GRAVITATION AND ELECTROMAGNETISM Introduction to the THEORY OF INFORMATONS by Antoine Acke

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1 GRAVITATION AND LCTROMAGNTISM Intodution to the THORY OF INFORMATONS by Antoine Ake PRFAC With the theoy of infoatons * we pesent a new theoy that explains in a siple way the phenoena and the laws of the avitational and the eletoaneti inteations. We intodue the te infoation in physis by naowin his eveyday eanin to a physial onept. We ive that te a speifi sense by definin it atheatially. The theoy of infoatons stats fo the idea that a physial objet anifests itself in spae by eittin infoatons. Infoatons ae dot-shaped entities whih ush away with the speed of liht ayin infoation about the position, the veloity and the eletial hae of the eitte. The ules fo the eission of infoatons by a point ass at est, and the attibutes of the infoatons ae defined by the postulate of the eission of infoatons. In the paaaphs I,...,IV of this pape we study the onsequenes of the postulate of the eission of infoatons fo the avitational and in the paaaph V fo the eletoaneti inteations. We ive a new eanin to the physial entity field and to the physial quantities that haateize a field (field, indution). We also dedue the laws to whih these quantities ae subjeted (laws of Maxwell) and the ules that anae the utual foes. We show that thee is a eat analoy between a avitational and an eletoaneti field, what iplies that the avitational field has a oponent that is analoous to the aneti field. In the paaaph VI we use the theoy of infoatons fo the study of eletoaneti waves and adiation. We intodue the idea that photons ae nothin but infoatons ayin an eney-paket. This leads to the view that the defletion of liht passin thouh a naow slit should be undestood as the visible effet of the tansition of an eney-paket fo one infoaton to anothe that osses his path. Finally we investiate the ipliations of the avity-eletoanetis analoy fo the existene of avitational waves and avitons. We hope to onvine the eade of the usefulness of the theoy of infoatons in the study of the phenoena and laws whih it fouses. Novebe 9 ant.ake@skynet.be * GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI Auteu: Antoine Ake - ant.ake@skynet.be - Uitave 8 Uiteveij: Nevelland, Industielaan 1, 931-Donen D/8/3988/1 The theoy of infoatons Antoine Ake

2 I. TH GRAVITATIONAL FILD OF A MASS AT RST 1. The postulate of the eission of infoatons The analoy between Newton s univesal law of avitation and Coulob s law suests that the ehaniss behind the inteations between asses and those between eletial haes ae of the sae natue. With the ai to undestand and to desibe these ehaniss, we intodue a new quantity in the asenal of physial onepts: INFORMATION. We suppose that infoation is tanspoted by ass- and eney-less dot-shaped entities that ush with the speed of liht () thouh spae. We all these infoation aies INFORMATONS. ah ateial objet ontinuously eits infoatons. An infoaton always aies - INFORMATION, whih is at the oot of avitation. Infoatons eitted by an eletially haed objet tanspot also e-information, the ause of the eletial inteation. The eission of infoatons by a point ass () anhoed in an inetial fae, is ovened by the POSTULAT OF TH MISSION OF INFORMATONS. A. TH MISSION is ovened by the followin ules: 1. The eission is unifo in all dietions of spae and the infoatons divee at the speed of liht ( /s) alon adial tajetoies elative to the loation of the eitte.. N &, the ate at whih a point-ass eits infoatons, is tie independent and popotional to the ass. So, thee is a onstant K so that: N & K. 3. The onstant K is equal to the atio of the squae of the speed of liht () to the Plank onstant (h): K 1,36.1 k. s h B. We all the essential attibute of an infoaton his -SPIN VCTOR. -spin vetos ae epesented as s en defined by: 1. The -spin vetos ae dieted towad the position of the eitte.. All -spin vetos have the sae anitude, naely: s ,18.1. s K. η 9 3 ( η 1,19.1 k. s. 4. π. G with G the avitational onstant) s, the anitude of the -spin-veto, is the eleentay -infoation quantity. The theoy of infoatons - - Antoine Ake

3 C. Infoatons eitted by an eletially haed point ass (a point hae q), have a seond attibute, naely the e-spin VCTOR. e-spin vetos ae epesented as s e and defined by: 1. The e-spin vetos ae adial elative to the position of the eitte. They ae entifual when the eitte aies a positive hae (q +Q) and entipetal when the hae of the eitte is neative (q -Q).. s e, the anitude of an e-spin veto depends on Q/, the hae pe unit of ass. She is defined by: 1 Q 4 Q 1 s. 8,3.1. N.. s. C e K. ε 1 ( ε 8,85.1 F / is the peittivity onstant).. The avitational field of a point ass Z P s O Y X Fi 1 In fi1 we onside an (eletially neutal) point ass that is anhoed in the oiin of an inetial fae. It ontinuously sends infoatons in all dietions of spae. The infoatons that o thouh afixed point P - defined by the position veto have two attibutes: thei veloity and thei -spin veto s : e and s.. e K. η K. η The ate at whih the point ass eits -infoation is the podut of the ate at whih it eits infoatons with the eleentay -infoation quantity: N&. s Of ouse, this is also the ate at whih it sends -infoation thouh any losed sufae that spans. η The theoy of infoatons Antoine Ake

4 The eission of infoatons fills the spae aound with a loud of -infoation. This loud has the shape of a sphee whose sufae oes away - at the speed of liht - fo the ente O, the position of the point ass. - Within the loud is a stationay state: eah spatial eion ontains an unhanin nube of infoatons and thus a onstant quantity of -infoation. Moeove, the oientation of the -spin vetos of the infoatons passin thouh a fixed point is always the sae. - One an identify the loud with a ontinuu: eah spatial eion ontains a vey lae nube of infoatons: the -infoation is like ontinuously spead ove the extent of the eion. We all the loud of -infoation suoundin, the GRAVITATIONAL FILD * o the - FILD of het point ass. Thouh any - even vey sall - sufae in the avitational field ae ushin, without inteuption, ountless infoatons: we an onside the otion of -infoation thouh a sufae as a ontinuous STRAM o FLOW OF -INFORMATION. We know aleady that the intensity of the flow of -infoation thouh a losed sufae that spans O is expessed as: N&. s η If the losed sufae is a sphee of adius, the intensity of the flow pe unit aea is iven by: 4. π.. η This is the density of the flow of -infoation in eah point P at a distane fo (fi 1). This quantity is, toethe with the oientation of the -spin vetos passin in the viinity of P, haateisti fo het avitational field at that point. Thus, the avitational field of the point ass is, in a point P, fully defined by the vetoial quantity : N& 4. π.. s 4. π. η.. e 4. π. η. 3. * The tie T elapsed sine the eeene of a point-ass (this is the tie elapsed sine the eeene of the univese) and the adius R of its field of avitation ae linked by the elation R.T. Assuin that the univese - sine its beinnin (1,8.1 1 yeas ao) - unifoly expands, a point at a distane fo uns away with speed v: onstant: H 1 4 1,7.1 T 1 v.. H. R T. H is de Hubble / s illionliht yeas The theoy of infoatons Antoine Ake

