general theory so this concept can Weber electrodynamics extendedto standard science. Here the sec ' include radiation causality does. 0H0 1 J.P. Wesley Conclusion Weiherdammstrasse 24, 7712 B/umberg, FFiG beg/5:,Th and other, speculations are all very ‘ ' Received: June 1985 en matrices and elliptic functions web but for. realizatio ' Chitfas to be forged in detail. Sotam only a case oft a recrpe’ 1'n search ofa n the mH , or better, acordon bleu. ”b References

1 Bohm D t (1980)., ., V/iO/eness and [he2 Imp/(care‑ Order. Routledge & Kevan P1l Ld

2 Clendinnen ' 3‘ (u I 'LOHdOt (1981). . 1.1., 'Phase termsI -‘ the iAXlOlTlv of~Choice', Specular. Sci chlznol 44 . Abstract Weber's law for the force between moving charges satisfies Newton’s Third Law, the conservation of energy, and yields Ampere‘s original empirical law for the force between current 4a gag/”10]”Clendinnen,) 6(5),l.l.,521‘Furt‐529her(1983)Remarks on Phase' versus the Axiom of Choice',I.Specular”“3me5n elements. Weber's law predicts the observed force between two closed current loops. It yields the observed temporal and motional electromagnetic induction, and the observed force on Ampere’s World,oten. PJ.7, tand Hersh. , R., 7'"\ll on‐Cantorian’ Set Tl " ' ' I aw is derived. This Weber field Bergm' pp. _12_220‘ W.H. Freeman. San Francisco “3:010 . .IWHI/ICHIHIICS in the Modem bridge. The electromagnetic field appropriate for the Weber force 1 is then extended to rapidly varying effects and radiation by introducing time retardation. An ann, P.G., Introduction to [I r _ . ( - )5).‑ additional electromagnetic wave, the Weber wave is obtained. Absolute space is included by York (1942). He [72me of Relamwy, Chap. 17. Prentice‐Hall. Net introducing time retardation using the phase velocity observed in a moving system as predicted by 6 Hancock ( ,H., Tl ‘I ’ ' the Voigt‐Doppler effect. 7 (1976).Well, A., EllipticwgiizgfIonsEllipticAccordingFunctions,to EisensteinDover Publicationsand KroneckerNewpYork89 Sprinogl(1953‘ 3“” . , , a , 2. 8 Cayle 9 Margenau,‘ Yr A-,H.,An TheEleme”WY. Treatise- ' on Elliptic Functions, Bell & Sons, London (1876). Introduction Nat - ,.~ . on 10 Edwards, A~W-F., FOIUIZZIIgeI'Of Eritrea! Rea/11% P422, McGraw-Hill, New York (1950). The electromagnetic theory of Weber,1 as first presented in 1846, is based (1977). [OILS ofMtJIhe/natical Genetics, p.21, Cambridae University Press D . the force between two moving point charges using the separation distance, the ll To”, .‑ plxms, R, and B' relative velocity, and the relative acceleration. His theory is the only electro‑ (1974). 1rd, C" The 566"” Life Of Plants, p.188, Penguin Books, London magnetic theory ever proposed th at satisfies both Newton’s Third Law and the Gordon R and y varying (1978). , ‘y Jacobs 0“: AG,«The Shaping‑ of Tissues in Embryos‘, Scicnr. Am, 84 conservation of energy. Weber’s original theory was limited to 810W! effects where time retardation and radiation were not involved. It is an ‘action‑ at-a-distance’ theory, no fields being necessary. It is now known that electro‑ magnetic waves exist and that a field theory is required to describe such waves. This paper, therefore, first expresses Weber’s original action-at‐a‐distance theory in terms of fields and then second introduces time retardation to yield electromagnetic waves. in this way, it is possible to obtain an electromagnetic theory compatible with all of the evidence which is consistent wrth Newton 5 Third Law and the Conservation of energy. . ' .~ .‑ Maxwell’s theory, being based upon the Biot‐Savart Law, does not satisfy Newton’s Third Law. Maxwell’s theory cannot, therefore, predzict the obseryed fOrCe 0“ Ampere’s bridge. Because Maxwell’s radiation theory 15ag6“?{?”j"' tion from erroneously assumed slowly varying effects it fails to predict 116 correct radiation field. An additional wave, the ‘Weber wave’, asderived here. is needed.

