Does the Velocity of Light Depend on the Source Movement?

Transcription

1 Issue 4 (Otober) PROGRESS IN PHYSICS Volume 12 (2016) Does the Veloity of Light Depend on the Soure Movement? Luis Bilbao Universidad de Buenos Aires. Consejo Naional de lnvestigaiones Científias y Ténias. Instituto de Físia del Plasma (INFIP). Faultad de Cienias Exatas y Naturales. Buenos Aires, Argentina. bilbao@df.uba.ar Data from spaerafts traking exhibit many anomalies that suggest the dependene of the speed of eletromagneti radiation with the motion of its soure. This dependene is different from that predited from emission theories that long ago have been demonstrated to be wrong. By relating the veloity of light and the orresponding Doppler effet with the veloity of the soure at the time of detetion, instead of the time of emission, it is possible to explain quantitatively and qualitatively the spaeraft anomalies. Also, a formulation of eletromagnetism ompatible with this oneption is possible (and also ompatible with the known eletromagneti phenomena). Under this theory the influene of the veloity of the soure in the speed of light is somewhat subtle in many pratial situations and probably went unnotied (i.e. below the detetion limit) in other measurements. 1 Introdution In these lines I intend to show that there exists onsistent evidene pointing to the need of revision and further study of what seem at present a settled issue, namely the independene of the speed of eletromagneti radiation on the motion of its soure. The main point in the evidene is the range disagreement during the Earth flyby of the spaeraft NEAR in Its range was measured near the point of losest approah using two radar stations, Millstone and Altair, of the Spae Surveillane Network, and ompared with the trajetory obtained from the Deep Spae Network [1]. As for the range, the two measurements should math within a meter-level auray (the resolution is 5 m for Millstone and 25 m for Altair), but atual data showed a differene that varies linearly with time (with different slopes for the two radar stations) up to a maximum differene of about 1 km, i.e. more than 100 times larger than the auray of the equipment used (see figure 10 of [1]). Further, when NEAR rossed the orbits of Global Positioning System (GPS) satellites, orbital radius 26,600 km, the measured range differene was 650 m, that is, a time differene of 2µs. Is it reasonable that any standard GPS reeiver performs better than the Deep Spae Network or the Spae Surveillane Network? There has not been a omplete explanation for the range disrepany. It is very diffiult to find any physial reason that may produe this anomaly, for any physial disturbane of the path of the spaeraft should manifest equally in the Deep Spae Network and the Spae Surveillane Network data. Guruprasad [2] proposed an explanation that points to a time lag in the Deep Spae Network signals proportional to the range, but the model is, at best, within 10% of the measured data (i.e. larger than the instrumental error) and, more important, it fails to explain an important feature, that is, the different slope for the two radars. If we assume that systems are working properly, then the measured range differene (time lag) ould be due to different propagation time of the employed signals. Additional points in the evidene ome from anomalies related to the traking of spaerafts, present in both Doppler and ranging data. The Pioneer anomaly [3] and the flyby anomaly [4] refer to small residuals of the differenes between measured and modeled Doppler frequenies of the radio signals emitted by the spaerafts. Although these residuals are very small (less than 1 Hz on GHz signals) the problem is that they follow a non-random pattern, indiating failures of the model. Aording to the temporal variation of those residuals the Pioneer anomaly exhibits a main term, an annual term, a diurnal term and a term that appears during planetary enounters. It should be larified that a few years ago an explanation of the Pioneer anomaly was published [5]. However, it is a very speifi solution that applies only to the main term of the Pioneer spaeraft anomaly, but left unresolved many other anomalies, inluding those of the spaeships Cassini, Ulysses and Galileo; the annual term; the diurnal term; the inreases of the anomaly during planetary enounters; the flyby anomaly; and the possible link between all them (it is hard to think that there are so many different auses for the mentioned anomalies). For all this, I believe that the issue an not be losed as it stands. 2 Range disagreement As a matter of fat, the range differene between the Spae Surveillane Network and the Deep Spae Network, δr, is perfetly fitted with R (t) v (t) δr (t)=, (1) where R (t) is a vetor range pointing from the spaeraft to the radar, v (t) the spaeraft veloity relative to the radar, Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement? 307

