On Physical Behavior of Elementary Particles in Force Fields

Transcription

1 On Physical Behavio of Elementay Paticles in Foce Fields Daniele Sasso * Abstact The physical behavio of elementay paticles, massive and enegetic, in foce fields is studied in this pape. In paticula let us conside the gavitational field and the electostatic field and elative to the electostatic field, as aleady it was done fo the gavitational field, we demonstate the theoetical validity of an electostatic petubation due to the motion of an electic chage into the electostatic field geneated by a pole chage. This electostatic petubation, on a pai with the gavitational petubation, has chaacteistics of continuity diffeently fom electomagnetic adiation, emitted by acceleated chages, fee o constained in complex stuctues, that instead has quantum chaacteistics. 1. Intoduction The object of this pape is that of expanding on the knowledge of the behavio of elementay paticles, whethe enegy o mass, in foce fields. Enegy quanta have a constant local physical speed c with espect to the pefeed inetial efeence fame whee they move and have a vaiable vecto elativistic speed with espect to any elative moving inetial efeence fame. The elativistic speed is given by the vecto sum of the constant local physical speed with the elative speed of the two efeence fames. The same behavio is valid also fo light, that is composed of photons, and in geneal fo electomagnetic waves. Chaged elementay paticles have an electodynamic mass that is constant at est and changes with the speed, unlike classical massive systems whose inetial mass is constant with the speed. It involves chaged elementay paticles have a elativistic inetial mass that depends on the speed and it is constant till the speed is constant. We know besides acceleated chaged elementay paticles inside a foce field have electodynamic mass that deceases when the speed inceases. Mass becomes zeo at the citical speed v c =1.41c, and becomes negative (antimass) at geate speeds than the citical speed whee elementay paticles become unstable. We will conside in the fist place the inetial field, successively the unifom foce field and at last the non-unifom foce field. In egad to non-unifom fields we will conside the gavitational field and the electostatic field, that both have cental symmety. * e_mail: dgsasso@alice.it 1

2 . Behavio of elementay paticles into the inetial field In the Theoy of Refeence Fames [1][] the Space-Time-Mass Domain is composed of thee autonomous physical quantities, linked mathematically: the thee-dimensional physical space, the one-dimensional physical time and mass fom which the physical time oiginates [3]. In that domain the inetial field is epesented by all efeence fames with inetial motion with espect to an inetial efeence fame supposed at est S[O,x,y,z,t]. Fo any moving inetial efeence fame S'[O',x',y',z',t'] with constant linea vecto speed v with espect to S, tansfomation equations of the space-time-mass ae P[S] = P'[S'] + v t dt = m dt' m' (1) Suppose that motion with constant speed v with espect to S happens along a adial diection (fig.1), then because of the spheical symmety we have = x + y + z () y z y S y 1 v O x y y' S 1 S' O 1 v 1 x 1 O' v S x' z' O x x z Fig.1 Motion with spheical cental symmety in the inetial field fo diffeent efeence fames Suppose still that at the initial instant t=0 the moving system is in the oigin O, the constant scala speed v is given by v=/t. In that case it is possible a gaphic epesentation of the inetial motion on the Minkowski two-dimensional plane (O,,t) with oigin in the point O..1 If the moving system S' with speed v is an enegy quantum, and if we assume symbolically that the physical speed v=c of the quantum with espect to S equals 1, then the space in metes coveed by the quantum with espect to S equals the time in seconds spent fo coveing it and the speed of light is epesented in the Minkowski gaph by the bisecto of the fist quadant, fo which '=45 (fig.).