5 We all this quantity the GRAVITATIONAL FILD STRNGHT o the -FILD STRNGHT. In any point of the avitational field of the point-ass, the oientation of oesponds with the oientation of the -spin-vetos of the infoatons who ae passin by in the viinity of that point. And the anitude of is the density of the -infoation flow in that point. Let us note that is opposite to the sense of oveent of the infoatons. Let us onside a sufae-eleent ds in P (fi,a). Its oientation and anitude ae opletely deteined by the sufae-veto ds (fi,b) ds ds. e n ds ds. en α P Fi,a Fi,b By dφ, we epesent the ate at whih -infoation flows thouh ds in the sense of the positive noal and we all this sala quantity the LMNTARY -FLUX THROUGH ds: dφ. ds. ds.osα Fo an abitay losed sufae S that spans, the outwad flux (whih we obtain by inteatin the eleentay ontibutions dφ ove S) ust be equal to the ate at whih the ass eits -infoation. The ate at whih -infoation flows out ust indeed be equal to the ate at whih the ass podues -infoation. Thus: Φ. ds η 3. The avitational field of a set of point-asses We onside a set of point-asses 1,, i, n whih ae anhoed in an inetial fae. In an abitay point P, the flows of -infoation who ae eitted by the distint asses ae defined by the avitational field stenths,...,,..., 1 i n. dφ, the ate at whih -infoaton flows, in the sense of the positive noal, thouh a sufae-eleent ds in P, is the su of the ontibutions of the distint asses: n n dφ ( i. ds) ( i ). ds. ds i 1 i 1 The theoy of infoatons Antoine Ake

6 Thus, the FFCTIV DNSITY OF TH FLOW OF -INFORMATION (the -field stenht) in P is opletely defined by: n i i 1 We onlude: The -field of a set anhoed point asses is in any point of spae opletely defined by the vetoial su of the field stenths aused by the distint asses. Let us note that the oientation of the effetive field stenth has no lone a elation with the oveent dietion of the passin infoatons. One shows easily that the outside -flux thouh a losed sufae in the -field of a set of anhoed point asses only depends on the spanned asses in : Φ in. ds η 4. The avitational field of a ass ontinuu We all an objet, in whih the atte is spead ove the oupied volue, in a tie independent anne, a ass ontinuu. In eah point Q of suh a ontinuu, the auulation of ass is defined by the (MASS) DNSITY ρ G. To define this sala quantity one onsides a volue eleent dv aound Q, and one deteines the enlosed ass d. The auulation of ass in the viinity of Q is defined by: d ρ G dv A ass ontinuu - anhoed in an inetial fae - is equivalent to a set of infinitely any infinitesial ass eleents d. The ontibution of eah of the to the field stenth in an abitay point P is d., the effetive field stenth in P, is the esult of the inteation ove the volue of the ontinuu of all these ontibutions. It eains evident that the outside -flux thouh a losed sufae only depends on the ass enlosed by the sufae. That an be expessed as follows: Futheoe, one an show that: div ot ρ G η what iplies the existene of a avitational potential funtion V fo whih: ***** ****** ***** ***** ***** ***** ***** adv The theoy of infoatons Antoine Ake

7 II. TH INTRACTION BTWN MASSS AT RST We onside a nube of point asses anhoed in an inetial fae. They eate and aintain a avitational field that, at eah point of spae, is opletely deteined by the veto. ah ass is iesed in a loud of -infoation. In eah point, exept its own anhoae, eah ass ontibutes to the onstution of that loud. Let us onside the ass anhoed in P. If the othe asses wee not thee, then should be at the ente of a pefetly spheial loud of -infoation. In eality this is not the ase: the eission of -infoation by the othe asses is esponsible fo the distubane of that syety and the extent of distubane in the diet viinity of is popotional to in P. Indeed in P epesents the intensity of the flow of -infoation send to P by the othe asses. If it was fee to ove, the point ass ould estoe the spheial syety of the - infoation loud in his diet viinity: it would be enouh to aeleate with an aount a. Aeleatin in this way has the effet that the exten field disappeas in the oiin of the eien-efeene fae * of. If it aeleates that way, the ass beoes blind fo the -infoation send to P by the othe asses, it sees only he own spheial - infoation loud. These insihts ae expessed in the followin postulate. 1. The postulate of the avitational ation A fee point ass aquies in a point of a avitational field an aeleation a so that the -infoation loud in its diet viinity shows spheial syety elative to its position. A point ass who is anhoed in a avitational field annot aeleate. In that ase it TNDS to ove. We an onlude that: A point ass anhoed in a point of a avitational field is subjeted to a tendeny to ove in the dietion defined by, the field stenth in that point. One the anhoae is boken, the ass aquies a VCTORIAL ACCLRATION a that equals. * The eien efeene fae of the point ass is the efeene fae anhoed at : is always at the oiin of his eien efeene fae. The theoy of infoatons Antoine Ake

8 . The onept foe - the avitational foe A point ass, anhoed in a avitational field, expeienes an ation beause of that field; an ation that is opensated by the anhoae. - That ation is popotional to the extent to whih the spheial syety of the avitational field aound is distubed by the exten -field, thus to the loal value of - It depends also on the anitude of. Indeed, the -infoation loud eated and aintained by is oe opat when is eate. That iplies that the distubin effet on the spheial syety aound by the exten -field is salle when is eate. Thus, to ipose the aeleation a the ation of the avitational field on ust be eate when is eate. We onlude: The ation that tend to aeleate a point ass in a avitational field ust be popotional to - the field stenth to whih the ass is exposed - and to the, anitude of the ass. We epesent that ation by F and we all this vetoial quantity the foe developed by the -field on the ass o the GRAVITATIONAL FORC on. We define it by the elation: F.. A ass anhoed at a point P annot aeleate, what iplies that the effet of the anhoae ust opensate the avitational foe. This eans that the distubane of the spheial syety aound P by ust be anelled by the -infoation flow eated and aintained by the anhoae. The density of that flow at P ust be equal and opposite to. It annot but the anhoae exets an ation on that is exatly equal and opposite to the avitational foe. That ation is alled a RACTION FORC. This disussion leads to the followin insiht: ah phenoenon that distubs the spheial syety aound a point ass, exets a foe on that ass. Between the avitational foe on a ass and the loal field stenth exists the followin elationship: F The aeleation iposed to the ass by the avitational foe is thus: F a The theoy of infoatons Antoine Ake