Speculations in Science and Technology, Vol. 10, No. 1, page 47 The WEber force 49 J.P, Wesley Weber. . assumed th at the ‑ Weber Electrodynamics posmons r3 61mg), U Of two interact' .1 no,- and it changes sign when th e subscripts 1and 3are interchanged to give and ri moving with the v 1110 D lenient Iidsi due to IzdSZ. €l0citie , iii: force oncurrent e The Biot‐Savart Law is quite U = qiqill/r ‐ (v-r)3/2c3r3] S‘3 and V1is and ‘Il at different; it 15 where c is the ve [‐ (d82‘d51)r + dsl(dso_~r)]/r3 (8) locity of light and (i) CZFB =1311dsg.\f(dsl.\fr)/r3 = 1211 r: ._ (8) clearly does notsatisfy Newton’s Third Law: the force r2 Tl, v=v,_vl The Biot‐Savart Law he subscripts i and 2does not yield The first term on th isnot directed along r, and interchanging t hat these laws energy. 6 right of equati '7 the negative for the force on 1,dsi due to Izdsz. It may be noted t V O“(I)- issimply the Couloinb L} When the s Porenlial (7) and (8) refer to moving charges by using the replacements the rate y C I ~ - t. 5 (11"1 = Ildsls (12V: 2 Izdsz (9) 5". Chan (3S i CNN 2 - . The absurdity of the Biot‐Savart Law (or any law violating Newton’s Third df (Clzflivr/r-‘m + V2/C3 _ 3(v _ -2 - .2 r) /2c°i +(r-dv/diyc2] (3) Law) can be immediately demonstrated. The self force on a closed current loop4 may be considered. Ampere’s Law (7), which satisfies Newton’s Third ing from each othe r and U dec ‑ Law, clearly yields zero for the self force on a closed current loop. Mecha‑ 5 result (3) may be written in therf‘oarslif nically coupling current element [2d52 togetlierwith current element Ildsi,the Biot‐Savart Law (8) predicts a net nonvanishing force on the two coupled the WebF er force‘ on charge (12 (4) due to charge q, is given by current elements equal to (10) w=(q2q1r/r3)[1 + 1/2/62 CZFB = 12111" X (dsl ><(dsi ><(ism/r3 (11)

p mole 1 by V1 and Caddinoc y‘15€21S 1C6 ‘ by V3 and Newwn's which need not vanish. By altering the way in which the loop is divided into WhereV2-d“1:11;;7/Cl vi.dPi/dr =(v2 ‐ “le2_dU/dr (6) portlons 1 and 2, which is merely a matter of labelling, the force predicted by equation (11) can be altered. Nothing need be changed physically. Interchan‑ Syéifffble-in ‘ ~‘ Thel aretotaltheegreqmenltja ofthe particles. This result (6) is immediatel! ging labels 1 antl 2 reverses the direction of the force. This net force on aclosed wn Straps dent of then depends Only guy + T> Where T is the kinetic ener I of thE current loop could be used in principle to lift a spaCe Ship by its 0 boot from the forces inside the space ship itself. And no energy h‘ilS {'0 be expended. thus , energythe Pathis coflServed.or the rate ofponChangethe 6ndof POints.the systemThe betweentotal enerthggIethlnplfifrii:g) d L The absurdity is clear. it is frequently claimed that only the net ponderomotive force between two closed current loops can be observed to test Proposed laws for the force between current elements or moving charges. Since the Blot‐Savfll'l' Law he absurdity' the Law of Biot‐Savart (equation (8)) and the Ampere Law (equation (7)) Yield Precisely the same “a he it appear that force between two closed current loopS; it is frequently claimed that it (1.065 not matter which law is used. To try to argue from an obviously false Premlsc, [he i -’ IS often nixulilgtfdefs Olilg‘m’ empirical law3 is satisfied the Blot‐Savart Law violating Newton’s Third Law, in order to obtain a‘coi'rect nipelilpal law. For examplgr force laWS that are not compatible conclusion is hardly satisfactory scientific thinking- Moreover, Observations are mem 172141” Ampere’s orioi mlany text books label the Blot‐Sa‑ not limited to the force between two closed current l00p5_ Three independent Ce 2 " 87 a curbrentna empmcal law forat r1theseparatedforce FAonby element [ids] Observations not limited to the force between two closed current loOPS are readily available to test the validity of any proposed force law between cuff-em _ '3 + elements or moving Charges: (1) the force on one portion of a closqdpcunent lflarl)’ satisf‘ ydszTMdSITer-l (7) 100p due to the remaining portion of the 1 bemeasurcd’thc mpclc 00p can ‘ the ‘ 168 N , ~ . harge mOVing in 'cuum ln ' eWton 8 Third Law: The force is directed brldge experlment.3 (2) The force on a C a va WeberE/ectrodynamics form any I . . (Persoml COmniunic. . ca tical without artifiCial conductor movino igtlfin) has shown that Ffhe 213136 Odbserved. (3} Mill To obtain an exact result in closed mathema _ . . localized Tl - ‘3 1‘3 Presence Of “C6 BleCtr‘ “ «fl “noul'iritiesm C it is convenient. to turn to . laminar geometry,- as indicated. - in. . . ie Induced . . . an external 1cfiridin grime 1 The laminar thickness 1.perpendicular to the page in the z direction is observatiOnsmemhc loop ascanre£luiredfigeldth Y the18erroneoUS“0t distributedFaradaunifOrClOiSEd+4me aromdCurrenttheloopWhat:i: not shown. The net force on Ampere’s bridge is then obtained by integrating element due to ah 6:8, bel used to demrmine the): aaweu theOll’. Miller}. [‐ 2J2-J./r3 + 3(J2-r)(,i1~r)/r>] (12) Merna Closed CLl . _ . 3 ci‘irA/ci-‘rgd-‘rl = r tions oftYPe (2) above). In principle, oneTrentcouldIOOPa](asalso reveal‘id bl’gleObsennCumin The case of a thin lamina (r small) of movin03 Charoesdirect‘ y ' unm S tea \Vhere J is the volume current density. be neglected in comparison to the 0 1 m a V39 ; but the Coulomb fosrlégithoe Sine heme” v small), where r w can V U probabl h narrow width (l and the f the circuit, is considered. The Biot‐Savart Law (8), other dimensions 0 e singularities, can be immediately converted to surface involving no possibl Force on Ampere’s bridge lving surface currents K, where K = I/w;thus, when A 3 integrals (t = 0) invo 6 bridge and A yis the surface area of the remainder of :mstraightforward integration of ti is the surface area of th 16 Ampere Lan (7) rmdpiere 3bridge3 yields a result com a . r ' _ for the farea 0 the circuit, 4 c over the past 160 years.”‑ Biotthe 6.xSrdvart Law (8) (see below) 8doesApsiiiipler10it ar“1thsltcraightforwardthe €XperiinemalintegrationObservatmn:ofthe c3123: I fang} jda1[‐(Kg-K1)r+K1(K2-r)]/r3 (13) A: A. ForSomI::?taleri observations. nor with selfieconsisftjfillta Compatible' Wham“‘ broken up into six portions, range . . C I. erngand the Bia‘rsera‘ssnt iltis frequently Claimed thatlthe AmPEre La 7‘, The surface areas A 3and A 1may be convenientlyridge may then be calculated imng r€pulsive force: bertweaew (8)1is correct. The experimentally estalilfslfeisl asindicated in Figure l. The force on Ampere’s b mpere Law 7 . n co inear current elem ' IS, A ents, as 0w i a Maxwelps EleCfrtZdyngfgt-157 frequently ignored or denied. The abccfntab) 1h} V which rejects the Am elCS,I:vhich is based upon the Biot‐Savart Last (gleiifd p re aw (7) has resulted in very expensive error; in .- O achieve thermo - . Bfldge particle accelerators. “Udear fusron and m the design Ofhigh-enemy “T 4___T__.._ _ The problem ofcalcula ' 5 the Ampere formula (gangoiheflfgrcgon Ampere’s bridge directly from either u __ __ mathematical difficulties. Cleveland" qitzt‐Savart formula (8) has met with or Wires of vanislting CrOSS-Section Wh tempted to use linear current elements, linear current elements goes to zero th en the separation distance between such l 6 4 arb-equation‘ . (7),. . tlien becomes inf' . 6 contribution to the force, according to l ltraly fmite Separati mite. Cleveland, therefore introduced asmall giredICted then becamgn :0 Obtain a finite result. Unforttinately the effect he ‐ “> W6‑ (1 iniéflnce'. RobertSOn,9 aIEOmMI-lly d'Cipendent upon his arbitrary separation oergrrauOns in terms of an ai‘bqimg- linear current elements, terminated his i 3 ‘ error-s t-O O,btain a finite resullt raiy diameter Of the wire he was COHSidering in USed lim Sign (not the same er. (B9th Cleveland and Richardson also madfi Smalle near current element ror) ”'1 their final formulas.) GraneauS has also st mterval fOr his C 8. To aVOid infinites he has arbitrarily chosena ______._‐‐-__ can be inVol , Omputer calculations. Because no arbitrary parameter 2 ' VECl 1n . F._.‐‐‐‐‐> ‐ x tlve predthlOnS.K ' . the PhySics,. these theories fail to provide adequate quantita‑ he Only Corre SiOns with three:t-theoretica. 1proced . . . . rem den A. dlmenSiOnal ure 1nV01ves gorng Simply to three dimen‑ 0 - - Ht - . . When the Separat.lnf1r}1tles can miss gemeflts- Using three‐dimenSional CUY‘ to zero_ 10“ dIStanCe betWeen v (inmbufiOns to integrals remain finite Ii the force due to (lie remainder of the circuit IS calculated entelements is allowed to20 Figure 1 AmparesA brtdgt. ) on wine. ' 0 ume curr ‑ rce law (7) and the Biol‐Suva” Law (8). direCIly using the Ampere original f0 52 V as . . . i the sum of nine integra Is. 8 . J.P. A ymmetry conSiderations reduc h Wes’ci/ Weber Electrodynamics. 53 nvolved. For example, the i e I 6 . 't are ogether there is then supposed to be a net menDral tor‘ the {O. I'C ‘ 13.0% Circui mechanically coupled t v force on the loop given by C2F.'~\(6,1)/[2 : . l: nonvanishing FB= 2(13/8) [111(1 + V1 + bz/az) ‐ ln(1+ V1 + bZ/(t, ~ 002)] (19) W { ‐ w W (_(l T (14') rce could be used to lift aspace ship or drive an automobile In principle, this to d.'_ al forces or without energy expenditure. This result (equan (l/wztz) (3f raj; CW2!r €123! dill!, dyi J dzl (‐ 2y/,.3 + 3Y3/r5) without any extern le of the absurdity already given by tion (19)) is merely a concrete examp uation 11 . _ equevelaiid actually measured the forces on the two portions of the closed : 1’71J 2 ‘ J1/3 + (2/3) ln2 + lIZ(Ot/€) + ln[(€‐a)/w] circuit. He found the forces were, in fact, equal and oppositely directed as required byNewton’s third law. Cleveland, thus, disproved the Biot‐Savart law Where Y = 7 _ ‘2 directly experimentally. been set eqii-al $1,311.; =1(x2 ‐ X02 + 0’2 ‘ yi)2 + (27 - z)23 d neglected COmpared Withe 0 SQuare cross‐section) and wherein; hn Elm straightforward anal s' bother dimenSlOI’IS of the circuit. In terrorist ten (7) is f0und to b . 3’ 15, t e.force on the bridge accordinoi a \ bm e in the posrtive y direction and actual to a 0 Amperes Lat. Weber force yields Ampere’s law rce law (7). Four forces act F = 2(13 2 rt/3 (1') A /c )[13/12 ‐ ‐ (2/3)an + i/ 1+ til/65 a Weber’s force law (5) yields Ampere’s empirical to 13due to an element ds. of onanelement of a conductor dsg carrying a current ‐ 111(1 + V] + b2/€2) + ln(b/w)] another conductor carrying a current 11: for w small com a d ‘ , (1) the force between positive stationary ions (+q2, v2 = 0; +611, Vi = 0): be neglected as' Pcompared“3‘ withWith6’‘, b,6,a,equationor t ‐ a.(15)If theyieldswidth of the bridgebmiii' (2) the force between the stationary positive ions in dsz and the movmg electrons in dsl (+q2, v2 = 0; ‐ q,, ‐ vl), F = 2 2 ationary positive A 2(1/c )[‐0.1i9i. . .+ lii(b/w)] (ml (3) the force between the moving electrons in dsz and the st ions in ds, (~q2, -v3; +q,, v1= 0), and oving electrons in Note that the large term involvin (4) the force between the movingelectrons in (152 and the m interaction of the parallel pOrtiogshéflilin equations (15) or (l6) arises from the dsi #V2; ~qi, and the force 0 4 d e loop near the contact, re,the force (#12, ~vi)‑ on 6 due to 1 Substituting the appropriate values indicated in the brackets into Weber’sLaW thus, depends prim '1 n ue to 3 (as shown in Figure l).The result(16). (5) and adding readily yields the net ponderomotive force on (153 carrying a as ' an y “P011 the repulsive force between colinear current elements current 12 due to an element ds, carrying a current 11 in agreement With ngxen Law (7). Carrying by Ampere’s Amperc’s empirical law (7). The Coulomb terms and the acceleration terms (8), the force onaflslimSa-r Stralghtforward integration of the Biot‐Savart Law 6 nClge is supposed to be in the y direction and equal to appearing in (S) cancel out in this case. FB=7([2/Cz) “ “1+ 2 2 7 7 [ 1+1?” -In(1+ 1+b-/t"-) (17) +1n(1 + x/my] which for b s mall COm . . will)” field for electrostatics and magnetostatics F8 : O pared With (7Of (1 ISSimply associated with the first term of It is deaf that the electrostatic potential to be n by the usual expressmn,. the Weber force (5), the Coulomb force, is give This BiOt S (13) c ( “ aVart result . . . 20 islgterd Ampere result ((1157))00r (18) ‘5 1"Eldically different from the directly cal‑ (13(1'2) = “f I J d3,.191(r1)/r ( ) agrege cement With the Am r (16). The strong repulsive force observed3M i5 1 Actthlitlt; 3:6 Weak or zergefrgrgesuhaThe experimental observations donot . , l 0t. 11. . ‘ . _e Bier.Sava e PFC _icted by the Biot' ‐Savart Law. where 91(r1) is the charge density distribution of the source. The Coulom; I‘Eniziiznderi-Ciii‘ttlfoes not (:CtlLiSISUtlriéN) ls absurd; as the force on the remainder ecir negative of this result The force on th€ forcc P61" unit volume charge density 92(r2) ISthen given by (21) equatiOn (17) and rgidlt may be readily obtained by simply changing the sign of ' 8C! 0 @2V2(P as n° (1by (3“ Ct. When the two portions of the closed fw(electrostatic) = ‐ V 54 55 For the rnagnetostatic case, where fields and forces ar ‘cs 27 JP. West-3 Iectrodynami q . I I Ir # (r‑dVlldt)/r3 ( ) currents in conductors, the Ampere force law e associated with neat Weber’s force law (5). In this case, the force weberECsz = (1241r[~ 2v3‘v1/r"2/7 ‘5]+ 3(v2 r)(\1r) density J2 due to a distributi ‐‐- til/[‘3 'i‘ 3(v1-r) .J esen stationary . th t betheshownforce 321:“, that this equation (7) in the form ,0 termS 1“ The last t\\ l b a currens uare brackets repr ‘11 . e due , roduced y C q t-carrying wire. It Wi ovm charg csz (magnetostatic) = Eharsispvery small and may 33;?“electedthis Weber force ontsenaccelfration term. orc , - socra 1mine . To Obtam the fielsgire it is only necessary. to en tostatic case, asgiven by ‐ fffriJZ‘Ji/l'3+(Jz'V2)(Ji'Vi)(1/r)ld3"1 [Oacurrent-C arrylna L m the magne charge (12 can be representfd qs d b , qu2. The force 0“ - 1(27) The Other terms ( 26) where J is replace ) J‐ is giVen from echiatior In order to remove J2 equationS (25) and f( l aiioe of the source Current 1 (r2) from the integral the followi due to a time‘ T3t6 0 C1 D considered: ng identities may be (28) rJi'V2(l/r) = ‐ arm/,3= r'Jivza/r) = Valor-rm r M by‐ iiid3i‘ir(r~8J1/ai)/"3: Using equation (23) the right‐hand side of equation (22) becomes (33} q‐ l

J2><(V2 ><fill/r) ~J2V2-IJ,/1~+(J2-V2)V2f (r-JQ/r (24) (178/8qu j j j dawn/r‐ j j j emit/r] =