3 The staight lines c 1 and c epesent always in the same gaph the elativistic speeds of both light and quanta with espect to two moving efeence fames S 1 [O 1,x 1,y 1,z 1,t 1 ] and S [O,x,y,z,t ] with elative speeds v 1 and v along the same adial diection. In the gaph of fig. the efeence fame S 1 has a concodant speed v 1 with the physical speed of light fo which the elativistic speed of quanta with espect to S 1, fo (1), is given by c 1 = c v 1 < c (3) c 1 = tg 1 < tg ' = c The efeence fame S has instead a discodant speed v with the physical speed of quanta fo which the elativistic speed, always fo (1), is given by c = c + v > c c = tg > tg ' = c (4) S, c >1 S', c=1 S 1, c 1 <1 O 1 ' t t Fig. Minkowski's kinematic gaph elative to enegy quanta in the inetial field. Massive elementay paticles have a dynamic behavio defined by the electodynamic mass that changes with the speed causing as pe the second of (1) a elativistic effect on paticle's time. Supposing that paticle moves along the adial diection with constant speed v=/t with espect to the esting efeence fame S. If in the moving efeence fame S' the esting constant electodynamic mass is m'=m o and paticle's time is t', with espect to the supposed at est efeence fame S we have 3

4 m = 1 v m' (5) c t = 1 v t' (6) c The Minkowski diagam (O,,t) fo diffeent constant values of v is given in fig.3, whee t and m ae gaphed on the hoizontal axis, and is gaphed on the vetical axis, The gaph develops in full in the fist and in the thid quadant of the Minkowski plane. In paticula we obseve in the fist quadant (v<v c ) values of t,m, ae positive, in the thid quadant (v>v c ) ae negative and they become zeo in O at the citical speed v c = c. v= 3c c 1.5c v c =1.41c c ct'/ c/ v=c/4 O v=0 -t', -m' t'/,m'/ t',m' t, m 1.5c c -ct' 3c Fig.3 Minkowski's kinematic diagam elative to the motion of elementay paticles in the inetial field 4

5 We can daw impotant physical meanings fom the Minkowski diagam, that ae altogethe coheent with physical data of the Feynman linea diagam [4][5] in fig.4 emitted enegy quanta 1 Absobed enegy 0 c 1,41c c 3c m=m o =m' m o / m =0 -m o -7m o / v m >0 m<0 zone of stability zone of instability Fig.4 Feynman's linea diagam elating to the behaviou of the acceleated paticle. In the fist quadant of Minkowski's diagam, whee the paticle's speed is smalle that the citical speed, the paticle has positive electodynamic mass m, positive chaacteistic time t and positive coveed distance =vt: in these conditions the paticle is stable. At the citical speed (oigin O of axes) all values become zeo and the paticle is on the vege of stability. In the thid quadant the paticle's speed is geate than the citical speed, chaacteistic values of m, t, ae negative, the paticle is unstable and its degee of instability inceases with the speed. The existence of the paticle in the thid quadant, chaacteized by instability, poves that negative values of electodynamic mass (antimass), negative chaacteistic time and negative coveed distance ae physically possible. Let us emind that in physics negative quantities ae eal and theefoe physically possible: they don't geneate poblems unlike imaginay quantities. In paticula the negative electodynamic mass, as we know, geneates instability of the paticle. The negative coveed distance is physically altogethe consistent with the (). Negative times, on a pai with mass, indicate paticle's instability; when it is fee the instability has a biefest duation, with a quick etun to the stability state and to the positive inetial time. These consideations demonstate that a stable univese exists in which time goes on in accodance with the positive flow past-pesent-futue of time. They pove also that an unstable univese exists in which the passage fom stability to instability is chaacteized by a time evesal with negative time intevals and the invese passage fom instability to stability is chaacteized by the etun to the positive inetial time. 3. Behavio of elementay paticles in the unifom field The unifom foce field is a field in which consideed efeence fames ae acceleated in unifom way (constant acceleation) though a constant foce with espect to the efeence fame S supposed at est (in ou easonings we don't conside pospective extenal esistant foces). In that case tansfomation equations of the space-time (1) become 5

