The Influence of Gravitation on the Speed of Light and an Explanation of the Pioneer 10 & 11 Acceleration Anomaly

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1 Applied Physics Research Vol. 3, No. 2; November 2011 The Influence of Graviaion on he Speed of Ligh and an Explanaion of he Pioneer 10 & 11 Acceleraion Anomaly Gocho V. Sharlanov Sara Zagora, Bulgaria 6014, EU Received: Augus 15, 2011 Acceped: Augus 29, 2011 Published: November 1, 2011 doi: /apr.v3n2p241 URL: hp://dx.doi.org/ /apr.v3n2p241 Absrac Consancy of he speed of ligh in ime-spaial area wih he same graviaional poenial (or in ime-spaial area wih equal level of conracion/expansion of he space-ime) is demonsraed. All of he experimens ( One-way, Two-way and Muliple-way measuremens) are made in ime-spaial area wih he same graviaional poenial (or in ime-spaial area wih equal level of conracion/expansion of he space-ime) his is he Earh s surface. Explanaion ha here is no change in he value of he speed of ligh in all of he above menioned experimens is given. The speed of ligh (or of he elecromagneic radiaion) is changing only when he ligh passes hrough ime-spaial areas wih differen graviaional poenials (or in ime-spaial areas wih differen levels of conracion/expansion of he space-ime). The Pioneer 10 and 11 Acceleraion Anomaly is acually a proving experimen of his realiy. Keywords: Speed of ligh, Consancy, One-way, Two-way, Ligh measuremen, Special relaiviy, Pioneer 10, Pioneer 11, Acceleraion anomaly, General relaiviy 1. Inroducion or more han niney years, many experimens have shown ha he speed of ligh is no consan. Some of he mos popular experimens are described by Sagnac, G. (1914), (Michelson, A.A,1925). and (Gale, H.E., 1925), (Miller, D.C.,1933), (Marme, P.,2000), (Kelly, A., 2005), (Gif, S.J.G., 2010). In all of hese experimens, he reference coordinae sysem is associaed wih he Earh's surface and he resuls are ligh speed angular dependence anisoropy. The resuls of he one-way measuremens of he speed of ligh, given in he paper (Gif, S.J.G., 2010), (which is analyzed in he nex poin of he aricle), also show ha if we associae he reference coordinae sysem wih he Earh's surface, we ge ligh speed anisoropy resuls. However, he ligh is propagaed in he space. Tha is why, i is correc o associae he reference coordinae sysem wih he space iself, where he Earh moves and warps he space around. In his reference coordinae sysem, he ligh goes hrough pahs wih differen lenghs, depending on he direcion. 2. One-Way Ligh Speed Deerminaion - Anoher poin of view The range managemen equaion is very imporan o he operaion of GPS. Le us examine One-Way ligh speed deerminaion which is done in he paper of (Gif, S.J.G., 2010) One-Way Ligh Speed Deerminaion Using he Range Measuremen Equaion of he GPS, using he same designaions. The ransmier, he receiver and he raveling pah (rajecory of he ligh) are in a spaial domain wih he same graviaional poenial. The ransmission and recepion saions are moving easward a he speed V of he Earh s surface a he same laiude. On an axis fixed in he Earh-Cenered Inerial frame along he line joining he wo saions wih he origin wes of saion A, he posiion of saion A is X A () a ime and he posiion of saion B is X B (). 2.1 The case Easward Transmission The saion A ransmis a signal easward a ime I o saion B which receives i a ime. Then, he ligh passes a paricular pah in he space (from he momen of ransmission I o he momen of receiving, from he poin X A ( I ) o he X B ( )) look a ig.1. This pah is equal o he disance beween he wo saions D plus he Published by Canadian Cener of Science and Educaion 241