9 Considein that the effet of the avitational foe is atually the sae as that of eah othe foe we an onlude that the elation between a foe F and the aeleation a that it iposes to a fee ass is: F. a 3. Newtons univesal law of avitation R P e 1 F 1 F 1 1 P 1 e 1 Fi 3 In fi 3 we onside two point asses 1 and anhoed in the points P 1 and P of an inetial fae. 1 eates and aintains a avitational field that in P is defined by the -field stenth: This field exets a avitational foe on : π. η e 1 In a siila anne we find F 1 : F.. e π. η 1 F. e 4. π. η F 1 This is the atheatial foulation of Newtons univesal law of avitation. ***** ***** ***** ***** ***** ***** ***** The theoy of infoatons Antoine Ake

10 III. TH GRAVITATIONAL FILD OF MOVING MASSS 1.The eission of infoatons by a point ass that desibes a unifo etilinea otion Z θ v θ s P P 1 θ P Fi 4 In fi 4 we onside a point ass * that oves with a onstant veloity v alon the Z-axis of an inetial fae. Its instantaneous position (at the abitay oent t) is P 1. The position of P, an abitay fixed point in spae, is defined by the veto 1 P P. The position veto - just like the distane and the anle θ - is tie dependent beause the position of P 1 is onstantly hanin. The infoatons that - with the speed of liht - pass at the oent t thouh P, ae eitted when was at P. Bidin the distane P P took the inteval t: t Duin thei ush fo P to P, the ass oved ove the distane fo P to P 1 : P P 1 v. t - The veloity of the infoatons is oiented alon the path they follow, thus alon the adius P P. * Fo easons that will beoe lea late, we indiate the ass who deteines the ate of the eission of infoatons - the est ass - as. The theoy of infoatons Antoine Ake

11 - Thei -spin veto s points to P 1, the position of at the oent t. This is an ipliation of ule B.1 of the postulate of the eission of infoatons. The lines who ay s and fo an anle θ. We all this anle, that is haateisti fo the speed of the point ass, the CHARACTRISTIC ANGL. The quantity s s. sin( θ ) is alled the CHARACTRISTIC -INFORMATION o the β- β INFORMATION of an infoation. We posit that infoatons eitted by a ovin point ass tanspot infoation about the veloity of the ass. This infoation is epesented by the GRAVITATIONAL CHARACTRISTIC VCTOR o β-vctor s whih is defined by: β s s β - The β-veto is pependiula to the plane foed by the path of the infoaton and the staiht line that aies the -spin veto, thus pependiula to the plane foed by the point P and the path of the infoaton. - Its oientation elative tot that plane is defined by the ule of the oksew : in the ase of fi 4, the β-vetos have the oientation of the positive X-axis. - Its anitude is: s s. sin( θ ), the β-infoation of the infoation. β We apply the sine ule to the tianle P P 1 P: It follows: s sin( θ ) sinθ v. t. t v s..sinθ s. β.sinθ s β β. v β is the oponent of the diensionless veloity β pependiula to s. Takin into aount the oientation of the diffeent vetos, the β-veto of an infoation eitted by a point ass with onstant veloity an also be expessed as: v s sβ The theoy of infoatons Antoine Ake

12 .The avitational indution of a point ass desibin a unifo etilinea otion We onside aain the situation fo fi 4. All infoatons in dv - the volue eleent in P - ay both -infoation and β-infoation. The β-infoation is elated to the veloity of the eittin ass and epesented by the haateisti vetos s : s v s s β With n, the density of the loud of infoatons at the oent t at P (nube of infoatons pe unit volue), the β-infoation in dv is deteined by the anitude of the veto: s v s n. sβ. dv n.. dv n. And the density of the the β-infoation (haateisti infoation pe unit volue) in P is deteined by: s v s n. s β n. n. β. dv We all this (tie dependent) vetoial quantity - that will be epesented by GRAVITATIONAL INDUCTION o het -INDUCTION in P: - Its anitude B deteines the density of the β-infoation at P. - Its oientation deteines the oientation of the β-vetos s β at that point. B - the 3.The avitational field of a point ass desibin a unifo etilinea otion w A point ass, ovin with onstant veloity v v. e z alon the Z-axis of an inetial fae, eates and aintains a loud of infoatons that ae ayin both - and β-infoation. That loud an be identified with a tie dependent ontinuu. That ontinuu is alled the GRAVITATIONAL FILD of the point ass. It is haateized by two tie dependent vetoial quantities: the avitational field stenth (shot: -field) and the avitational indution (shot: -indution) B. - With N the density of the flow of infoatons in P (the ate pe unit aea at whih the infoatons oss an eleentay sufae pependiula to thei dietion of oveent), the -field at that point is: N. s - With n, the density of the loud of infoatons in P (nube of infoatons pe unit volue), the -indution at that point is: The theoy of infoatons Antoine Ake

13 B n. s β Between N and n the next elationship exists: N n If v - the speed of het point ass - is uh salle than - the speed of liht - the distane P P 1 is neliible opaed to the distane P 1 P. Then: N N& K. 4. π. 4. π. N& and n K. 4. π.. 4. π.. Futhe (I.): s K. η K. η e Thus, if we ae easonin not elativisti *, the -field in P is expessed as: N s 4. π. η.. 3. Then, we wok out the foula that deteines the -indution at P. We find: v s v ( N. s ) 1.( v ) B n. sβ n π.. η And, intoduin the onstant ν by the definition: ν 1. η the -indution in P is expessed as: B ν. 4. π..( ) v 3 * Fo the esults of the elativisti easonin s, see: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk II (Nevelland 8) The theoy of infoatons Antoine Ake

