NEWTONIAN TORSION PHYSICS

Transcription

1 NWTONIAN TOION PHYI William. Alk INTAK, IN., 77. tat t 9, t 5-38 Prsott Vall, AZ 834, UA Phon: (98) mailto:william.alk@intalk.om ABTAT: Th purpos of this book is to plor onpts rlatd to F nrg and th ontrol of Grait/Antigrait that ar basd ntirl within th framwork of tndd lassial Nwtonian phsis alld Nwtonian Torsion Phsis. It is shown that th aus of grait is a tp of marosopi torqu btwn inrtial frams whr th origin of th torqu ours within imaginar or ompl spa. Th fft manifsts in ral spa as unirsal mass attration, or grait. A orrlation has bn disord btwn mass, indutors, and apaitors, thrb rlating th imaginar or ompl origin of torqu to grait, and how this sam torqu affts ltromagntism. A simplifid torsional mass rlatiit modl alld Natural latiit (N) Thor is prsntd and dirtl rlatd to grait. This thor is thn orrlatd to instin's pial latiit () Thor, and as a onsqun, rats a orrtd Prinipl of quialn Thorm showing th origin of grait and antigrait oms from imaginar or ompl spa. A tmporal rotation oprator is introdud using ulr s Idntit, whih shows th imaginar or ompl (i.., tim-past and tim-futur) motion of mattr as positi or ngati displamnt into imaginar spa, whih mbodis th fundamntal onpt of tim tral. Th spd of light, Plank's onstant h, prmabilit μ, prmittiit ε, Boltzmann's onstant k, ltri harg q, and th Fin trutur onstant α ar inariant btwn inrtial frams and thrfor, unafftd b torqu baus th flutuation or uratur of th fundamntal paramtrs that ompos ths onstants ar shown to aluat to unit gain. In othr words, ths onstants rmain onstant anwhr within a gin torqu fild or grait wll. Graitomagnti Thor shows that th magnti fild nrg produd b a moing ltron is shown to b a spial rlatiisti mass flutuation, and thrfor rats a ral torqu, whih oupls to grait as a sondar graitational fft. This motion an ithr ha a ral loit, or an imaginar or ompl (i.., tim-past or tim-futur) loit. If th loit is ompl, thn th spial rlatiisti mass flutuation or orrsponding graitational or antigraitational fft, whih onsquntl produs a ompl (i.., tim-past or timfutur) magnti fild. This is th origin of th fft alld grait or antigrait. In addition, th olum of th total fild nrg of a ompl magnti fild an ithr b positi or ngati, whih an add or subtrat from th nrg produd b a ral magnti fild. In th Bohr modl of th Hdrogn atom, an Amprian urrnt is dsribd as an ltron irulating around a nulus at a rlatiisti spd. This rats a magnti indution mrging from th ntr of th nulus. Flutuating this fild b appling an trnal magnti indution auss th loit of th ltron to bom ompl. Th prsn of NGATIV ITAN, th prodution of NGATIV NGY, and th ontrol of GAVITY/ANTIGAVITY our b flutuating th mass of an objt in ompl spa. Th thor prsnts a onptual brakthrough for th dlopmnt of nrg and high-spd fild propulsion thnologis. ± of an ltron an b ithr positi or ngati, and hibits a INTODUTION Puthoff (99) oind th phras, mtri nginring, and Puthoff, ittl and Ibison () onsidr th auum to b a polarizabl mdium, and that it an b prssd in trms of tnsor formulations of urd spa-tim. Th bnding of light passing nar a massi objt is ausd b indud spatial ariation in th rfrati ind of th auum nar th objt. This is orrlatd to hangs in prmabilit μ and prmittiit ε of th auum. hangs ourring in th auum also afft th mass of objts, th lngth and bnding of rulrs, th frqun of loks, th nrg of light, t. This book both simplifis and links grait with ltromagntism b prsnting formulations of urd spa-tim in trms of tndd lassial Nwtonian phsis, whih ar ausd b

2 Nwtonian Torsion Phsis INTAK, IN. 3.8 rlatiisti flutuations of mass, indutan, and apaitan of an objt. For ampl, whn an objt with mass naturall falls downward in a gin grait wll, its natural rlatiisti mass + inrass du to Nwtonian Graitation, or unirsal mass attration. Th nw mass of an objt + is displad to a nw position within this wll, thn mass-nrg rmains onsrd b rturning th mass to its pla of origin, or +. In othr words, b onrting this inras in rlatiisti mass + to nrg +, a for ats upon th objt, and th nw mass is now displad bak to its original position that was highr rtiall in th wll. Th objt hibits an antigraitational fft b rmoing or subtrating from. Th rat of hang of this flutuation ould aus th spd of th objt to asil d th spd of light. This is baus th rlatiisti graitational mass of th objt, whih is shown to b onrgnt, is moing at right angls to a rlatiisti inrtial mass, whih is shown to b dirgnt. in th spd of th objt with rlatiisti graitational mass has no known uppr limit, th rsulting spd through dp spa ould b normous and nssitats th us of th warp fator 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 idntial sphrs as sn b an obsrr on th arth. ass and olum of mattr ar undr th influn of diffrnt grait. hown in Fig. abo ar two idntial 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 idntial sphrs hang in mass and olum rlati to position of th obsrr. William Alk Pag 9//7

3 Nwtonian Torsion Phsis INTAK, IN. 3.8 PH on th lft is undr th influn of grait of th oon and PH on th right rmains undr th influn of grait of th arth. in 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 fft of uratur of spa and tim upon mattr ausd b torsion originating from imaginar or ompl spa and obsrd in ral spa as unirsal mass attration, or grait. APPYING TH PODUT U armt () onsidrs sparatl th influn of a graitational potntial upon mattr, and assums for th momnt that kinti nrg is zro. Th kinti nrg and graitational nrg ar aluatd indpndntl and thrfor ar onsidrd mutuall lusi. For Kinti nrg sstms, and gin a fram of rfrn, th following inrtial-basd paramtrs mass, indutor, and apaitor, ar onsidrd inariant. Howr, for Graitational nrg sstms, and gin an quipotntial surfa of grait rfrn, th following torsionalbasd paramtrs rlatiisti mass ±Δ, rlatiisti indutor ±Δ, and rlatiisti apaitor ±Δ, flutuat or ur btwn inrtial frams. o, b appling th produt rul, this prinipl is mathmatiall prssd as, Whr, th Inrtial Trm is gin as, And th Torsional Trm is gin as, d da db () t ( ab) b + a ba + ab b Δ a + a Δb dt dt dt t () ba b Δ a t () ab a Δb Th first trm is rgardd as inrtial, and thrfor is onsidrd kinti or flus, and is Nwtonian-basd. Th sond trm is rgardd as torsional, and thrfor, oupls to grait. Whn aluatd, 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 Graitational nrg ma b positi or ngati. This prinipl tnds Nwtonian-basd phsis to inlud Nwtonian Torsion Phsis, and is formulatd and analzd in th dirtion of grait. William Alk Pag 3 9//7

4 Nwtonian Torsion Phsis INTAK, IN. 3.8 TOIONA A FUTUATION FUTUATING A ± + r r g FIGU 3. Th flutuating mass of an objt du to grait. Appling th produt rul, th omplt idal momntum modl is omposd 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 surfa of grait g Y. Th Torsional Trm is Y, and hanging mass flutuats btwn quipotntial surfas of grait. For a mass flutuating sstm, th Torsional Trm is NOT zro Nwtons. o, gin an objt haing mass moing at onstant loit 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 in has units of rsistan in mns m, its dirtion of hang ould ithr b POITIV or NGATIV. If is ngati, it has units of ngati rsistan or, < mns m (4) Now, th instantanous graitationall indud powr P of a flutuating mass P () t f () t (5) Y Y o, for rtain alus of, th total instantanous powr P an b NGATIV or, P () t < Watts () Thn, intgrating P with rspt 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 9//7

5 Nwtonian Torsion Phsis INTAK, IN. 3.8 If is positi, it has units of positi rsistan or, > mns m (8) Now, th instantanous graitationall indud powr P of a flutuating mass P () t f () t (9) Y Y o, for rtain alus of, th total instantanous powr P an b POITIV or, P () t > Watts () Thn, intgrating P with rspt to tim rsults in ss 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 flutuating mass quialnt of nrg (4) Y o, th graitational momntum modl f (5) () t Y Y Y Y tting d dt, th Torsional For Trm Y B rarranging trms, th flutuating nrg quialnt of mass f () t () () f t (7) Th total nrg ontaind within mattr () t () t (8) William Alk Pag 5 9//7

6 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th hang in this total nrg (9) B rarranging trms, th hang in total mass () o, th tim driati form of th Torsional ass Trm f () t () Th driati form d f d () Th diffrn form Δ Δ f (3) William Alk Pag 9//7

7 Nwtonian Torsion Phsis INTAK, IN. 3.8 TOIONA INDUTIV A FUTUATION + I FUTUATING INDUTAN ± g + - FIGU 4. Th flutuating indutan of an objt du to grait. Appling th produt rul, th omplt idal indutor modl is omposd of two trms, d di d ν () t ( I) + I I + I (4) dt dt dt Whr, th Inrtial Trm is I, and indutan is inariant within an quipotntial surfa of grait g Y. Th Torsional Trm is I, hanging indutan flutuats btwn quipotntial surfas of grait. For an induti flutuating sstm, th Torsional Trm is NOT zro olts. B appling a onstant urrnt I through indutor, 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 () in has units of rsistan in ohms, Ω, its dirtion of hang ould ithr b POITIV or NGATIV. If is ngati, it has units of ngati rsistan or, < Ω (7) Now, th instantanous graitationall indud powr P of a flutuating indutor P () t I ν () t I (8) o, for rtain alus of, th total instantanous powr P an b NGATIV or, P () t < Watts (9) Thn, intgrating P with rspt to tim whn th total powr is lss than zro watts rsults in NGATIV nrg of indutor or, William Alk Pag 7 9//7

8 Nwtonian Torsion Phsis INTAK, IN. 3.8 If is positi, it has units of positi rsistan or, (3) () () < t P dt I dt I t Jouls > Ω (3) Now, th instantanous graitationall indud powr P of a flutuating indutor P () t I ν () t I (3) o, for rtain alus of, th total instantanous powr P an b POITIV or, P () t > Watts (33) Thn, intgrating P with rspt to tim rsults in ss POITIV nrg of indutor 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 flutuating mass quialnt of nrg I (39) Y Y o, th graitational indutor modl I f (4) () t Y Y Y Y Y tting d dt, th Torsional Induti For Trm Y William Alk Pag 8 9//7

9 Nwtonian Torsion Phsis INTAK, IN. 3.8 B rarranging trms, th flutuating nrg quialnt of mass () () t f t (4) () f t (4) Th total nrg ontaind within mattr () t () t (43) Th hang in this total nrg (44) B rarranging trms, th hang in total mass () t I I () t f I () t t () () t (45) o, th tim driati form of th Torsional Induti Trm () t () t f () t (4) Th driati form d d f (47) Th diffrn form Δ Δ f (48) William Alk Pag 9 9//7

10 Nwtonian Torsion Phsis INTAK, IN. 3.8 TOIONA APAITIV A FUTUATION + FUTUATING APAITAN ± + - g i V + V - FIGU 5. Th flutuating apaitan of an objt du to grait. Appling th produt rul, th omplt idal apaitor modl is omposd of two trms, d dv d i() t ( V) + V V + V (49) dt dt dt Whr, th Inrtial Trm is V, and apaitor is inariant within an quipotntial surfa of grait g Y. Th Torsional Trm is V, and hanging apaitan flutuats btwn quipotntial surfas of grait. For a apaiti flutuating sstm, th Torsional Trm is NOT zro amps. B appling a onstant oltag aross apaitor, 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) in has units of ondutan in mhos,, its dirtion of hang ould ithr b POITIV or NGATIV. If is ngati, it has units of ngati ondutan or, < (5) Now, th instantanous graitationall indud powr P of a flutuating apaitor is P () t i () t V V (53) o, for rtain alus of, th total instantanous powr P an b NGATIV or, P () t < Watts (54) Thn, intgrating P with rspt to tim whn th total powr is lss than zro watts rsults in NGATIV nrg of apaitor or, William Alk Pag 9//7

11 Nwtonian Torsion Phsis INTAK, IN. 3.8 (55) () () < t P dt V dt V t Jouls If is positi, it has units of positi ondutan or, > (5) Now, th instantanous graitationall indud powr P of a flutuating apaitor P () t i () t V V (57) o, for rtain alus of, th total instantanous powr P an b POITIV or P () t > Watts (58) Thn, intgrating P with rspt to tim rsults in ss POITIV nrg of apaitor 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 flutuating mass quialnt of nrg V (4) Y Y o, th graitational apaitor modl V f (5) () t Y Y Y Y Y tting d dt, th Torsional apaiti For Trm Y William Alk Pag 9//7

12 Nwtonian Torsion Phsis INTAK, IN. 3.8 B rarranging trms, th flutuating nrg quialnt of mass f () t () () f t (7) Th total nrg ontaind within mattr () t () t (8) Th hang in this total nrg (9) B rarranging trms, th hang in total mass f() t V V () t V () t t () () t (7) o, th tim driati form of th Torsional apaiti Trm () t () t f () t (7) Th driati form d f (7) d Th diffrn form Δ Δ f (73) William Alk Pag 9//7

13 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 +Δ (AFT),378.. g g 7. g 9.8 AATION DU TO GAVITY m s g n FIGU. Th natural mass flutuation of an objt du to graitational fr fall. Natural unirsal mass attration or lassi Nwtonian grait is a for f that ats through a ntr of mass of th arth with mass and a tst mass sparatd b a distan, G f g (74) o, gin, Graitational onstant ass of th arth adius of arth G.759 Nm kg kg.378 m Th surfa grait g of th arth g 4 (.759 N m kg )( kg ) (.378 m) G 9.85m s (75) William Alk Pag 3 9//7

