The Ritz Ballistic Theory & Adjusting the Speed of Light to c near the Earth and Other Celestial Bodies

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1 College Park, MD 11 PROCDINGS of the NPA 1 The Ritz Ballistic Theory & Ajusting the Spee of Light to c near the arth an Other Celestial Boies Nina Sotina PhD in Physics, Mosco State University 448 Neptune Avenue, Apt. 1, Brooklyn, NY nsotina@gmail.com Naia Lvov Assistant Professor, Division of Mathematics an Physics ssex County College, 33 University Ave., Neark, NJ 71 lvov@essex.eu In 198 Walter von Ritz suggeste that the spee of light is equal to the constant c only hen measure relative to the source. Ritz systematically reevelope Maxellian electroynamics bringing it into agreement ith this hypothesis. Assuming that c is the spee of light at the output of the light source an that the la of velocity aition from classical mechanics is vali for the case of a moving source, the results of the famous Michelson-Morley experiment, the aberration of starlight, an a number of other relate experimental results come into agreement. The single objection to the hypothesis at that time as provie by astronomical observations of the motion of binary stars. The Ritz theory came to an en ith the ork of W. e Sitter (1913) ho claime to have a convincing argument for shoing that the hypothesis of Ritz as inconsistent ith the results of spectroscopic observations of binary stars. A hien postulate in e Sitter s argument, hoever, is that the spee of light propagating from the stars is not affecte by anything. To refute e Sitter s argument, it oul be sufficient to assume that the spee of light ajusts to the value of c at the vicinity of arth an other celestial boies. The authors sho that this assumption ae to the Ritz hypothesis explains ell spectroscopic observations of the binary stars. This combine hypothesis: the Ritz ballistic hypothesis an the ajustment of the spee of light to c near celestial boies (in particular near the arth), also explains experiments performe at CRN in An aitional argument in favor of the suggeste hypothesis is the erivation of the formula for the transverse Doppler ffect presente in this ork. 1. The Pre-relativistic Perio in Physics It is interesting to look into the pre-relativistic perio of the history of physics an recall the cause of the so-calle crisis in physics that as settle ith the evelopment of the Special Theory of Relativity (SR). It as knon at the time that the propagation of light in a vacuum as escribe by Maxell s equations, hich ere not invariant uner the Galilean transformations, but ere invariant uner the Lorentz transformations. The mere fact that the linear ave equation u/ t a u is invariant uner the Lorentz transformations is of little importance. For example, an equation of this type escribes the longituinal vibrations in a ro, but no one conclues from this fact that the Galilean principle is not vali an that it is necessary to change the geometry of space. In the case of a ro, physicists kno that the equation escribing the vibrations is approximate. It is essential only that the classical la of velocity aition is vali for the velocity of the ro s translational motion an of the elastic vibrations propagation. So at the en of the 19 th century it as expecte that the same situation is also true for the velocity of light, provie that light propagates through some elastic meium, that is, the ether. To ifferent points of vie existe, hoever, as to hether the arth orbits the Sun ithout imparting any motion to the ether or hether the ether is ragge along ith the earth (as is the case ith air). From the observations of the aberration of light (if interprete from the viepoint of the ave theory of light) it folloe that the ether surrouning the earth oes not share the earth s motion. It also folloe from the Michelson-Morley experiment that, on the contrary, the ether must be carrie ith the earth. Having iscare the hypothesis of the "luminiferous" ether efining a preferre reference frame an having introuce a moel of four-imensional pseuo- ucliian space ith metric s x y z c, SR provie an explanation for the aberration of stellar measurements, the results of the Michelson-Morley experiment an other experiments for the etection of the "ether in". Was there a compelling necessity to link space an time together an go beyon the frameork of the three-imensional moel of ucliean space? Di another logical ay out exist for overcoming the ifficulties encountere by physics at the beginning of the th century? Yes, in fact, such a ay as propose by Walter von Ritz in 198 [1]. The beginning of tentieth century as a point of ivergence on the evolutionary path of Physics. The logical path on hich the science coul be further evelope epene on external factors occurring at that time rather than on the internal logic of the science itself. Ritz suggeste that the spee of light as equal to c only hen measure relative to the source. The so-calle Ritz emission theory is in accor ith the observation for the aberration of star positions, the Fizeau experiments, the original Michelson- Morley experiment, an also most other experiments carrie out for etermining the "ether in". W. e Sitter (1913) claime, hoever, to have a convincing argument that the hypothesis of Ritz as inconsistent ith the results of spectroscopic observations of binary stars []. The argument of e Sitter in his on ors is as follos. If the source of light has spee u in the positive x irection, accoring to the Ritz theory the spee of light raiate in the same irection is c + u, here c is the spee of light ith respect to the source (Fig.1). Let us imagine there is a binary star an an observer place at a large istance at the orbit plane. Accoring to Ritz, the