6 P[S] = P[S'] + a t dt = m dt' m' (7) whee a is the constant acceleation of the moving efeence fame S' with espect to the efeence fame S supposed at est. Supposing that, like in the case of inetial field, also now the motion of S' happens along the adial diection of S and that at the initial instant of time t=t'=0 the moving system is in the oigin O with null initial speed, the constant acceleation is given by a=v/t fom which v=at. In that case the gaphic epesentation of acceleated motion of S' in the Minkowski bidimensional kinematic plane (O,,t) with oigin in the point O is paabolic (fig.5) being = at (8), ' '=ct+at / S', v=at, =at / c, =ct S[O,,t] blue: c' = c+at ed: c' = c-at O t '=ct-at / Fig.5 Minkowski's kinematic gaph of motion of a quantum in an unifom foce field 3.1 Fo enegy quanta that tavel with the physical speed c with espect to the efeence fame S supposed at est, the elativistic speed, with espect to the efeence fame S' that is povided with an unifom acceleated motion a, is given by c' = c + at (9) in which t'=t, as pe the (7), because enegy quanta don' t have a vaiable eal physical mass. The sign + depends on the fact that the speed v of S' can be discodant o 6

7 concodant with the diection of the photon physical speed. The pefomed space is given by '=ct + at / (+ in blue and - in ed). 3. Let us conside now the case in which a massive elementay paticle moves along a adial diection with constant acceleation a and velocity v=at with espect to the esting efeence fame S. If m' is the esting electodynamic mass and t' is the paticle time in the moving efeence fame S', with espect to the esting efeence fame S we have m = 1 a t m' (10) c dt = 1 a t dt' (11) c whee m and t ae the electodynamic mass and the time of elementay paticle in S. Setting in the (11) k t =a/ c and integating we have [6] t = 1 tgh(k t t') (1) k t with t<t'. Chating in the Minkowski kinematic diagam the values of t, m, fo diffeent values of v=at, we obtain a simila gaph to diagam of fig Behavio of elementay paticles in the non-unifom field Supposing acceleation changes with linea law a(t)=yt whee Y[Y x,y y,y z ] is a vecto constant [7], tansfomation equations of the Space-Time-Mass domain become P[S] = P'[S'] + Y t 3 dt = m dt' m' 6 (13) In that case, we have poved [7] the gaph of the non-unifom acceleated motion on a two-dimensional plane (O,x,t) with oigin in the point O is epesented by cubic paabolas instead of quadatic paabolas. Consequently the elativistic behavio of physical systems into the field of non-unifom foce is simila to the behavio into the field of unifom foce and theefoe the Minkowski kinematic diagam in that situation is still simila to the diagams epesented in fig3 and in fig.5. Let us want to expand on the behavio of elementay paticles elative to two paticula non-unifom fields: the gavitational field and the electostatic field (in that case only fo chaged massive paticles). Both fields have cental symmety and aen't unifom because thei intensity changes with the distance. 7

8 4.a The gavitational field Let us distinguish still enegy paticles fom massive paticles. 4.a.1 Suppose that quantum enegy paticle comes fom an inetial field with the constant physical speed c o and goes into a gavitational field geneated by a pole mass M o (fig.6). In geneal the diection of the speed of the quantum can be any, but let us conside two paticula cases: adial diection and tangential diection. M o O c o c o Fig.6 Repesentation of an enegy quantum coming fom two paticula diections Supposing that the quantum (povided with enegy hf) comes fom infinite (geatest) distance, because of both its equivalent mass m f =hf/c o and the action of the gavitational field geneated by the pole M o, the quantum undegoes an attaction foce that in the event of adial diection poduces a vaiable adial speed, given [1][8] by c() = c o + GM o (14) In the event of tangential diection the quantum undegoes a deflection [8] with espect to the pole M o, that being o =90, on the suface of the mass M o, at distance R (n=1), is given by = GM o (15) c o R whee R is the adius of the pole M o. In the event of the sun =0,873 acseconds, while fo the eath =0,87x10-3 acseconds. We note that the value of gavitational deflection hee calculated fo the sun is diffeent fom the value calculated in the ef[8]. The diffeence of values is due to diffeent used efeence fames. In fact in the ef[8] values have been calculated with espect to the eath's obseve. 8