14 4.The avitational field of a set of point asses desibin unifo etilinea otions We onside a set of point asses 1,, i, n whih ove with onstant veloities v1,..., v i,..., v n in an inetial fae. This set eates and aintains a avitational field that in eah point of spae is haateised by the veto pai (, B ). - ah ass i eits ontinuously -infoation and ontibutes with an aount i to the -field at an abitay point P. As in I.3 we onlude that the effetive -field defined as: i in P is - If it is ovin eah ass i eits also β-infoation, theeby ontibutin to the -indution in P with an aount B. It is evident that the β-infoation in the volue eleent dv in P at eah oent t is expessed by: Thus, the effetive -indution ( B i B in P is:. dv ) ( B dv i i ). B B i 5. The avitational field of a stationay ass flow The te stationay ass flow indiates the oveent of a hooeneous and inopessible fluid that in an invaiable way flows thouh a eion of spae. The intensity of the flow at an abitay point P is haateised by the flow density J G. The anitude of this vetoial quantity equals the ate pe unit aea at whih the ass flows thouh a sufae eleent that is pependiula to the flow at P. The oientation of J oesponds to the dietion of that flow. If v is the veloity of the ass eleent ρ. G dv that at the oent t flows thouh P, then: J G ρ. v G G The ate at whih ass flows thouh a sufae eleent ds in P in the sense of the positive noal, is iven by: dig J G. ds The theoy of infoatons Antoine Ake

15 And the ate at whih the flow tanspots - in the positive sense (defined by the oientation of the sufae vetos ds ) - ass thouh an abitay sufae S, is: i J. ds We all i G the intensity of the ass flow thouh S. G S Sine a stationay ass flow is the aosopi anifestation of ovin ass eleents ρ.dv, it eates and aintains a avitational field. And sine the veloity v G of the ass eleent in eah point is tie independent, the avitational field of a stationay ass flow will be tie independent. It is evident that the ules of I.4 also apply fo this tie independent -field: - div ρ G η - ot what iplies: adv One an pove that the ules fo the tie independent -indution ae: - divb what iplies B ota otb ν. J - G G 6. The laws of the avitational field We have shown that ovin (inlusive otatin) asses eate and aintain a avitational field, that in eah point of spae is haateised by two tie dependent vetos: the (effetive) -field and the (effetive) -indution B. The infoatons that - at the oent t - pass in the diet viinity of P with veloity ontibute with an aount ( N. s ) to the instantaneous value of the -field and with an aount ( n. s ) tot the instantaneous -indution at that point. β s and s β espetively ae thei -spin vetos and thei β-vetos. They ae linked by - the elationship: s s β - N is the instantaneous value of the density of the flow of infoatons with veloity at P and n is the instantaneous value of the density of the loud of those infoatons in that point. N and n ae linked by the elationship: N n The theoy of infoatons Antoine Ake

16 One an pove * that in a atte fee point of a avitational field followin laws: 1. div. div B en B obey the ot otb B t 1. t The fist law expesses the onsevation of -infoation, the seond the fat that the β- veto of an infoaton is always pependiula to the plane foed by his spin veto and his veloity. Laws 3 and 4 expess that a hane in tie of B ( ) is always elated to a hane in spae of ( B ). A ass eleent at a point P in a ass ontinuu is always an eitto of -infoation, and - - if it oves - also a soue of β-infoation. The instantaneous value of ρ G at P ontibutes with an aount ρ G η to the instantaneous value of div at that point. And the ontibution of the instantaneous value of J G to otb is G ν.j. In an abitay point of a avitational field the pevious laws beoe: 1. div. div 3. B ot ρ G η B t 1 4. otb. ν. J G t These ae the avitational analoues of Maxwell laws. ***** ***** ***** ***** ***** ***** ***** * The oplete atheatial deivations an be found in: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk III (Nevelland 8) The theoy of infoatons Antoine Ake

17 IV. TH INTRACTION BTWN MOVING MASSS We onside a nube of point asses ovin in an inetial fae O. They eate and aintain a avitational field that in eah point of spae is defined by the vetos and ah ass is iesed in a loud of -infoation and of β-infoation. In eah point, exept its own position, eah ass ontibutes to the onstution of that loud. Let us onside the ass that, at the oent t, oes thouh the point P with veloity v. - If the othe asses wee not thee, the -field in the viinity of (the eien -field of ) should be syeti elative to the aie of the veto v. Indeed, the -spin vetos of the infoatons eitted by duin the inteval (t - t, t + t) ae all dieted to that line. In eality that syety is distubed by the -infoation that the othe asses send to P., the instantaneous value of the -field in P, defines the extent to whih this ous. - If the othe asses wee not thee, the β-field in the viinity of (the eien β-field of ) should otate aound the aie of the veto v. The vetos of the veto field defined by the veto podut of v with de -indution that haateizes the eien β-field of, should - as - be syeti elative to the aie of the veto v. In eality this syety is distubed by the β-infoation send to P by the othe asses. The veto podut v B ) of the instantaneous values of the veloity of and the -indution at P, ( defines the extent to whih this ous. If it was fee to ove, the point ass ould estoe the speifi syety in its diet viinity by aeleatin with an aount a' + ( v B ) elative to its eien inetial fae *. In that anne it should beoe blind fo the distubane of syety of het avitational field in its diet viinity. These insihts fo the basis of the followin postulate. B. 1. The postulate of the avitational ation A point ass, ovin in a avitational field (, B ) with veloity v, tends to beoe blind fo the influene of that field on the syety of its eien field. If it is fee to ove, it will aeleate elative to its eien inetial fae with an aount a ' : a' + ( v B ) * The eien inetial fae of the point ass is the efeene fae that at eah oent t oves elative to O with the sae veloity as. The theoy of infoatons Antoine Ake

18 . The avitational foe The ation of the avitational field (, B ) on a ovin point ass (veloity v ) is alled the GRAVITATIONOL FORC F G on. In extension of II., we define F G [ + ( v B )]. F G as: is the RST MASS of the point ass: it is the ass that deteines the ate of the eission of infoatons by the ass within any efeene fae. One an pove * that the avitational foe is the ause of a hane of the linea oentu p of the point ass when it is fee to ove in the inetial fae O: the ate of hane of the linea oentu equals the foe: dp dt F G The linea oentu of a ovin point ass is defined as: p. v 1 β. v In this ontext is its RLATIVISTIC MASS. Between both asses exist the elation: et 1 β v β The elativisti ass deteines the ate of eission of infoatons in a efeene fae O if the tie is deteined by a lok that is anhoed at the ovin ass. 3. The inteation between two unifo linea ovin point asses The point asses 1 and (fi 5) ae anhoed in the inetial fae O that is ovin elative to the inetial fae O with onstant veloity v v. ez. The distane between the asses is R. In O the asses don t ove. They ae iesed in eah othe s -infoation loud and they attat - aodin Newton s law of avitation - one anothe with an equal foe: ' ' ' ' 1 1. F' F1 F π. η R * Fo the atheatial deivation, see: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk II, 6. (Nevelland 8) The theoy of infoatons Antoine Ake