2 Sotina & Lvov: The Ritz Ballistic Theory & Ajusting the Spee of Light to c Vol. 8 light raiate by the star at point A reach the observer in time /(c + u), an the light raiate at point B in time /(c - u). (Here A an B are points on the opposite ens of the orbital iameter perpenicular to the irection from the star to the observer). Let us esignate T half of the orbital perio (the orbit is consiere to be circular). As a result, the time interval of the star motion from point A to point B ill be T + u/c, an the time interval uring hich the star as at the secon half of its perio ill be T u/c. Assuming further that u/c is of the same orer of magnitue as T, it ill be impossible, if the Ritz theory ere vali, to agree the observations ith the Kepler s las. For all spectroscopic binary stars u/c is not only of the same orer of magnitue as T, but, in most cases, may be even greater. If e assume, for example, that u equals 1 km/sec, T = 8 ays, /c = 33 years (that is, the parallax is.1 ), then T u/c =. All these quantities are of the same orer of magnitue, hich is often so for ell knon spectroscopic binaries. (Most parallaxes ill be less than.) The existence of spectroscopic binary stars an the fact that in most cases the observe linear velocity is in complete agreement ith the Kepler s las represent strong evience in favor of invariance of the spee of light. B c - u c + u Fig. 1. A binary star: a system of to stars A an B. A hien postulate in e Sitter s argument, hoever, is that the spee of light propagating from the stars is not affecte by anything. There ere attempts to prove the consistency of Ritz's theory using the extinction theorem, the most important contribution being mae by J.G. Fox [3]. The theorem states that if an incient electromagnetic ave traveling ith spee c associate ith a vacuum enters a ispersive meium, its fiels are cancele by part of the fiels of the inuce ipoles (macroscopically by the polarization) an replace by another ave propagating ith a phase velocity characteristic of the meium. The incient ave is extinguishe by interference an replace by another. The motion of the source an the spee of light relative to it are irrelevant accoring to this theorem. There are, hoever, some experiments hose results are not explaine by the extinction theorem. The experiment performe at CRN, Geneva, in 1964 [4] as consiere to be the most convincing evience against the Ritz theory. In this experiment the spee of 6 GeV photons prouce in the ecay of very energetic neutral pions as measure by time-of-flight over paths up to 8 meters in length. The pions ere prouce by the bombarment of a beryllium target ith 19. GeV protons having spees (inferre from the measure spees of charge pions prouce in the same bombarment) of.99975c.. Ajusting the Spee of Light to c near Celestial Boies What conclusion can be erive from the CRN experiment? The only conclusion that follos from that experiment is that the spee of photons equal c as measure ith respect to the arth (ithout taking into account the rotational motion of the arth about its axis). At least to other hypotheses can be suggeste for the explanation of this fact besies SR, that are in agreement ith the Ritz theory. (Note that SR also agrees ith the Ritz theory since the spee of a photon accoring to SR equals c in the frame of reference of the source.) The first hypothesis: assume (as Ritz i) that there is no ether, an the photon leaves a source ith velocity c relative to the source. From the Ritz viepoint the velocity of the photon must remain c ith respect to the source an c u ith respect to arth, here u is the velocity of the source. The CRN experiment, hoever, shoe that the spee of photon ith respect to arth is c inepenent of the source motion. This result may have the folloing explanation: the spee of the photon ajusts to the value of c at the vicinity of arth or other celestial boies ue to the interaction of the photon ith the fiels (possibly unknon yet) associate ith these boies. This iea in a ay is extension of the extinction theorem. The secon hypothesis: the ether is ragge along ith the earth (or the celestial boy), an c is the spee of the photon ith respect to the ether. Besies e assume that light is not a regular linear ave propagating in the ether, an a photon has inertial properties like a soliton in orinary liqui. Moreover, the photon has quantum properties like structures existing in superfluis. (The folloing interesting process is observe, for example, in superflui He-3: a structure, calle a hegehog, having a spin propagates ith a high spee in a superflui like a particle). The emitte photon in this case is a process that propagates through the ether ith the spee c. Any of the above hypotheses makes the Sitter s argument unconvincing an is in accor ith observations for the aberration of star positions, the original Michelson-Morley experiment, an other experiments carrie out for etermining the "ether in". In this context it is interesting to give the conclusion of L. Brilluoine s analysis of the principal experiments of SR: the isotropic ucliian space ith the variable spee of light might represent a moel that oul be most consistent ith the experimental physical observations. [5] We sho belo, that it is possible on the basis of any of the above to hypotheses to obtain the relativistic formula for Doppler ffect [6, 7]. 