9 I would want to conside now an open impotant question: does the deflection of quantum electomagnetic adiations in gavitational fields depend on fequency? Fom the (15) we deduce the deflection is independent of fequency. The question is equivalent to anothe question: that is if the fall of bodies in gavitational fields depends on mass of body. This question has been debated at length since Galileo's time and still today a sue answe to this question doesn' exist elative to known main theoies: the Newtonian Dynamics and the Einsteinian Electodynamics. Fo this eason I would want to give an answe in the ode of the Theoy of Refeence Fames. In TR the complete law of motion is not given by the only Newton law that epesents the intenal esistant foce (F=mdv/dt) but it needs to conside also the extenal esistant foce. In that event of the fall of bodies in gavitational fields the extenal esistant foce is defined by atmosphee of celestial body that geneates the gavitational field. When the atmosphee is pesent (like fo the eath, the sun, etc..) then the fall of bodies depends on the body mass [][6]. In a vacuum instead, and fo celestial bodies that ae devoid of atmosphee, the fall of bodies is independent of the mass of body. Theefoe the fall of bodies elative to the eath, the sun and all othe celestial bodies that have atmosphee, depends on mass of falling body. As pe this analogy what we can say about the dependence on fequency of the deflection of quantum electomagnetic adiations? We know quantum adiations, fo all fequencies as fom infaed ays, ae physical events of pue enegy and in the ode of the Theoy of Refeence Fames the deflection of those adiations in gavitational fields is explained by the equivalent mass that can be associated with evey single quantum of enegy (o electomagnetic nanowave) that oiginates adiation. Fom the Planck elation we deduce evey quantum has an enegy E=hf and consequently, as pe the Einstein elation E=mc o, an equivalent mass m=hf/c o. If the equivalent mass in its motion of deflection doesn't undego extenal esistant foces then we can affim cetainly the deflection of quantum adiations is independent of fequency: it is cetainly tue in a vacuum and fo celestial bodies without atmosphee. It is valid in geneal also fo continuous electomagnetic adiations. 4.a. If elementay paticle is massive, with a esting electodynamic mass m', its behavio into the gavitational field is altogethe simila to the behavio of an odinay inetial mass, and theefoe in the absence of extenal esistant foces, the paticle takes on the speed v() = G M o o (16) o whee o epesents the initial point fom which the massive paticle falls into the gavitational field geneated by M o. In the absence of extenal esistant foces the paticle fall is theefoe independent of mass, if instead extenal esistant foces (like atmosphee) ae pesent, then the paticle motion and its speed v() depend on the electodynamic mass of paticle. We know electodynamic mass of chaged paticles changes with the speed and into the gavitational field it assumes the expession 9

10 m = m' 1 - v = m' 1 - GM o o - (17) c o c o o We obseve the electodynamic mass of the moving paticle into the gavitational field deceases when the distance deceases and it becomes zeo at the distance R = o (18) 1 + o R s whee R s =GM o /c o is the Schwazschild distance. Mass is negative fo < R and consequently paticle is unstable in this zone of the field (fig.7). m m' R o Fig.7 Tend of the electodynamic mass of a moving elementay paticle into the gavitational field. We think a massive elementay paticle in fall into a gavitational field would have to geneate a smallest gavitational petubation [1] like an odinay body in fall. It needs also to specify this smallest gavitational petubation has nothing to do with electomagnetic enegy emitted in quantum shape by acceleated paticle at the expense of electodynamic mass of paticle. It is inteesting to see now if the vaiable electodynamic mass into the gavitational field influences the petubation. The space length p, the duation T p and the petubation speed c p have the same tend of odinay masses and consequently ae independent of paticle mass; the petubation enegy W p () depends instead on the electodynamic mass of paticle. In that case in fact we have and calculating W p () = GM o o - m' 1 - v (19) o c o W p () = GM o m' o c o - GM o o - (0) o o c o 10

