altr th local grait wll. Th mass of ths sstms is conrtd to css fild nrg during th magntizing/charging phas. During th dmagntizing/discharging phas, css lctrical nrg is collctd, and mass is rstord aftr this phas. Thn, th ccl bgins again. As a consqunc, clocks runs fastr du to brokn smmtr of mass-nrg consration in th proimit of ths dics bcaus mass is conrtd to NGATIV nrg. William Alk Pag 5/4/8

107 Nwtonian Torsion Phsics INTAK, IN. 3.9 AN INDIATO OF X F NGY IPU DU TO X FUX IN O (NGATIV NGY) UNT (AP) i AGNTIZING UNT (POITIV NGY) TI () t FIGU 44. css fr nrg is harstd as NGATIV nrg. Th diagram abo shows that an impuls function occurs whn css rsidual magntic flu is found in th cor of a coil bing magntizd at th start of th nt ccl, t sc. If harstd, th nrg of this function manifsts as NGATIV nrg and coupls to POITIV nrg forming a compl dirct currnt. This currnt consists of both ral and imaginar componnts whr th ral currnt i is tim-forward and th imaginar currnt ji is timfutur. Th ral currnt componnt is considrd to b classic HOT UNT and th imaginar currnt componnt is considrd to b OD UNT. Dpnding upon how much rsidual flu is aailabl in th cor, th nrg in this impuls function could b quit substantial. FIGU 45. css nrg found in N. Za s dic. William Alk Pag 7 5/4/8

108 Nwtonian Torsion Phsics INTAK, IN. 3.9 FOU TINA DVI j i θ j, θ i θ, θ TI t TI t OU DIPO + IN 3 OPX FID GNATO Δ Δc 4 + OUT OAD DIPO TPOAY A DUTION TWO TINA DVI j i θ, θ OU/ OAD DIPO TOT + IN + OUT IN TI t TI t j i θ, θ ( OUT ) + Jouls OUT + OP. IN OPX FID GNATO Δ Δ c TPOAY A DUTION DNOT HOT TI-FOWAD NGY FOW DNOT OD TI-FUTU NGY FOW DNOT HOT/OD TI-ADVAND NGY FOW WITHD OPATION: Tim Forward urrnt i Tim Adancd urrnt i ON OFF ON OFF t t NOT: AU IDA YT FIGU 4. Two trminal / four trminal compl fild mass fluctuating sstms. Th diagram abo shows a tpical configuration of four trminal and two trminal compl fild mass fluctuating sstms. In th four trminal sstms, nrg from th sourc dipol (i.., a battr) ntrs through trminals and. css nrg las through trminals 3 and 4 and chargs th load dipol. In th two trminal sstms, th sourc dipol also acts as th load dipol. nrg las th sourc dipol through trminals and and css nrg las through th sam trminals at Tim t latr. William Alk Pag 8 5/4/8

109 Nwtonian Torsion Phsics INTAK, IN. 3.9 FIGU 47. Th martpak/zpod Workstation. FIGU 48. Th ZPOD in opration. William Alk Pag 9 5/4/8

110 Nwtonian Torsion Phsics INTAK, IN. 3.9 IN OUT TYPIA TANFO ATION OUT IN TH ZPOD: INDUTIV A FUTUATO t PIAY ID (7mH) P-3 IN OUT TH ZPOD P- P- T- ONDAY ID (.H) OUT IN t P-4 μ o (H + ) OI/O ABI X NGY t FIGU 49. Th css nrg of th ZPOD. William Alk Pag 5/4/8

111 Nwtonian Torsion Phsics INTAK, IN. 3.9 FIGU 5. Th Bik using martpak tchnolog. FIGU 5. Th Bik using a martpak 3-3. William Alk Pag 5/4/8

112 Nwtonian Torsion Phsics INTAK, IN. 3.9 TA OPX FID GNATO A QUIVANT IUIT PW i G G + V A + N N - Δ Δ c F - BG μh N + j i θ, θ > F F ( F) +Δ t sc + - j H ik θ, θ > H - + K - - j K θ, θ > + + j i θ, θ > j θ, θ > FIGU 5. Nikola Tsla s U patnt 58,7. Nikola Tsla was th first to dlop th phnomnon of compl filds back in th 88's. H disd a sris of machins patntd in th 89's that gratl amplif this phnomnon, which h latr calld ADIANT NGY. As shown abo, th pioting magntic domains cratd b Amprian urrnts of th frromagntic matrial ar ordrd in th dirction of fild B G b magntizing coil G. agntizing th high inductanc coils crat an opposing fild μ H that acts upon th ordrd domains of th matrial, thus cancling or partiall cancling th ral magntic fild cratd b th Amprian urrnts. An imaginar magntic fild jb mrgs du to this j cancllation and coupls back into th magntizing dirct currnt as i θ, whr θ >. Thrfor, th magntizing dirct currnt bcoms compl bcaus th circulating motions of th lctrons ar rotating into th imaginar ais. William Alk Pag 5/4/8

113 Nwtonian Torsion Phsics INTAK, IN. 3.9 j As shown abo, bfor switch F is closd, th capacitors H ar chargd with a compl dirct currnt i θ producd b an opposing flu from coils. Th compl fild nrg is stord in capacitors H. At th momnt of switch F closur t sc, th compl dirct currnt flows through coil K, rapidl discharging capacitors H. j A r larg compl lctric potntial θ is obsrd across th scondar coil. OU DIPO + IN j i θ, θ G TI t INPUT 3 TA OPX FID GNATO Δ Δc OUTPUT 4 j i θ, θ K TI t K + OUT DNOT HOT TI-FOWAD NGY FOW DNOT OD TI-FUTU NGY FOW DNOT NUTA TI-ADVAND NGY FOW NOT: AU IDA YT FIGU 53. Tsla s four trminal compl fild gnrator. William Alk Pag 3 5/4/8

114 Nwtonian Torsion Phsics INTAK, IN. 3.9 TH HUTHION FFT XPAIND FIGU 54. tal sampls from John Hutchison s lab. As shown abo, John Hutchison succssfull applid th Tsla compl fild to mtal sampls with amazing rsults. Ths bulk mtal sampls wr mltd at room tmpratur without an application of hat. Th compl filds inducd cold dd currnts within th mtal, which in turn, causd th mtal to cold mlt. As th mtal softnd, John insrtd bits of othr mtals and organic matrial as shown. With th fild turnd off, th mtal rsolidifid trapping ths matrials within th mtal lattic structur. FIGU 55. John Hutchison in his lab. William Alk Pag 4 5/4/8

115 Nwtonian Torsion Phsics INTAK, IN. 3.9 K j ji i θ, θ 9 K K OPX UNT j K + j N NGATIV FID NGY X ji GION OF OD TING N NGATIV FID NGY Y ji j BX - + j B X j B Y - + j BY OPX FID j X TA AP j Y OD DDY UNT INDUD IN TA FIGU 5. old dd currnts bing inducd in a mtal sampl. As shown abo, cold dd currnts ar inducd in th mtal block with th application of compl magntic filds. A compl currnt flowing through th coils producs ths magntic filds. Th magntic fild nrg surrounding ths coils is NGATIV, and th mtal sampl in th prsnc of this fild will cold mlt du to induction. FIGU 57. Anothr cold mltd mtal sampl. William Alk Pag 5 5/4/8