3. The Doppler ffect for a Photon The equations for the transverse an longituinal Doppler ffect are erive belo. Note that any of the above to hypotheses can be use in the erivations, because they have to ieas in common: the first is that the spee of a photon ith respect to the source is equal to the funamental constant c an that the la of velocity aition from classical mechanics is vali, an seconly, that the spee of the photon ajusts to the value c near the arth. The equations are erive from the photon s point of vie, hoever, some clarifications to this vie have to be mae, because there are various efinitions of photon that are use in ifferent branches of physics. Such a ifference in the use of the term reflects, in particular, the fact that there is no unifie point of vie on the nature of the material carrier of the associate quantum of energy, that is, the photon. Belo e presume a photon to be a hypothetical particle hich accounts for

3 College Park, MD 11 PROCDINGS of the NPA 3 the signal at the output of a photoetector. Although there is no strict efinition of the photon in the frameork of any consistent theory, the photon as a particle (ith the ave properties characteristic of the particle) is use in a number of optical stuies here an attempt is mae to go beyon the frameork of the conventional (Copenhagen) interpretation. It is orth noting that the first corpuscular moels of the light fiel consisting of elementary particles, each possessing the energy h of a quantum of light, here is the raiation frequency, ere evelope after A. Compton s experiments on X-ray scattering (19). The observe change in the frequency of the scattere raiation as explaine by the elastic collision of an electron ith a particle possessing energy h an impulse p / c. In 199, G.H. Leis calle this particle a photon. Belo, the equation for Doppler's effect is erive for the case of a circularly polarize photon in the pure state. In this context particular properties of the photon can be iscusse: its polarization, energy, mass. First e erive the equation for the energy of the photon emitte by a moving source. Consier an inertial frame of reference linke to the observer here the source of light ith mass M moving in a vacuum ith velocity u. The energy of the source is compose of kinetic energy Mu / an internal energy of the excite atoms. When a photon is emitte, the internal energy of the source is change an becomes *. In aition the source unergoes a recoil ue to the emission pressure: its spee gains an increment of u u (here u is the spee of the source after emission of the photon). From the las of conservation of energy an momentum for the photon an the source respectively, it follos that M m u Mu * ph (1) Mu Mm u m o here m is the mass carrie aay by the photon emitte ith spee с ith respect to the source, ph is the photon energy in the observer s frame of reference, an cu is the photon velocity in the same frame. Note that the vector is irecte toars the observer. observer Fig.. Velocity aition for the photon emitte by a moving source. From q. (), e obtain for u : Mum cu u (3) M m After emission of the photon, the internal energy of the atom is ecrease by the amount h, here is the natural frequency of the atom, that is, * h. Taking this an q. (3) into account, q. (1) can be expresse as follos: o c u () ph Mu Mu m cu h (4) mu m m / M u c c u 1 m / M If the mass M of the source is much greater than that of a photon, the terms containing m / Mmay be ignore. In this approximation, q. (4) takes the form: mu ph h muc (5) Using the relation mc h (note that this is not a consequence of special relativity), q. (5) can be represente in to equivalent forms: u m h ph h u 1 (6) c c here c u ucos (7) Here e enote as the angle beteen the velocity of the source an the irection from the source to the observer, i.e. the angle beteen vectors u an. Consier a special case u. In this case q. (6) implies: mc h h. (8) A very important result follos from q. (6) an q. (8): the energy of a photon, as an entity ith mass m, can be represente ith to components, the first being the kinetic energy of the center of mass, here e assume all of the photon s mass is concentrate; the secon is the energy associate ith the motion about the centre of mass, hich is characteristic of the photon s intrinsic egrees of freeom. (This important result as first obtaine by L. Bolyreva an N. Sotina [6, 7]). No let us take into consieration the arth influence on the spee of the photon. Case 1: Suppose that a source of light is at rest ith respect to the arth, an an observer is moving ith a constant spee u relative to the arth. In the frame of reference of the arth, the mass of the photon emitte by the source is equal to m an there is no reason hy it shoul change in the observer s frame of reference prior to interaction of the photon an the receiver. It is experimentally establishe that the absorption of light occurs in quanta of energy h, here is the etecte frequency. Assume that all the energy of the photon is equal to the energy etecte by the measuring system (hich is no ifferent than that of conventional physics). Uner this assumption, from q. (6) e obtain, to ithin u/ c u u 1 c c inclusively, (9) If u, that is, u, then the expression for the transverse Doppler effect follos from q. (7): 1. (1)