11 Consideing the Schwazschild distance the petubation enegy can be witten also in the shape R s = GM o (1) c o W p () = GM o m' o R s () o o When the point of fall beginning of paticle o coincides with the half of the Schwazschild distance the enegy of the gavitational petubation is null. Fo o <R s / the enegy is negative and fo o >R s / the enegy is positive (fig.8). Because the Schwazschild distance is smallest it is possible to deduce that geneally o >R s /. W p () R s / o Fig.8 The blue gaph epesents the enegy of the gavitational petubation fo an odinay mass, the ed gaph epesents the enegy of the gavitational petubation fo a massive paticle. Note: Louis Rancout has announced futhe esults of his expeiment on inteactions between light and mass, that I sum up hee: 1. when the shaft of light passes hoizontally ove the tial mass placed into the eath's gavitational field, the mass wheight deceases.. when the shaft of light passes unde the tial mass the mass weight inceases. The Rancout effect is explicable in TR though a change of the gavitational field poduced by the shaft of light: the field and wheight decease because of a decease of the gavitational constant G and incease because of an incease of the constant G: it shows the existence of an effect of light and enegy quanta on both the gavitational field and the gavitational constant G. Pospective effects of heating and cooling of mass have been consideed and excluded. 11

12 Meantime Paviz Pavin has communicated always in ReseachGate his oiginal and vey inteesting intuition on possible inteactions among photons and between beams of photons. It allows to complete the symmetical goup of inteactions Mass-Light-Mass (symmety MLM o M L ): 1. Inteaction Mass-Mass (Newton law);. Inteaction Mass-Light (Einstein second effect); 3. Inteaction Light-Mass (Rancout effect); 4. Inteaction Light-Light (Pavin effect). 4.b The electostatic field The electostatic field is a paticula state of electomagnetic field that happens when all electic chages ae constant and motionless. In that event the magnetic field is null and the electic field is static, fo which an emission of electomagnetic enegy thee isn't. The cental system is defined by a constant positive electic chage +Q (pole) that geneates an electostatic field with cental symmety [][6]. An elementay paticle with chage -q undegoes an attactive foce (accoding to the theoy of the electostatic field) given by the Coulomb law F = Q q (3) 4 o The motion law of elementay paticle into the field is m o dv(t) + Kv(t) = Q q (4) dt 4 o whee m o =m' is the esting electodynamic mass of paticle. Let's suppose that extenal esistant foces ae null (k=0), we have m o dv(t) = Q q (5) dt 4 o Let's suppose still that at the initial instant t=0 the paticle is placed at distance o fom the cental chage with null initial speed v(0)=v( o )=0. Solving [6] the (5) we obtain fo evey distance the speed v() = Q q o - (6) o m o o The (6) tell us an elementay paticle into an electostatic field has a behavio like into a gavitational field [1]. Now nevetheless we obseve in the electostatic field, also in the absence of extenal esistant foces (k=0), the paticle's speed depends on the electodynamic mass fo which paticles with diffeent mass have diffeent speeds, unlike what happens into the gavitational field. Because then the elativistic electodynamic mass of paticle changes with the speed accoding to the elationship 1

13 we deduce m = m o 1 v (7) c o We obseve besides at the citical distance m = m o 1 - Q q o - (8) 4 o m o o c o c = Qq o (9) Qq + 4 o m o o c o electodynamic mass becomes zeo (m=0). Fo smalle distances the speed inceases, the electodynamic mass becomes negative and the paticles becomes unstable. If the distance o is geatest, on the vege of infinite, we have (because Qq is negligible) c = Qq (30) 4 o m o c o If the cental chage is a poton and the seconday chage is an electon, both have electic chage equal to the electon: in that event we have c =,8x10-15 m, that coincides with the adius of the nucleus of hydogen atom. The distance c epesents the citical distance because at that distance fom the cente of cental chage the paticle's electodynamic mass becomes zeo; fo geate distances electodynamic mass is positive and fo smalle distances is negative. At the citical distance the paticle's speed equals the citical speed v c = c. At smalle distances the paticle's speed is geate than the citical speed. It is manifest that a moving chaged elementay paticle into an electostatic field is unable to geneate a gavitational petubation but the question is if it is able to geneate anothe type of petubation: the electostatic petubation. 5. Effects of electostatic field Let us conside now two physical situations concening the motion of an electic chage -q into an electostatic field with cental symmety in which the pole is epesented by a constant chage +Q. 5a. Electostatic petubation Like the fall of an odinay mass o a massive paticle into a gavitational field geneates a gavitational petubation, so also the motion of an electical chage into an electostatic field geneates an electostatic petubation that popagates though space with space 13