14 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th grait g at GAVITATIONA FN position g 4 (.759 N m kg )( kg ) ( 9.9 m) G.537 m s (7) Th grait g at position g 4 (.759 N m kg )( kg ) ( 7.59 m) G m s (77) armt () quats for f produd b a flutuating tst mass d to th graitational for f, Th driati form of a flutuating tst mass d f () t f () t (78) d f d g d (79) Th driati form of th graitational D HIFT (or BU HIFT) of tst mass d and th nrg quialnt of tst mass d displad d within a gin grait wll g d d g d (8) armt stats th quation abo shows a alulatd hang of nrg lls as a funtion of graitational potntial is in prft agrmnt with th Pound and bka and also th Pound and nidr primnts. Thrfor, nrg inrass as a funtion of downward or positi displamnt 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 g dyg (8) g ln (8) g Y g g ln ln ln ( ) ( ) ( g g ) (83) g g (84) g g (85) William Alk Pag 4 9//7

15 Nwtonian Torsion Phsis INTAK, IN. 3.8 g g (8) o, th Pound, bka and nidr primnt usd ossbaur sptrosop to masur th ltromagnti 57 graitational D HIFT (or BU HIFT) of 4.4kV gamma ras mittd from F through a rtial distan of.m. With th gamma ras mittd upward, th showd th D HIFT was within on prnt (%) of this rsult, G g g Δ Δ HIFT (87) HIFT 8 ( m s) 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 s) 4 (.759 N m kg )( kg ) (.378 m) (.378 m) (9) HIFT (9) Now, th for f produd b a flutuating indutor d is quatd to th graitational for f, Th driati form of a flutuating indutor d f () t f () t (9) d f d g d (93) Th driati form of th graitational D HIFT (or BU HIFT) of indutor d displad d within a gin grait wll g d g d (94) t dy g g d, th ponntial solution of th driati form of an indutor d g dyg (95) g William Alk Pag 5 9//7

16 Nwtonian Torsion Phsis INTAK, IN. 3.8 ln (9) g Y g g ln ln ln ( ) ( ) ( g g ) (97) g g (98) g g (99) o, th graitational D HIFT (or BU HIFT) of an indutor G g g Δ HIFT () Now, th for f produd b a flutuating apaitor d is quatd to th graitational for f, Th driati form of a flutuating indutor d f () t f () t () f d g d d () Th driati form of th graitational D HIFT (or BU HIFT) of apaitor d displad d within a gin grait wll g d d g d (3) t dy g g d, th ponntial solution of th driati form of a apaitor d g dyg (4) g ln (5) g Y g g ln ln ln ( ) ( ) ( g g ) () William Alk Pag 9//7

17 Nwtonian Torsion Phsis INTAK, IN. 3.8 g g (7) g g (8) o, th graitational D HIFT (or BU HIFT) of a apaitor G g g Δ HIFT (9) William Alk Pag 7 9//7

18 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 hang of rlatiisti mass du to grait. Th stablishmnt of a GAVITATIONA FN is dfind as a fid point of rfrn within a gin grait wll g. This point ma b loatd in a plan of quipotntial surfa of grait, and is usd throughout this papr. Natural rlatiisti hangs of mass, olum, frqun, nrg, t. flutuat or ur as a funtion of displamnt ±Δ from this point of rfrn. This displamnt dfins a nw point within a nw plan of quipotntial surfa of grait g ±Δ, and th grait at that point ma b inrasd or drasd basd upon th sign of th displamnt. armt () inoks th prinipl of mass-nrg onsration rgarding th displamnt of mattr btwn plans. For ampl, an objt of mass displad a distan Δ hangs bak to its original mass whn rturnd to its original position within a gin grait wll. Thrfor, a nw and simplifid rlatiit modl is introdud. For graitational nrg sstms, and gin an quipotntial surfa of grait rfrn, th following paramtrs inluding rlatiisti mass ±Δ, rlatiisti indutan ±Δ, and rlatiisti apaitan ±Δ, flutuat or ur btwn quipotntial surfas of grait b displamnt ±Δ. Again, th kinti nrg of graitational nrg sstms is assumd to b zro. o, gin a ommon quipotntial surfa of grait rfrn g, an inras in grait auss a natural rlatiisti inras in mass, nrg quialnt of mass (graitational nrg), indutan, and apaitan. ikw a dras in grait auss a natural rlatiisti dras in th sam mtris. Gin an objt with a rst mass apaitan, th nw rst mass and th nw apaitan ar,, an quialnt nrg of th rst mass, th nw quialnt nrg of th rst mass, an indutan, and a, th nw indutan, γ ±Δ () N γ ±Δ () N γ ±Δ () N γ ±Δ (3) N William Alk Pag 8 9//7

19 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th natural rlatiisti gamma γ N g g γ N (4) Th diffrn forms and th ponntial forms of th natural rlatiisti mass modl, nrg quialnt of mass modl, indutor modl, and apaitor modl at position ±Δ within a gin grait wll g ar, g g g g ±Δ ± g g g g +Δ ± g g g g +Δ ± g g g g ±Δ ± (5) () (7) (8) In summar, Natural latiit (N) Thor dsribs th natur of th primar graitational fft. William Alk Pag 9 9//7

20 Nwtonian Torsion Phsis INTAK, IN. 3.8 PIA ATIVITY THOY dt ds dt A TATIONAY OBV dr dt r B OBV IN OTION FIGU 8. Th dfinition of a spa-tim intral rlati to Obsrr B in motion. instin (95) formulatd his thor of spial rlatiit and is dsribd as Obsrr B, moing at loit r rlati to a stationar Obsrr A, undrgos a rlatiisti fft. This fft hangs th mass, lngths, tim intrals, frqun and nrg of th obsrr in motion. It s prssd as a Pthagoran-tp quantit alld a spa-tim intral, and aluats as a orntz tmporal orrtion shown blow. ds + dr dt (9) ds dt dr () in th loit r of Obsrr B r dr r () dt dr dt () r o, ds dt dt (3) r dtr r ds dt dt (4) in th spd of light ds dt s (5) William Alk Pag 9//7

21 Nwtonian Torsion Phsis INTAK, IN. 3.8 ds dt () o, th orntz tmporal orrtion rlati to Obsrr B dt dt r (7) dt dt r (8) dt dt r (9) Thrfor, rlati to Obsrr B in motion with a tim intral dt B, stationar Obsrr A s lok with a tim intral dt A will b tiking fastr or BU HIFTD, and ha th following orntz tmporal orrtion, dt A dt B r (3) dt > dt (3) A B ikw rlati to stationar Obsrr A with a tim intral dt A, Obsrr B s lok at tim intral dt B will b tiking slowr or D HIFTD, and ha th following orntz tmporal orrtion, dt B r dta (3) dt < dt (33) B A William Alk Pag 9//7

22 Nwtonian Torsion Phsis INTAK, IN. 3.8 TI FUTU t TI FOWAD DAD GAVITY + j Δ Δ GAVITATIONA FN INITIA A, AT T AND t s UVATU DU TO VOITY +Δ g INAD GAVITY t + Δ FIGU 9. A hang of rlatiisti mass du to loit. Gin th rst mass of an objt, th spial rlatiisti mass objt moing at loit modl prsntd b instin (95) shows an γ + d (34) Th gamma γ γ (35) Implmnting th binomial pansion of th abo quation, Using th st ordr trm of th pansion shown abo whr γ (3) , th nw spial rlatiisti gamma γ γ + (37) Th driati form of th spial rlatiisti mass modl moing at loit γ ± d ± (38) William Alk Pag 9//7

23 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th driati form of a flutuating mass d d (39) An objt an mo at a ral (i.., tim-forward) loit, at an imaginar (i.., tim-futur) loit j, or at a loit that is a ombination of th two. Th ral and imaginar omponnts ar rotatd about th tmporal ais and thrfor, an b dsribd as ompl 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 ompl numbr uss th ulr s idntit θ, whih funtions as a tmporal rotation oprator. jθ osθ + jsinθ (4) o, th driati form of th inrtial D HIFT (or BU HIFT) of mass d, nrg quialnt of mass d, indutor d, or apaitor d of an objt moing at a ral loit or a ompl loit j d d d d HIFT (4) Th ponntial solution of th driati form of mass d (4) ln ( ) (43) ln ( ) ln ( ) ln (44) (45) (4) (47) (48) (49) William Alk Pag 3 9//7

24 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, th inrtial D HIFT (or BU HIFT) of a mass, an nrg quialnt of mass a apaitor, an indutor, and Δ Δ Δ Δ HIFT (5) Th spial rlatiisti gamma γ γ (5) Th diffrn forms and th ponntial forms of th spial rlatiisti mass modl, nrg quialnt of mass modl, indutor modl, and apaitor modl of an objt moing at a ral loit or a ompl loit j ar, ±Δ ± ±Δ ± ±Δ ± +Δ ± (5) (53) (54) (55) William Alk Pag 4 9//7

25 Nwtonian Torsion Phsis INTAK, IN. 3.8 DID INTIN GT IT IGHT, O NOT? instin s Gnral latiit Thor (9) quats Nwton s sond law of motion, f ma i, whr m i is th inrtial mass to Nwton s graitational for, f mg g, whr m g is th graitational mass. Is this onpt orrt? instin usd this to formulat his quialn prinipl and statd, Thr is no primnt a prson ould ondut in a small olum of spa that would distinguish btwn a graitational fild and an quialnt uniform alration. Is this statmnt orrt? ts tst instin s prinipl 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 alrating in spa. As shown abo, th natural rlatiisti mass flutuation of an lator at rst on th surfa of th arth is zro, or d. Howr, th sond ordr spial rlatiisti mass flutuation of th sam lator alrating in spa is non-zro or d >, and as a onsqun, radiats ltromagnti was. Aording to Woodward (998), radiation ration is obsrd in bodis bing alratd basd upon Nwton s sond law of motion, f ma. Thrfor, gin this snario, th graitational mass an t b quialnt to its inrtial mass du to thir diffrns in mass flutuations. William Alk Pag 5 9//7

26 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 onstant loit in spa. As shown abo, an lator traling a distan + d in fr fall and th sam lator moing at a onstant loit at right angls to fr fall produ irtuall no radiation ration. o, gin this sond snario, ths mass flutuations ar onsidrd quialnt, hn, stablishing a nw Prinipl of quialn 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.9 ±. j 8 7 ± 7.5 j 7 ± 5. j 7 ±.5 j. VOITY (m/s) FIGU. Vloit profil of a kg inrtial mass. William Alk Pag 9//7

27 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th inrtial D HIFT of an objt du to loit Δ HIFT (5). GAVITATIONA A (kg) DAING GAVITY GAVITATIONA FN g DAING GAVITATIONA A (BU HIFT) g g INAING GAVITATIONA A (D HIFT) DIPANT FO NT OF ATH (m) FIGU 3. Displamnt profil of a kg graitational mass du to arth s grait wll. And sin th graitational D HIFT of th sam objt du to grait g G g g Δ HIFT (57) B quating an inrtial D HIFT to a graitational D HIFT, a nw Prinipl of quialn Thorm is dtrmind as, G g g (58) William Alk Pag 7 9//7

28 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, an objt displad loit, ±Δ within th arth s grait wll g is quialnt to th sam objt moing at ompl ( ) g g G (59) 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/s). INAING INTIA A (D HIFT) FIGU 4. quating an inrtial D (BU) HIFT to a graitational D (BU) HIFT. As shown abo, if th displamnt Δ of an objt is POITIV, thn th objt is moing at a ral loit. Howr, if th displamnt tim-futur) loit Δ is NGATIV, thn th sam objt is moing at a ompl (i..,, or loit j, whr j. Th ral and imaginar omponnts ar rotatd William Alk Pag 8 9//7

29 Nwtonian Torsion Phsis INTAK, IN. 3.8 about th tmporal ais as a ompl loit. Th rotation is gin as θ 9, whr th ral ais is θ j and th imaginar tim-futur ais is θ 9. Th ompl numbr uss th ulr s idntit θ, whih funtions as a tmporal rotation oprator. jθ osθ + jsinθ () o, gin an objt moing at a ompl loit, th quialnt displamnt to position within th arth s grait wll g, whr < or G g + G + g () Thrfor, th quialnt displamnt Δ within th arth s grait wll g Δ + G + G () Th quialnt maimum ompl loit ma at is + (3) G ma G (4) o, gin th quialnt maimum ompl loit ma, th minimum mass min at G min + G (5) In summar, this nw Prinipl of quialn Thorm dsribs an objt moing at on-half th squar of a ral loit is quialnt to th sam objt haing falln down a displamnt + d within a gin grait wll g. This objt naturall aquirs mor rlatiisti mass, indutan and apaitan as it mos at a ral loit, and augmnts its own graitation with othr objts. On th othr hand, th sam objt moing at on-half th squar of a ompl loit j is quialnt to th sam objt haing falln up a displamnt d in th sam grait wll. This objt naturall loss mor rlatiisti mass, indutan and apaitan as it mos at a ompl loit j, and diminishs its own graitation with othr objts. Thrfor, spial rlatiit is onsidrd to b a sondar graitational fft. William Alk Pag 9 9//7