19 ZZ v R F 1 F 1 O Y 1 X O Y X Fi 5 In the fae O both asses ae ovin in the dietion of the Z-axis with the speed v. The avitational field of a ovin ass is haateized by the veto pai (, B ) and the utual attation is now defined by: F F F.( v. B ) 1.( 1 v. B 1) 1 1 In elativisti iustanes *, the -fields ae haateised by: 1 1. en 4πη R 1 β πη R β 1 And the -indutions by: 1 B 1.. 4πη R en 1 B.. 4πη R 1 β v 1 1 β v Substitution ives: F F πη R β We an onlude that the oponent of the avitational foe due to the -indution is β ties salle than that due to the -field. This iplies that, by speeds uh salle than the speed of liht, the effets of het β- infoation ae asked. ***** ***** ***** ***** ***** ***** ***** * Fo the atheatial deivation of these foulas see: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk II, 1. en. (Nevelland 8) The theoy of infoatons Antoine Ake

20 V. LCTROMAGNTISM 5.1. The eleti field of a point hae at est Fo the postulate of the eission of infoatons follows that an eletially haed point ass at est in an inetial fae, eits infoatons that not only tanspot - but also e- infoation. Z P s e s O, q Y X Fi 6 In fi 6 we onside a ateial point, with ass and (positive) hae q, that is anhoed in het oiin of an inetial fae. The infoatons oin thouh the fixed point P - defined by the position veto - have thee attibutes: thei veloity, thei -spin veto s and thei e-spin veto s :.. e 1 1 K. η K. η s.. e se.... e q 1 q 1 K. ε K. ε e The avitational field of the point ass, we have studied unde I, is the aosopi anifestation of het -spin vetos of the infoatons. Thei e-spin veto leads to an analoue entity: the LCTRIC FILD o the e-fild OF TH POINT CHARG q that is haateised by the LCTRIC FILD STRNGHT o de e- FILD. In the sae way as we linked unde I. the -field to the density of the -infoation flow, so we link the e-field to the density of the e-infoation flow by: N& 4. π.. s e q 4. π. ε.. e q 4. π. ε. 3. The theoy of infoatons - - Antoine Ake

21 The ole played by the fato ( ) in the definition of q is taken by the fato ( ) in het η ε definition of. By a easonin analoue to that unde I.3, we show that the eleti field of a set of anhoed point haes is the vetoial supeposition of the eleti fields of the diffeent haes. We extend this to a hae ontinuu (opae with I.4) and haateize the spatial hae distibution by definin the auulation of hae in a point by the eleti hae density ρ : ρ Fo the analoy avitation-eletiity we onlude that het eletial field obeys to two laws (opae with I.4): 1. div ρ ε. ot, what iplies : adv dq dv. The inteation between haes at est We onside a nube of point haes anhoed in an inetial fae. They eate and aintain an eleti field that, at eah point of spae, is opletely deteined by the veto. ah hae is iesed in a loud of e-infoation. In eah point, exept in its own anhoae, eah hae ontibutes to the onstution of that loud. Let us onside the hae q anhoed in P. If the othe haes wee not thee, then q should be at the ente of a pefetly spheial loud of e-infoation. In eality this is not the ase: the eission of e-infoation by the othe haes is esponsible fo the distubane of that syety and the extent of distubane in the diet viinity of q is popotional to in P. Indeed in P epesents the intensity of the flow of e-infoation send to P by the othe haes. If it was fee to ove, the point hae q ould estoe the spheial syety of the e- infoation loud in his diet viinity: it would suffie to aeleate with an aount q a.. Aeleatin in this way has the effet that the exten field disappeas in the oiin of the eien-efeene fae of q. If it aeleates that way, the hae beoes blind fo the e-infoation send to P by the othe haes, it sees only its own spheial e- infoation loud. These insihts ae expessed in the followin postulate. q A fee point hae q aquies in a point of an eleti field an aeleation a. so that the e-infoation loud in its diet viinity shows spheial syety elative to its position. The theoy of infoatons Antoine Ake

22 A point hae that is anhoed in an eleti field annot aeleate. In that ase it TNDS to ove. We an onlude that: A point hae anhoed in a point of an eleti field is subjeted to a tendeny to ove in the dietion defined by, the field in that point. One the anhoae boken, the hae aquies a VCTORIAL ACCLRATION a that equals q.. The ation exeted by the field on q is alled the LCTRIC FORC onlude: F q. F ON q. Fo II. we In fi 7 we onside two anhoed point haes. R q P e 1 F 1 q 1 P 1 F 1 e 1 Fi. 7 It is easy to show (opae with II.3) that the utual eleti foes ae expessed as: F q. q q. q 1 1. e 1 4. π. ε. R en 1 F1. e 4. π. ε 1. R This is the atheatial foulation of COULOMB s LAW. Thee is a foal analoy with Newton s univesal law of avitation. Howeve thee is a diffeene: Coulob s law indiates that the eleti inteation an be as well populsive (the haes have the sae sin) as attative (the haes have opposite sins), whee Newton s law only peits attation (ass is always positive). The theoy of infoatons - - Antoine Ake

