GRAVITOELECTROMAGNETISM AND NEWTON S LAW OF UNIVERSAL GRAVITATION

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1 GAVITOELECTOMAGNETIM AND NEWTON LAW O UNIVEAL GAVITATION Antoine Ake etied Pofesso, Depatent Industial ienes Uniesity Collee Kaho int-lieen Gent - Beliu ant.ake@skynet.be Abstat In this atile it is shown that Newton s law of uniesal aitation pefetly an be dedued in the faewok of aito-eletoanetis (GEM). This eans that a eto theoy of aity does not neessay lead to epulsion. Keywods: aito-eletoanetis, aitation, theoy of infoatons INTODUCTION In aito-eletoanetis [],[],[3] (GEM) we think about the foe atin between two asses and in tes of aitational fields :. Mass sets up a aitational field in the spae aound itself;. The field ats on ass, this shows up in the foe that expeienes. Genealized: in GEM the aitational field plays an inteediay ole in the inteation between asses.. The aitational field is set up by a ien distibution of - whethe o not oin - asses and it is, just as the eletoaneti field, defined by two thee-diensional intetwined eto fields: the -field E and the -indution B. These eto fields eah hae a alue defined at eey point of spae and tie and ae thus, elatie to an inetial efeene fae O, eaded as funtions of the spae and tie oodinates. Just like the eletoaneti field ( E, B ), the aitational field ( E, B ) is atheatially desibed by a set of fou patial diffeential equations, the GEM-equations (o the Maxwell-Heaiside equations ) that desibe how E and B ay in spae due to thei soues - the asses and the ass flows - and how they ae intetwined. In 4 of Gaitoeletoanetis explained by the theoy of infoatons [4], the GEM equations ae dedued in the faewok of the theoy of infoatons. It is shown that at a point P of a aitational field - whee ρ G is the ass density and J G is the density of the ass flow - E and B ust obey to the followin equations:

2 . di E =. di = B 3. ote ρ G η B = t E 4. otb = ν. J G t And: η. ν = with η = G. In 5 of Gaito-eletoanetis explained by the theoy of infoatons [4] it is shown that the aitational inteations ae the effet of the tendeny of a ateial objet to aeleate in ode to beoe blind fo the aitational fields eneated by othe objets. The ation of the aitational field on a point ass is desibed by the foe law of GEM, a law analo to Loentz foe law: A point ass, that is - elatie to an inetial efeene fae O - oin with eloity in a aitational field ( E, B ), will aeleate elatie to its pope inetial efeene fae O with an aount a ': a' = E + ( B We an intepet this by sayin that the aitational field exets an ation on a point ass in that field. We all that ation the aitational foe G. It is defined as: G =. a' =. ) [ E + ( B )] whee is the est ass of the point ass. In 5 of Gaito-eletoanetis explained by the theoy of infoatons [4] it is shown that the effet of the aitational foe on the state of oeent of the point ass is expessed by: dp G = dt p =. is the linea oentu of the point ass elatie to the inetial efeene fae O. It is the podut of its elatiisti ass = with its eloity in O. The linea oentu of a oin point ass is a easue fo its inetia, fo its ability to pesist in its dynai state. GEM an be onsideed as an upade of Newtonian aity. Unlike Newton s law of uniesal aitation, GEM takes the effet of the kinetis of the aitatin objets into aount. It has been show [7],[8] that etain onete peditions ade on the basis of the

3 3 aito-eletoaneti desiption of aity ae pefetly in line with the esults of osoloial obseations. Aodin to the theoy of infoatons [4] - that explains the aitational phenoena and laws as the aosopi anifestations of eleentay infoation aies, alled infoatons -the aitational field is not a puely atheatial onstution. It is not just an eleent of ou thinkin about natue but a substantial eleent of natue. The substane of the aitational field is alled -infoation. The statin point of GEM diffes fundaentally fo the statin point of GT, beause in the desiption by GEM of the aitational phenoena and laws spae and tie don t play an atie ole. It ae eleents of the desiption of natue that do not patiipate in the physial poesses. NEWTON UNIVEAL LAW O GAVITATION The phenoenon of the aitational inteation between two patiles at est is desibed by Newton s uniesal law of aitation [5] : The foe between any two patiles hain asses and sepaated by a distane is an attation atin alon the line joinin the patiles and has the anitude.. = G. =. whee G = is a uniesal onstant hain the sae alue fo all pais of patiles. We will show that this law pefetly an be dedued in the faewok of GEM. P e e P i In fi we onside two point asses with est asses and anhoed at the points P and P of an inetial efeene fae.. eates and aintains a aitational field that at P is defined by the -field: E =. e. η.