Mylar/a: fl aA/ar) where the notation for the volume integr . . a ations has been abbreviated. _ ' lds the Weber force on Introducing the usual vector potential 7 , and (28) the,“ yie A and a magnetic scalar potential f, Combining equationls 1 c A, and I‘,defined by the Weber magnetostatic potential field ' I' tie(21),v ‑lbcéiiy v in apotential field (I), becomes charge (1movrng “1t1 29 cA=fffd3r1J‘/r, equations (20) and (25), + v X (M)_ WA + (mm ( > CF=fffd3r1J1-r/r (25) ch = q[- chl) ‐- aA/a, + ar/at trent 100p gourCes are I i confined CU ‘ _ “2 force. For the limiting Maxwell case, where only - ce3to the Lorei In terms of these potenti al fields, A and F the force per unit volume onthe 'invol ved and V-A = F = O,The Weber force (29) iedu current density J2 due to the steady current distribution J] is cfw (magnetostatic) = J ><(V X A) ‐ JV'A + (J'VWF (26) . ' ' __ ‘ G where the subscripts zl ‘ lave been dropped. Weber induction for Stationary Grants to force on the (filectlogsftgtrlge For the special limiting case when V-A = F = 0 this result (2,6) [BdUFES {10. ' b defined as the electromagne 1 nduCtOr' The induce. l as 21 the Maxwell theory. It may be shown that this limitng C355 mVOlVCS 0;) Induction may e 't've by COW/BMW“) 1“ a cO‘h t acts on the met3 the contained closed current loop sources. In general this need not be true. 0: carriers, counted as90:11 ihe onderomotive force thhe induced 'fOrCe 0.“ on example, to predict the force on Ampere’s bridge the source mUSt betaken a may be CODtYaStéfi 1"“ n thepfixed positive ions)- e separation.T£1efO\x?\§:ber whole (or essential y 0 duce acurl'em 0r acharg eseparation- “‘6 e (is the portion of circuit apart from the bridge where the current does not in closed loops and is not contained. rm electrons in a metal can prO neither current nor chaff;rr ing wirC is the sain rte the positive ions can prOdl:lceced by “Other currentéga) Oi for distribute.d c1c(Inge forcethe forceon theonelectronsacharge asproMatti/onu d given(29),bywhereeQuatlonby(COnvention the carriers Weber force on a movin and current sources y e g charge due to a current-carrying Wire electrons) are counted as p051t' ive. ' ’1metal. " 1'he lorces“ ‘ induced A moving charge (1», ta trons flow' the . . , . - . . ' nary Since electrons are n average accelerated iii.( When elec ions in a wire where thekenforceasposmve,involve can interact With the posmve statiO i A 0t on - (I force 0“ the b balanced by other forcesn the '“dgcc - oduce interact With the negative mov 5: (+02, +V2; +5113 VI= 0); and ”Ci“ 0n the electrons must 6 induced force is balanCCd by an OhmiCow, thendrag-a thfge separation must pI' ‘Qi,a movino*vl).Addingch these two forces,ing electronsusing equationwhere the(5),forceyieldsinvolves:the Weber(Miami on electrons can result in' no cuffCmC65fl the Induced. f0rce. c arge (12 due to a current carrying conductor as an electrostatic field that balan Hall effect J~P- Wesley Weber Electrodynamics . . of the election- s . 'tten‘ '15 the sum of the velocity frelative t: Vetgcrty In this case, currents do.not chanobe with time and the con elocrttes and the w“ of theC conductor‘ itse' lf v’ . The orceofonthe ary, The Hall arises when the the ductors are station‑ effect direction of in for Vconductor v ' 'th the velocrtyvg' ' + v4_ 18.then the. sum out. electrons is perpendicular to the flow of electrons. In this duced force on the [hoesitive charge +q2 tn ovmgiZiis't‘ve +q1 in the source movmg. wrthhttltile6 gawk?! can the case, charoe direction, noOhmic drag balance induced force. In this a s force given by the post: [Ithe negative electrons ~q1, movr gupdts eparation must occur in the direction of the induced field to balance the induc v; and the force given ') (5) and summing the two forces yte the effect on a current density instead of on a single movinoed field.CharoeConsideringc (3‘ ‐v + vl. Using equation 5 (33) replaced by Qand qv by J to yield the force per unit volumebf. n12 hill :iiec 2 ‐‐ r f.‐ 2v1-(v2 + V3)/7 + (v1 ~ C Fw ' (12511 1 a I 2 .3 Iz/rs may then be obtained from equation (29) by neglecting (I) and the rim:l I i '3 3 '1‘) [(V7 + Vé)-r]/r variations and by considering only the force perpendicular to J. The induced "