23 3. The influene of a dieleti on the eleti field Dieletis in an eleti field ae POLARISD. The oleules of a dieleti behave as eleti dipoles. These ae neutal stutues onsistin of two equal and opposite point haes (-Q, +Q) whih ae sepaated by a sall distane a and haateised by thei dipole oent p a. Q. e p. ( e p is oiented fo -Q to +Q.) leti dipoles in an eleti field have a tendeny fo alinent with that field: the dieleti beoes polaised. The extend of polaisation in a point P of a dieleti is haateized by the POLARISATION P. P depends on the field in P and is defined by: κ is the suseptibility of the dieleti in P. P κ. ε. One an show * that the eleti field in an abitay point of spae an be haateised by the veto D, that not depends on the natue of the atte at that point. This vetoial quantity is alled the DILCTRIC INDUCTION. It is defined by: D. + P The law that expesses the onsevation of e-infoation (V.1) an be enealized to: ε divd ρ Let us finally note that thee doesn t exist ass dipoles. That iplies that in avitation thee is no analoue fo dieleti polaisation. 4. The eletoaneti field of a unifo etilinea ovin point hae The infoatons eitted by a point hae q, desibin a unifo etilinea otion (fi 8) tanspot - besides e-infoation - also infoation elatin to the veloity v of the eitte. If the point hae oves, the lines ayin s e and no lone ae paallel: they fo an anle θ. This anle is the CHARACTRISTIC ANGL intodued in III.1 beause s e and s ae aied by the sae line. We all the quantity s s. sin( θ ) that - in this ontext - is epesentative fo het b e haateisti anle, the CHARACTRISTIC e-information o the MAGNTIC INFORMATION o the b-information of an infoation. We posit that infoatons eitted by a ovin point hae tanspot infoation about the veloity of that hae. This infoation is epesented by the LCTRIC CHARACTRISTIC VCTOR o b-vctor s whih is defined by: b * See: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk IV, 4 (Nevelland 8) The theoy of infoatons Antoine Ake

24 s s b The oientation of s b is defined by ule of the oksew. If q > (fi 8), s b is dieted into the plane of the dawin; if q < then s b points out of the plane. The anitude of s b is the b-infoation of the infoation. e Z θ s e v θ P P 1 q θ P Fi 8 As in III,1 one poves: v s sb e Consequently, the by q eitted infoatons whih ae oin thouh the fixed point P - defined by the tie dependant position veto - have two attibutes that ae in elation with the fat that q is a ovin point hae: thei e-spin veto s e and thei b-veto s b : s e q 1 q 1.. e.. and K. ε K. ε se v s s b These attibutes aosopi anifest theselves as, espetively the LCTRIC FILD STRNGTH (the e-fild) and the MAGNTIC INDUCTION (the b-induction) B in P. - With N the density of the flow of infoatons in P (the ate pe unit aea at whih the infoatons oss an eleentay sufae pependiula to thei dietion of oveent), the e-field in that point is: e The theoy of infoatons Antoine Ake

25 N. s e - With n, the density of the loud of infoatons in P (nube of infoatons pe unit volue), the e-indution in that point is: B n. s b If v - the speed of the point hae q - is uh salle than - the speed of liht - the distane P P 1 is neliible opaed to the distane P 1 P. Then as in III.3: q µ. q. and B.( v ) π.. 4. π. ε 1 with µ ε. The e-infoation loud defined by the veto pai (, B ) is alled the LCTROMAGNTIC FILD of q. It has two oponents: the LCTRIC FILD and the MAGNTIC FILD. 5. The eletoaneti field of a set of ovin point haes The ontibution of eah hae q i to the eletoaneti field in P is defined by The effetive eletoaneti field is haateised by (analoue to III.4): i and B Bi i and B i. 6. The eletoaneti field of a stationay hae flow The te stationay hae flow indiates the oveent of an hooeneous and inopessible haed fluid that - in an invaiable way - flows thouh a eion of spae. The intensity of the flow in an abitay point P is haateised by the flow density J. The anitude of this vetoial quantity equals the ate pe unit aea at whih the hae flows thouh a sufae eleent that is pependiula to the flow at P. The oientation of J oesponds to the dietion of the flow of positive hae aies and is opposite to the dietion of the flow of neative hae aies (In what follows the flow of neative hae aies is eplaed by a fitive flow of positive aies in the opposite dietion). If v is the veloity of the hae eleent ρ dv that at the oent t flows thouh P, then:. J ρ. v The ate at whih hae flows thouh a sufae eleent ds in P in the sense of the positive noal, is iven by: di J. ds The theoy of infoatons Antoine Ake

26 And the ate at whih the flow tanspots - in the positive sense (defined by the oientation of the sufae vetos ds ) - hae thouh an abitay sufae S, is: i J. ds S We all i, the intensity of the hae flow thouh S, the LCTRIC CURRNT thouh S. Sine a stationay hae flow is the aosopi anifestation of ovin hae eleents ρ.dv, it eates and aintains an eletoaneti field. And sine the veloity v of the hae eleent in eah point is tie independent, the eletoaneti field of a stationay hae flow will be tie independent. It is evident that the ules of V.1 also apply fo this tie independent e-field: - div ρ ε - ot what iplies: adv One an pove that the ules fo the tie independent aneti indution ae: - divb what iplies B ota otb µ. J - Let us onside the speial ase of a LIN CURRNT. A line uent is the stationay hae flow thouh a - whethe o not staiht - ylindial tube. The ate at whih hae is tanspoted thouh an abitay setion S, is defined by: i J. ds S This - tie and position independent - quantity is alled the LCTRIC CURRNT TROUGH TH LIN. The haes flow paallel to the dietion of the axis of the ylindial tube and all hae eleents dq ae ovin with the sae speed v. We an identify the tube with a stin thouh whih a uent i flows. ah hae eleent is ontained in a line eleent dl of the stin. The quantities that ae elevant fo the eleti uent in the stin ae elated to eah othe: v. dq i. dl i. dl is alled a CURRNT LMNT. The theoy of infoatons Antoine Ake

27 The aneti indution db, aused in a point P by a uent eleent is found by substitutin v.dq by i. dl in the foula that we deived unde V.4 fo a ovin point hae. ( defines the position of P elative to the uent eleent). Thus: µ. i db 4. π..( dl ) 3 This is the atheatial foulation of LAPLAC S LAW. 7. The eletoaneti field of a onduto We an undestand the uent in a onduto as the dift oveent of fitive positive hae aies thouh a lattie of iobile neative haed entities. A onduto in whih an eleti uent flows auses a aneti field, but not an eleti one. Indeed, the uent is a stationay hae flow and thus the ause of a stationay aneti field oposed by ontibutions defined by Laplae s law. He doesn t ause an eleti field, beause the e-spin vetos of the infoatons eitted by the ovin hae aies ae neutalized by the e-spin vetos of the infoatons eitted by the lattie. Unlike a β-field - that neve exists without a -field - a aneti field an exist without an eleti field, what iplies that a aneti field is not neessaily asked in evey day iustanes. 8. The eletoaneti inteation Consideations as unde IV lead to the POSTULAT OF HT LCTROMAGNTIC INTRACTION: A point hae q, ovin in an eletoaneti field (, B ) with veloity v, tends to beoe blind fo the influene of that field on the syety of its eien field. If it is fee to ove, it will aeleate elative to its eien inetial fae with an aount a ' : a' q.{ + ( v B)} The ation exeted by the eletoaneti field on the ovin hae q is alled the LORNTZ FORC F ON q. Fo II. we onlude: M F M [ + ( v )] q. B The theoy of infoatons Antoine Ake