4 4 Indeed. The fist GEM-equation - that is the atheatial expession of the onseation of -infoation [4] - states that the flux of the aitational field thouh an abitay losed sufae is deteined by the enlosed ass in aodin to the law: in E. d = () η Let us apply this equation to an hypothetial sphee with adius enteed on P. - Beause of the syety, E is at eey point of that sphee pependiula to its sufae and has the sae anitude. o, at an abitay point P of the sphee, E an be expessed as E = E whee e and E espetiely ae the unit eto and the oponent (with onstant anitude) of E in the dietion of P P.. e uthe, at eey point of the sufae of the sphee: d = d. e. With this infoation we alulate E. d: E. d E. e. d. e = E. d = E. d = E =.4π () - The enlosed ass is, so in = (3) Takin into aount () and (3), () beoes: E.4π η = (4) We onlude: at a point P at a distane fo P the aitational field is pointin to P and deteined by: E = E. e =. e In patiula at the point P : E =. e η.. If was fee, aodin to the postulate of the aitational inteation [4] it would aeleate with an aount a : a = o the aitational field of exets a aitational foe on : E

5 5.. e = a =. E =. 4. π. η. In a siila anne we find. : =. e = η..the INTEACTION BETWEEN TWO MOVING POINT MAE Z=Z X X O Y O Y i Two point asses with est asses and (fi ) ae anhoed in the inetial fae O that is oin elatie to the inetial fae O with onstant eloity =. ez. The distane between the asses is. elatie to O the asses ae at est. Aodin to Newton s law of uniesal aitation, they exet on eah othe equal but opposite foes: ' = ' = '. = G... =. η elatie to O both asses ae oin with onstant speed in the dietion of the Z-axis. o the tansfoation equations between an inetial fae O and anothe inetial fae O, in whih a point ass expeienin a foe is instantaneously at est, we an iediately dedue the foe that the point asses exet on eah othe in O [6] ae: = = = '. ( ) = '. We will show that also this fo of Newton s law of uniesal aitation pefetly an be dedued in the faewok of GEM.

6 6. Z=Z P =O θ P O Y X i 3 In 3. of Gaito-eletoanetis explained by the theoy of infoatons [4] it is shown that - at a point P whose position is deteined by the tie dependent position eto (fi 3) - the aitational field ( E, B ) of a patile with est ass that is oin with onstant eloity =. ez alon the Z-axis of the inetial efeene fae O (fi 3) is deteined by: w E =.. =.. e (.sin θ ) (.sin θ ) B =..( ) 3 3. (.sin θ ) with =, the diensionless speed of. One an eify that these expessions satisfy the laws of GEM.. In the inetial fae O of fi, the asses and ae oin in the dietion of the Z- axis with speed. oes thouh the aitational field eneated by, and oes thouh that eneated by. Aodin the aboe foulas, the anitude of the GEM field eated and aintained by at the position of is deteined by: E =. and B =.. And aodin to the foe law.[ E + ( B )] G =,, the anitude of the foe exeted by the aitational field ( E, B) on - this is the attation foe of on - is: =.( E. B ) Note that E is pointin to the atual position of the patile and not to its liht-speed delayed position.

7 7 Afte substitution: ' =.. =. In the sae way we find: ' =.. =. We onlude that the oin asses attat eah othe with a foe: = = = '. This esult pefetly aees with that based on..t. 3.CONCLUION o the aboe we an onlude that it s easy to atheatially dedue all aspets of Newton s law fo the laws of GEM. The sin of the esult indiates that the aitational inteation between asses is always attatie. That eans that a eto theoy about aity not neessay leads to epulsion. efeenes.heaiside, Olie. A Gaitational and Eletoaneti Analoy, Pat I. sl : The Eletiian 893, Vol Jefienko, Ole. Causality, Eletoaneti Indution, and Gaitation. sl : Eletet ientifi 99, Vol Ake, Antoine. Gaitatie en elektoanetise. Gent : Uiteeij Neelland, 8. 4.Ake, Antoine. Gaito-eletoanetis explained by the theoy of infoatons. Hadoni Jounal, Vol. 36, Nube 4, Auust 3 5.esnik, Daid and Halliday, obet. undaentals of Physis. New Yok - London - ydney - Toonto : John Wiley & ons, esnik, obet. Intodution to speial elatiity. New Yok, London, ydney : John Wiley & ons, In, Abab I. Abab. The enealized Newton s law of aitation esus the eneal theoy of aity. Jounal of Moden Physis, Vol. 3 No. 9,, pp ( 8.Taja, M. and de Matos, C.J. Adane of Meuy Peihelion explained by Coaity. 3. axi: -q/344. (