30 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl. Gin th loit profil abo of an objt haing a mass moing at a spial rlatiisti timforward loit, omput th nw spial rlatiisti inrtial mass o, gin, Dirtion of tim θ ass of objt.kg 8 Vloit of objt. m s Th tim-forward loit of an objt. jθ 8 j 8. s. s () m m Th nw spial rlatiisti inrtial mass 8 (. m s) 8 ( m s) (. kg) (7) Th inrtial mass of th objt was inrasd b,.57kg (8).57kg. kg.57kg (9) ampl. Gin th loit profil abo of an objt haing a mass moing at a spial rlatiisti loit tim-futur j, omput th nw spial rlatiisti inrtial mass. o, gin, Dirtion of tim θ 9 ass of objt.kg 8 Vloit of objt. m s Th tim-futur loit of an objt jθ 8 j9 8. s. s (7) m j m Th nw spial rlatiisti inrtial mass 8 (. j m s) 8 ( m s) (. kg) (7) Th inrtial mass of th objt was rdu b, kg (7) kg. kg.54kg (73) William Alk Pag 3 9//7

31 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl 3. Gin th graitational profil abo of an objt haing a mass within arth s grait wll o, gin, ass of objt g, omput th nw natural rlatiisti graitational mass.kg Objt on arth s surfa.378 m 8 Objt displad to. m 8 pd of light m s Graitational onstant G.7 Nm kg 4 ass of th arth kg Th alration du to grait at surfa of arth displad to a position Δ. g 4 (.7 N m kg )( kg ) (.378 m) G 9.85m s (74) Th alration du to grait at altitud. 8 m abo th arth g 4 (.7 Nm kg )( kg) 8 (. m) G m s (75) Gin th ponntial solution of th natural rlatiisti mass modl, th nw graitational mass 8 (.39894m s )(. m) ( 9.85m s )(.378 m) g g 8 ( m s) kg (7) (. ) kg (77) Th graitational mass of th objt was rdud b, (78) kg kg kg ampl 4. Assuming thr ar no othr graitational influns bsids th arth, omput th nw minimum natural rlatiisti graitational mass min of an objt at. o, gin, ass of objt.kg Objt on arth s surfa.378 m 8 pd of light m s Graitational onstant G.7 Nm kg 4 ass of th arth kg William Alk Pag 3 9//7

32 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th minimum graitational mass min at 4 (.7 N m kg )( kg ) G 8 (.378 m)( m s) kg (79) min. Th graitational mass of th objt was rdud b, min kg (8) (8) kg kg kg HOW GAVITY AFFT TH VOU OF OBJT An objt of olum V (lngth, width W, and hight grait wll g. ikw th sam th olum V dilats as a funtion of position H ) ontrats as a funtion of position +Δ within Δ in th sam grait wll. o, th diffrn form of th graitational D HIFT (or BU HIFT) of an objt of olum ΔV V displad Δ within a gin grait wll g Δ ΔW ΔH g g W H (8) Th diffrn forms and ponntial forms of th natural rlatiisti objt of olum V at position ±Δ g g g g Δ (83) g g g g Δ W W W W W (84) g g g g Δ H H H H H (85) An objt of olum V (lngth th sam objt of olum HOW VOITY AFFT TH VOU OF OBJT, width W, and hight V dilats moing at a ompl loit H ) ontrats moing at a ral loit. ikw o, th diffrn form of th inrtial D HIFT (or BU HIFT) of an objt of olum ΔV V moing at a ral loit or a ompl loit j j. Δ ΔW ΔH W H (8) William Alk Pag 3 9//7

33 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th diffrn forms and ponntial forms of th spial rlatiisti objt of olum V moing at a ral loit or a ompl loit j Δ (87) W W Δ W W W (88) H H Δ H H H (89) within grait wll as a funtion of position HOW GAVITY AFFT TH FQUNY OF TI A mhanial osillator ibrating at a frqun f ontrats (i.., slows down) as a funtion of position +Δ g. ikw th sam mhanial osillator ibrating at a frqun f dilats (i.., spds up) Δ in th sam grait wll. o, th diffrn form of th graitational D HIFT (or BU HIFT) of an osillator ibrating at a frqun Δ f f displad Δ within a gin grait wll g Δ f g g (9) f Th diffrn form and ponntial form of th natural rlatiisti frqun f of an osillator at position ±Δ g g g g Δ f f f f f (9) HOW VOITY AFFT TH FQUNY OF TI A mhanial osillator ibrating at a frqun f ontrats (i.., slows down) whil moing at a ral loit. ikw th sam mhanial osillator ibrating at a frqun f dilats (i.., spds up) whil moing at a ompl loit j. o, th diffrn form of th inrtial D HIFT (or BU HIFT) of an osillator ibrating at a frqun Δ f f whil moing at a ral loit or a ompl loit j Δ f (9) f William Alk Pag 33 9//7

34 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th diffrn form and ponntial form of th spial rlatiisti frqun f of an osillator moing at a ral loit or a ompl loit j f f Δ f f f (93) HOW GAVITY AFFT AN INTVA OF TI A mhanial osillator ibrating for an intral of tim t ontrats (i.., slows down) as a funtion of position +Δ within grait wll g. ikw th sam mhanial osillator ibrating for an intral of tim t dilats (i.., spds up) as a funtion of position Δ in th sam grait wll. o, th diffrn form of th graitational D HIFT (or BU HIFT) of an osillator ibrating for an intral of tim Δ ttdisplad Δ within a gin grait wll g Δ t g g (94) t Th diffrn form and ponntial form of th natural rlatiisti tim intral t of an osillator at position ±Δ g g g g Δ t t t t t (95) HOW VOITY AFFT AN INTVA OF TI A mhanial osillator ibrating for an intral of tim t ontrats (i.., slows down) whil moing at a ral loit. ikw th sam mhanial osillator ibrating for an intral of tim t dilats (i.., spds up) whil moing at a ompl loit j. o, th diffrn form of th inrtial D HIFT (or BU HIFT) of an osillator ibrating for an intral of tim Δ ttwhil moing at a ral loit or a ompl loit j Δ t (9) t Th diffrn form and ponntial form of th spial rlatiisti tim intral t of an osillator moing at a ral loit or a ompl loit j t t Δ t t t (97) William Alk Pag 34 9//7

35 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th momntum grait wll sam grait wll, HOW GAVITY AFFT INA ONTU p of an objt of mass g. ikw th momntum moing at loit inrass as a funtion of position p of th sam objt drass as a funtion of position p +Δ within Δ in th (98) o, th diffrn form of th graitational D HIFT (or BU HIFT) of momntum displad Δ within a gin grait wll g Δ p p of an objt Δ p g g (99) p Th diffrn form and ponntial form of th natural rlatiisti momntum p at position ±Δ g g g g ±Δ ± p p p p p () HOW VOITY AFFT INA ONTU Th momntum th sam objt drass moing at a ompl loit p of an objt of mass inrass moing at a ral loit. ikw th momntum p j, p of () o, th diffrn form of th inrtial D HIFT (or BU HIFT) of momntum ral loit or a ompl loit j Δ p p of an objt moing at a Δ p () p Th diffrn form and ponntial form of th spial rlatiisti momntum loit or a ompl loit j p of an objt moing at a ral p p ±Δ p p ± p (3) Th angular momntum funtion of position inariant as a funtion of position HOW GAVITY AFFT ANGUA ONTU of an objt of mass moing at loit 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 objt is r (4) William Alk Pag 35 9//7

36 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, th diffrn form of th graitational D HIFT (or BU HIFT) of angular momntum objt displad Δ within a gin grait wll g Δ of an Δ (5) Th diffrn form and ponntial form of th natural rlatiisti angular momntum at position ±Δ () HOW VOITY AFFT ANGUA ONTU Th angular momntum of an objt of mass is inariant moing at a ral loit with a radius r. ikw th angular momntum of th sam objt is inariant moing at a ompl loit j, r (7) o, th diffrn form of th inrtial D HIFT (or BU HIFT) of angular momntum moing at a ral loit or a ompl loit j Δ of an objt Δ (8) Th diffrn form and ponntial form of th spial rlatiisti angular momntum of an objt moing at a ral loit or a ompl loit j (9) William Alk Pag 3 9//7

37 Nwtonian Torsion Phsis INTAK, IN. 3.8 TH PA-TI DIA O TH ATH Z ε TI t Z G Z μ B FIGU 4. Th spa-tim mdia or athr. Aording to Puthoff (99) and Puthoff, ittl and Ibison (), th auum is dsribd as haing magnti prmabilit μ and diltri prmittiit ε, and ats to impd th propagation of light and th motion of mattr. Dirt modifiation of ths omponnts hangs 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 objts undrgoing natural unirsal mass attration. Th ati auum of spa, or spa-tim mdia (i.., th athr) is omposd of unondnsd rlatiisti mass. An objt mad of mattr (i.., atoms) and gin a GAVITATIONA FN point undrgos unirsal mass attration (i.., graitational fr fall) with anothr objt. Both objts aquir rlatiisti mass b a natural mans from th surrounding spa-tim mdia as a funtion of displamnt +Δ btwn th two objts. This mdia ondnss onto both objts as mor rlatiisti mass, thrb inrasing thir total mass n +Δ n, indutan n +Δ n, and apaitan n + Δ n. This ation hangs th rlatiisti momntum of both objts rsulting with inrasing for of attration. Th spa-tim mdia btwn ths objts rarf or rlatiisti mass ondnss out of th mdia thrb affting both th magnti prmabilit μ and th diltri prmittiit ε of fr spa. This rarfation of mdia is rfrrd to as a grait wll, and as a onsqun, auss th olum of spa oupid b both objts and th spa btwn thm to b rdud. Th spa-tim mdia in a rarfing stat mans grait btwn ths objts is inrasing, whih auss light passing nar ths objts to amplif in nrg λ and inras in frqun f λ as pron b th Pound and bka primnt (94). This bhaior of spa-tim mdia ats as an impdan upon th natural motion of mattr and th propagation of light. William Alk Pag 37 9//7

38 Nwtonian Torsion Phsis INTAK, IN. 3.8 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. ltromagnti was propagating within a gin grait wll. hown abo is th BU HIFTING of an ltromagnti wa du to grait. lati to a GAVITATIONA FN point or quipotntial surfa of grait within a gin grait wll g, PHOTON A drass in nrg λ and frqun f λ as it propagats through drasing grait g Δ. ikw PHOTON B inrass in nrg λ and frqun f λ as it propagats through inrasing grait g +Δ. This fft was dmonstratd in th Pound, bka and nidr primnt, whih usd ossbaur sptrosop to masur th ltromagnti 57 graitational D HIFT (or BU HIFT) of 4.4kV gamma ras mittd from F through a rtial distan of.m. Using th diffrn form of flutuating nrg Δ λ of an ltromagnti wa propagating through grait wll g and th gamma ras mittd upward, th D HIFT was within on prnt (%) of this rsult, Δ g g λ HIFT λ (9.858 s )(.378 ) 9.85 s.378 HIFT 8 ( m s) m m m m () () HIFT () William Alk Pag 38 9//7

39 Nwtonian Torsion Phsis INTAK, IN. 3.8 And with th gamma ras mittd downward, th BU HIFT was, HIFT 9.85 ms.378 m (9.858ms )(.378 m) ( m s) 8 (3) HIFT (4) Th diffrn form and ponntial form of th natural rlatiisti ltromagnti nrg λ at position ±Δ g g g g ±Δ ± λ λ λ λ λ (5) in th nrg λ of a singl photon Thn, th Plank's onstant h hf () λ λ λ h (7) f Th diffrn form of th graitational D HIFT (or BU HIFT) of frqun Δ fλ fλ of an ltromagnti wa propagating Δ within a gin grait wll g λ Δ f g g λ (8) f λ Th diffrn form and ponntial form of th natural rlatiisti ltromagnti frqun f λ at position ±Δ g g g g ±Δ ± fλ fλ fλ fλ fλ (9) o, th natural rlatiisti Plank's onstant h ranging from position Δ to +Δ aluats to unit gain or, h g g λ λ g g fλ fλ λ h f λ () Thrfor, th natural rlatiisti Plank's onstant h is inariant btwn quipotntial surfas of grait or, 34 h.755 Joul s () William Alk Pag 39 9//7

40 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th spd of light λ f λ () Th diffrn form of th graitational D HIFT (or BU HIFT) of th walngth ltromagnti wa displad Δ within a gin grait wll g Δ λ λ of an Δ λ g g (3) λ Th natural rlatiisti walngth λ at position ±Δ g g g g Δ λ λ λ λ λ (4) o, natural rlatiisti th spd of light ranging from position Δ to +Δ aluats to unit gain or, g g g g λ λ λ λ λ λ f f f (5) Thrfor, th natural rlatiisti spd of light is inariant btwn quipotntial surfas of grait or, m s () HOW GAVITY AFFT TH PABIITY OF PA-TI DIA Th prmabilit μ of spa-tim mdia is gin as, μ π (7) 7 4 H m Th diffrn form of th graitational D HIFT (or BU HIFT) of indutan within a gin grait wll g Δ displad Δ Δ g g (8) Th indutan of spa-tim mdia at position ±Δ g g g g Δ (9) William Alk Pag 4 9//7

41 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th diffrn form of th graitational D HIFT (or BU HIFT) of lngth Δ displad Δ within a gin grait wll g Δ g g (3) Th lngth of spa-tim mdia at position ±Δ g g g g Δ (3) o, th natural rlatiisti prmabilit unit gain or, μ of spa-tim mdia ranging from position Δ to +Δ aluats to g g g g μ μ (3) Thrfor, th natural rlatiisti prmabilit surfas of grait or, μ of spa-tim mdia is inariant btwn quipotntial μ 7 4π H m (33) HOW GAVITY AFFT TH PITTIVITY OF PA-TI DIA Th prmittiit ε of spa-tim mdia is gin as, ε F m (34) Th diffrn form of th graitational D HIFT (or BU HIFT) of apaitan Δ within a gin grait wll g Δ displad Δ g g (35) Th apaitan of spa-tim mdia at position ±Δ g g g g Δ (3) William Alk Pag 4 9//7