4 4 Sotina & Lvov: The Ritz Ballistic Theory & Ajusting the Spee of Light to c Vol. 8 Using q. (9) an q. (7) e obtain the etecte frequency of the photon for any value of : 1 cos c 1cos cos O q. (11) agrees, to ithin an accuracy of (11) u/ c inclusively, ith that of the equation escribing the Doppler ffect in SR. Note also that the q. (11), has to solutions hen the frequency oes not change ( ) 1) hen the relative spee of the photon is zero ( u ), an ) hen u ccos. In these cases c an, consequently, the total energy of the photon is the same in both frames of reference. The relativistic equation for the Doppler ffect also has to solutions hen the frequency of light is unchanging, hoever, in SR the secon solution agrees ith the erive solution above only approximately (ith an accuracy of inclusively) an oes not have an obvious physical interpretation. The fact that in our consieration the secon solution (corresponing to the case hen the frequency is unchanging) is the exact solution of q. (11), an has a simple physical interpretation is an aitional argument in favor of the theory evelope in this ork. Case : No suppose that an observer is at rest ith respect to the earth, an a source is moving ith constant spee u relative to the observer. In this case, there is one more entity, namely the arth, hich can have an influence on the spee, mass, an frequency of the photon. Making the folloing to assumptions, namely that: 1. the emitte photon has the spee с an energy h in the frame of reference of the source, an. in the frame of reference of the observer, the spee of the photon also equals c, but its energy has value h (hich is no ifferent than that of conventional physics) 3. e again can obtain q. (11) for the Doppler effect, ( in this case is the photon s frequency ith respect to an observer at rest). Inee the emitte photon has energy given by q. (6) in the frame of reference of the observer. After the photon s spee ajusts to the value of c ith respect to the earth its energy assumes the value h. Substituting h in q. (6) for ph e obtain q. (11) for the Doppler ffect. Note, that in the process of ajustment of the spee to c, the photon s total energy in the frame of reference of the observer remains constant but its momentum, frequency an mass change. The change in the photon s mass supports hypothesis (see above), hich states that the photon is not a particle, but rather is some sort of process, like a soliton in a superflui. The surprising coincience of the corresponence of q. (11) ith the equation that escribes the Doppler ffect in SR (for / they coincie up to 3 inclusive) can be reaily explaine. The same to ieas can be foun in SR: 1) the Ritz iea, that the spee of the photon equals c ith respect to the source, an ) the fact that the spee of the photon also equals to c in the reference frame of the observer. A funamental question arises: hy oes q. (11), erive here on the basis of the la of conservation of energy agrees to such high accuracy ith the equation from SR erive from kinematic consierations? From the fact that relativistic kinematics correctly explains the results of certain optical experiments, it can be conclue that in the four-imensional kinematic formalism of SR there are ynamics hien in the geometry of space. In other ors, the interaction of light ith evices (or fiels associate ith arth) appears to behave in a ay such that optical experiments can be escribe through the kinematic of SR [7]. 4. Light Curve for clipsing Binary Stars Let us go back to the iscussion of the Ritz theory. As it as explaine above, this theory is in accor ith most experiments carrie out for etermining the "ether in". The Ritz emission hypothesis, hoever, is inconsistent ith the results of spectroscopic observations of binary stars an also the experiment performe at CRN, Geneva. Hoever, if e a the assumption that the spee of the photon ajusts to c near arth an other celestial boies to the Ritz hypothesis, the latter comes in agreement ith the observation of the motion of binary stars. Furthermore, this combine hypothesis provies alternative explanations for all funamental experiments of SR. It also has been emonstrate earlier, that the equation for not only the longituinal but also the transverse Doppler ffect can be erive on the basis of this hypothesis. It is important to note that explanation of the transverse Doppler ffect up to no has been consiere the sole prerogative of SR. The question arises as to hether there are any phenomena hich give ifferent results hen explaine ith SR versus ith our theory. The anser is yes; one such phenomenon is seen ith the behavior of light in the vicinity of binary stars. Specifically, a light curve plotte on the basis of SR is ifferent than the curve plotte on the basis of our theory. Accoring to the first postulate