28 The Loentz foe is the ause of the hane of the linea oentu p of a point hae that feely oves in an eletoaneti field (see IV.): F M dp dt Let us eview the situation of fi 5 and assue that the two point asses that ae anhoed in the ovin inetial fae O ay the haes q 1 and q. A easonin entiely analoous to that unde IV.3 leads to the onlusion that the anitude of the utual eletoaneti foe in O is ( 1 β )-ties salle than the anitude of that foe in O. And that the aneti oponent of that foe is (β ) ties salle than the eleti oponent. In this situation, the effet of the aneti indution is asked in evey day iustanes. Only if thee is no eleti field, as in the ase of two ondutos, the aneti foe anifests itself. 9. The influene of a aneti ateial on the aneti field A aneti ateial beoes MAGNTIZD if it is plaed in a aneti field. Its oleules behave as aneti dipoles: neutal stutues havin a aneti oent beause they ae the seat of iula uent loops. Maneti dipoles in a aneti field have a tendeny fo alinent with that field. The extent of the anetization in a point P of a aneti ateial is haateized by the MAGNTIZATION M. M depends on the indution in P and is defined as: M χ B. µ χ is the aneti suseptibility of the aneti ateial at P. One an show * that the aneti indution in an abitay point of spae an be haateised by the veto H, that not depends on the natue of the atte in that point. This vetoial quantity is alled the MAGNTIC FILD STRNGHT. It is defined by: H B M The aneti field stenth at a point P is elated to the flow density at that point: This is a enealization of V.6 µ oth J * See: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - Hoofdstuk IV, 9 (Nevelland 8) The theoy of infoatons Antoine Ake

29 1. Maxwell s laws Auents siila to those of III.6 lead to the followin elations that stand in an abitay point in an eletoaneti field. 1. divd ρ. divb 3. B ot t 1 D 4. oth. + J t ***** ***** ***** ***** ***** ***** ***** The theoy of infoatons Antoine Ake

30 VI. WAVS AND RADIATION 1. The eletoaneti field of an aeleated point hae Z v a ϕ e e θ + θ ' P P s e θ P 1 e P O Y X Fi 9 In fi 9 we onside a point hae q that, at the oent t, oes thouh P 1. The instantaneous values of its veloity and its aeleation ae: v v. ez and a a. ez. We suppose that the speed v eains uh salle than the speed of liht. The infoatons that on the oent t ae ushin thouh the fixed point P - defined by the tie dependent position veto - ae depated fo P. Thei veloity is on the sae aie line as P P. Thei e-spin veto is on the aie line P P. In V.I.1 of A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI we show that P is ahead of the point hae. In the ase of a unifo aeleated etilinea otion: 1 a. P 1P. P P1 The haateisti anle (between the ayin lines of s e en ) has two oponents: v( t ) - θ sin( θ ). sinθ, the haateisti anle elated to the veloity of q at the oent ( t ) when the onsideed infoatons wee eitted (V.4). The theoy of infoatons Antoine Ake

31 a( t ). - θ' sin( θ '). sinθ, the haateisti anle elated to the aeleation of q at the oent ( t ) when the onsideed infoatons wee eitted. If the aeleation is tie independent, then a ( t ) a( t) a Takin into aount that P P 1 - the distane tavelled by q duin the inteval t - an be neleted opaed to P P - the distane tavelled by the liht duin the sae inteval - one an onlude that an be identified with (and θ with θ ). Thus: v( t ) a( θ + θ.sinθ + ' t ).. sinθ The aosopi effet of the eission of e-infoation by the aeleated hae q is an eletoaneti field (, B ). We intodue the efeene syste ( e, e, eϕ ) (fi 9) and find * : q 4. π. ε. B µ. q 4. π.. e q + { 4. π. ε.. µ. q. v( t ).sinθ +. a( t 4. π.. { µ. q. v( t ).sinθ +. a( t ).sinθ}. e 4. π. ).sinθ}. e ϕ. The eletoaneti field of an haonially osillatin point hae In fi 1 we onside a point hae q that haonially osillates aound the oiin of the ω inetial fae O with fequeny ν.. π We suppose that the speed of the hae is always uh salle than the speed of liht and that it is desibed by: v( t) V.osωt The elonation z(t) and the aeleation a(t) ae than expessed as: V π π z ( t).os( ωt ) en a ( t) ω. V.os( ωt + ) ω * See: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - V.I., V.I.3, V.I.4 (Nevelland 8) The theoy of infoatons Antoine Ake

32 e Z P e ϕ e P 1 q 1 e θ e θ O Y φ X Fi 1 We estit ou onsideations to points P that ae suffiiently fa away fo the oiin O. Unde this ondition we an posit that the flutuation of the lenth of the veto P1 P 1 is vey sall elative to the lenth of the position veto, that defines the position of P elative to the oiin O. In othe wods: we aept that the aplitude of the osillation is vey sall elative to the distanes between the oiin and the points P on whih we fous. j. Statin fo V V. e - the oplex quantity epesentin v(t) - we deive the oponents of the eletoaneti field in P. We find * : With qv. j. k. η j. ω. µ µ..(. qv. j. k. 1 j. k e + ).sinθ and B θ ϕ. e.( + ). sin 4. π 4. π ω 1 µ k the phase onstant, and η µ. 1. π the intinsi ipedane ε. ε of fee spae. So, an haonially osillatin point hae eits an eletoaneti wave that expands with the speed of liht elative to the position of the hae: * See: A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI - V.3 (Nevelland 8) The theoy of infoatons Antoine Ake