42 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th diffrn form of th graitational D HIFT (or BU HIFT) of lngth Δ displad Δ within a gin grait wll g Δ g g (37) Th lngth of spa-tim mdia at position ±Δ g g g g Δ (38) o, th natural rlatiisti prmittiit ε of spa-tim mdia ranging from position unit gain or, Δ to +Δ aluats to g g g g ε ε (39) Thrfor, th natural rlatiisti prmittiit ε of spa-tim mdia is inariant btwn quipotntial surfas of grait or, ε F m (4) HOW GAVITY AFFT TH VITUA ITAN OF PA-TI DIA Th spa-tim mdia has irtual rsistan or impdan Z, and thrfor, isn't apabl of absorbing or dissipating ltromagnti nrg. Its A rsistan is infinit or,. This mdia srs to impd th propagation of light and th motion of mattr and is alulatd as, Z μ (4) ε in it has bn shown th prmabilit quipotntial surfas of grait, it follows th natural rlatiisti impdan position Δ to +Δ aluats to unit gain or, μ and prmittiit ε of spa-tim mdia ar inariant btwn Z of spa-tim mdia ranging from Z μ Z (4) ε Thrfor, th natural rlatiisti impdan of grait or, Z of spa-tim mdia is inariant btwn quipotntial surfas Z 37.73Ω (43) William Alk Pag 4 9//7

43 Nwtonian Torsion Phsis INTAK, IN. 3.8 HOW GAVITY AFFT TH PD OF IGHT Th spd of light btwn spa-tim mdia (44) μ ε in it has bn shown th prmabilit μ and prmittiit ε of spa-tim mdia ar inariant btwn quipotntial surfas of grait, it follows th natural rlatiisti spd of light through spa-tim mdia ranging from position Δ to +Δ aluats to unit gain or, (45) μ ε Thrfor, th natural rlatiisti spd of light through spa-tim mdia is inariant btwn quipotntial surfas of grait or, m s (4) HOW GAVITY AFFT BOTZANN' ONTANT Th Boltzmann's onstant k is gin as, k (47) N in th Idal Gas onstant and Aogadro's Numbr it follows th natural rlatiisti Boltzmann's onstant k ranging from position gain or, N ar inariant btwn quipotntial surfas of grait, Δ to +Δ aluats to unit k k (48) N Thrfor, th natural rlatiisti Boltzmann's onstant k is inariant btwn quipotntial surfas of grait or, 3 k.3858 Jouls K (49) HOW GAVITY AFFT AN TI HAG A fundamntal ltri harg q is gin as, q f (5) Th ltri for f inrass with th squar of a drasing distan, and th ltri fild also inrass with th squar of a drasing distan at position + d. ikw th ltri for f drass with th squar of a William Alk Pag 43 9//7

44 Nwtonian Torsion Phsis INTAK, IN. 3.8 inrasing distan, and th ltri fild it follows th natural rlatiisti ltri harg q ranging from position also drass with th squar of a inrasing distan at position Δ to d, +Δ aluats to unit gain or, q f q (5) Thrfor, th natural rlatiisti ltri harg q is inariant btwn quipotntial surfas of grait or, q oul (5) HOW GAVITY AFFT TH FIN TUTU ONTANT Th Fin trutur onstant α q α (53) ε h in an ltri harg q, th spd of light, th prmittiit ε, and Plank's onstant h ar inariant btwn quipotntial surfas of grait, it follows th natural rlatiisti Fin trutur onstant α ranging from position Δ to +Δ aluats to unit gain or, α q α (54) ε h Thrfor, th natural rlatiisti Fin trutur onstant grait or, α is inariant btwn quipotntial surfas of α (55) William Alk Pag 44 9//7

45 Nwtonian Torsion Phsis INTAK, IN. 3.8 A TYPIA TOAGNTI WAV B FAT PA-TI DIA t FIGU 7. Propagation of ltromagnti wa in flat spa-tim. B t t FIGU 8. Tpial B and Filds. William Alk Pag 45 9//7

46 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 ltromagnti wa in rarfid spa-tim. B t t FIGU. Inrasing magnitud and frqun of B and Filds b graitational funtion. William Alk Pag 4 9//7

47 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 ltromagnti wa in omprssing spa-tim. B t t FIGU. Drasing magnitud and frqun of B and Filds b graitational funtion. William Alk Pag 47 9//7

48 Nwtonian Torsion Phsis INTAK, IN. 3.8 FIGU 3. A Global Positioning atllit. ampl 5. A Global Positioning atllit (GP) transmits an ltromagnti signal at a frqun f λ AT of ~.3Hz down to th arth from an altitud of,8.8km, and has an orbital loit of km s. Th natural rlatiisti BU HIFT du to grait and th spial rlatiisti D HIFT du to loit hangs th frqun of this transmittd signal. o, gin th orrtd transmittd frqun f λ AT, omput th BU HIFT and D HIFT suh that a ground-basd rir will rad a signal f λ X that is prisl 3. Hz. Th signal frqun of th satllit is adjustabl down to μ Hz. o, gin, Altitud of satllit Δ.88 m 3 Orbital loit m s orrtd frqun of satllit f Hz λ AT ir loatd on surfa of arth.378 m 8 pd of light m s Graitational onstant G.7 Nm kg 4 ass of th arth kg Th initial radius of th satllit abo th arth m m m +Δ (5) William Alk Pag 48 9//7

49 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th alration du to grait at altitud.549 m abo th arth g 4 (.7 N m kg )( kg ) (.549 m) G.553m s (57) Th alration du to grait at altitud 7.59 m abo th arth g 4 (.7 N m kg )( kg ) (.378 m) G 9.85m s (58) Gin th ponntial solution of th natural rlatiisti frqun modl, th graitational BU HIFTD frqun ( 9.85m s )(.378 m) (.553m s )(.549 m) g g 8 ( m s) f f Hz (59) λ λ ( ) f Hz f () λ λ Gin th ponntial solution of th spial rlatiisti frqun modl, th D HIFTD frqun of th BU HIFTD frqun omputd abo 3 ( m s) 8 ( m s) f f Hz () λ λ ( ) f 3. Hz f () λ o, a ground-basd rir will rad a signal that is prisl 3. Hz with a satllit frqun f λ AT gin abo. λx FIGU 4. A onstllation of 4 Global Positioning atllits (GP) orbiting th arth. William Alk Pag 49 9//7

50 Nwtonian Torsion Phsis INTAK, IN. 3.8 GAVITOAGNTI THOY P db r UNT NT θ AGNTI INDUTION I d FIGU 5. Th magnti indution produd b a positi urrnt lmnt. A onstant positi ltri urrnt I must rat a stabl magnti fild B around a wir. This stabl fild is du to th flow of ltri urrnt shown abo. Th hang of magnti indution db at a fid point P produd b a urrnt lmnt d is alulatd using th Biot-aart s aw, db μ I d r 4π r (3) 3 Or, μ I sin ( θ ) d db (4) 4π r in harg q is quantizd in a singl ltron passing a fid point pr hang of tim dt or, thn, ltri urrnt I is dfind as quantit N of hargs dq d N I q (5) dt dt And loit of an ltron passing a fid point is dfind as hang of distan d pr hang of tim dt or, d () dt William Alk Pag 5 9//7

51 Nwtonian Torsion Phsis INTAK, IN. 3.8 Thn, th ltri urrnt I is rdfind as, d( N ) I (7) d o, th hang of magnti indution db at a fid point P produd b quantit N of hargs loit moing at db μ sin ( θ ) d( N ) (8) 4π r To find th magnti indution B produd b a singl ltron at point P whn θ 9 intgrat, and N, thn μ B 4π r db (9) Th total nrg dnsit u B of magnti fild B ontaind within olum V u B U B B V μ (7) Thrfor, th total fild nrg Th hang of magnti fild nrg Th total nrg U B of magnti fild B ontaind within olum V U ontaind within mattr B B μ V V (7) 4 μ 3π r du B ontaind within a hang of olum d V B μ du B d V d V (7) 4 μ 3π r (73) quat total magnti fild nrg U B to th total nrg U B ontaind within mattr, (74) o, th hang of magnti fild nrg du B du B d B (75) William Alk Pag 5 9//7

52 Nwtonian Torsion Phsis INTAK, IN. 3.8 Thrfor, th flutuating magnti mass d B ontaind within a hang of olum d V d B ( ) du μ B d V (7) 4 3π r ω r ma r min FIGU. Th olum V of an ltron is modld as a hollow sphroid. in th nrg of an ltron is finit, no fild omponnt an b prsnt at its ntr. o, th olum of an ltron is modld as a hollow sphroid, Th flutuating magnti mass π rma rmin ma V π sin ω d ω r dr 4π r dr (77) r rmin d B ontaind within a hang of olum d V of a hollow sphroid ( ) μ ( ) r ma (78) rma ( 4π r ) 4 min rmin μ d B d r dr d dr 3π r 8π r Gin th radius of a flutuating magnti mass r, th driati form of a moing ltron r d ranging from a lassi ltron radius r to infinit, or Th flutuating magnti mass d B d B ( ) μ dr 8π (79) r r d B ( ) μ (8) 8π r William Alk Pag 5 9//7

53 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, gin th rst mass of an ltron moing at loit is, th diffrn form of th spial rlatiisti mass of an ltron γ ± d ± (8) B quating th flutuating magnti mass d B to th spial rlatiisti mass d, Th quation rdus to, ( ) μ (8) 8π r ( ) o, gin, 7 Prmabilit of fr spa μ 4π H m Fundamntal harg of an ltron.77 5 lassi ltron radius r.8794 m st mass of an ltron μ (83) 8π r 3 kg 9 ( π ) 5 8π (.8794 m) H m kg (84) This shows th flutuating magnti mass of a moing ltron is idntial to th spial rlatiisti mass at an loit, Thrfor, th flutuating magnti mass (85) d B is th flutuating mass d B d of an ltron, d (8) o, th magnti mass B and th mass of th ltron B ( ) μ (87) 4π r And th flutuating magnti mass Δ B and th flutuating mass Δ ( ) μ ( ) μ B 8π r 4π r Δ Δ (88) William Alk Pag 53 9//7

54 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, th loit of an ltron π r Δ Δ (89) μ ( ) Thrfor, if th flutuating mass is positi, thn th loit of th ltron is ral. Howr, if th flutuating mass is ngati, thn th loit 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 magnti flutuating mass. Now, th diffrn form of th inrtial D HIFT (or BU HIFT) of th magnti mass Δ B B and th mass Δ of a partil moing at a loit Δ B Δ (9) B A partil an mo at a ral (i.., tim-forward) loit, at an imaginar (i.., tim-futur) loit j, or at a loit that is a ombination of th two. Th ral and imaginar omponnts ar rotatd about th tmporal ais and thrfor, an b dsribd as ompl 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 ompl numbr uss th ulr s idntit θ, whih funtions as a tmporal rotation oprator. Th ompl loit Gin th rst mass of an ltron rlatiisti magnti mass jθ osθ + jsinθ (9) or th lassi ltron radius r, th diffrn forms of th spial, whr θ 9 ar, modl of a partil moing at a ompl loit ±Δ ± ( ) μ ( ) 4π r 4π r μ ±Δ ± (9) (93) William Alk Pag 54 9//7

55 Nwtonian Torsion Phsis INTAK, IN. 3.8 Now, appl th nw Prinipl of quialn Thorm whr th flutuating magnti mass of a moing ltron is quialnt to natural rlatiisti mass du to th arth s grait wll, μ ( ) ( g g ) Δ G (94) 8π r ( ) g g G (95) Th position of an ltron moing at a loit within arth s grait wll g Y whr < or G Δ g g + + g g (9) Δ + + G G (97) Th quialnt maimum ompl loit ma at ma G (98) Gin th quialnt maimum ompl loit ma, th minimum graitational mass min at G min + G (99) Th quialnt maimum flutuating graitational mass of th ltron ma min Δ at G Δ (3) o, th diffrn form of th graitational D HIFT (or BU HIFT) of th magnti mass Δ B B and th mass Δ of a partil displad a distan Δ within a gin grait wll g Y ( g g ) Δ Δ B (3) B William Alk Pag 55 9//7

56 Nwtonian Torsion Phsis INTAK, IN. 3.8 Gin th rst mass of an ltron or th lassi ltron radius r, th diffrn forms of th natural rlatiisti mass modl of a partil displad a distan Δ within a gin grait wll g Y ar, g g ( g g ) ±Δ ± g g ( ) ( g g ) μ ( ) μ ±Δ ± 4π r 4π r (3) (33) In summar, Graitomagnti Thor shows that a moing ltron produs an inras in rlatiisti mass that tnds from its lassi radius r to infinit, and oupls to grait. This motion an ithr ha a loit or a ompl (i.., tim-futur) loit j. If th loit is ompl, thn th ltron will hibit an antigraitational fft, and produ a ompl (i.., tim-futur) magnti fild jb. In addition, th total fild nrg U B of a ompl magnti fild jb ontaind within a olum V is NGATIV. ampl. An ltron moing through a wir at a tim-forward loit whr θ produs a timforward magnti indution B at a distan r. Gin, Dirtion of tim is forward θ Vloit of ltron through a wir. m s 7 Prmabilit of fr spa μ 4π H m 9 Fundamntal harg of an ltron.77 3 st mass of an ltron kg adius r.m Graitational onstant G.7 Nm kg adius of surfa of arth.378 m ass of th arth Th tim-forward loit, whr θ 4 kg m m Th tim-forward magnti indution B at distan r B jθ j. s. s (34) 7 9 ( 4π H m)(.77 )(. m s) μ 4π r 4π. (35) ( m) B 8.77 T (3) William Alk Pag 5 9//7