of SR, in any inertial frame of reference, light propagates isotropically, inepenent of the motion of its source, an the spee of light is equal to the ellknon constant c. It follos from this postulate, that the light curve for eclipsing binary stars stuie in the ork of W. e Sitter, shoul be a horizontal straight line ith rops of intensity corresponing to eclipses. Consier the case of eclipsing binary stars, a system of to stars A an B, hose plane of orbit lies in the line of sight of the observer. Accoring to our hypothesis the spees of photons emitte by star A are equal to c ith respect to that star, an similarly the spees of photons emitte by star B are equal to c ith respect to star B. Because the stars are orbiting the common center of mass ith a linear velocity u (for simplicity consier u to be the same for both stars), the spees of photons moving in the irection of the line-of-sight of the observer shoul be ifferent. After some time, hoever, the spees of the to sets of photons can equalize an have the same value c, for example, ue to their motion near another celestial boy. Of course, the problem is that e on t kno the mechanism for this equalization. If e assume that the photons' spees ajust their values to c in the ether, then the question remains concerning ho the

5 College Park, MD 11 PROCDINGS of the NPA 5 ether moves through space. We can say ith certainty, hoever, from the above argument that the light curve of a binary star is not a straight line. Belo e sho this mathematically. Let be the istance at hich spees of photons equalize. Obviously, the light curve plotte by the observer locate at some istance from the binary system (call this point M) is the same as the curve plotte by the observer on arth (because the photons travel further ith the same spee ). The relationship beteen the current time t an the time of the photon s arrival at the point M (for both stars A an B) is given by the folloing equation: t 1 c 1 cost (1) for the photon emitte by star A, an t 1 c 1 cost (13) for the photon emitte by star B. Let inicate the angular spee of the stars orbital motion about the common center of mass, /T, here T is the orbital perio, an u/ c. The position of the stars at the initial moment of time t is shon on Figure 1. Assume that the number of photons emitte per unit time n is the same for both stars. Let m1 be the number of photons per unit time arriving at the point M from the star A, an m be the number of photons per unit time arriving at the point M from the star B. In the time interval t each star emits nt photons. The number of photons arriving at point M are therefore an m respectively. Then for star A e have an for star B: n t m m11 t m 1 1 1, (14) nt m m t (15) here 1 / can be foun from q. (1) as 1 sint 1 c 1 cost an / can be foun from q. (13) as sint 1 c 1 cost, (16) (17) We are stuying the change in light intensity in the frame of point M. Thus, e have to substitute 1 an for t in q. (16) an q. (17) respectively. Accoring to q. (14) an q. (15) the relative ensity of photons arriving at point M from star A is m1 1 1/ 1 t 1 (18) n The relative ensity of photons arriving at point M from star B is: m 1/ t (19) n So, the total relative ensity s of photons arriving at point M is as follos: m m s () n 1 / / From the viepoint of SR, s, an the graph of s versus time shoul be constant. In our case the graph of the function s given by q. () shos that the curve, hich represents the rela- s s t/ T as measure at the point M, is a tive photon ensity perioic function ith the perio T/ (here T is the orbital perio of the star system) (Fig.3). s Fig. 3. Light curve for an eclipsing binary star. The variations from s epens on the istance from the star to the point M, (the point here the photons spees equalize). Using ata for the binary system WW Aurigae, e obtain that at a istance 1 AU, , an for 1 AU, In the case of WW Aurigae, is small an probably not etectable in observations. Light curves shoing uneven brightness, hoever, are often observe. Besies the rops in intensity ue to eclipses, there are observe eviations from constant values in the regions of light curve beteen these rops. Astronomers have ifferent explanations for these variations, some of hich are quite obviously contrive. This topic clearly requires further stuy to arrive at a creible resolution. An yet the ne results of the observation of binary stars might provie ne arguments in favor of the Ritz hypothesis, to hich e have ae the hypothesis of the ajustment of the spee of light to c near celestial boies. Acknolegment We oul like to thank Anatoly Sukhorukov for his contribution to calculation of the light curve for binary stars, an to Konstantin Kouptsov for helping us on Mathematica softare. Our special thanks to Robert Finch for his help ith the translation of this article an valuable comments. References T/4 3T/4 [ 1 ] W. Ritz, Annales e Chimie et e physique 8: 145 (198). [ ] W. Sitter, Physikalische Zeitschrift XIV: 49 (198). [ 3 ] J. G. Fox, Am. J. Phys. 33: 1 (1965). [ 4 ] T. Alvager & J. M. Bailey, Phys. Letters 1: 6 (1964). [ 5 ] L. Brillouin, Relativity Reexamine (Aca. Press, 197). [ 6 ] L. B. Bolyreva & N. B. Sotina, A Theory of Light ithout Special Relativity? (Mosco: Logos, 1999). [ 7 ] L. B. Bolyreva & N. B. Sotina, Galilean lectroyn. 13 (6):