33 (, ; )...sin. 1+ (, ; ) θ t µ qv θ k B θ t.os( ωt k + ) 4π Φ ϕ with t Φ k In points at a eat distane of the osillatin hae, speifially thee wee this expession equals asyptotially: >> 1, k ω B ϕ µ. q. a( t ).sinθ µ. k. qv..sinθ µ. q. ω. V.sinθ.sin( ωt k).sin( ωt k) 4π 4π 4π The intensity of the fa field is invesely popotional to, and is deteined by the oponent of the aeleation of q, that is pependiula to the dietion of. In A. Ake - GRAVITATI N LKTROMAGNTISM - D INFORMATONNTHORI, we expand this onsideations to the eletoaneti field of a Hetz dipole. e 3. Poyntin s theoe An eletoaneti field is fully defined by the vetoial funtions ( x, y, z; t) and B ( x, y, z; t). Poyntin s theoe states that the expession B. ds µ defines the ate at whih eney flows thouh the sufae eleent ds in P in the sense of the positive noal. B So, the density of the eney flow in P is. This vetoial quantity is alled Poyntin s veto. It is epesented by S : µ B S µ The aount of eney tanspoted thouh the sufae eleent ds in the sense of the positive noal duin the inteval dt is: B du. ds. dt µ 4. The eney adiated by an haonially osillatin point hae Unde VI. we have showed that an haonially osillatin point hae q adiates an eletoaneti wave that in a fa point P is defined by (see fi 1): The theoy of infoatons Antoine Ake

34 µ. q. ω. V.sinθ. e.sin( ωt k). e 4π µ. q. ω. V.sinθ B Bϕ. eϕ.sin( ωt k). e 4π ϕ The instantaneous value of Poyntin s veto in P is: µ. q. ω. V.sin θ S.sin ( ωt 16. π.. k). The aount of eney that, duin one peiod T, flows thouh the sufae eleent ds that in P is pependiula on the oveent dietion of the infoatons, is: e du T P. dt. ds µ. q. ω. V.sin 16. π.. θ T.. ds. π And with ω : T µ. q du. V.sin θ ds ν 8.. ds dω is the solid anle unde whih ds is seen fo the oiin. So, the osillatin hae adiates, pe peiod, an aount of eney pe unit of solid anle in the dietion θ: µ. q u Ω. V.sin 8 θ. ν The density of the flux of eney is eatest in the dietion defined by θ 9, thus in the dietion pependiula on the oveent of the hae. 5. The eission of photons by an haonially osillatin point hae In VI.4 we have studied the eney tanspoted by the eletoaneti wave that is adiated by an haonially osillatin point hae. The adiated eney is popotional to the fequeny of the wave, thus popotional to the fequeny at whih the hae osillates. We posit that an osillatin hae q loads soe of the infoatons that it eits with a disete eney paket hν. Infoatons ayin an eney paket ae alled PHOTONS. Thus, we postulate that the eletoaneti eney adiated by an osillatin point hae is tanspoted by infoatons. This iplies that photons ush thouh spae with the speed of liht. The theoy of infoatons Antoine Ake

35 So, the nube of photons eitted by an osillatin point hae q pe peiod and pe unit of solid anle in the dietion θ, is aodin to VI.4: µ. q. V.sin N θ f Ω 8h It follows that the total nube of photons that it eits pe peiod is: π. q. V 3 π.. sin. d.. q. µ µ N f π 8h θ θ 3 h. Let us opae N f with N, the nube of infoatons that the eletially haed osillatin point ass eits duin the sae inteval: V. 1 5 N N. T.. 1,36.1. and h ν ν π. µ N f 3. h. 18. q. V 6,63.1. q. V If the osillatin entity is an eleton, we obtain: 1,4.1 N and ν N f 19 1,7.1. V Sine the instantaneous speed annot eah the speed of liht, we an find an absolute uppe liit fo N f : N f 19 < 1,7.1. 1,53.1 It is ipossible fo an osillatin eleton to eit oe than 1, photons pe peiod. Fo the definition of a photon it follows that the nube of photons eitted duin a peiod ust be salle than the nube of infoatons eitted duin the sae inteval: So : ν < 8,1.1 1 Hz. 1,4. 1 1,53.1 < ν We onlude that 8,1.1 1 Hz is an absolute uppe liit fo the fequeny of the eletoaneti waves that an be adiated by an osillatin eleton. If the soue of adiation is an osillatin poton the fequeny of the eletoaneti wave ust be salle than 1,5.1 5 Hz. 5. Gavitational waves - avitons If we apply the easonin of VI. on the -infoation eitted by a - whethe o not haed - haonially osillatin point ass, we find the desiption of the fa avitational field: The theoy of infoatons Antoine Ake

36 B ϕ ν... a t ν k V θ ν ω V θ θ ( )....sin....sin.sin( ωt k).sin( ωt k) 4π 4π 4π This expession desibes a avitational wave, that expands with the speed of liht. 1 Let us alulate the eney adiated by a avi tational wave usin the sae ethod as in the ase of an eletoaneti wave. If we aept that the eney in both situations is tanspoted by photons (h.ν ), we ust onlude that the nube of photons eitted by pe peiod and pe unit of solid anle, is: ' ν.. V.sin θ N f Ω 8h Takin into aount the data dedued unde VI.6 fo an osillatin haed patile with ass and hae Q, we find the followin elation between N - the nube of photons that, pe peiod, is taken with the avitational wave - and N f - the nube of photons that in the sae inteval is taken with the eletoaneti one: ' ν 1 N f N f..( ) 7,43.1.( ). N µ Q Q ' f f Fo an eleton, this ives ' 37 f N f N,41.1. N and in the ase of a poton we find ' 43 f N 8,1.1.. We note that alost all photons that ae eitted by an osillatin patile ae elated to its hae and oupled to the eletoaneti wave. The eission of a photon by a neutal patile is vey unlikely. This onlusion justifies the assuption that a avitational wave tanspots eney in the fo of GRAVITONS. Gavitons ae eney pakets h.ν that ae eitted by the osillatin ass and tanspoted thouh spae by infoatons. The nube of avitons eitted pe peiod by on osillatin ass is: f ' N f π ν.. 3 h'.. V Fo a poton (and a neuton): ' N f 9,15.1 h' 89., and sine the speed always ust V 7 ' 8,4.1 be salle than the speed of liht: N f <. A poton also is a soue of h' π µ photons, naely N f pe peiod. We know (VI.4) that: N <.. q. 1,53. 3 h. 1 f. If we aept that the nube of eitted avitons is of the sae anitude as the nube of eitted photons, we find the followin oufh estiation fo h : 7 h ' 5,4.1 J. s The theoy of infoatons Antoine Ake