57 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th POITIV flutuating mass Δ of th ltron (. m s) 8 ( m ) Δ kg s 3 ( ) (37) 5 Δ kg (38) Appling th nw Prinipl of quialn Thorm, (.378 m) (.378 )(. s) 4 ( Nm kg )( kg) + m m G (39) o, th quialnt POITIV displamnt m (3) Δ is graitational within th arth s grait wll Δ m (3) 5.98 ampl 7. An ltron moing through a wir at a tim-adand loit whr < θ < 9 produs a tim-adand magnti indution B at a distan r. Gin, Dirtion of tim is adand θ 45 Vloit of ltron through a wir. m s 7 Prmabilit of fr spa μ 4π H m 9 Fundamntal harg of an ltron.77 3 st mass of an ltron kg adius r.m Graitational onstant G.7 Nm kg adius of surfa of arth.378 m 4 ass of th arth kg Th tim-adand loit, whr θ 45 m j m jθ j s s (3) Th tim-adand magnti indution B at distan r B ( 4π H m)(.77 )( j m s) μ + 4π r 4π. (33) ( m) 8 8 B j T + (34) William Alk Pag 57 9//7

58 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th IAGINAY flutuating mass Δ of th ltron ( j m s ) ( m ) Δ kg s (35) Δ (3) j kg Appling th nw Prinipl of quialn Thorm, (.378 m) ( )( s) (.7 Nm 4 kg )( kg) + m j m G + (37) o, th quialnt IAGINAY displamnt Th maimum tim-futur loit m j m (38) Δ is shown to b non-graitational within th arth s grait wll Δ j m (39) 5.98 ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (3) j m (3) 4 ma.84 s ampl 8. An ltron moing through a wir at a tim-futur loit whr θ 9 produs a timfutur magnti indution B at a distan r. Gin, Dirtion of tim is futur θ 9 Vloit of ltron through a wir. m s 7 Prmabilit of fr spa μ 4π H m 9 Fundamntal harg of an ltron.77 3 st mass of an ltron kg adius r.m Graitational onstant G.7 Nm kg adius of surfa of arth.378 m ass of th arth Th tim-futur loit, whr θ 9 4 kg m j m jθ j9. s. s (3) William Alk Pag 58 9//7

59 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th tim-futur magnti indution B at distan r B 7 9 ( 4π H m)(.77 )(. j m s) μ (33) ( m) 4π r 4π. 8 B.77 j T (34) Th NGATIV flutuating mass Δ of th ltron (. j m s) 8 ( m ) Δ kg s 3 ( ) (35) 5 Δ kg (3) Appling th nw Prinipl of quialn Thorm, (.378 m) (.378 )(. s) 4 ( Nm kg )( kg) + m j m G (37) o, th quialnt NGATIV displamnt.3785 m (38) Δ is antigraitational within th arth s grait wll Th maimum tim-futur loit Δ m (39) 5.98 ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (33) j m (33) 4 ma.84 s William Alk Pag 59 9//7

60 Nwtonian Torsion Phsis INTAK, IN. 3.8 TH ATIVITY OF OBITA PIN z ω r P r P A linar spa-tim intral is dfind as, FIGU 8. Th dfinition of a rotating spa-tim intral. ds + dr dt (33) in z, r + + z + (333) dr d + d + dz d + d (334) Aording to Fok (94), a rotating spa-tim intral is dfind as, This rdus to, osω t+ sinω t (335) sinω t+ osω t (33) ( ω ) ω ds + dt d d dt d + d + dz (337) ( ω ) ω ds r dt d d dt dr (338) William Alk Pag 9//7

61 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 omplt ompl Bohr modl of th Hdrogn atom. In th Bohr modl of th Hdrogn atom, ltrons mo at rlatiisti spds in disrt irular orbits around a nulus. It has bn dtrmind th inras in rlatiisti mass of th ltron is in th form of total magnti fild nrg produd b th irulating ltron. o, as a onsqun of this motion, a magnti indution B is produd at th ntr of th orbit. If an trnal magnti fild is applid to this indution, th loit of th ltron boms ompl b partiall rotating into th imaginar ais. Th loit of th ltron ma inras or dras as a funtion of th applid trnal fild. If th fild opposs th indution B, th ral loit will appar to dras as it rotats into th imaginar ais. If th ltron s loit is full rotatd into th imaginar ais and thrfor moing at a tim-futur loit j, a tim-futur magnti fild jb will mrg from th ntr. Th omplt ompl Bohr modl inluds th following haratristi quations shown blow. Ths quations ontain th ral and imaginar omponnts of a moing ltron that is rotatd about th tmporal ais as ompl motion. Th rotation is gin as θ 9, whr th ral ais is θ and th imaginar tim-futur ais is θ 9. Th ompl numbr uss th ulr s idntit o, gin, Dirtion of tim θ Frqun of orbit f Prmabilit of fr spa μ Fundamntal harg of an ltron lassi st Bohr orbital radius r st mass of an ltron pd of light Graitational onstant G an radius of surfa of arth ass of th arth an radius of surfa of un ass of th un UN j θ, whih funtions as a tmporal rotation oprator. William Alk Pag 9//7

62 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th ompl frqun of orbit f, whr θ 9 Th ompl Amprian urrnt i of th ltron Th ompl agnti Dipol omnt μ of th ltron jθ f f f osθ + j f sinθ (339) i f (34) μ π π (34) r i r f Th ompl angular loit ω of th ltron ω π f (34) Th ompl loit of th ltron rω π r f (343) Th ompl magnti fild B at th ntr 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 ) (344) μi μ μ μ f μ ω μ B (345) 3 r π r r 4π r 4π r Th magnti for F of th ltron dirtd upon th nulus F B (34) μ μ μ ω μ i μ 4 π ( ) f F μ π (347) π r 4π 4π r Th dirtion of ltron motion is suh that th magnti for F is an attrati for btwn th ltron and th nulus. Th spial rlatiisti mass of th irulating ltron ±Δ ± (348) William Alk Pag 9//7

63 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th hang in rlatiisti mass of th ltron produd b th irulating ltron. Δ is in th form of th hang in magnti fild nrg Δ U B Δ UB Δ Δ (349) Th diffrn form of th inrtial D HIFT (or BU HIFT) of th mass Δ of an ltron moing at a loit o, th ompl loit of th ltron Δ π r i μ π r f r ω (35) r r π F Δ (35) μ Th ompl Amprian urrnt i of th ltron i F Δ μ π π r (35) Th ompl agnti Dipol omnt μ of th ltron μ π F Δ r r (353) μ Th ompl frqun of orbit f of th ltron f F Δ (354) μ π π r Th ompl angular loit ω of th ltron π F Δ ω (355) μ r o, th ompl magnti for F of th ltron F dirtd upon th nulus ( ) ( ) ( ) Δ Δ ΔU B π r π r π r μ μ μ (35) And th diffrn form of th inrtial D HIFT (or BU HIFT) of th mass Δ of an ltron Δ π r F (357) μ William Alk Pag 3 9//7

64 Nwtonian Torsion Phsis INTAK, IN. 3.8 Appling th nw Prinipl of quialn Thorm, r ω π r f π r i μ π r F Δ (358) r o, th ompl loit of th ltron ( ) ( ) μ ( ) ( g ) g Δ G (359) ( ) g g G (3) Th ompl angular loit ω of th ltron ω ( g ) g G r r (3) Th ompl frqun of orbit f of th ltron f g g G π r π r (3) Th ompl Amprian urrnt i of th ltron g g G i π r π r (33) Th ompl agnti Dipol omnt μ of th ltron g g G μ r r (34) Th ompl magnti for F of th ltron dirtd upon th nulus μ μ g g G F π r π r (35) William Alk Pag 4 9//7

65 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th quialnt displamnt to position of an ltron moing at a loit within arth s grait wll g Y whr < or G g + G + g (3) 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 (37) (38) (39) (37) (37) Th diffrn form of th graitational D HIFT (or BU HIFT) of th mass Δ of a partil displad a distan Δ within arth s grait wll g Y ( g g ) Δ G (37) Gin th rst mass of an ltron displad a distan, th diffrn forms of th natural rlatiisti mass Δ within arth s grait wll g Y ar, modl of a partil g g ( g g ) ±Δ ± (373) William Alk Pag 5 9//7

66 Nwtonian Torsion Phsis INTAK, IN. 3.8 G ±Δ ± G (374) In summar, if th ral omponnt of th magnti fild is anlld, or B, du to an trnall applid magnti fild B XT, th loit of th irulating ltron is ompl, or j and a ompl magnti fild jb mrgs. This ompl magnti fild is blid to b prsnt in th Aharono-Bohm primnt, whih afftd j th flow of ltrons. Th ompl Amprian urrnt uss th tmporal rotation oprator or ulr s idntit θ, whr θ 9. As th motion of an ltron rotats from ral to imaginar, or θ 9, th ltrons spial rlatiisti mass Δ in th form of magnti fild nrg Δ U B drass. In addition, th ltrons rst mass as wll as its harg is inariant during alration or dlration. 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 ltron irulats around th nulus at a rlatiisti loit as shown abo. This rats a magnti indution B mrging from th ntr of th nulus. o, gin, Dirtion of tim is forward θ 5 Frqun of orbit f.8 Hz 7 Prmabilit of fr spa μ 4π H m Fundamntal harg of an ltron.77 lassi st Bohr orbital radius r m 3 st mass of an ltron kg 8 pd of light m s Graitational onstant G.7 Nm kg an radius of surfa of arth.378 m 9 William Alk Pag 9//7

67 Nwtonian Torsion Phsis INTAK, IN. 3.8 ass of th arth kg Th tim-forward frqun of orbit f, whr θ Th tim-forward Amprian urrnt i jθ 5 j 5 f f Hz Hz.8.8 (375) i f Hz Amps (37) Th tim-forward magnti fild B at th ntr 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 (377) (378) Th tim-forward angular loit ω of th ltron Th tim-forward loit of th ltron ω π π (379) 5 f.8 Hz 4.75 Hz rω m Hz m (38) Th tim-forward magnti for F of th ltron s dirtd upon th nulus 9 (.77 )(.945 s)( ) F B m T (38) F N (38) Th dirtion of ltron motion is suh that th magnti for F is alwas an attrati for btwn th ltron and th nulus. Th POITIV flutuating mass Δ of th ltron (.945 m s) 8 ( m ) 3 35 Δ ( kg) kg s (383) Th inrasd spial rlatiisti mass of th ltron kg kg kg +Δ + (384) William Alk Pag 7 9//7

68 Nwtonian Torsion Phsis INTAK, IN. 3.8 Appling th nw Prinipl of quialn Thorm, (.378 m) (.378 )(.945 s) 4 ( Nm kg )( kg) + m m G (385) o, th quialnt POITIV displamnt m (38) Δ is graitational within th arth s grait wll Δ m (387) 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-adand Bohr modl of th Hdrogn atom. ampl. In th tim-adand Bohr modl of th Hdrogn atom, th ral magnti fild ratd b an ltron irulating at rlatiisti spds is partiall anlld b an trnall applid magnti fild B XT. Th ltron rats b rotating its loit into th imaginar ais as shown abo. As a onsqun of this ompl loit j 45 j 45, a ompl magnti fild B mrgs. o, gin, Dirtion of tim θ 45 5 Frqun of orbit f.8 Hz 7 Prmabilit of fr spa μ 4π H m Fundamntal harg of an ltron.77 lassi st Bohr orbital radius r m 3 st mass of an ltron kg 8 pd of light m s Graitational onstant G.7 Nm kg 9 William Alk Pag 8 9//7

69 Nwtonian Torsion Phsis INTAK, IN. 3.8 an radius of surfa of arth.378 m 4 ass of th arth kg 8 an radius of surfa of un.9 m 3 ass of th un.9889 kg UN Th tim-adand frqun of orbit f, whr θ 45 Th tim-adand Amprian urrnt i jθ 5 j f f Hz j Hz (388) i f j Hz (389) 4-4 i j Amps + (39) Th tim-adand magnti fild B at th ntr 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) (39) Th tim-adand angular loit ω of th ltron B jt (393) 5 5 ω π f π j Hz (394) ω + j Hz (395) Th tim-adand loit of th ltron rω m j Hz (39) j m s (397) Th maimum tim-futur loit ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (398) j m (399) 4 ma.84 s William Alk Pag 9 9//7

70 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th tim-adand loit of th ltron Th maimum tim-futur loit far ds oupling 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 s Th tim-adand loit of th ltron Th tim-adand magnti for F of th ltron far ds oupling to un s grait wll! dirtd upon th nulus F B (4) 9 (.77 )( s)( ) F + j m + jt F j N (43) Th dirtion of ltron motion is tim-adand or rotatd into th futur suh that th magnti for F is alwas an attrati for btwn th ltron and th nulus. Th IAGINAY flutuating mass Δ of th ltron ( j m s ) ( m ) Δ kg s (44) Δ (45) j kg Th spial rlatiisti mass of th ltron 3 35 ( ) ( ) +Δ kg + j kg (4) j kg + (47) Appling th nw Prinipl of quialn Thorm, (.378 m) (.378 )( s) (.7 N m 4 kg )( kg ) + m j m G + (48) jm (49) William Alk Pag 7 9//7

71 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, th quialnt IAGINAY displamnt 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 magnti fild ratd b an ltron irulating at rlatiisti spds is bing anlld b an trnall applid magnti fild B XT. Th ltron rats b rotating its loit into th imaginar ais as shown abo. As a onsqun of this ompl loit j, a ompl magnti fild jb mrgs. o, gin, Dirtion of tim θ 9 5 Frqun of orbit f.8 Hz 7 Prmabilit of fr spa μ 4π H m Fundamntal harg of an ltron.77 lassi st Bohr orbital radius r m 3 st mass of an ltron kg 8 pd of light m s Graitational onstant G.7 Nm kg an radius of surfa of arth.378 m 4 ass of th arth kg 8 an radius of surfa of un.9 m 3 ass of th un.9889 kg UN Th tim-futur frqun of orbit f, whr θ 9 9 William Alk Pag 7 9//7