62F“, = q2q1r[‐ iI%/r3 + 3(v1-r)2/2r5] (33 F = I I I d3i'lr-J1(r1, t ‐ r/c)/r i This force is very small and has been neglected above. en by equation" (29).. The. just small is, specific numerical example ’ ‘ “ on a chai'oe moungin1' ' this field .-is givd To demonstrate how this force a completely by equations may be considered where the force on apositive charge qgseparated adistance “liiifdieidefsebeerex » electrod;namics is then prescnbe I) from an infinitely long straight wire with a current I is calculated. Let qt be 41 and (29). ‘ . ‘ " ' " " ns; the charge of the conduction electrons per unit length in the wire, 0in :didsii ( "Bhe integral expi‘essmns (41) can a1so beexpressed‑ asdifferential equatio The force on the charge (12, which is perpendicular to the Wire, isobtaine an thus, 1/ equation thus, <42) (38) by integrating along the wire (in they d‘recmn); [33(1) = ‐ 45m, C] 2A ~‐ ‐- 47:. 6 ‘ 4 4 = Strap/act Fw =(q21v1b/c2) f dy(‐ 2/r3 + 3y2/r5) = ‐ right/6217 (39) 7 7 2 2 1VZA : __ X , ' 1 Ct where El[V$*a/a(a)]r‐ : V“ ‐ 8 /8(ct) 7 am . ‘ VfiniteVXA+VV-Asource, H R wave, 0 . - '2 vanish for a _‘ . t omagnehii'd of equationsI ‘‑ For the particular val ues q2 = 10-10 c, 1 A, 111 = 10 cm/S,<”mdb:1cm the force is Fw = =103 smce Fdoe? “Otfm airtiiediiikfl) yields an ziclditi%n:lrelcl:; the F field must 10‐S dyne, a truly negligible effea' . - h sewn“S The velocity squ (41) or the thud ? eqt rediCth by the Maxwell t. (it-0y“. Of energy for slowly arise from a very sared terms involving Vi are always neghglble’ ast is due I0 the ‘Weber \vaLe ’ r[1(C))11’:‘.)”1“hird Law and the conseivaeis’ cannot be doubted. . , mall apparent decrease in the charge Ofthe Elemod that is their motion. An effective positive charge may, thus, be assum? harm? EXISUOvarying 5311;:3’5e ' , ti: physical existence of. ‘Weber wa Proportional to C11 = q ivi/cz. For a current-carrying wire the effecnve C D per unit length is then approximately dqi/ds. = [VI/C2 = I’m/10c Absolute space ' uation' (5), is" valid.‑ where - moving Ch 1’ is measured in am The original web“ force law betwictnwo moving C‘hrffgeséciK/hen, ,. Ids equationsthis force(29),law electrons in a metal is only peres. Since the drift velocity V; 0f the only for relative coordinates be??? and magnetostatlcf {ffere’nce' asthe fields ”finals: . . . , 05a _ . o‘r ’ . - ,-U ‑ charge distribution is extre of the order of centimetres per second; the e.eiion 15written 1“.‘e.‘"”.‘5 Of-elecir in the laboratOIy {ran}; of the observd‘g 1.11%) due to the v? terms in eqmely Small. The effect on a static Charge dlsmbil be (25), and (20), it is valid onoyf the frame of re'fererlas given by equations ( . , neglected. uations (38), (27) and (33) may. thus, alwa)s are defined only in terms Ion, radial ments. The Weber theory extended to 60 . 61 inbvolves time retardatio rodynamtcs 1'1 assuming' Slmply‘ a V61 J>P.Wesley Weber Elect 3 server, in particular, ocrty c betw a velocity 0 relativ References oes not, therefore, inc e to he observer. ' lude the effect of absolut bli. Leibnizens Ges., Leipzig, 316 (1346); Alm- der Phys., 73, 229 (1848); The velocit pro te space. l Weber. W.E-~ A _ y of energy a ' I-1]» Webers’ Wetke,. ., Volumes 1‐6 , Julius Springer,. Berlin_ (1893)., 4 be fixed relative to absolutepspgaflctefil‘gf Electromagnetic wayes is observed to and not fixed rel Slhfiiigll 1C. Treatise on Electricity and Magnetism, (reprint 1891 3rd Edn), Volumes I observer . The result 41 ' ative. to the movino y valid for an absolut and 11, Dover, New York (1954). 823), Memoires sur l’Eleetrodynamique, Vol. '1, estationary observei or for 12/0 negligible.( ) 15, thus, 0111 Ampere, A.M., Meni. Acad. Sci., 6, 175 (1 Absolute s a . . 25. Gauthier Villars, Paris (1882). Should be, inpfatcxe Iggy be introduced by noting that the r t Wesley, J.P., Bull. Am. pliys. 506., 28, 1310 (1983). (411 . Inst. Elect. Engng, 42, 311 (1923). in the ms of the apparent retardeilrdffd poremms Haring, C., Trans. Am moving laboraltlclfd ”filer Wed Mag. Suppl, 2], 416 (1936). Cleveland, F.F., Phil. therefore , be Inter‘ ry. e veIOCitY Cin equations' e emas, Obse Cimento, 768, 189 (1983). Pappas, RT,11 Nuovo laboratory. The wageretcd 3'8 the Phase VClOClty: c’ 013:”), find 14215h0u1d,he moving '5., 53, 6648 (1982); Phys. Lett., 97A, 253 (1983). Graneau, P., J. Appl. Ph) asa Phase velocit Thequatlons (42) clearly indicateithat rte mtinterpreted therefore needegi' ephase velocity ct observed in the Cmu‘St be Robertson. 1.A.. Phil. Mag, 36, 32 (1945). aboratory is, Kennard, E., Phil. Mag, 33, 179 (1917). . ty of energy and Wesley, J.P., Proc. Int. Conf. SplICC‐Tlme pmpagafi’on ct” _ m equations (41) and (42) and not trinmimgl' Wesley, J.P., in Editors Marinov, 8., 982); Causal Quantum Theory, oc1ty of the observer, at laboratory 1,515 has er‐e vdm :here V0is the absolute V61 6 “3100‘ Absolute/1e33, pp. 168‐174, East-West, Graz, Austria (1 - , ' a y een stre 17 in an absolutel m ' SSCd’ Electromaonetic T i ' Chap. 4, Benjamin Wesley, Blumberg, (1983). phase VCIocity Cy, Elna/1111i 3:?qu mittst have two velocifies andaghit‘jirsitofsentfid Sagnac, (3., Complex Retulus, 157, 708, 1410 (1913); J. Phys., 4, 177 (1914). t , 0 en . S, 116.1 e Michelson, A.A., and Gale, H.Ci., Astropliys. J., 61, 137 (1925). h?f;:me magnitude nor directizmocr ergy Propagationc ‘ . They need not have Conklin, E.K., Nature, 222. 971 (1969). ongmai Web - ' Henry, P.S., Nature, 231, 516 (1971). 1.GravitaL, 12, 57(1980); Tltorny source and observer'esrotffieorf/ 18based only on relative coordinates bet“, time r€tardati0n miist be e fect of absolute space can only beObserved Mien Marinov,S., Chechosl. .1. Phys, 824, 965 (1974); Gen. Re Way of Truth 11, pp. 68-81, East~West._ Graz, Austria (1984). mathematical eXpressionse 'ttak'en into account, To obtain the appmpiiafi: Wesley. J.P., Found. Pliys., 16, 817 (1986); Found Phys, 10, 503 (1980); Causal Quantum effectl7,18 f0 r e1 .1 IS_sufficient_ tO conSider' the ‘ _ Theory, Chap. 4, Benjamin Wesley, Blumberg (1983). trated” the vogctt‐fgmagnetic radiation in absolute space As has/1:231(Ifeoppier Voigt. W.. Gan. Nae/nu, 41 (1887). 34, 333, 427 (1887); Astrophys. J., 37, 190 Michelson, A.A.,and Morley, E.W.,Am. J. Sci., propagation of electcgcjplgr eff?“ GXplains all of the known observations I(1)110life (1913). observations of Roemerrrifigclngtlcdravfis in absolute space in particular the S .‐ I ‘ ra . ’ .’ 0111:0(rhle,; Conklin,14v15 and Mariizév filChelson‐Morley,”Sagnac,”Michel‑ a ra iatin sou ‘ - ' k', w',gphasr§::110\{mg [With the velocity vSthe propagation constant frequency oc1ty c , and the velocity of energy propagation c*in a SYStem movin w' pler effect yieldiwlth the absolute velocity v0along the x axis the Voigt-Dop‑

CYs(1 ‘ VO'c/c2)(1 ‐ VS‘c/CZ) (43) c,(D = £05700 ‐ VO'C/C2)/YS(1 ‐ vs-c/cz)

C* == (C.\'c _- v V0) eX + (Cyey + CZeZ)/YO

Where eh e O . - , e a ‑ Scripts 3 refer’ ’ Z re unit veCtors alo ‘ ' ' ' 1/ 1 _ 10 the source a rig Cartesran coordinate directions, sub‑ tent withvi/CZ and Y0: l/\/Ig\d§zuhbjscripts 0 refer to the observer, and y, = quations (41) and (423/031; Th€§€ wave parameters (43) are consis‑ 1 re c is replaced by e’. 1,2