Light Transmission and the Sagnac Effect on the Rotating Earth

Transcription

1 Light Transmission and the Sagna ffet on the Rotating arth Stephan J. G. Gift Department of letrial and Computer ngineering Faulty of ngineering The University of the West Indies St. Augustine, Trinidad and Tobago, West Indies mail: Abstrat: Light transmission on the surfae of the rotating arth is examined using the Langevin metri of general relativity. It is shown that this metri whih yields the rigorously tested and verified algorithm for lok synhronization in the Global Positioning System (GPS) also predits east-west light speed anisotropy that is inonsistent with light speed isotropy postulated to hold at a loal level on the rotating arth. This light speed anisotropy is further demonstrated using experimentally onfirmed light travel time in a simple speed alulation as well as the lassial method of light speed relative to a terrestrial observer rotating with the arth for light travel in the arth-centred Inertial (CI) frame. These theoretial results are onfirmed by experimental findings from GPS measurements and lead to the re-interpretation of the Sagna effet normally treated as a time orretion in GPS operation. Keywords: general relativity, priniple of light speed onstany, GPS, range equation, one-way speed of light, CI frame, Sagna ffet. 1. Introdution A entral tenet of modern physis is the priniple of light speed onstany aording to whih light travels at a onstant speed in all inertial frames. Numerous verifiation experiments yielding light speed have been onduted leading to the almost universal belief that the priniple has been onfirmed. However Zhang [1] has shown that while two-way light speed invariane has been verified, one-way light speed onstany has not. Also, although the priniple is formulated as applying in inertial frames, the majority of light speed tests laiming its onfirmation have been onduted in the noninertial frame of the rotating arth [-9]. Rindler [10] justifies this by arguing we do not expet to find suh extended or perfet inertial frames in nature. It is the equivalene priniple that provides the bridge between the ideal [speial relativity] model and the real world. Aording to it, we an find at eah event a set of loal inertial frames, whih may

2 be small or large depending on (i) the distribution of nearby masses, and (ii) the auray we require. It is to these frames (or other frames not differing too muh from these frames) that [speial relativity] is applied in pratie, and with great suess. In other words the surfae of the rotating arth an be treated as an approximately inertial frame by onfining onsiderations to suitably restrited regions suh that the speed of light is loally isotropi in this otherwise non-inertial frame. This onlusion is supported by many authors inluding Rizzi and Tartaglia [11], Rizzi and Tartaglia [1], Rizzi and Ruggiero [13], Pasual-Sánhez et al.[14] and Kassner [15]. Thus on a rotating platform Rizzi and Tartaglia [11] argue for light speed onstany both ast and West and Pasual- Sánhez et al. [14] support light speed onstany both loally and globally. Additionally, Tartaglia and Ruggiero [16] have shown in the framework of general relativity that angular momentum effets do not measurably affet light travel times in Mihelson- Morley type experiments. Perhaps the most ompelling indiation of the aeptane of the priniple of light speed onstany and its appliability in the terrestrial frame is its use in the SI definition of the metre requiring light speed invariane in the frame of the rotating arth. There is however some disagreement about the physis of light transmission on a rotating platform. Speifially a few authors argue for light speed anisotropy around suh a platform and the onsequent inappliability of the priniple of light speed onstany [17, 18]. Selleri [17] in partiular advaned a proof of anisotropy in the speed of light in a referene frame that is ommoving with the edge of a rotating platform. ven Rizzi and Tartaglia who initially argued for light speed isotropy [11], later relaxed their position regarding global light speed anisotropy in a rotating frame [1]. An entire book addressing this issue has in fat been published [19]. Thirty years ago in a paper presented at a Preise Time and Time Interval meeting desribing the results of time transfer experiments using laser light pulses, Alley and others [0] noted that the metri assoiated with general relativity predits an asymmetry in the one-way speed of light travelling in the east-west and west-east diretions. It was suggested then that this differene if real may eventually be measurable by experiment. In a later paper Alley and his olleagues [1] outlined the general relativity theory predition of light speed anisotropy in the east-west diretion and desribed an experiment that diretly searhed

3 3 for this anisotropy. This predition of light speed anisotropy in the framework of general relativity diretly onflits with the loal priniple of light speed onstany on the surfae of the arth and this apparent inonsisteny has never been resolved. The advent of the very suessful Global Positioning System (GPS) where light transmission on the rotating arth is an on-going physial ativity provides an opportunity for diret experimental resolution of the ontroversy relating to the physis of light travelling in rotating frames. GPS operation is based on aurate atomi loks that are synhronized using an algorithm derived within the same general relativity metri [, 3] that predits east-west light speed asymmetry. The aepted interpretation is that light speed is onstant in GPS lok synhronization but a time adjustment sometimes referred to as the Sagna orretion is neessary beause of the arth s rotation. Similar to the ase of light speed onstany in a rotating frame, this interpretation has been subjet to hallenge [4-30]. Marmet [4] and Kelley [5] have argued that observed travel time differenes in the GPS for east-west light transmission is evidene of light speed anisotropy and Gift has supported this using the rigorously verified GPS lok synhronization algorithm [6] and the GPS range equation [7]. Hayden [31] previously arrived at this same onlusion after onsidering several experiments inluding Sagna, Mihelson-Gale and Brillet-Hall. In this paper we re-examine the issue of light transmission on the rotating arth with partiular referene to the GPS and analyze the problem using general relativity in a rotating frame of referene. In setion we derive the transmission time for a pulse of light travelling on the surfae of the arth using the Langevin metri in general relativity. This yields the result given by Ashby and aepted by the CCIR for lok synhronization. In setion 3 we use the same metri to determine the orresponding eastwest light speeds on the rotating arth and revisit the problem of asymmetrial light speeds. Supporting experimental evidene from the GPS is presented. In setion 4 based on the experimentally onfirmed time of travel result light speed in any diretion on the surfae of the arth is alulated using the ratio distane over time. In setion 5 light speed in any diretion is also determined based on light travel in the arth-centered Inertial (CI) frame relative to the rotating arth. A full disussion of the findings and their impliations is then presented in setion 6.

4 4. Derivation of the Travel Time of a Light Pulse in General Relativity In this setion we derive the transmission time of a light pulse travelling on the surfae of the arth. In doing so, we follow the proedure presented by Ashby [3]. From general relativity and ignoring gravitational potentials, the metri in the CI frame where spae-time is Minkowskian is in ylindrial oordinates given by [3-34] ds ( dt ) dr r d dz (1) The transformation from the oordinate system ( t, r,, z) in the CI frame where light speed is to a oordinate system ( t, r,, z) in the arth Centered arth Fixed frame whih is rotating at the uniform angular speed is given by t t, r r, t, z z () The transformation t t in () means that time t in the rotating frame is the same as the time t in the assoiated CI frame where the measuring loks an be instein synhronized. This results in the Langevin metri in the rotating frame given by where ds ( 1 d r )( dt) r ddt d (3) dr r d dz (4) is the square of the oordinate distane. Applying equation (3) to the propagation of light on the rotating arth by setting ds 0 yields a quadrati equation for dtgiven by Solving for ( dt) gives r r d (1 )( dt) ( dt) d 0 (5) r d dt r d r ( ) 4(1 ) d r (1 ) Taking the dominant term under the square root gives r d d dt r ( 1 ) (6) (7)

5 5 Noting that r 1and taking the positive sign redue equation (7) to r d dt d As pointed out by Ashby [3] the quantity r d/ orresponds to the infinitesimal area da z in the rotating frame that is swept out by a line onneting the axis of rotation to the light pulse and projeted onto a plane parallel to the equatorial plane. Thus (8) an be written as dt d da z From (9) the total time for light to travel a given path as measured in the rotating frame is given by d dt da z path path path (8) (9) (10) quation (10) gives the light travel time observed on the surfae of the rotating arth. As a GPS lok synhronization proedure it has been rigorously and exhaustively tested and verified and has been published in a standard by the CCIR (International Radio Consultative Committee) in 1990 and 1997 for synhronizing loks at different points on the arth. Using (10) the time tw for light to travel eastward between two points fixed on the surfae of the arth a short distane l apart is given by [6] l lv t W (11) where v is the surfae speed of the arth at the partiular latitude. The time to travel westward between these same two points from (10) is given by [6] tw for light l lv t W (1) This GPS east-west light travel time differential t t 0derived using the CCIR algorithm (10) formally establishes the fat that light takes longer to travel ast than West between fixed points on the surfae of the arth, an experimental observation first highlighted by Marmet [4] and Kelley [5]. W W

6 6 Ashby however interprets the first term d / in (10) as the time in the rotating frame for the light to traverse the path dat speed while he interprets the seond term da z as the additional time determined in the underlying inertial frame for the light to ath up to the moving referene point. The assoiated physial phenomenon is sometimes referred to as the Sagna ffet. Aording to Ashby Observers fixed on the earth, who were unaware of earth rotation, would use just d / for synhronizing their lok network and this would lead to signifiant error. Towards aurate lok synhronization he states that orretions of the form da / based on his interpretation of equation (10). path z must be applied, this From this disussion, the overall situation for the observer fixed on the surfae of the rotating earth is that light travels between fixed points on the arth s surfae at speed onsistent with the priniple of light speed onstany but that a Sagna orretion must be applied to the resulting travel time beause of the rotation of the arth. Ashby has published several papers promoting this interpretation [3, 35-37] and it is now widely aepted by physiists. This interpretation is however open to question sine as indiated previously the Langevin metri used to derive the lok synhronization algorithm also yields anisotropi light speed in the east-west diretion in the rotating frame [0, 1]. Moreover as demonstrated above, equation (10) shows that t W t W in the following setions. implying asymmetrial east-west light speeds. We examine this situation 3. Light Speed in the ast-west Diretion in General Relativity Following Alley et al. [1], onsider light transmission in the east-west diretion on the rotating arth as shown in Fig.1 in whih ase d z 0. These authors assumed d r 0 in their derivation of east-west light speed sine the hanges are inremental. In order to demonstrate this, starting in the diretion of a line of latitude OB, the light pulse travels from point O on the surfae of the arth along a straight line to the point A where B is on the surfae of the arth and O is on the axis. For right-angled triangle O OA,

7 7 d rtan d rd sine d is an infinitesimal hange and hene from (4), d r 0. Using d rd redues equation (7) to O d r O rd d B dr A Fig.1 ast-west Light Transmission on the Surfae of the arth r d r rd rd ( 1) dt r (13) r r ( 1 ) (1 )(1 ) For light travelling in the east-west diretion, d is negative suh that d d. Sine dtis positive, then the negative sign in ( r 1) in (13) is hosen giving r rd(1 ) rd dt r r r (1 )(1 ) (1 ) This gives rd dt ( r ) (14) (15) Now rd d is the east-west distane travelled in time dtand r v is the speed of the earth s surfae at the partiular latitude. Hene Therefore the east-west light speed W d dt (16) ( v) on the rotating earth is given by

8 8 W d d v dt d /( v) (17) For light travelling in the west-east diretion, d is positive and therefore d d. Sine dtis positive, then the positive sign in ( r 1) in (13) is hosen giving This redues to whih gives r rd(1 ) rd dt r r r (1 )(1 ) (1 ) rd dt ( r ) (18) (19) d dt (0) ( v) Therefore the west-east light speed W on the rotating earth is given by W d d v dt d /( v) (1) Thus at any point on the surfae of the rotating arth, the general relativity alulation produes light speed v from ast to West and light speed v from West to ast. Alley and his team [1] noted this asymmetrial light speed predition by the general relativity metri but were unlear whether the predition was observable sine the metri of equation (3) seems to assume that the observer is loated at the entre of the rotation. This unertainty has however been removed as light speeds v in the eastwest diretion on the surfae of the arth have been verified by several researhers using GPS tehnology. Around the time of these attempts by Alley and his group to detet ast-west light speed differentials, unequal travel time of about 300 nanoseonds for eletromagneti signals travelling in opposite diretions around the arth were diretly demonstrated by Allan and his olleagues using atomi loks and signal refletions off orbiting satellites [38]. Following this Marmet [4], using GPS measurements observed

9 9 that a light signal takes about 8 nanoseonds longer to travel eastward from San Franiso to New York than to travel westward from New York to San Franiso. Kelly [5] also noted that measurements using the GPS reveal that a light signal takes 414 nanoseonds longer to irumnavigate the arth eastward at the equator than in the westward diretion around the same path. This is as predited by GPS equations (11) and (1). Both Marmet and Kelley onluded that these observed travel time differenes in the GPS measurements in eah diretion our beause light travels at speed eastward and v v westward relative to the surfae of the arth at the partiular latitude. Gift [6] onfirmed and generalized these anisotropi east-west light speeds v by using the GPS lok synhronization algorithm to determine light travel time for arbitrary distane. (See setion 4) Wang [8] used the range equation operating in the CI frame to demonstrate light travel time differenes depending on the observer s uniform motion relative to the CI frame. Gift [7] applied Wang s approah by employing the range equation to determine elapsed time for light traveling between two adjaent points fixed on the surfae of the rotating arth at the same latitude then using the known distane between the two fixed points to show that the one-way speed of light in the east-west diretion is v. This east-west light speed anisotropy has also been observed by Hath [9] for light transmission between the GPS reeivers on two Gravity Reovery and Climate xperiment satellites and by Sato [30] who showed that in the operation of the GPS the Sagna effet provides experimental evidene that the speed of light varies aording to the rotational motion of the arth. It is evident therefore that the asymmetrial light speed predition of general relativity has atually been observed, the inonsisteny with the priniple of light speed onstany notwithstanding. In order for general relativity to predit light speed onstany on a rotating platform, it seems that the assoiated field equation must be modified. Based on researh onduted by Yilmaz [39, 40] a suitable modifiation is adding the stress energy tensor of the gravitational field tto the stress energy tensor for matter Ton the right side of the equation. The equation then beomes R 1 8G gr ( T ) 4 t ()

10 10 where Ris the Rii tensor onstruted from a nonlinear ombination of the g and their first and seond derivatives, R is the salar urvature and G is the Newtonian gravitational onstant. The relevant metri when solved for east-west light travel yields light speed onstany given by [1] d r dt However while light speed derived using the modified field equation is known to produe inaurate lok synhronization when used without a Sagna orretion, it will be shown that light speeds v derived using the original field equation do not. (3) 4. Light Speed Using GPS Time Measurements Sine the time of travel given by GPS equations (11) and (1) has been rigorously verified and is programmed into the operation of the GPS, this represents an atual time of travel measurement that an be used to test the asymmetrial east-west light speed predition of general relativity based on simple kinematis as was done in [6]. Thus using the GPS time tw in (11), the one-way speed of light W traveling eastward between two points fixed on the surfae of the arth a distane l apart is given by W l t Similarly using the GPS time W l tw l lv westward between the two loks is given by W l t W l v (1 ) 1 v, v in (1), the one-way speed of light W l lv v (1 ) 1 v, v (4) traveling The results in (4) and (5) are exatly the light speeds (1) and (17) predited by general relativity. This means that the GPS diretly onfirms light speed anisotropy in the arth Centered arth Fixed frame. Stated simply, the GPS shows that light travels faster West than ast between two points fixed on the surfae of the rotating arth. (5) It is possible to use the GPS to demonstrate a more general form of the asymmetrial east-west light speed predition of general relativity. Thus in the rotating

11 11 frame the light pulse travels a oordinate distane hene the light speed R in the rotating frame of the arth is given by R d in the time dtgiven in (9) and d d (6) dt d r d In Fig. O is on the axis of the arth, O is on the surfae and d is parallel to the equatorial plane. Let the angle between the diretion of the light pulse on the surfae of the arth and the line of latitude OX at that point be. Then Realling that using (7), (6) beomes r d d os (7) r v is the speed of the earth s surfae at the partiular latitude and R d (8) d vd os Az O da z d r O d X Fig. Distane d travelled by the Light Pulse This redues to R v 1 (1 os ) vos, v (9) For light transmission in the west-east diretion, R o 0 and therefore (9) gives o v. For light transmission in the east-west diretion, 180 and hene (9) yields R v. These light speed values are exatly those found using the general relativity metri in setion 3 and experimentally onfirmed using the GPS [4-30]. Thus the light speed in (9) determined in the arth s rotating frame using the CCIR timing algorithm (9) and (10) yields one-way light speed R vos relative to

12 1 the surfae of the arth and not light speed R required by the loal priniple of light speed onstany. It is therefore now lear why lok synhronization using d / alone results in signifiant error. The error ours beause light speed in the rotating frame is vos and not and hene lok synhronization should use d /( vos ) and not d /. To onfirm this we determine the time dtfor light to travel the oordinate distane dat speed vos. This is given by Then, From Fig., R d d d ( vos ) d ( vos ) dt, v vos ( v os ) R Substituting (3) in (31) yields (30) d d r os dt (31) d os r/ da z (3) dt d da z From (33) the time for light to travel a given path as measured in the rotating frame is therefore given by d dt da z path path whih is equation (10) given by Ashby and published by the CCIR for lok synhronization. We have therefore onfirmed that lok synhronization using d / where R vos results in aurate lok synhronization. Ashby s R interpretation that synhronization using (34) is really the use of travel time d / with a orretion A / promotes the illusion that the atual speed of light in the d z path (33) (34) rotating frame is onsistent with the loal priniple of light speed onstany when in fat the speed is vos as has now been demonstrated. In view of these results Ashby s interpretation must be rejeted.

13 13 5. Derivation of Light Speed Using Relative Veloity in the CI Frame Aording to the IS-GPS-00 Interfae Speifiation [], GPS signals propagate in straight lines at the onstant speed in the CI frame, a frame that moves with the arth in its orbital motion but does not share the arth s rotational motion. The experimentally established isotropy of the speed of light in the CI frame is utilized in the GPS range equation given by [, 3] r r ( tr s s r s ) r ( t ) ( t t ) (35) where ts is the time of transmission of an eletromagneti signal from a soure, tr is the time of reeption of the eletromagneti signal by a reeiver both times determined using synhronized loks, r t ) is the position of the soure at the time of transmission of the s ( s signal and r t ) is the position of the reeiver at the time of reeption of the signal. r ( r quation (35) enables aurate determination of the instantaneous position of objets whih are stationary or moving on the surfae of the arth. This light speed onstany in the CI frame provides us with a third approah to onfirming light speed anisotropy in the rotating frame of the surfae of the arth. R C v B v A v Fig. 3 Light Speed in the CI Frame and Observer speed due to arth s Rotation Thus in the CI frame light travels at speed relative to the CI frame while the arth on whose surfae the light transmission is observed is rotating at speed v relative to the CI frame. Consider a light pulse direted at an angle with respet to the line of latitude at a point A on the arth. This is shown in Fig. 3 where the light is travelling at speed in the CI frame and the observer on the surfae of the arth is moving at speed

14 14 v beause of the rotating arth. In order to determine veloity of the light relative to the moving observer a veloity v that is equal and opposite to v is applied in order to bring the observer to rest relative to the CI frame. Then the speed of the light R relative to the rotating arth is the resultant of and v given by R v vos(180 ) v vos ( vos ) ( vsin ) (36) Sine v, then (36) redues to R vos (37) whih is exatly the speed (9) derived in setion (4). Considering the right-angled triangle ABC in Fig.3, AB ( vos ) and BC vsin. Hene the assoiated angle is given by BC vsin tan 0, v (38) AB vos From (38) 0and therefore the speed of light R relative to the surfae of the rotating arth is R vos at an angle with the line of latitude. The time dtto travel the oordinate distane dat speed vos is given by R d d( v os ) dt, v R whih as shown in setion (4) leads to the CCIR synhronization equation (10) given by d dt da z path path path (39) (40) It is instrutive to ompare this situation with the ase of a vehile moving uniformly on the surfae of the arth and observed by a pedestrian. In order to have a meaningful omparison we again onsider the time tw for light to travel eastward between two points fixed on the surfae of the arth a short distane l apart given in equation (11) by [6] l lv t W (41) where, as before, v is the speed of the arth s surfae at the partiular latitude. Reall the light is travelling at speed in the CI frame while the observer is moving on the rotating arth at speed v relative to the CI frame. Light travel time is also given by [6] tw

15 15 l l lv t W, v (4) v Now onsider the situation in Fig.4 where a vehile at a position A is moving at veloity vc relative to the surfae S (orresponding to light transmission at veloity relative to the CI frame) and an observer a distane L away at B walking in the same diretion at veloity v relative to S with v vc (orresponding to the observer a distane l away moving on the rotating arth at speed v relative to the CI frame). v A S L v B Fig. 4 Vehile at A and Observer at B both moving on Surfae S Then from lassial mehanis the speed of the vehile relative to the moving observer is given by v C v and the time T for the vehile to ath up with the observer is given by L T (43) v v C xpanding (43) and retaining only terms up to first-order this redues to L Lv T (44) v C v C Comparing (44) and (41) it is lear that the situations are ompletely analogous. In the ase of the moving vehile however, (44) is not interpreted as the time L / for vc the vehile to travel at speed vc relative to the observer with a orretion Lv/ v C beause of the movement of the observer. Instead the aepted and orret interpretation of (44) is this is the time /( v v) for the vehile to travel to the observer L C at speed v C v relative to the observer. Similarly, in the GPS the interpretation of (41) as the time l / for the light to travel at speed relative to the observer on the rotating arth with a orretion lv / beause of the rotating arth is artifiial and not tenable. Instead, as demonstrated above, the orret interpretation of (41) is that it is the time l /( v) for the light to travel to the observer at speed v relative to the observer.

16 16 6. Disussion The results of this investigation reveal that the Langevin metri of general relativity whih produes the rigorously verified CCIR lok synhronization algorithm, also yields noninvariant east-west light speeds v in the frame of the rotating arth. This is ontrary to the light speed invariane priniple postulated to hold in an approximately loal inertial frame on the arth and assumed true in the SI standard of length measurement. This light speed anisotropy has been experimentally onfirmed by several researhers [4-30] using the high-preision tehnology of the GPS. Moreover, by using elementary kinematis involving onfirmed GPS time and arbitrary distane measurements, a more general expression R vos for light speed relative to the surfae of the rotating arth was derived whih easily yielded the CCIR lok synhronization algorithm. It was demonstrated that aurate lok synhronization uses d /( vos ) and not d / sine light speed in the frame of the rotating arth is vos and not. The notion that the CCIR lok synhronization algorithm works sine light travels at speed with the so-alled Sagna orretion neessary beause of the rotation of the arth is an invalid interpretation that enourages belief in a onstant light speed. Light transmission in the CI frame at speed relative to this frame and modeled by the GPS range equation r t ) r ( t ) ( t t ) enabled a omplete and aurate r ( r s s r s representation of the situation. Sine the CI frame moves with the arth but does not rotate with it, an observer fixed on the surfae of the arth moves at speed v relative to the CI frame. Therefore the relative speed of light R travelling in the CI frame and observed on the surfae of the rotating arth was determined using the lassial priniples of relative veloity and shown to be R vos. This is exatly the expression derived using the experimentally determined GPS light transmission time and simple kinematis. To further illuminate the disussion, well-understood relative veloity ourring with low-speed vehiular motion was outlined and the equations shown to be ompletely analogous to those derived from the CCIR lok synhronization algorithm. The appliability of lassial mehanis and relative speed to light transmission in the CI

17 17 frame was therefore revealed. These fully onsistent theoretial and experimental results demonstrating light speed anisotropy in the arth Centered arth Fixed frame suggest that the priniple of light speed onstany really is inappliable in the rotating frame of the surfae of the arth. Suh a view appears to be supported by Ashby who, despite his interpretation of the Sagna ffet as a time orretion, said [36, p44] the priniple of the onstany of annot be applied in a rotating referene frame! Selleri [17] has shown that an unavoidable paradox arises when speial relativity is applied to rotating platforms sine the ratio of one-way east-west light speeds (both W 1 v / loally and globally) is 1. This is inonsistent with the light speed 1 v / W invariane postulate of the theory whih requires 1. Several attempts have been made to resolve this issue [11, 1, 41-43] but Selleri in a later paper [44] reaffirmed the legitimay of the finding 1. He sought a resolution of this problem [45] by examining the most general set of spae-time transformations whih satisfy the experimentally observed onditions of onstant two-way light speed and time dilation and whih differ only by a lok synhronization parameter e 1. This allowed him to identify from among all possible transformations (inluding the Lorentz transformation) the single transformation that aords with all existing experimental data and for whih the paradox does not arise. This turned out to be the Inertial transformation [46, 47] orresponding to e 1 0 in the general set whih has been independently onfirmed [48]. This transformation predits one-way light speed on the rotating arth as R for whih 1 ( v / )os Using the anisotropi light speed 1 v / thereby resolving the paradox. 1 v / R, Selleri [45] alulated the 1 ( v / )os time for an eletromagneti signal to travel between two points on the arth via a geostationary satellite and thereby fully demonstrated the orretion term A /. d z This result is exatly that obtained in this paper using light speed R vos. This equivalene ours sine light speed R redues to 1 ( v / )os

18 18 R (1 ( v / )os ) vos v 1 ( v / )os 1 ( v / ) os, (45) As a result of Selleri s derivation of the orretion, he onluded The proedure whih we suggest to experimentalists is to avoid using a wrong veloity of light and orreting the result with an ad ho term, but rather to use from the beginning the veloity of light [ R ] of the inertial transformations. 1 ( v / )os Finally in the determination of light speed, synhronized loks are required for the timing of a light pulse as it propagates between two fixed points. In this regard, the I 1588 Standard for a Preision Clok Synhronization Protool for Networked Measurement and Control Systems defines synhronized loks as follows [49]: Two loks are synhronized to a speified unertainty if they have the same epoh and measurements of any time interval by both loks differ by no more than the speified unertainty. The timestamps generated by two synhronized loks for the same event will differ by no more than the speified unertainty. From this, loks are synhronized if they indiate the same times for the same events and this is realized using a suitable synhronization proedure. Some researhers however employ ertain other lok synhronization proedures that result in different modes of lok operation whih they refer to as synhronized loks. Light speeds determined using suh loks will show a dependene on these different lok synhronization shemes sine differently synhronized loks will measure different time intervals for the same light signal transmission. In fat virtually any speed an be obtained by suitably synhronizing the measuring loks and Will [50] has pointed out that a partiularly perverse hoie of synhronization an make the apparent speed infinite! These apparent speeds are artifiial and bear no relation to physial reality; they are meaningless. A proper lok synhronization method must result in loks that indiate the same times for the same events, preisely as ours in the GPS. In this system it has been experimentally demonstrated that the use of any other lok synhronization algorithm would result in major timing and navigational errors and therefore all suh alternatives are invalid. Selleri addressed this issue in his onsideration of the Sagna ffet [45]. In addition to resolving the paradox by identifying the inertial transformation, he presented

19 19 a new proof of absolute simultaneity by deduing the ondition e 0 from the universal set of spae-time transformations. In this way absolute simultaneity is shown to be neessary in all theories and like the GPS it is not true that the synhronization proedure an be hosen freely Conlusion In their paper of 1988, Alley and his o-authors [1, p6] expressed the view that A fully suessful theory of spae, time, and gravity must be founded upon atual experiene with the behaviour of loks and the propagation of light pulses in gravitational fields and in aelerated frames of referene. The remarkable stability of urrent atomi loks and the preision of short pulse laser ranging and time transfer systems now allow new types of experiments to be undertaken. These will allow the neessary experiene to be gained. In keeping with this approah, the appliation of available GPS atomi loks in simple time-measuring experiments disussed in this paper has enabled us to gain valuable information about the behaviour of light as it travels in the arth Centered arth Fixed frame. In partiular the GPS has onfirmed in equations (4) and (5) and elsewhere that light travels faster West than ast relative to the surfae of the rotating arth ontraditing the widely aepted priniple of light speed onstany. This is an objetive fat validated by observational experiene using synhronized loks in the real-world time measurement of travelling light. The Langevin metri used in general relativity to derive the suessful CCIR lok synhronization algorithm was shown to also predit anisotropi east-west light speeds v. This predition was supported using light travel times based on the GPS timing algorithm and simple kinematis as well as lassial mehanis involving relative veloity in the CI frame. Both methods yielded v for east-west light travel between fixed points on the surfae of the arth. This was onfirmed by atual experimental data from the GPS. Both approahes also produed the more general light speed expression R vos for light travelling at an angle with respet to a line of latitude. This anisotropi result is onsistent with Selleri s light speed R predited by his Inertial transformation but inonsistent with the light 1 ( v / )os

20 0 speed invariane priniple requiring light speed in the otherwise non-inertial terrestrial frame. This expression R whih is assumed to hold loally R vos for light speed relative to the surfae of the rotating arth was used to derive the CCIR lok synhronization algorithm that has been instrumental in the suessful operation of the GPS. Here it was demonstrated that aurate lok synhronization uses is d /( vos ) and not d / beause light speed in the frame of the rotating arth vos and not. Selleri has shown that the one-way light speed arth whih redues to R R on the rotating 1 ( v / )os vos ompletely resolves the problem of the Sagna orretion. In an online dialogue involving authors of papers in the book on rotating frames [19p399], he stated My viewpoint about Sagna-like orretions is that they arise from the anisotropi propagation of light in the arth rotating frame. These orretions are fully aounted for if this anisotropy is properly taken into aount, as I showed in my paper [45p60-63]. These sentiments are in onsonane with the results presented in this paper as well as with previous findings [4-31]. Thus these entirely onsistent theoretial results and objetive experimental fats provide inontrovertible evidene of light speed anisotropy in the arth Centered arth Fixed frame that deserves the attention of the sientifi ommunity. It was given attention long ago by Ives [51] who after investigation argued that the priniple of light speed onstany is not supported by objetive matters of fat. We onlude that this light speed anisotropy, manifested in the physial world as light travelling faster West than ast, renders the priniple of light speed onstany inappliable on the rotating arth. Suh anisotropy leads to a definitive re-interpretation of the CCIR lok synhronization algorithm: The Sagna effet should no longer be viewed as a neessary time orretion in GPS operation arising from the rotation of the arth sine no suh orretion is neessary if the true speed of light is used in the travel time determination. Instead the Sagna effet should be reognised as simply the time differene between separate light pulses arising from their different speeds as they travel in the rotating frame of the surfae of the arth.

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