72 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th tim-futur Amprian urrnt i jθ 5 j9 5 f f Hz j Hz.8.8 (4) i f j Hz j Amps (4) Th tim-futur magnti fild B at th ntr 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 (43) (44) Th tim-futur angular loit ω of th ltron Th tim-futur loit of th ltron Th maimum tim-futur loit ω π π (45) 5 f.8 j Hz 4.75 j Hz rω m j Hz j m (4) s ma within th arth s grait wll 4 ( Nm kg )( kg) (.378 m) G ma (47) j m (48) 4 ma.84 s Th tim-futur loit of th ltron Th maimum tim-futur loit far ds oupling to arth s grait wll. ma within th un s grait wll 3 ( Nm kg )( kg) (.9 m) G (49) UN ma 8 j m (4) 5 ma.754 s Th tim-adand loit of th ltron Th magnti for F of th ltron far ds oupling to un s grait wll! dirtd upon th nulus William Alk Pag 7 9//7

73 Nwtonian Torsion Phsis INTAK, IN (.77 )(.945 s)( ) F B j m jt (4) F N (4) Th dirtion of ltron motion is tim-futur or rotatd into th futur suh that th magnti for F is alwas an attrati for btwn th ltron and th nulus. Th NGATIV flutuating mass Δ of th ltron (.945 j m s) 8 ( m ) 3 35 Δ ( kg) kg s (43) Th drasd spial rlatiisti mass of th ltron kg kg 9.93 kg +Δ + (44) Appling th nw Prinipl of quialn Thorm, (.378 m) (.378 )(.945 s) 4 ( Nm kg )( kg) + m j m G (45) o, th quialnt NGATIV displamnt 5.8 m (4) Δ is antigraitational within th arth s grait wll Δ m (47).3785 William Alk Pag 73 9//7

74 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 omplt ompl ltron drift loit modl in a oppr wir. If a oppr wir is onntd to a battr, an ltri fild will b st up at r point within th wir. This fild will at on ltrons and will gi thm a rsultant motion. An ltri urrnt I is stablishd if a nt harg q u passs through an ross stional ara A of th ondutor in tim t. Th ltri fild that ats on th ltrons dosn t produ a nt alration baus th ltrons kp olliding with th atoms that mak up th ondutor. Th ltrons, thrfor, mo at an arag drift loit. If th ltron drift loit j is timfutur, th assoiatd ltri fild j and magnti fild jb ar also tim-futur. Th omplt ompl ltron drift loit modl inluds th following haratristi quations shown blow. Ths quations ontain th ral and imaginar omponnts of a moing ltron that is rotatd about th tmporal ais as a ompl partil. Th rotation is gin as θ 9, whr th ral ais is θ and th imaginar tim-futur ais is θ 9. Th j ompl numbr uss th ulr s idntit θ, whih funtions as a tmporal rotation oprator. o, gin, Dirtion of tim θ urrnt flowing through a ondutor I Fundamntal harg of an ltron adius of oppr wir r Dnsit of ondutor matrial ( ) D atom Numbr of ondution ltrons pr atom of ondutor k atom Aogadro s Numbr N Atomi wight of ondutor matrial gmnt lngth of ondutor pd of light st mass of an ltron adius of surfa of arth Graitational onstant G ass of th arth W atom sistiit of ondutor matrial ( ) ρ atom Th ompl urrnt I flowing through a ondutor, whr θ 9 William Alk Pag 74 9//7

75 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th ompl urrnt dnsit J jθ I I Iosθ + jisinθ (48) J I I (49) A π r Th olum V of a sgmnt of a ondutor V A π r (43) Th quantit of ondution ltrons n atom in a olum of ondutor n D N k atom atom atom (43) Watom Th nt harg q atom in a olum of a ondutor q n V (43) atom atom Th ompl loit (433) t Th ompl urrnt I flowing through a ondutor q n V t atom atom I π r natom (434) o, th ompl drift loit of an ltron moing through a ondutor I J π rn n (435) atom atom Th flutuating mass Δ of th ltron Δ (43) Appling th nw Prinipl of quialn Thorm, ( g ) g Δ G (437) William Alk Pag 75 9//7

76 Nwtonian Torsion Phsis INTAK, IN. 3.8 g g G (438) ( ) g g G (439) Th quialnt displamnt to position of an ltron moing at a loit within arth s grait wll g Y whr < or G g + g (44) + G (44) Th rsistiit ρ Atom of a ondutor is gin as, ρ Atom V V (44) J I I A π r Th rsistan of a sgmnt of ondutor V ρ Atom ρatom (443) I A π r GNT OF OPP WI TON DIFT A r I A TPOA OTATION θ FIGU 34. Th tim-forward ltron drift loit in a oppr wir. William Alk Pag 7 9//7

77 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl. A tim-forward ltri urrnt I is stablishd if a nt harg q u passs through an ross stional ara A of th ondutor in tim-forward t. Th ltrons mo at an arag tim-forward drift loit. o, gin, Dirtion of tim θ urrnt through oppr wir I. Amps 9 Fundamntal harg of an ltron.77 3 adius of AWG oppr wir r.94 m 3 Dnsit of oppr ondutor ( ) Du 8.9 gm m Numbr of ondution ltrons pr atom of oppr ku ltron atom 3 Aogadro s Numbr N.37 atoms mol Atomi wight of oppr ondutor Wu 3.54 gm mol gmnt lngth m 8 pd of light m s 3 st mass of an ltron kg Graitational onstant G.7 Nm kg an adius of surfa of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of oppr ondutor ( ) Th tim-forward urrnt I flowing through a ondutor, whr θ Th tim-forward urrnt dnsit J j jθ I I. Amps. Amps (444) J (. Amps) I I.9 Amps m A π r π m 3 (.94 ) (445) Th olum V of a sgmnt of oppr wir 3 3 V A π r π.94 m m 5. m (44) Th quantit of ondution ltrons n u in a olum of oppr wir n u n D N k u u u (447) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( ltron atom) (448) ( 3.54gm mol) nu ltrons m (449) Th nt harg q u in a olum of oppr wir William Alk Pag 77 9//7

78 Nwtonian Torsion Phsis INTAK, IN. 3.8 u u ( )( 5. )(.7733 ) q n V ltrons m m (45) qu 4 7. (45) Th tim-forward loit (45) t Th tim-forward urrnt I flowing through a oppr wir qu nu V I π rnu π rnu. Amps t (453) o, th tim-forward drift loit of an ltron moing through a oppr wir (.9 Amps m ) ( )(.7733 ) I J π rn n ltrons m u u (454) 4.43 m s (455) Th POITIV flutuating mass Δ of th ltron 4 (.43 m s) 8 ( m ) Δ kg s 3 ( ) (45) 5 Δ 9.98 kg (457) Th POITIV flutuating mass of an ltron is almost 5 ordrs of magnitud blow its rst mass Appling th nw Prinipl of quialn Thorm,. (.378 m) 4 (.378 )(.43 s) 4 ( Nm kg )( kg) + m m G (458) o, th quialnt POITIV displamnt.378 m (459) Δ is graitational within th arth s grait wll 9 Δ m (4).87 Gin a tim-forward oltag V and a tim-forward urrnt I, th rsistiit ρ u of oppr wir is gin as, William Alk Pag 78 9//7

79 Nwtonian Torsion Phsis INTAK, IN. 3.8 ρ u V V J I A I π r 8.8 Ω (4) m Th rsistan of a sgmnt of oppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (4) GNT OF OPP WI TON DIFT j45 r j45 j45 j45 A j45 I A TPOA OTATION θ 45 FIGU 35. Th tim-adand ltron drift loit in a oppr wir. ampl 3. A tim-adand ltri urrnt I is stablishd if a nt harg q u passs through an ross stional ara A of th ondutor in tim-adand t. Th ltrons mo at an arag tim-adand drift loit. o, gin, Dirtion of tim θ 45 urrnt flow through oppr wir I. Amps 9 Fundamntal harg of an ltron.77 3 adius of AWG oppr wir r.94 m 3 Dnsit of oppr ondutor ( ) Du 8.9 gm m Numbr of ondution ltrons pr atom of oppr ku ltron atom 3 Aogadro s Numbr N.37 atoms mol Atomi wight of oppr ondutor Wu 3.54 gm mol gmnt lngth m 8 pd of light m s 3 st mass of an ltron kg Graitational onstant G.7 Nm kg an adius of surfa of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of oppr ondutor ( ) William Alk Pag 79 9//7

80 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th tim-adand urrnt I flowing through a ondutor, whr θ 45 Th tim-adand urrnt dnsit J j45 jθ I I. Amps jamps (43) ( jAmps) I I J A r j Amps m m π π 3 (.94 ) (44) Th olum V of a sgmnt of oppr wir A π r π.94 m m 5. m 3 3 V (45) Th quantit of ondution ltrons n u in a olum of oppr wir n u n D N k u u u (4) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( ltron atom) (47) ( 3.54gm mol) nu ltrons m (48) Th nt harg q u in a olum of a oppr wir u u ( )( 5. )(.7733 ) q n V ltrons m m (49) qu 4 7. (47) Th tim-adand loit (47) t Th tim-adand urrnt I flowing through a oppr wir qu nu V I π r nu j Amps t (47) o, th tim-adand drift loit of an ltron moing through a oppr wir ( j Amps m ) ( )(.7733 ) I J π rn n ltrons m u u (473) William Alk Pag 8 9//7

81 Nwtonian Torsion Phsis INTAK, IN. 3.8 j m s (474) Th flutuating mass Δ of th ltron ( j m s ) ( m ) Δ kg s (475) Δ (47) j kg Th flutuating mass of an ltron is almost 5 ordrs of magnitud bond its rst mass Appling th nw Prinipl of quialn Thorm, and is imaginar. (.378 m) ( )( s) (.7 N m 4 kg )( kg ) + m j m G + (477) o, th quialnt IAGINAY displamnt.378 m (478) Δ is shown to b non-graitational within th arth s grait wll 9 Δ j m (479).4 Gin a tim-adand oltag V and a tim-adand urrnt I, th rsistiit ρ u of oppr wir is gin as, ρ u V V J I A I π r 8.8 Ω (48) m Th rsistan of a sgmnt of oppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (48) William Alk Pag 8 9//7

82 Nwtonian Torsion Phsis INTAK, IN. 3.8 GNT OF OPP WI TON DIFT j j A r j j ji A TPOA OTATION θ 9 FIGU 3. Th tim-futur ltron drift loit in a oppr wir. ampl 4. A tim-futur ltri urrnt + ji is stablishd if a nt harg q u passs through an ross stional ara A of th ondutor in tim-futur t. Th ltrons mo at an arag tim-futur drift loit + j. o, gin, Dirtion of tim θ 9 urrnt flow through oppr wir I. Amps 9 Fundamntal harg of an ltron.77 3 adius of AWG oppr wir r.94 m 3 Dnsit of oppr ondutor ( ) Du 8.9 gm m Numbr of ondution ltrons pr atom of oppr ku ltron atom 3 Aogadro s Numbr N.37 atoms mol Atomi wight of oppr ondutor Wu 3.54 gm mol gmnt lngth m 8 pd of light m s 3 st mass of an ltron kg Graitational onstant G.7 Nm kg an adius of surfa of arth.378 m 4 ass of th arth kg 8 ρ u.8 Ω m sistiit of oppr ondutor ( ) Th tim-futur urrnt I flowing through a ondutor, whr θ 9 Th tim-futur urrnt dnsit J j9 jθ I I. Amps. j Amps (48) (. jamps) I I J A r.9 j Amps m m π π 3 (.94 ) (483) William Alk Pag 8 9//7

83 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th olum V of a sgmnt of oppr wir A π r π.94 m m 5. m 3 3 V (484) Th quantit of ondution ltrons n u in a olum of oppr wir n u n D N k u u u (485) Wu 3 3 ( 8.9 gm m )(.37 atoms mol)( ltron atom) (48) ( 3.54gm mol) nu ltrons m (487) Th nt harg q u in a olum of a oppr wir u u ( )( 5. )(.7733 ) q n V ltrons m m (488) qu 4 7. (489) Th tim-futur loit (49) t Th tim-futur urrnt I flowing through a oppr wir qu nu V I π r nu π r nu. j Amps t (49) o, th tim-futur drift loit of an ltron moing through a oppr wir (.9 j Amps m ) ( )(.7733 ) I J π rn n ltrons m u u (49) j m 4.43 s (493) Th NGATIV flutuating mass Δ of th ltron 4 (.43 j m s) 8 ( m ) Δ kg s 3 ( ) (494) 5 Δ 9.98 kg (495) William Alk Pag 83 9//7

84 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th NGATIV flutuating mass of an ltron is almost 5 ordrs of magnitud blow its rst mass Appling th nw Prinipl of quialn Thorm,. (.378 m) 4 (.378 )(.43 s) 4 ( Nm kg )( kg) + m j m G (49) o, th quialnt NGATIV displamnt.378 m (497) Δ is antigraitational within th arth s grait wll Δ m (498) 9.33 Gin a tim-futur oltag V and a tim-futur urrnt I, th rsistiit ρ u of oppr wir is gin as, ρ u V V J I A I π r 8.8 Ω (499) m Th rsistan of a sgmnt of oppr wir ( m) V 8 3 u (.8 m) I ρ A Ω 3.93 Ω m π 3 (.94 ) (5) William Alk Pag 84 9//7