2 Volume 12 (2016) PROGRESS IN PHYSICS Issue 4 (Otober) and the speed of light. Figure 1 shows this fit and its omparison with measured data. The orbital and measured data were taken from [1]. Although the exat loation of the radar stations are unknown to the author (approximate values are: Millstone 42.6 N W, and Altair 9.18 N E), the fit is statistially signifiant for both radar stations (p < 10 3 ) inluding the first outliers points. It reprodues the (almost) linear dependene with time during the measured interval, and the two different slopes for Millstone and Altair stations due to their different loations. δr (m) :12:13 06:18:49 06:25:25 06:32:01 Date/Time 06:38:36 06:45:12 06:51:48 Fig. 1: Range disagreement between the Spae Surveillane Network and the Deep Spae Network, for 1998 NEAR flyby (Millstone blue points, upper trae, and Altair red points, lower trae). Also the fit (1) is plotted (full lines, Millstone in blue and Altair in red). For Millstone, the error bars refer to the unertainties in the extration of the data from figure 10 of [1], rather than to its traking error (5 m), while for Altair, the auray is 25 m. Sine range measurements are based on time-of-flight tehniques, the validity of (1) means that the eletromagneti waves (mirowave) of the Deep Spae Network and the Spae Surveillane Network travel at different speeds. Speifially, in the radar frame of referene, if the Spae Surveillane Network waves travel at, then the Deep Spae Network waves travel at plus the projetion of the spaeraft veloity in the diretion of the beam, in sharp ontrast with the Seond Postulate of the Speial Relativity Theory. In view of the above result one may ask what is established, at present, about the relation of the speed of eletromagneti radiation (light for short) to the motion of the soure. In order to elaborate this point the following questions are of relevane: 1. Are there simultaneous measurements of the speed of light from different moving marosopi soures (not moving images) with different veloities?; 2. Sine ballisti (emission) theories are ruled out (see, for example, DeSitter [6, 7], Breher [8] and Alväger et al [9]), how else ould the speed of light depend on the soure movement?; 3. How is it possible that there is a first order differene in v/ in spaeraft range measurements, while at the same time there are many experiments on time dilation that are onsistent with Speial Relativity Theory to seond order inv/ (see, for example, [10])?; 4. If the veloity of light depend on the veloity of the soure, why has this not been observed in other phenomena in the past? In answer to the previous questions, so far as the author is aware, there is no known experimental work that simultaneously measures the speed of light from two different soures (not images), or that simultaneously measures the speed of light and that of its soure. For example, in the work by Alväger et al, [9] the speed of light is measured at a later time ( 200 ns) than the emission time, and there is no measurement of the speed of the soure at the time of the detetion of the light. Note that measurements involving moving images produe different results from those produed by mobile soures. For example, under Speial Relativity Theory, a moving soure is affeted by time dilation while a moving image is not. Therefore, to ensure the independene of the speed of light from its soure movement, it is essential to have two soures with different movements. Although ontroversial and beyond the sope of the this note, time dilatation phenomena may be of different physial origin from first order terms, as it may be inferred from the work of Shrödinger [11]. Thus, measurements of time dilatation phenomena in aordane with Speial Relativity Theory, does not neessarily imply the independene of the speed of light with the movement of the soure. The experiments mentioned above [6 9] only rule out ballisti theories in whih radiation maintains the speed of the soure at the time of emission, but do not rule out other ideas, like Faraday s 1846 [12]. 3 Faraday s ray vibrations In order to remove the ether, Faraday introdued the onept of vibrating rays [12], in whih an eletri harge is oneived as a enter of fore with attahed rays that extend to infinity. The rays move with their enter, but without rotating. Aording to this view, the phenomenon of eletromagneti radiation orresponds to the vibration of these rays, that propagates at speed relative to the rays (and the enter). That is, the radiation remains linked to the soure even after emitted. Today we ould desribe the interation as a kind of entanglement between the harge and the photon. A framework for the eletromagneti phenomena aording to Faraday s ideas was developed. It was alled Vibrating Rays Theory [13] in referene to Faraday s vibrating rays. Under Faraday s idea, the veloity of radiation at a given epoh will be equal to plus the veloity of the soure at the same epoh, in ontrast with ballisti theories in whih 308 Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement?

3 Issue 4 (Otober) PROGRESS IN PHYSICS Volume 12 (2016) the emitted light retains the speed of the soure at the emission epoh. In this sense the radiation is always linked to the harge at every time after the emission. Consequently, the measured Doppler Effet orresponds to the speed of the soure at the time of reeption, as well. Further, a differene between ative and passive refletion is expeted, sine the latter is still related to the original soure aording to Vibrating Rays Theory. The Deep Spae Network works with the so alled ative refletion (the spaeraft re-emits in real time a signal in phase with the reeived signal from Earth), while the Spae Surveillane Network works with passive radar refletion. In onsequene, the down-link signal from the approahing spaeraft will propagate faster that the refleted one. Using the available orbital data [1] we found that, under Vibrating Rays Theory, the theoretial time-of-flight differene between ative and passive refletion gives exatly the same range disagreement as (1), see Part 6 of [13]. 4 Pioneer anomaly The Pioneer anomaly refers to the fat that the reeived Doppler frequeny differs from the modeled one by a blue shift that varies almost linearly with time, and whose derivative is d( f ) Hz/s, (2) dt where f is the frequeny differene between the measured and the modeled values. In the ase of a soure with variable speed, the main differene in Doppler (to first order) between Vibrating Rays Theory and Speial Relativity Theory, is that Speial Relativity Theory relates to the speed of the soure at the time of emission, while Vibrating Rays Theory relates to the speed of the soure at the time of reeption. Preisely, this differene seems to be present in the spaeraft anomalies. If Vibrating Rays Theory is valid, it automatially invalidates all alulations and data analysis of spaeraft traking whih are based on Speial Relativity Theory. So, it is not easy to make a diret omparison between the expeted results from Speial Relativity Theory and Vibrating Rays Theory. However, to see whether or not the main features predited by Vibrating Rays Theory are present in the measurements, we an evaluate the residual by simulating a measured Doppler signal assuming that light propagates in aordane to Vibrating Rays Theory but analyzed aording to Speial Relativity Theory. Calling t 2 the emission time of the downlink signal from the spaeraft toward Earth and t 3 the reeption time at Earth, the first order differene of the Doppler shift between Vibrating Rays Theory and Speial Relativity Theory is (see [13] Part 4) f=f VRT f S RT f 0ˆr v2 v 3, (3) where v 2 and v 3 represent the veloities of the spaeraft at the orresponding epoh, ˆr is the unit vetor from the spaeship to the antenna, and f 0 the proper frequeny of the signal. That is, the veloity used in the Speial Relativity Theory formula is that at the time of emission while aording to Vibrating Rays Theory is that orresponding at the time of reeption. Sine the spaeraft slows down as it moves away, then ˆr (v 2 v 3 ) > 0, therefore the differene orresponds to a small blue shift mounted over the large red shift, as it has been observed in the Pioneer anomaly. It should be noted that this differene appears beause of the ative refletion produed by the on-board transmitter. In ase of a passive refletion (for example, by means of a mirror) the above differene vanishes. 4.1 Main term An estimate of the order of magnitude of 3 is obtained by using that the variation of the veloity of the spaeraft between the time of emission and reeption is approximately v 2 v 3 a (t 2 t 3 ), (4) where a is a mean aeleration during the down-link interval. An estimate for the duration of the down-link is simply t 3 t 2 r, (5) where r is a mean position of the spaeship between t 2 and t 3, therefore r a f f 0. 2 Sine a= GM ˆr, r 2 where G is the gravitational onstant, and M the mass of the Sun, then, the time derivative beomes d ( f ) dt f 0 v a 2. (6) If the differene (6) is interpreted as an anomalous aeleration we get a a v a, (7) that is, the so-alled anomalous aeleration is v/ times the atual aeleration of the spaeraft. Using data from HORIZONS Web-Interfae [14] for the spaeraft ephemeris, some harateristi value for a a an be obtained. Consider the anomalous aeleration deteted at the shortest distane of the Cassini spaeraft during solar onjuntion in June, The spaeraft was at a distane of 7.42 AU moving at a speed of 5.76 km/s. The anomalous aeleration given by (7) is a a m/s 2 of the same order of the measured one ( m/s 2 ). Also, the losest distane at whih the Pioneer anomaly has been deteted was Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement? 309

4 Volume 12 (2016) PROGRESS IN PHYSICS Issue 4 (Otober) about 20 AU. the anomalous aeleration predited by (7) at that distane is a a m/s 2 of the same order as the measured one. The anomaly given by (7) dereases in time in a way that has not been observed. Note, however, that aording to Markwardt [15] the expeted frequeny at the reeiver inludes an additional Doppler effet aused by small effetive path length hanges, given by f path = 2 f 0 dl dt, (8) where dl/dt is the rate of hange of effetive photon trajetory path length along the line of sight. This is a first order effet that an partially hide the differene between Speial Relativity Theory and Vibrating Rays Theory. Therefore, a more areful analysis should take into aount the additional ontribution of (8) in (7). Further, other first order effets may appear, for example, by a slight rotation of the orbital plane. Due to spaeraft maneuvers or random perturbations the orbital parameters are obtained by periodially fitting the measurements with theoretial orbits. Therefore there is no straightforward way to weight the importane of these fittings in (7). In other words, data aquisition and analysis may hide part of the Vibrating Rays Theory signature. 4.2 Annual term Apart from the residual referred to in the preeding paragraph there is also an annual term. Aording to Anderson et al [16] the problem is due to modeling errors of the parameters that determine the spaeraft orientation with respet to the referene system. Anyway, Levy et al [17] laim that errors suh as errors in the Earth ephemeris, the orientation of the Earth spin axis or the stations oordinates are strongly onstrained by other observational methods and it seems diffiult to modify them suffiiently to explain the periodi anomaly. The advantage of studying the annual term over the main term, is that the former is less sensitive to the first order orretion mentioned above, and, for the ase of Pioneer, also to the thermal propulsion orretion [5]. Clearly, the Earth orbital position does not modify those terms. As before, the annual term is explained by the differene between the veloity of the spaeraft at the time of emission and that at the moment of detetion, whih depends on whether the spaeship is in opposition or in onjuntion relative to the Sun. When the spaeraft is in onjuntion, light takes longer to get bak to Earth than in opposition. The time differene between emission and reeption will be inreased by the time the light takes in rossing the Earth orbit. Speifially, taking into aount the delay due to the position of Earth in its orbit, in opposition equation (5) should be written as t 3 t 2 r+r orb, (9) while in onjuntion it would be t 3 t 2 r R orb, (10) where R orb is the mean orbital radius of Earth. Therefore, an estimate of the magnitude of the amplitude of the annual term is f f 0 ar orb 2. (11) For the ase of Pioneer 10 at 40 AU we get and at 69 AU f 14 mhz, (12) f 4.8 mhz, (13) in good agreement with the observed values. Using data from HORIZONS Web-Interfae [14] a more omplete analysis of the time variation of f has be performed. The residual (that is, simulated Doppler using Vibrating Rays Theory but interpreted under Speial Relativity Theory) during 12 years time span is plotted in figure 2. Also the dumped sine best fit of the 50 days average measured by Turyshev et al [18] is plotted showing an exellent agreement between measurements and Vibrating Rays Theory predition. The negative peaks (i.e., maximum anomalous aeleration) our during onjuntion when the Earth is further apart from the spaeraft, and positive peaks during opposition. Also, the amplitude is larger at the beginning of the plotted interval and dereases with time, as it was observed [4, 18]. 5 Flyby anomaly Like the Pioneer anomaly, the Earth flyby anomaly an be assoiated to a modeling problem, in the sense that relativisti Doppler inludes terms that are absent in the measured signals. The empirial equation of the flyby anomaly is given by Anderson et al [4], whih, notably, an be derived using Vibrating Rays Theory, as is done in Part 6 of [13]. Consider the ase of NEAR traked by 3 antennas loated in USA, Spain, and Australia (a full desription of the traking system is found in a series of monographs of the Jet Propulsion Laboratory [19]). The reeiving antenna was hosen as that having a minimum angle between the spaeraft and the loal zenith. Using available orbital data, a simulated Doppler signal has been alulated using Vibrating Rays Theory. Thus, the simulated residual is obtained by subtrating the theoretial Speial Relativity Theory Doppler, from the Vibrating Rays Theory alulation. We observed, however, that the term that ontains the veloity of the antennas, that is d= γ u 3 γ u1 1 ˆr 23 u 3 / 1 ˆr 12 u 1 /, (14) 310 Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement?

5 Issue 4 (Otober) PROGRESS IN PHYSICS Volume 12 (2016) f (mhz) Doppler Residual (Hz) :00: :30: :00: :30: :00: :30: :00:30 Date Date and time Fig. 2: Annual variation of the frequeny differene between Vibrating Rays Theory and Speial Relativity Theory (full line) and anomalous dumped sine best fit of the 50 days average measured by Turyshev et al [18] (dashed line), for Pioneer 10 from January 1987 to January Fig. 3: Fitting the pre- (right half, in red) and post-enounter (left half, in blue) X-band Doppler data residual, for the NEAR flyby under an ideal hyperboli orbit. Solid lines simulated aording to Vibrating Rays Theory. Crosses, atual data extrated from referene [4]. is not enough to ompletely remove the first order (in u/) Earth signature (u is the veloity of the antenna, 1 refers to the emission epoh and 3 to the reeption epoh, as in [13] Part 4). This is so beause the veloity of the antennas is not uniform and the evaluation of the emission time is different for Vibrating Rays Theory and Speial Relativity Theory. Then, a small first order term remains. Anyway, sine orbital parameters are obtained by periodially fitting the measurements to theoretial orbits, thus a similar proedure is needed for Vibrating Rays Theory. Curiously, by doing so, the first order term is removed. The only differene between orbits adjusted by Speial Relativity Theory and Vibrating Rays Theory is a slight rotation of the orbit plane, as mentioned above. Note that in the ase of range disagreement (disussed above) two different orbital adjustment would be needed by the Deep Spae Network and the Spae Surveillane Network due to the different propagation speed. In onsequene, it will be impossible to fit a simultaneous measurement, as it seems to happen with the range disagreement. The final result shows that eah antenna produes a sinusoidal residual with a phase shift at the moment of maximum approah. Therefore, if we fit the data with the pre-enounter sinusoid a post-enounter residual remains and vie versa. In figure 3 are simultaneously plotted the result of fitting the residual by pre-enounter data (right half in red, orresponding to figure 2a of [4]) and by post-enounter data (left half in blue, orresponding to figure 2b of [4]). Note that the simulated plots are remarkably similar to the reported ones, inluding the amplitude and phase (i.e., minima and maxima) of the orresponding antenna. The fitting of post-enounter data (blue) an be improved by appropriately setting the exat swithing times of the antennas (whih are unknown to the author). The flyby Doppler residual exhibits a lean signature of the Vibrating Rays Theory. 6 Conlusions In this work I have presented observational evidene favoring a dependene of the speed of light on that of the soure, in the manner implied in Faraday s ideas of vibrating rays. It is remarkable and very suggestive that, as derived from Faraday s thoughts, simply by relating the veloity of light and the orresponding Doppler effet with the veloity of the soure at the time of detetion, is enough to quantitatively and qualitatively explain a variety of spaeraft anomalies. Also, it is worth mentioning that a formulation of eletromagnetism ompatible with Faraday s oneption is possible, as shown in [13] Part 8, whih is also ompatible with the known eletromagneti phenomena. The most remarkable fat of this new formalism is the simultaneous presene of instantaneous (stati terms) and delayed (radiative terms) interations (i.e., loal and nonloal phenomena in the same interation). Finally, under Vibrating Rays Theory the manifestation of the movement of the soure in the speed of light is more subtle than the naive +kv hypothesis (k is a onstant, 0 k 1) usually used to test their dependene [8]. Thus, it is also of fundamental importane the fat that, from the experimental point of view, it is very diffiult to detet differenes between Vibrating Rays Theory and Speial Relativity Theory, as disussed in [13], whih is also manifest in the smallness of the measured anomalies, and in the non lear manifestation of the effet in usual experiments and observations. For example, it produes a negligible effet on satellite positioning systems, see Part 7 of [13]. I am aware of how ounterintuitive these oneptions are to the modern sientist, but also believe that, given the above evidene, a onsientious experimental researh is needed to settle the question of the dependene of the speed of light on that of its soure as predited by Vibrating Rays Theory, and Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement? 311

6 Volume 12 (2016) PROGRESS IN PHYSICS Issue 4 (Otober) that has been observed during the 1998 NEAR flyby. As a losure, I reall Fox s words regarding the possibility of onduting an experiment on the propagation of light relative to the motion of the soure: Nevertheless if one balanes the overwhelming odds against suh an experiment yielding anything new against the overwhelming importane of the point to be tested, he may onlude that the experiment should be performed [20]. Aknowledgements I am thankful to Fernando Minotti who read this paper and improved the manusript signifiantly, although he may not agree with all of the interpretations provided in this paper. Referenes Submitted on July 4, 2016/Aepted on July 8, Antreasian P.G., Guinn J. R. Investigations into the unexpeted Delta-V inreases during the Earth gravity assists of Galileo and NEAR. AIAA Paper No presented at the AIAA/AAS Astrodynamis Speialist Conferene and Exhibit (Boston, August 10-12, 1998). 2. Guruprasad V. Observational evidene for travelling wave modes bearing distane proportional shifts. EPL, 2015, v. 110, Anderson J.D., Laing P.A., Lau E.L., Liu A.S., Nieto M.M., Turyshev S.G. Indiation, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Aeleration. Phys. Rev. Lett., 1998, v. 81, Anderson J.D., Campbell J.K., Ekelund J.E., Ellis J., Jordan J.F. Anomalous Orbital-Energy Changes Observed during Spaeraft Flybys of Earth. Phys. Rev. Lett., 2008, v. 100, Turyshev S.G., Toth V.T., Kinsella G., Lee S.-C., Lok S.M., Ellis J. Support for the Thermal Origin of the Pioneer Anomaly. Phys. Rev. Lett, 2012, v. 108, de Sitter W. Ein astronomisher Beweis für die Konstanz der Lihgeshwindigkeit. Z. Phys., 1913, v. 14, de Sitter W. Über die Genauigkeit, innerhalb welher die Unabhängigkeit der Lihtgeshwindigkeit von der Bewegung der Quelle behauptet werden kann. Z. Phys., 1913, v. 14, Breher K. Is the Speed of Light Independent of the Veloity of the Soure? Phys. Rev. Lett., 1977, v. 39, Alväger T., Farley F.J.M., Kjellman J., Wallin I. Test of the seond postulate of speial relativity in the GeV region. Phys. Lett., 1964, v. 12, Botermann B., Bing D., Geppert C., et al. Test of Time Dilation Using Stored Li+ Ions as Cloks at Relativisti Speed. Phys. Rev. Lett., 2014, v. 113, Shrödinger E. Die erfüllbarkeit der relativitätsforderung in der klassishen mehanik. Ann. der Physik, 1925, v. 77, Faraday M. Thoughts on ray-vibrations. Phil. Mag. Series 3, 1846, v. 28, Bilbao L., Bernal L., Minotti F. Vibrating Rays Theory. arxiv: Markwardt C.B. Independent Confirmation of the Pioneer 10 Anomalous Aeleration. arxiv: gr-q/ Anderson J.D., Laing P.A., Lau E.L., Liu A.S., Nieto M.M., Turyshev S.G. Study of the anomalous aeleration of Pioneer 10 and 11. Phys. Rev. D, 2002, v. 65, Levy A., Christophe B., Reynaud S., Courty J-M., Brio P., Mtris G. Pioneer 10 data analysis: investigation on periodi anomalies. Journées sientifiques de la SF2A, Paris, Frane, 2008, (hal ). 18. Turyshev S.G., Anderson J.D., Laing P.A., Lau E.L., Liu A.S., Nieto M.M. The Apparent Anomalous, Weak, Long-Range Aeleration of Pioneer 10 and 11. arxiv: gr-q/ DESCANSOTeam, Jet Propulsion Laboratory, California Institute of Tehnology. (aessed July 2014). 20. Fox J.G. Experimental Evidene for the Seond Postulate of Speial Relativity. Am. J. Phys., 1962, v. 30, 297. Editorial Comment This paper plays an importane in the understanding of the physial observable veloity of light that differs from the world-invariant in the General Theory of Relativity. Defining physial observable quantities in the General Theory of Relativity is not a trivial problem. This is beause we are looking at objets in a four-dimensional spae-time, and we have to determine whih omponents of these four-dimensional tensor quantities are physially observable. A omplete mathematial theory for alulating physially observable quantities in the four-dimensional spae (spae-time) of General Relativity was introdued in 1944 by Abraham Zelmanov, and is known as the theory of hronometri invariants. Landau and Lifshitz in 84 of their The Classial Theory of Fields also introdued physially observable time and observable three-dimensional intervals similar to Zelmanov. But they limited themselves only to this partiular ase, while only Zelmanov arrived at the versatile mathematial theory. A ompendium of Zelmanov s theory of physial observable quantities an also be found in the books. In short, physially observable are the projetions of four-dimensional quantities onto the time line and the three-dimensional spatial setion of the observer, whih an be non-uniform, deformed, urved and rotating. These projetions are alulated through the speial projeting operators whih take all the aforementioned fators into aount. In partiular, the physial observable veloity of light differs from the world-invariant, and is depended on the gravitational potential and the rotation veloity of the observer s spae. In ultimate physial onditions, as is shown in Chapter 5 of Partiles Here and Beyond the Mirror, the observable veloity of light an even beome zero, that is verified by the frozen light experiment (Lene Hau, 2001). Even more. In a physial spae (spae-time metri) wherein is a shift at one of the spatial diretions (that means a spatial anisotropy), the observable veloity of light is depended on the signal soure s veloity at this preferred diretion. We drafted suh a spae-time metri in the last deade. Einstein s postulates have now only a historial meaning. One Einstein moved his theory on the mathematial basis of Riemannian geometry, he found that all the postulates are the manifestations of geometry of Riemannian spaes. It is as well true about the world-invariant of the veloity of light. In a spae, whih is free of gravitation, is uniform, non-deformed, and non-rotating, the physial observable veloity of light oinides with the world-invariant. However in a real physial spae it does not. For this reason the experimental ompendium and the analysis presented in Bilbao s paper will maybe give a new fresh stream in searh for the further theoretial preditions of the General Theory of Relativity. Dmitri Rabounski, Editor-in-Chief Larissa Borissova, Asso. Editor Zelmanov A. Chronometri invariants. Amerian Researh Press, Rehoboth (NM), Zelmanov A. Chronometri invariants and aompanying frames of referene in the General Theory of Relativity. Soviet Physis Doklady, 1956, v. 1, Borissova L. and Rabounski D. Fields, Vauum, and the Mirror Universe. 2nd ed., Svenska fysikarkivet, Stokholm, Rabounski D. and Borissova L. Partiles Here and Beyond the Mirror. 3rd ed., Amerian Researh Press, Rehoboth (NM), Luis Bilbao. Does the Veloity of Light Depend on the Soure Movement?