2 Applied Physics Research Vol. 3, No. 2; November 2011 disance Δ ha he saion B has passed during he ime inerval ( I ) a he speed V: As a resul we ge he expression: Pah D D V I I (1) c c c D I (2) c V On he base of his equaion he speed of he ligh was claimed o be equal o (c-v). Bu he righ inerpreaion of (2) is: if he ligh has raveled he pah D during he ime inerval ( I ), hen is speed would be (c-v). However, he real pah in he space is (D+Δ) and in he space where he ligh is propagaed, he speed of ligh appears o be consan. 2.2 The case Wesward Transmission The saion A ransmis a signal wesward a ime I o saion B which receives i a ime. In his case we apply he same approach. Then, he ligh passes a paricular pah in he space (from he momen of ransmission I o he momen of receiving, from he poin X A ( I ) o he X B ( )) look a ig.2. This pah is equal o he disance beween he wo saions D minus he disance Δ ha he saion B has passed in he space during he ime inerval ( I ) a he speed V: Pah D D V I I (3) c c c D I (4) c V The inerpreaion of (4) is no ha he speed of he ligh is equal o (c+v). Indeed, if he ligh has raveled he pah D during he ime inerval ( I ), hen is speed would be (c+v). However, he real pah of ligh in he space is (D-Δ) and in he space where i is propagaed (he spaial domain wih he consan graviaional poenial) - he speed of he ligh is consan. Or in he wo cases he ligh ravels differen pahs during differen ime inervals ( I ), bu wih a consan speed of ligh. 3. Two-Way Ligh Speed Ascerainmen. Michelson-Morley Experimen Analysis Le us apply he same approach - o associae reference coordinae sysem wih he space iself, where he Earh moves and warps he space around. The objecs of he ses of Michelson-Morley Experimen (and also he Eher-Drif Experimen of D.C. Miller) are a he same graviaional poenial - a he Earh s surface. Therefore, he speed of ligh is consan. The inerferomeer used in Michelson-Morley experimen see ig.3: The ligh source, deecor, SSM (Semi-silvered mirror) and he mirrors are horizonally locaed (a he same graviaional poenial). The SSM, mirror A and mirror B are in he general case a he differen laiudes (L SSM, L A and L B ) wih he corresponding speed of he Earh s surface (V SSM, V A and V B ). If he disances beween (SSM-Mirror A) and (SSM-Mirror B) are D, he lenghs of he Two-way pah which he ligh passes beween (SSM-Mirror A) and (SSM-Mirror B) will depend on, which will be differen (V SSM, V A and V B are differen) and his difference will change as he angle α (he orienaion of he se of he experimen) changes. Tha is why, he change of he speed of ligh will be regisered in he Earh-Cenered Inerial reference frame. This difference is oo small o deec, bu in case of Muliple-way pah, obained by he D.C.Mill s Inerferomeer, he difference grows repeaedly. or example, in he special case of hese experimens, when α=45 0 or α=225 0 (see ig.3) he laiudes of he mirror A and mirror B are equal and we will have he same pah of he ligh in he space. Hence, in his paricular case even if we use D.C.Mill s Inerferomeer (associaed wih he Earh-Cenered Inerial reference frame), he change of he speed of ligh canno be regisered. In all of he above menioned cases, he objecs of he ses of he experimens are a he same graviaional poenial. The poenials of hese objecs in relaion o he Sun and heir poenials o he global locaion of he 242 ISSN E-ISSN

3 Applied Physics Research Vol. 3, No. 2; November 2011 Solar sysem in he Galaxy can be ignored, because he graviaion o he Earh is dominan. According o he aricle by Alber Einsein On he Influence of Graviaion on he Propagaion of Ligh, he speed of ligh is differen in is passage hrough he ime-spaial domains wih differen graviaional poenial: If we call he speed of ligh a he origin of co-ordinaes c 0, hen he speed of ligh c a a place wih he graviaion poenial Φ will be given by he relaion: c c (5) c The principle of he consancy of he speed of ligh holds good according o his heory in a differen form from he one ha usually underlies he ordinary heory of relaiviy. This approach also gives an explanaion for he Pioneer 10 and 11 Acceleraion Anomaly. The oal graviaional poenial (or he level of conracion/expansion of he space-ime) of cerain small spaial domain in he Universe corresponds o he GULW (Global Universe Level of Warping), or o he conracion/expansion of he space-ime of his domain. The speed of ligh increases/decreases in correspondence wih GULW of he spaial domains in he Universe, hrough which he ligh or elecromagneic radiaion passes. Or in any ime-spaial domain in he Solar sysem, GULW depends on (GL P +GL S +GL G ), where GL P is his level depending on he graviaional poenial relaed o he neares plane; GL S is his level depending on he graviaional poenial relaed o he Sun; and GL G is his level depending on he graviaional poenial relaed o he curren locaion of he Solar sysem in he Galaxy. 4. Discussion The observed anomaly of he acceleraion of he spaceships Pioneer 10 and Pioneer 11 is because of he fac ha he communicaional signals beween spacecraf and Earh (he elecromagneic radiaion) are wih much higher speed (and increasing) when he spaceships escape from he Sun graviy. urhermore, he par of rajecory of he communicaional elecromagneic signals from he spaceship o he Earh, in which he speed of ligh is much higher han he speed of ligh a he Earh surface, is increasing oo. As a resul, he expeced ravel ime of he communicaional elecromagneic signals (based on he consancy of he speed of elecromagneic radiaion) beween he spacecraf and Earh urns ou o be much more han he real ravel ime. So we regiser backward aracion (acceleraion) of he ship o he Sun. This explanaion of he Pioneer 10 and 11 Acceleraion Anomaly is acually anoher es of Einsein's conclusion in his aricle On he Influence of Graviaion on he Propagaion of Ligh. 5. Conclusion Acually, his paper gives a new explanaion of discrepan resuls abou he consancy of he speed of ligh, unambiguously obained from he one-way, wo-way and muliple-way measuremen experimens. The speed of he ligh is changing only as a resul of he change in he graviaional poenial (or he change of conracion/expansion of he space). Anoher new conribuion is he accepance ha he "eher" is considered o be he "warped space-ime of he Universe" iself. I is rue ha for more han 100 years scieniss make experimens o discover exisence of he "eher. Noes: The Special Relaiviy is based on he posulae of he consancy of he speed of ligh a he same graviaional poenial, bu regardless of he reference sysem. Tha is why, he Special Relaiviy has o be revised. We have o develop a new inerpreaion of he General Relaiviy based on he Uncerainy principle of he macro-world suggesed by (Sharlanov, G.V., 2011). As a consequence, his aricle (The posulae Invariance of he Speed of Ligh ) will give a soluion of problems such as he acceleraed expansion of he Universe, as well as he explanaion of he dark maer and he dark energy in he Universe, which has been under research for a long ime. References Einsein, А. (1911). On he Influence of Graviaion on he Propagaion of Ligh, originally from Annalen der Published by Canadian Cener of Science and Educaion 243

4 Applied Physicss Research Vol. 3, No. 2; November Physik [35]. Michelson, A..A., and Gale, H.E. (1925). Effec of he Earh s Roaion on he Velociy of Ligh, Asrophysical J., 61, 140. hp:/ //dx.doi.org/ / Miller, D.C. (1933). The Eher-Drif Experimen and he Deerminaion of he Absolue Moion he Earh, Reviews of Modern Physics,, 5. hp://dx.doi.org/ /revmodphys Marme, P. (2000). The GPS and he Consan Velociy of Ligh, Aca Scieniarum, 22, Kelly, A. (2005). Challenging Modern Physics, BrownWalker Press, lorida. Gif, S.J.G. (2010). One-Way Ligh Speed Deerminaion Using he Range Measuremen Equaion of he GPS, Applied Physics Research, Vol. 3, No. 1. Sharlanov, G.V. (2011). The Posulae Invariance of he Speed of Ligh, submied o Physics Essays. igure 1. igure ISSN E-ISSN

5 Applied Physics Research Vol. 3, No. 2; November 2011 igure 3. Published by Canadian Cener of Science and Educaion 245