85 Nwtonian Torsion Phsis INTAK, IN. 3.8 OPX ITO I + j V θ - V + - FIGU 37. Th omplt ompl rsistor. j Gin a ompl oltag sour V with a tmporal rotation oprator θ, whr θ 9 is ating upon th oltag, a ompl dirt urrnt flows through rsistor. A ompl oltag V appars aross th rsistor. Th rsulting instantanous powr P is dissipatd or absorbd b th rsistor. o, gin, Dirtion of tim θ Voltag suppl V sistor Th ompl oltag suppl V Th ompl urrnt I flowing through rsistor jθ V V V osθ + jvsinθ (5) Th ompl oltag V aross rsistor Th rsistan I V (5) V I V (53) V (54) I Th instantanous powr P dissipatd and/or absorbd b th rsistor V P V I I (55) William Alk Pag 85 9//7

86 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl 5. Gin a tim-forward oltag sour V and a known rsistor alu, omput th tim-forward urrnt and powr dissipatd b th rsistor. o, gin, Dirtion of tim θ Voltag our V.Volts sistor.5ω Th tim-forward oltag V Th tim-forward urrnt I j jθ V V.Volts.Volts (5) I (.Volts) (.5Ω) V 4. Amps (57) Th instantanous powr P dissipatd b th rsistor ( Volts) (.5Ω) V. P 4.Watts (58) ampl. Gin a tim-adand oltag sour V and a known rsistor alu, omput th tim-adand urrnt and powr bing dissipatd and absorbd b th rsistor. o, gin, Dirtion of tim θ 45 Voltag our V.Volts sistor.5ω Th tim-adand oltag V Th tim-adand urrnt I j45 jθ V V.Volts jvolts (59) 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 adiabati. William Alk Pag 8 9//7

87 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl 7. Gin a tim-futur oltag sour V and a known rsistor alu, omput th tim-futur urrnt and instantanous powr absorbd b th rsistor. o, gin, Dirtion of tim θ 9 Voltag our V.Volts sistor.5ω Th tim-futur oltag V Th tim-futur urrnt I j9 jθ V V.Volts. jvolts (5) I (. jvolts) (.5Ω) V 4. jamps (53) Th instantanous powr P absorbd b th rsistor ( jvolts) (.5Ω) V. P 4.Watts (54) OPX INDUTO i t s + + j V θ FIGU 38. Th omplt ompl magntizing indutor. j Gin a ompl oltag sour V with a tmporal rotation oprator θ, whr θ 9 is ating upon th oltag, whn swith loss at t s, a ompl dirt urrnt i flows through rsistor and magntizs indutor. A ompl oltag appars aross th rsistor and a ompl oltag appars aross indutor. Th rsulting instantanous powr P is dissipatd and/or absorbd b th rsistor, th instantanous powr P stord in th indutor, and th nrg stord in th indutor. o, gin, Dirtion of tim θ Tim t Voltag suppl V Indutor William Alk Pag 87 9//7

88 Nwtonian Torsion Phsis INTAK, IN. 3.8 sistor Th ompl oltag suppl V Th ompl oltag aross th rsistor Th ompl oltag aross th indutor jθ V V V osθ + jvsinθ (55) t i t (5) di (57) () t dt tting t s, th ompl urrnt i flowing through th rsistor and th indutor di + + (58) () () () V t t i t dt V () t di dt i + (59) 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 (5) (53) (54) (55) William Alk Pag 88 9//7

89 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P dissipatd and/or absorbd b th rsistor V P() t () t i() t i () t t (5) Th instantanous powr P stord in th indutor di P() t () t i() t i V i() t i () t (57) dt t t t t t t V V V V P () t (58) tting t s, th nrg stord in th indutor di t P dt i dt i di i t i t dt t t i() t () () ( ) t t i( t ) (59) V t t t t V V () t V () t t (53) (53) ampl 8. Gin a tim-forward oltag sour V, a known rsistor alu and indutor alu, omput th tim-forward urrnt and powr dissipatd b th rsistor, and th nrg stord in th indutor. o, gin, Dirtion of tim θ Tim.s t.s Voltag suppl V.Volts Indutor 47mH sistor.5ω Th tim-forward oltag suppl V j jθ V V.Volts.Volts (53) Th tim-forward urrnt i flowing through th rsistor and th indutor at t.s (.Volts) (.5Ω) (.5Ω) t ( 47 mh ) V t i () t (533) i.s 3.98 Amps (534) William Alk Pag 89 9//7

90 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P dissipatd b th rsistor at t.s (.5Ω) t ( 47 mh ) (.Volts) (.5Ω) V t P () t (535) P.s 39.9Watts (53) Th instantanous powr P stord in th indutor at t.3s and at t.s (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) (.Volts) (.5Ω) V P () t (537) P P.3s.Watts (538).s.95Watts (539) Th nrg stord in th indutor from t.s to t.s (.5Ω) t t ( 47 mh ) ( 47 mh )(.Volts) ( Ω) V () t.5 (54).s 3.73 Jouls (54) ampl 9. Gin a tim-adand oltag sour V, a known rsistor alu and indutor alu, omput th tim-adand urrnt and powr dissipatd and absorbd b th rsistor, and th nrg stord in th indutor. o, gin, Dirtion of tim θ 45 Tim.s t.s Voltag suppl V.Volts Indutor 47mH sistor.5ω Th tim-adand oltag suppl V j45 jθ V V.Volts jvolts (54) Th tim-adand urrnt i flowing through th rsistor and th indutor at t.s ( jVolts) (.5Ω) (.5Ω) t ( 47 mh ) V t i () t (543) i.s j Amps (544) William Alk Pag 9 9//7

91 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P dissipatd and absorbd b th rsistor at t.s (.5Ω) t ( 47 mh ) ( jVolts) (.5Ω) V t P () t (545) P.s 39.9 jwatts (54) Th instantanous powr P stord in th indutor at t.3s and at t.s (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) ( jvolts) (.5Ω) V P () t (547) P P.3s. jwatts (548).s.95 jwatts (549) Th nrg stord in th indutor from t.s to t.s (.5Ω) t t ( 47 mh ) ( 47 mh )( jvolts) ( Ω) V () t.5 (55).s 3.73 j Jouls (55) ampl. Gin a tim-futur oltag sour V, a known rsistor alu and indutor alu, omput th tim-futur urrnt and powr absorbd b th rsistor, and th ngati nrg stord in th indutor. o, gin, Dirtion of tim θ 9 Tim.s t.s Voltag suppl V.Volts Indutor 47mH sistor.5ω Th tim-futur oltag suppl V j9 jθ V V.Volts. jvolts (55) Th tim-futur i flowing through th rsistor and th indutor at t.s (. jvolts) (.5Ω) (.5Ω) t ( 47mH ) V t i () t (553) i.s 3.98 j Amps (554) William Alk Pag 9 9//7

92 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P absorbd b th rsistor at t.s (.5Ω) t ( 47 mh ) (. jvolts) (.5Ω) V t P () t (555) P.s 39.9Watts (55) Th instantanous powr P stord in th indutor at t.3s and at t.s (.5Ω) (.5Ω) t t t t ( 47 mh ) ( 47 mh ) (. jvolts) (.5Ω) V P () t (557) P P.3s.Watts (558).s.95Watts (559) Th nrg stord in th indutor from t.s to t.s (.5Ω) t t ( 47 mh ) ( 47mH )(. jvolts) ( Ω) V () t.5 (5).s 3.73 Jouls (5) i t s Gin nrg oltag, whn swith loss at FIGU 39. Th omplt ompl dmagntizing indutor. stord in indutor with a tmporal rotation oprator j θ, whr 9 θ is ating upon th t s, a ompl dirt urrnt i flows through rsistor. Th indutor dmagntizs into th rsistor. A ompl oltag appars aross th rsistor. Th rsulting instantanous powr P and nrg o, gin, Dirtion of tim θ Tim t Initial urrnt through indutor I Indutor sistor ar dissipatd and/or absorbd b th rsistor. William Alk Pag 9 9//7

93 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th ompl urrnt I through th indutor At t s, th oltag V aross th rsistor jθ I I Iosθ + jisinθ (5) V I (53) Th ompl oltag aross th rsistor Th ompl oltag aross th indutor t i t (54) di (55) () t dt tting t s, th ompl urrnt i flowing through th rsistor and th indutor it () t t (5) di (57) () i t dt i di (58) dt () t di dt (59) 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 (57) i ( t) ( t t ) I (573) () t i t I (574) William Alk Pag 93 9//7

94 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P dissipatd and/or absorbd b th rsistor () () () () t P t t i t i t I (575) tting t s, th nrg dissipatd and/or absorbd b th rsistor () t t t t t (57) t P dt I dt t t t t I () t I I I () t t (577) (578) ampl. Gin a tim-forward oltag V aross indutor, a known rsistor alu and indutor alu, omput th tim-forward urrnt flowing through th rsistor, and th powr and nrg dissipatd b th rsistor. o, gin, Dirtion of tim θ Tim.s t.s Initial urrnt through indutor I 4. Amps Indutor 47mH sistor.5ω Th tim-forward urrnt I through th indutor j jθ I I 4. Amps 4. Amps (579) Th tim-forward urrnt i flowing through th rsistor and th indutor at t () (.5Ω) t ( 47 mh ) t.s and at t.s i t I 4. Amps (58) i i.s 4. Amps (58).s. Amps (58) Th instantanous powr P dissipatd b th rsistor at t.s and at t.s t ().5 ( Ω) t ( 47 mh ) P t I.5Ω 4. Amps (583) P P.s 4.Watts (584) 4 (.s) 9.59 Watts (585) William Alk Pag 94 9//7

95 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th nrg dissipatd b th rsistor at t.s.5 ( Ω) t ( 47 mh )( 4. Amps) t ( 47 mh ) I () t (58).s 3.7 Jouls (587) ampl. Gin a tim-adand oltag V aross indutor, a known rsistor alu and indutor alu, omput th tim-adand urrnt flowing through th rsistor, and th powr and nrg dissipatd and absorbd b th rsistor. o, gin, Dirtion of tim θ 45 Tim.s t.s Initial urrnt through indutor I 4. Amps Indutor 47mH sistor.5ω Th tim-adand urrnt I through th indutor j45 jθ I I 4. Amps jamps (588) Th tim-adand urrnt i flowing through th rsistor and th indutor at t () (.5Ω) t ( 47 mh ) t.s and at t.s i t I j Amps (589) i i.s j Amps (59).s j Amps (59) Th instantanous powr P dissipatd and absorbd b th rsistor at t.s and at t.s Th nrg t ().5 ( Ω) t ( 47 mh ) P t I.5Ω j Amps (59) P.s 4. jwatts (593) 4 (.s) 9.59 P j Watts (594) dissipatd and absorbd b th rsistor at t.s and at t.s.5 ( Ω) t ( 47 mh )( j Amps) t ( 47 mh ) I () t (595).s 3.7 j Jouls (59) William Alk Pag 95 9//7

96 Nwtonian Torsion Phsis INTAK, IN. 3.8 ampl 3. Gin a tim-futur oltag V aross indutor, a known rsistor alu and indutor alu, omput th tim-futur urrnt flowing through th rsistor, and th powr and nrg absorbd b th rsistor. o, gin, Dirtion of tim θ 9 Tim.s t.s Initial urrnt through indutor I 4. Amps Indutor 47mH sistor.5ω Th tim-futur urrnt I through th indutor j9 jθ I I 4. Amps 4. jamps (597) Th tim-futur urrnt i flowing through th rsistor and th indutor at t.s and at t.s t () (.5Ω) t ( 47 mh ) i t I 4. j Amps (598) i i.s 4. j Amps (599).s. j Amps () Th instantanous powr P absorbd b th rsistor at t.s and at t.s Th nrg t ().5 ( Ω) t ( 47 mh ) P t I.5Ω 4. j Amps () P P.s 4.Watts () 4 (.s) 9.59 absorbd b th rsistor at t.s and at t.s Watts (3).5 ( Ω) t ( 47mH )( 4. j Amps) t ( 47mH ) I () t (4).s 3.7 Jouls (5) William Alk Pag 9 9//7

97 Nwtonian Torsion Phsis INTAK, IN. 3.8 OPX APAITO i t s + + j V θ FIGU 4. Th omplt ompl harging apaitor. j Gin a ompl oltag sour V with a tmporal rotation oprator θ, whr θ 9 is ating upon th oltag, whn swith loss at t s, a ompl dirt urrnt flows through rsistor and hargs apaitor. A ompl oltag appars aross th rsistor and a ompl oltag appars aross apaitor. Th rsulting powr P is dissipatd and/or absorbd b th rsistor and th nrg o, gin, Dirtion of tim θ Tim t Voltag suppl V apaitor sistor Th ompl oltag suppl V Th ompl oltag aross th rsistor Th ompl urrnt i through a apaitor is stord in th apaitor. jθ V V V osθ + jvsinθ () t i t (7) d (8) () i t dt tting t s, th ompl oltag aross th apaitor V t + t i t + t (9) d () () t V dt d dt t V () () William Alk Pag 97 9//7

98 Nwtonian Torsion Phsis INTAK, IN. 3.8 () t t d dt t () t V () () t t ln ( () t V) t (3) t t V ln ( () t V) ln ( V) ln tt V ( t t ) t t V V t V V V t t () (4) (5) () Th instantanous powr P dissipatd and/or absorbd b th rsistor Th instantanous powr P stord in th apaitor () ( V ()) t t V t P() t () t i () t (7) () () () d dt ( V t ( t) ) (8) P t t i t t t t t t t V V V V P () t (9) tting t s, th nrg stord in th apaitor 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 () () ampl 4. Gin a tim-forward oltag sour V, a known rsistor alu and apaitor alu, omput th tim-forward urrnt and powr dissipatd b th rsistor, and th nrg stord in th indutor. o, gin, Dirtion of tim θ William Alk Pag 98 9//7

99 Nwtonian Torsion Phsis INTAK, IN. 3.8 Tim.s t.s Voltag suppl V.Volts apaitor 47 μf sistor.kω Th tim-forward oltag suppl V j Th tim-forward oltag aross th apaitor at t.s jθ V V.Volts.Volts (3) t t (.kω)( 47 μf) () t V (.Volts) (4).s 8.89Volts (5) Th instantanous powr P dissipatd b th rsistor at t.s and at t.s (.Volts) (.kω) V t P () t t (. kω)( 47μF) () P P.s.Watts (7) 3 (.s).49 Th instantanous powr P stord in th apaitor at Watts (8) t.33s and at t.s (.Volts) (. kω) V t t t t (. kω)( 47 μf) (. kω)( 47 μf) P () t (9) P P.33s.45Watts (3).s.5Watts (3) Th nrg stord in th apaitor from t.s to t.s ( 47 μf )(.Volts) (. kω)( 47 μf) V t t () t (3).8 t Jouls (33) ampl 5. Gin a tim-adand oltag sour V, a known rsistor alu and apaitor alu, omput th tim-adand urrnt and powr dissipatd and absorbd b th rsistor, and th nrg stord in th indutor. o, gin, William Alk Pag 99 9//7

100 Nwtonian Torsion Phsis INTAK, IN. 3.8 Dirtion of tim θ 45 Tim.s t.s Voltag suppl V.Volts apaitor 47 μf sistor.kω Th tim-adand oltag suppl V j45 Th tim-adand oltag aross th apaitor at jθ V V.Volts jvolts (34) t.s t t (. kω)( 47 μf) () t V ( jvolts) (35).s jvolts (3) Th instantanous powr P dissipatd and absorbd b th rsistor at t.s and at t.s ( jVolts) (.kω) V t P () t t (. kω)( 47μF) (37) P.s. jwatts (38) 3 (.s).49 Th instantanous powr P stord in th apaitor at P j Watts (39) t.33s and at t.s ( jVolts) (.kω) V t t t t (. kω)( 47 μf) (.kω)( 47 μf) P () t (4) P P.33s.45 jwatts (4).s.5Watts (4) Th nrg stord in th apaitor from t.s to t.s ( 47 μf )( jvolts) (. kω)( 47 μf) V t t () t (43).8 t jjouls (44) ampl. Gin a tim-futur oltag sour V, a known rsistor alu and apaitor alu, omput th tim-futur urrnt and powr absorbd b th rsistor, and th nrg stord in th indutor. William Alk Pag 9//7

101 Nwtonian Torsion Phsis INTAK, IN. 3.8 o, gin, Dirtion of tim θ 9 Tim.s t.s Voltag suppl V.Volts apaitor 47 μf sistor.kω Th tim-futur oltag suppl V Th tim-futur oltag aross th apaitor at j9 jθ V V.Volts. jvolts (45) t.s t t (. kω)( 47 μf) () t V (. jvolts) (4).s 8.89 jvolts (47) Th instantanous powr P absorbd b th rsistor at t.s and at t.s (. jvolts) (.kω) V t P () t t (. kω)( 47μF) (48) P P.s.Watts (49) 3 (.s).49 Th instantanous powr P stord in th apaitor at Watts (5) t.33s and at t.s (. jvolts) (.kω) V t t t t (.kω)( 47 μf) (. kω)( 47 μf) P () t (5) P P.33s.45Watts (5).s.5Watts (53) Th nrg stord in th apaitor from t.s to t.s ( 47 μf )(. jvolts) (. kω)( 47 μf) V t t () t (54).8 t Jouls (55) William Alk Pag 9//7

102 Nwtonian Torsion Phsis INTAK, IN. 3.8 i t s Gin nrg th oltag, whn swith loss at FIGU 4. Th omplt ompl disharging apaitor. stord in apaitor with a tmporal rotation oprator j θ, whr θ 9 is ating upon t s, a ompl dirt urrnt i flows through rsistor. Th apaitor dishargs into th rsistor. A ompl oltag appars aross th rsistor. Th rsulting instantanous powr P and nrg o, gin, Dirtion of tim θ Tim t Initial oltag aross apaitor V apaitor sistor At ar dissipatd and/or absorbd b th rsistor. t s, th oltag V aross th rsistor V I (5) Th ompl oltag aross th rsistor Th ompl urrnt i through a apaitor t i t (57) d (58) () i t dt tting t s, th ompl oltag aross th apaitor d (59) () () () t t i t dt d dt () t () () t t d dt V t () t () William Alk Pag 9//7

103 Nwtonian Torsion Phsis INTAK, IN. 3.8 () t t ln ( () t ) t () V t ( t) ln ( () t ) ln ( V ) ln tt V (3) ( t) ( t t ) t V (4) () t Th instantanous powr P dissipatd and/or absorbd b th rsistor t V (5) t t V P() t () t i () t () tting t s, th nrg dissipatd and/or absorbd b th rsistor t t V t () t P t dt dt t (7) V t t t t V () t V () t V t (8) (9) ampl 7. Gin a tim-forward oltag V aross apaitor, a known rsistor alu and apaitor alu, omput th tim-forward urrnt flowing through th rsistor, and th powr and nrg dissipatd b th rsistor. o, gin, Dirtion of tim θ Tim.s t.s Initial oltag aross apaitor V.Volts apaitor 47 μf sistor.kω Th tim-forward oltag V aross th apaitor Th tim-forward oltag aross th apaitor j jθ V V.Volts.Volts (7) t () t (. kω)( 47 μf) t V.Volts (7) William Alk Pag 3 9//7

104 Nwtonian Torsion Phsis INTAK, IN. 3.8.s.Volts (7).s.9Volts (73) Th instantanous powr P dissipatd b th rsistor at t.s and at t.s t. ( Volts) (.kω) V P () t t (. kω)( 47μF) (74) Th nrg P dissipatd b th rsistor at P.s.Watts (75) 3 (.s).49 Watts (7) t.s and at t.s ( μf )( Volts) (. kω)( 47 μf) V t 47. t () t (77).s.3 Jouls (78) ampl 8. Gin a tim-adand oltag V aross apaitor, a known rsistor alu and apaitor alu, omput th tim-adand urrnt flowing through th rsistor, and th powr and nrg dissipatd and absorbd b th rsistor. o, gin, Dirtion of tim θ 45 Tim.s t.s Initial oltag aross apaitor V.Volts apaitor 47 μf sistor.kω Th tim-adand oltag V aross th apaitor j45 Th tim-adand oltag aross th apaitor jθ V V.Volts jVolts (79) t () t (. kω)( 47 μf) t V jvolts (8).s jvolts (8).s jvolts (8) William Alk Pag 4 9//7

105 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th instantanous powr P dissipatd and absorbd b th rsistor at t.s and at t.s ( + jvolts) (.kω) V P () t t t (. kω)( 47μF) (83) Th nrg P.s. jwatts (84) 3 (.s).49 P j Watts (85) dissipatd and absorbd b th rsistor at t.s and at t.s ( μf )( + jvolts) (. kω)( 47 μf) V t t () t (8).s.3 j Jouls (87) ampl 9. Gin a tim-futur oltag V aross apaitor, a known rsistor alu and apaitor alu, omput th tim-futur urrnt flowing through th rsistor, and th powr and nrg absorbd b th rsistor. o, gin, Dirtion of tim θ 9 Tim.s t.s Initial oltag aross apaitor V.Volts apaitor 47 μf sistor.kω Th tim-futur oltag V aross th apaitor Th tim-futur oltag aross th apaitor j9 jθ V V.Volts. jvolts (88) t () t (. kω)( 47 μf) t V. jvolts (89).s. jvolts (9).s.9 jvolts (9) Th instantanous powr P absorbd b th rsistor at t.s and at t.s t. ( jvolts) (.kω) V P () t t (.kω)( 47μF) (9) P.s.Watts (93) William Alk Pag 5 9//7

106 Nwtonian Torsion Phsis INTAK, IN. 3.8 Th nrg P 3 (.s).49 absorbd b th rsistor at t.s and at t.s Watts (94) ( μf)( jvolts) (. kω)( 47 μf) V t 47. t () t (95).s.3 Jouls (9) OPX FID A FUTUATION THNOOGI in a thortial link was stablishd btwn grait and ltromagntism, two mass flutuation thnologis ar prsntl undr instigation. Both thnologis ar ltrial dis with th first bing induti-basd, and th sond bing apaiti-basd. hown blow is a simplifid shmati 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 ompl fild mass flutuating sstms. Ths sstms ar li, and altr th loal grait wll. Th mass of ths sstms is onrtd to ss fild nrg during th magntizing/harging phas. During th dmagntizing/disharging phas, ss ltrial nrg is olltd, and mass is rstord aftr this phas. Thn, th l bgins again. As a onsqun, loks runs fastr du to brokn smmtr of mass-nrg onsration in th proimit of ths dis baus mass is onrtd to NGATIV nrg. William Alk Pag 9//7

107 Nwtonian Torsion Phsis INTAK, IN. 3.8 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. ss fr nrg is harstd as NGATIV nrg. Th diagram abo shows that an impuls funtion ours whn ss rsidual magnti flu is found in th or of a oil bing magntizd at th start of th nt l, t s. If harstd, th nrg of this funtion manifsts as NGATIV nrg and oupls to POITIV nrg forming a ompl dirt urrnt. This urrnt onsists of both ral and imaginar omponnts whr th ral urrnt i is tim-forward and th imaginar urrnt ji is timfutur. Th ral urrnt omponnt is onsidrd to b lassi HOT UNT and th imaginar urrnt omponnt is onsidrd to b OD UNT. Dpnding upon how muh rsidual flu is aailabl in th or, th nrg in this impuls funtion ould b quit substantial. FIGU 45. ss nrg found in N. Za s di. William Alk Pag 7 9//7

108 Nwtonian Torsion Phsis INTAK, IN. 3.8 FOU TINA DVI j i θ j, θ i θ, θ TI t TI t OU DIPO + IN 3 OPX FID GNATO Δ Δ 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 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 Adand urrnt i ON OFF ON OFF t t NOT: AU IDA YT FIGU 4. Two trminal / four trminal ompl fild mass flutuating sstms. Th diagram abo shows a tpial onfiguration of four trminal and two trminal ompl fild mass flutuating sstms. In th four trminal sstms, nrg from th sour dipol (i.., a battr) ntrs through trminals and. ss nrg las through trminals 3 and 4 and hargs th load dipol. In th two trminal sstms, th sour dipol also ats as th load dipol. nrg las th sour dipol through trminals and and ss nrg las through th sam trminals at Tim t latr. William Alk Pag 8 9//7

109 Nwtonian Torsion Phsis INTAK, IN. 3.8 FIGU 47. Th martpak/zpod Workstation. FIGU 48. Th ZPOD in opration. William Alk Pag 9 9//7

110 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 ss nrg of th ZPOD. William Alk Pag 9//7

111 Nwtonian Torsion Phsis INTAK, IN. 3.8 FIGU 5. Th Bik using martpak thnolog. FIGU 5. Th Bik using a martpak 3-3. William Alk Pag 9//7

112 Nwtonian Torsion Phsis INTAK, IN. 3.8 TA OPX FID GNATO A QUIVANT IUIT PW i G G + V A + N N - Δ Δ F - BG μh N + j i θ, θ > F F ( F) +Δ t s + - 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 ompl filds bak in th 88's. H disd a sris of mahins patntd in th 89's that gratl amplif this phnomnon, whih h latr alld ADIANT NGY. As shown abo, th pioting magnti domains ratd b Amprian urrnts of th frromagnti matrial ar ordrd in th dirtion of fild B G b magntizing oil G. agntizing th high indutan oils rat an opposing fild μ H that ats upon th ordrd domains of th matrial, thus anling or partiall anling th ral magnti fild ratd b th Amprian urrnts. An imaginar magnti fild jb mrgs du to this j anllation and oupls bak into th magntizing dirt urrnt as i θ, whr θ >. Thrfor, th magntizing dirt urrnt boms ompl baus th irulating motions of th ltrons ar rotating into th imaginar ais. William Alk Pag 9//7

113 Nwtonian Torsion Phsis INTAK, IN. 3.8 j As shown abo, bfor swith F is losd, th apaitors H ar hargd with a ompl dirt urrnt i θ produd b an opposing flu from oils. Th ompl fild nrg is stord in apaitors H. At th momnt of swith F losur t s, th ompl dirt urrnt flows through oil K, rapidl disharging apaitors H. j A r larg ompl ltri potntial θ is obsrd aross th sondar oil. OU DIPO + IN j i θ, θ G TI t INPUT 3 TA OPX FID GNATO Δ Δ 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 ompl fild gnrator. William Alk Pag 3 9//7

114 Nwtonian Torsion Phsis INTAK, IN. 3.8 TH HUTHION FFT XPAIND FIGU 54. tal sampls from John Huthison s lab. As shown abo, John Huthison sussfull applid th Tsla ompl fild to mtal sampls with amazing rsults. Ths bulk mtal sampls wr mltd at room tmpratur without an appliation of hat. Th ompl filds indud old dd urrnts within th mtal, whih in turn, ausd th mtal to old mlt. As th mtal softnd, John insrtd bits of othr mtals and organi matrial as shown. With th fild turnd off, th mtal rsolidifid trapping ths matrials within th mtal latti strutur. FIGU 55. John Huthison in his lab. William Alk Pag 4 9//7

115 Nwtonian Torsion Phsis INTAK, IN. 3.8 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 urrnts bing indud in a mtal sampl. As shown abo, old dd urrnts ar indud in th mtal blok with th appliation of ompl magnti filds. A ompl urrnt flowing through th oils produs ths magnti filds. Th magnti fild nrg surrounding ths oils is NGATIV, and th mtal sampl in th prsn of this fild will old mlt du to indution. FIGU 57. Anothr old mltd mtal sampl. William Alk Pag 5 9//7