14 acceleation a (). This acceleation has physical dimensions of the fequency f e and is given by a () = f e = - dv() = 1 Qq o ( o -) (31) d ( o -) o m o Physical chaacteistics of electostatic petubation ae simila to chaacteistics of gavitational petubation petubation length e = o - petubation duation T e =1/a =1/f e (3) petubation speed c e = e /T e = e f e The speed of the font of electostatic petubation, fo evey, is given by c e () = o v() = Qq( o -) (33) o m o o Electostatic petubation has the same gaphic epesentation as gavitational petubation (fig.9). q o v 3 o 4 =0 Q e e e Fig.9 Gaph of cicula electostatic petubation fo diffeent values of and diffeent values of e. e Besides electostatic petubation has an enegy given by W e () = Qq( o -) (34) 4 o o 14

15 Natually it is valid whethe fo chaged paticles o fo chaged odinay bodies. Let us obseve duation and speed depend on whethe the two electic chages o the mass of moving chaged paticle, enegy depends only on two chages while the length is independent of whethe chages o mass. Fo gavitational petubation instead duation and speed depend only on pole mass, enegy depends on the two masses and length is independent of mass. 5b. Electomagnetic adiation Electostatic petubation is due to the non-unifom motion of the chage q caused by the electostatic field. We know an acceleated chaged massive elementay paticle in an electostatic field epesents a vaiable nanocuent which geneates an electomagnetic nanofield which is subject to the Maxwell equations [][6]. Besides paticle's electodynamic mass deceases with the speed and simultaneously it emits quantum electomagnetic enegy fo pecise values of speed. In paticula the acceleated paticle, at the physical speed c of light, has an electodynamic mass equal to half of the esting electodynamic mass and emits a fist gamma quantum of electomagnetic enegy; at the citical speed v c = c it emits a second gamma quantum with simultaneous zeoing of the electodynamic mass. Both gamma quanta move with the physical speed of light. The two effects of electostatic field (electostatic petubation and electomagnetic emission) ae independent of each othe and both ae due to the acceleated motion of the chaged massive elementay paticle into the electostatic field: the petubation is due to the acceleated motion into the electostatic field, while the electomagnetic emission is due to the vaiation of electodynamic mass with speed. Besides the two effects pesent a fundamental diffeence: in fact the electostatic petubation has continuous natue and it is geneated fo evey value of the distance, the electomagnetic adiation instead has quantum natue and it is emitted by paticle only fo a few chaacteistic discete values of electodynamic mass, speed and distance. Refeences [1] D. Sasso, Physics of Gavitational Field, vixa.og, 014, id: [] D. Sasso, Physico-Mahematical Fundamentals of the Theoy of Refeence Fames, vixa.og, 013, id: [3] D. Sasso, Relativity and Quantum Electodynamics in the Theoy of Refeence Fames: the Oigin of Physical Time, vixa.og, 011, id: [4] D. Sasso, On the Stability of Electodynamic Paticles: the Delta Radiation, vixa.og, 01, id: [5] D. Sasso, Physical Natue of Mesons and Pinciple of Decay in the Non-Standad Model, vixa.og, 01, id: [6] D. Sasso, Dynamics and Electodynamics of Moving Real Systems in the Theoy of Refeence Fames, axiv.og, 010, id: [7] D. Sasso, Relativistic Physics of Foce Fields in the Space-Time-Mass Domain, vixa.og, 014, id: [8] D. Sasso, Pedictions on Obsevations and Measuements of the Deflection of Light on the Occasion of 015 Sola Eclipse Accoding to the Theoy of Refeence Fames, vixa.og, 014, id: