PRECISION MEASUREMENT OF THE ONE-WAY SPEED OF LIGHT AND IMPLICATIONS TO THE THEORY OF MOTION AND RELATIVITY

Transcription

1 PRECISION MEASUREMENT OF THE ONE-WAY SPEED OF LIGHT AND IMPLICATIONS TO THE THEORY OF MOTION AND RELATIVITY C. S. Unnikrishnan Gravitatin Grup/FI-Lab Tata Institute f Fundamental Research, Mumbai unni@tifr.res.in, Intrductin The speed f light, withut dubt, is the mst discussed and the mst imprtant aspect in theries f mtin and relativity. Its large value, relative t speeds familiar r practically imaginable in daily life, implies that sme f the relativistic effects are t small and subtle t be nticed except in specialized experiments, whereas certain ther effects, like the energy released in cnversin f matter t energy, are larger than ne culd pssibly imagine frm experience. Its fundamental essential rle in the thery f relativity, and the special relativistic assertin that the speed f light is a universal cnstant independent f the speed f the surce r f the bserver are familiar and well knwn. Peple ften say that if there is ne thing that is abslute in the thery f relativity, it is the speed f light. It is this assumptin that allws special relativity t assert that an bserver in inertial mtin in empty space is cmpletely equivalent t an bserver at rest. In this backdrp, it will be surprising, and perhaps shcking t sme, t nte that the cnstancy f the speed f light relative t a mving bserver is nt an experimentally established fact 1. What is experimentally well established is the fact that the tw-way speed f light that is measured in a reference frame is independent f the speed f the frame, and that the results are identical t a measurement perfrmed in a frame at rest. T understand the fundamental difference between this measurement and the ne in which the ne-way speed f light is t be measured, we need t first discuss certain aspects f the prpagatin f waves in a medium and f the measurement f the velcity f prpagatin. We will als discuss a nvel technique fr the measurement and cmparisn f the ne-way speed f light. This will be fllwed by a brief review f the relevant experiments, which will establish that the ne-way speed has never been measured directly befre. Then we will present the result frm a recent experiment that shws that the speed f light relative t an bserver depends n the velcity f the bserver in exactly the same way the speed f ther familiar waves. These results will clearly establish the lgical and peratinal circularity that was present in the special thery f relativity regarding the speed f light relative t mving bservers. Als, the experimental results supprt strngly the predictin f first rder anistrpy f the ne-way speed f light in the thery f csmic relativity 2 based n the gravitatinal influence f the matter filled universe n entities mving thrugh the preferred frame f the istrpic universe 3. Cnceptual and mathematical aspects Cnsider an experiment t measure the speed f a wave-train. One needs t fix a standard distance (fr the time being we will assume that this is knwn, thugh fr the measurement f the speed f light this aspect has t be defined crrectly, as we will d later). Figure 1 indicates the scheme. Figure 1: Tw clcks are required in a cnventinal ne-way speed measurement. Clearly, the measurement f ne-way speed requires tw clcks that are pre-synchrnized. Again, fr familiar measurements (speed f water waves fr example) the synchrnizatin is nt a prblem. The ne-way speed will be given by the expressin

2 v = L/( t2 t1) (1) The measurement can als be dne using just ne clck if the wave-train is reflected back at the end f the track such that it reaches back t the starting pint. This avids the need t synchrnize tw clcks; nly ne stable clck is required, since a clck is synchrnus with itself. Then the tw-way speed is given by v = 2 L/( t1' t1) (2) tw The difference between the tw measurements becme apparent when we cnsider the situatin where the entire measurement scheme f the frame f reference including the clcks, start and finish pints etc. mve relative t the medium in which the wave-train is mving. See figure 2. Figure 2: Diagram t explain the imprtant cnceptual and physical difference between the measurements f the ne-way speed and the tw-way speed. The upper panel explains the situatin when the reference frame is mving t the right as the wave-train is prpagating at its natural speed c relative t the medium. Since the reference pint B mves away, the waves have t catch up a further distance befre they reach B where the clck is, and it takes mre time t cver the distance L as judged by the bserver in the mving frame. During the time t taken by the wave-train t reach frm pint A t B, the pint B wuld mve ut by the distance vt. Therefre the effective ne-way speed v t = L + vt ' L v = v v t v is smaller. We see that the speed f the waves in the medium is independent f the speed f the surce, but it is dependent n the speed f the bserver. This is the general situatin regarding all knwn waves in situatins where the wave-speed is determined by the prperties f a preferred frame r medium. Nw cnsider the lwer panel f figure 2. Here the wave is reflected back at B and it mves twards A, retracing its earlier trajectry. In this tw-way prpagatin, the pint A mves t the right by a distance vt and catches up with the waves during the time T the waves takes t cmplete the tw-way prpagatin. The ttal time taken fr the tw-way trip is L L 2L T = + = v v v + v v (1 v / v ) 2 Therefre, the effective tw-way speed f the waves relative t the mving bserver is 2L v ( 1 2 / 2 tw = v v v ) (5) T It is this mdified velcity dependent tw-way speed that Michelsn and Mrley sught t cmpare with the tw-way speed in a directin perpendicular t the mtin f the reference frame. What is imprtant t nte is that the tw-way speed has n first rder dependence n the velcity f the bserver s frame whereas the ne-way speed des have such dependence. If ne wants t avid using any clck at all in such measurements, then a cmparisn f speeds in tw different directins may be dne, and this is what Michelsn and Mrley attempted. Fr example the effective tw-way speed in a perpendicular directin is ' (3) (4)

3 v = v 1 v / v (6) tw and interestingly the ne-way speed in this directin is identical. Therefre, when ne cmpares the tw speeds by frming an interfermeter, the experiment is sensitive t nly the rati f the tw velcities and that is given by vtw 1 v / v v = (7) tw Therefre, the Lrentz-Fitzgerald hypthesis that the arm f the interfermeter that is parallel t 1 v / v the velcity f the frame cntracts by the factr explains the null result in the M-M experiment. Since these details are well knwn, we will fcus n the fact that such a cancellatin des nt happen if ne is dealing with the ne-way speed f light. Then the rati is v v (1 v/ v ) = 1 v/ v v v v v tw tw 1 / (8) There is a first rder crrectin. But such a measurement is nt pssible, as we will see later. What is hwever pssible is a cmparisn f the ne-way speeds in exactly ppsite directins, ne parallel t the velcity f the bserver and anther anti-parallel. Then als the rati and the difference f the tw ne-way speeds depend n the velcity f the bserver t first rder in v v. In fact, if we culd measure the ne-way speed f light in the parallel and antiparallel / directin ver a length L, the difference in time taken by the tw wave-trains is expected (frm ur analysis s far) t be L L 2Lv δ T = = 2 c v c+ v c (1 v / c ) withut cnsidering secnd rder effects like length cntractin. (We have nw written the speed f the waves with symbl c, t cnfrm t standard usage.) Even if thse effects are cnsidered, the first rder term des nt change. Nte the crucial difference between a ne-way cmparisn and a tw-way cmparisn. It is clear frm this discussin that the dependence f the speed f light n the velcity f the bserver, if any, cannt be studied using measurements that use a tw-way prpagatin technique when there are physical effects like length cntractin. Such studies require a new technique that will allw cmparing ne-way speeds directly. Befre we discuss the basic idea, let us briefly state hw the special thery f relativity (SR) deals with the empirical results f tw-way speed cmparisns. In SR, there is n length cntractin in the rest frame because mdificatins f time and length in SR depend nly n relative speeds. The fundamental hypthesis is SR is that the speed f light is a universal cnstant in all inertial frames, even thugh the experimental evidence is restricted t tw-way speed cmparisns. Therefre, the time taken t prpagate a length L is always is L/ c irrespective f whether the standard reference length is mving r nt. Indeed, inertial mtin is cmpletely equivalent t a state f rest in SR. This implies that if it is pssible t cmpare the ne-way speeds in tw ppsite directins relative t a reference frame mving inertially at velcity v, the difference in time the tw light pulses r wave-trains take t prpagate a length L is expected t be null in SR. The expressin in equatin 9 is zer is special relativity. Sme earlier experiments There have been n experiments that directly measured the ne-way speed f light relative t a mving reference frame. Hwever, sme experiments have been interpreted by the experimenters as an effective measurement f the speed f the ne-way prpagatin, r as a cmparisn f the ne-ways speed in tw ppsite directins. Sme f these measurements actually cmpare anistrpy f Dppler shifts f light emitted by mving surces and then try t interpret it as equivalent t a measurement f the anistrpy f the ne-way speed f light. But mst experimenters d nt seem t realize that the ld ether thery that has first rder anistrpy in the speed f light relative t mving bservers predict the same null results in such experiments, and therefre these are nt experiments that can demarcate between Einstein and (9)

4 Lrentz, r mre generally, between special relativity and a thery f relativity with a preferred frame. We will briefly mentin just ne f these mdern experiments t clarify that such experiments d nt measure r cmpare the ne-way speed f light. Cnsider the experiment by Krisher et al that cmpared Hydrgen maser clcks separated by 21 km, statinary in earth s frame, using a stable fiber ptical link 4. Each clck generates a stable utput signal at 100 MHz lcal frequency that is used t mdulate a laser signal that passes frm ne clck t the ther thrugh the fiber ptic link. If light takes additinal path length alng ne directin cmpared t the ther, due t the first rder anistrpy, there will be fixed ffset between the tw clcks, which f curse cannt be measured since there is n abslute synchrnizatin. But if the anistrpy is time dependent, due t the rtatin f the earth, then ne can hpe t see a time dependent phase difference between the tw clcks, in the tw channel netwrk analyzers at each site, ne channel fed by the lcal clck and the ther by the signal frm the distant clck. But, a diple anistrpy signal was nt seen even at the level f 1 part in The quadruple anistrpy was even smaller. What is frgtten in the analysis f such experiments is that the clck time dilatin itself cntains exactly the same term in the preferred frame theries, since the clck delays nw depend n the abslute speed thrugh the preferred frame, rather than n their relative speed 5. Therefre, the clcks have different time dilatins even when they are at relative rest. The time dependent phase change f the clck cmpensates exactly the time dependent delay in the prpagatin f the light, and the tw cancel, and a null signal results. Therefre, these experiments d nt test the anistrpy f the ne-way speed f light, being affected by the first rder time dilatin f the surce f the reference signal itself. Measuring the ne-way speed f light It is pssible t measure the ne-way speed f light and ther waves, and particles with just ne clck, withut the need t synchrnize tw distant clcks. The idea is extremely simple, and perhaps this is why it has been cmpletely missed in the usual discussins. T see the pint, cnsider the experiment discussed in the cntext f figure 1, but mdified slightly as in figure 3. Figure 3: Measurement f the ne-way speed alng a curved track. The cmparisn track is bent in a shrt sectin, but ne is still measuring the ne-way speed alng the path frm A t B. Nte that the speed f the waves are nt changing, and we have kept the ttal length t be traversed as L as in the previus experiments. In this experiment the results will be identical t the ne btained with the linear track. In fact, we are very familiar with this situatin since this is hw ne-way sprint races are cmpared in situatins where the track needs t be larger than abut 100 meters. Nw cnsider the same situatin where the start pint A is mved t the right at speed v and the end pint B is mved t the left with speed v synchrnusly. This can be achieved fr measuring ne-way speed f water waves, fr example by cnnecting a string f fixed length between the tw pints and by pulling the tw reference pints tgether. This situatin is exactly the same as the ne in figure 2 as far as the measurement f the ne-way speed is cnsidered. All the reference markers in the bserver s frame are mved in the same directin alng the track at speed v such that by the time the wave reaches pint B, it has mved by a distance vt, exactly the same way we had in figure 2. Again, the mathematical results are exactly the same as in the situatin in figure 2. In particular, if we reflect the waves at B and perfrm a tw-way speed

5 measurement, the first rder dependence n the velcity f the bserver will cancel ut and nly secnd rder differences will remain. Hwever, it is nt pssible t d the experiment fr the case f light in this cnfiguratin fr the simple reasn that synchrnus mvement f the tw reference marks require synchrnizing signals t be sent between the tw pints. Behaviur if such signals in different theries are different and the analysis can becme circular in lgic. Hwever, a simple mdificatin eliminates this prblem 6. The mdified cnfiguratin in figure 4 uses nly ne clck. The surce, the detectr, the clck etc. are all in the same frame, at the same reference pint and yet, the experiment measures the ne-way speed f the wave-train! This is achieved by bringing the pint B s clse t A, after winding nce arund the track, that they seem identical. It is imprtant t nte, hwever, that the physical distance frm A t B is still L. Figure 4: Measurement f the ne-way speed using a single clck, relative t an inertially mving reference frame. See text fr details. In the left panel we have a measurement f the ne-way speed f the wave-train, relative t an inertially mving reference frame A that carries just ne clck. The panel n the right deals with the cmparisn f the ne-way speeds f wave-trains in tw ppsite directins relative t a reference frame that is inertially mving in ne directin with respect t sme preferred frame. Nte that the bserver A is always in inertial mtin during the experiment, since we assume that the speed f the waves is much larger than the bserver s velcity; the waves trains reach back after ne rund trip in a time shrt cmpared t the time it takes fr the bserver t mve a significant distance alng the track. The secnd measurement f the cmparisn f arrival times can be dne interfermetrically, and then the clck is nt required. One will mnitr the shift in the interference fringes as the velcity f the bserving frame with respect t the preferred frame is changed. The predictin f special relativity in these situatins is clear. Since the inertially mving bserver is equivalent t an bserver at rest, and since the speed f light is identical in bth directins relative t the mving frame as well, the tw wave-trains have t reach back simultaneusly, as calculated in the rest frame f A. The distances frm A t A alng bth directins are identical by cnstructin, and if the speeds f the waves are als identical then the predictin f simultaneus arrival with respect t A is unambiguus (with respect t an external frame relative t which A is mving, the wave-trains will nt reach simultaneusly accrding t the theries f relativity we are cmparing here). The experiment Ideally, the experiment has t be dne with hllw ptical fiber guides, all rigidly attached t a cnveyr belt platfrm such that the platfrm n which the surce and the detectr fr light are lcated mves linearly at unifrm speed alng ne directin. The experiments that I have perfrmed were either with nrmal ptical fibers r in free space with reflecting mirrrs. (It is easy t argue that all these cnfiguratins give the same result, thugh intuitively, and naively, ne might want t argue that hllw ptical fibers shuld be used, and this demand can be satisfied withut much technical prblems.) The cnfiguratin is shwn in figure 5.

6 Figure 5: Schematic diagram f the experimental set up. The shaded rectangular regin represents the mving platfrm n which the surce, beam splitters and the detectr are rigidly fixed. The fur mirrrs serve t fld the ptical path. The reference platfrm carried the surce and the pht-detectr. The mving platfrm is n a standard linear ptical bench, with the mvement made smther by a layer f grease. A rller bearing ptical stage with its springs remved and an air bearing stage have been tried as well. In the velcity range in which mst measurements have been dne (less than 1 m/s), the greased ptical bench was sufficient. The sensitivity is sufficient t detect a shift that is less than 1/10 4 f the width f the fringe, but the mvement causes sme vibratins and this limits the sensitivity t abut 1/3000. This can be imprved by a factr f 10 using essentially the same cnfiguratin by imprving the stability f the fringes (the signal t nise at the detectr is high enugh t detect 1/10 6 f a fringe, in principle). The ttal ptical path is between 1.3 m and 2 m in the several runs cnducted. Ignring secnd rder effects, the expected shift in a preferred frame thery, in which the speed f light des depend n the velcity f the bserver, can be calculated using the equatin 9 fr the arrival time difference. The ptical path length difference with respect t the platfrm is δl = cδt = 2Lv 2Lv c(1 v / c ) c (10) Then the shift in the fringe per meter f the ptical path (L=1 m), fr a wavelength f 633 nm is δ l 2Lv δ s = 0.01 v( m/ s) λ = cλ (11) We get a shift f abut 1/1000 f a fringe when the speed is abut 0.1 m/s. This is measurable and mst f the data is taken with speeds in the range f 0.05 t 0.4 m/s. The fllwing graph (figure 6) summarizes the results frm ne such experiment, in which the arrival time difference f the wavefrnts, δ T, in the tw directins is pltted as a functin f the linear velcity f the reference platfrm. Clearly, the linear dependence n the velcity f the reference platfrm is unambiguusly established. The line indicates the expectatin in csmic relativity in which the speed f light depends n the velcity f the reference platfrm. The same result is expected in the ld ether thery as well, and the trend prves that the speed f light behaves in exactly the same way as the speed f ther familiar waves behaves in relatin t an inertially mving bserver. Therefre, the special relativistic assertin f the universality and istrpy f the speed f light applies nly t the tw-way speed f light and nt t the physical speed f light in ne directin. This implies that the results f thse experiments in which ne-way speed becmes relevant, as in clck cmparisns, the predictins f special relativity will nt hld gd, and this has already been pinted ut and discussed in detail, with further empirical evidence 7.

7 Figure 6: Arrival time differences between the wavefrnts f light traveling in ppsite directins relative t the inertial mtin f the reference platfrm as a functin f its velcity in the experiment depicted in figure 5. The time difference is derived frm the shift f the interference fringes. The experimental results are identical when an ptical fiber is used, even thugh naively ne might have expected that the ptical phase difference wuld have been larger fr a given velcity f the reference platfrm because light takes mre time t cmplete the rund trip. In the ether thery, there is a Fresnel drag that carried light in the fiber which cmpensates the time delay in the rund trip. In Csmic Relativity, the ne-way speed f light in a mving frame is mdified due t the gravitatinal vectr ptential A g (r the ff-diagnal metric cmpnents) generated by the matter current f the csms as seen in the mving frame, and therefre the mdificatin f the rund trip phase is simply prprtinal t the integral. This is the A g path csmic gravitatinal Aharanv-Bhm phase induced due t mtin relative t the matter in the universe. This des nt depend n the speed with which light cmpletes the rund trip, and als explains beautifully why the difference in the rund trip time in the tw ppsite directins in ptical as well as matter wave Sagnac interfermeters is identical, and independent f the speed f the entity (phtn, atm, electrn etc.) circulating in the interfermeter. Cnclusins The experiment described in this paper, and its many pssible variatins, establish that the speed f light is nt a universal istrpic cnstant relative t inertially mving bservers. This finding invalidates the fundamental assumptin f the special thery f relativity, and supprts a thery f relativity with a preferred frame relative t which all velcities are t be referred fr discussing velcity dependent physical effects like the time dilatin. It is argued elsewhere that the preferred frame is the massive istrpic frame f the matter filled universe, and nt the frame f the statinary ether 8. All relativistic kinematical effects are in fact gravitatinal effects f the matter in the universe. Therefre, the apparent success f the special thery f relativity is cnfined t situatins invlving tw-way cmparisns, r in thse situatins similar Lrentz factrs n time and length cancel each ther. There are several experimental situatins where this des nt happen, as in the measurements described here and in rund trip clck cmparisn experiments described elsewhere 9, and then the results unambiguusly suggest replacing special relativity with a thery f relativity in which the istrpic frame f the universe is the preferred frame. This new thery called csmic relativity is described in detail in references 2 and 3. While it may be expected that such a paradigm change will take cnsiderable time because it is difficult t change majrity beliefs that are entrenched deep, the shift frm special relativity t csmic relativity is inevitable because unambiguus and new empirical evidence, apart frm the requirement f cnsistency with the existence f a matter filled universe with its all pervading gravity, dictate such a change. dx

8 1 C. S. Unnikrishnan, Denying experience in the physical wrld: Cnsciusness misled, t appear in the prceeding f the cnference n Cnsciusness, Experience and Ways f Knwing: Perspectives frm Science, Philsphy and the Arts (Ed. Sangeetha Menn, 2006). 2 C. S. Unnikrishnan, Csmic Relativity: The fundamental thery f relativity, its implicatins and experimental tests, E-preprint, available at gr-qc/ (2004). 3 C. S. Unnikrishnan, Csmic Relativity: The nly cnsistent ntlgical fundatin fr the thery f space-time and relativity, t appear in Fundatins f Science, Editr, B. V. Sreekantan (PHISPC, New Delhi, 2006). 4 T. P. Krisher et al, Test f the istrpy f the ne-way speed f light using hydrgen maser frequency standards, Phys. Rev. D 42, (Rapid. Cmm.) References 2 and 3. 6 I cnceived this technique fr measuring the ne-way speed f light arund the year Initially it was used as linear Sagnac phase detectr in which the reference frame is inertial, in cntrast t the cnventinal Sagnac interfermeter. Sn it was realized that measurement f the phase difference is essentially the same as the measurement f time, nce the frequency f the emitter is fixed. Then the measurement is als equivalent t a rund trip clck cmparisn. Since the phase difference is equivalent t the difference in path length between the tw prpagatin directins, the same experimental set up cmpares the ne-ways speeds f light in tw ppsite directins relative t the inertial mtin f the reference platfrm. 7 References 2 and 3. 8 References 2 and 3. 9 C. S. Unnikrishnan, Discvery f a new csmic gravitatinal effect revealed as the faster aging f a transprted atmic clck, t be published. See als reference 2.