Clocks,+Aberration+and+Ether+Drag鐘,畸變和拖曳以太

1、Clocks, Aberration and Ether Drag 鐘，畸變和拖曳以太Against Ether DragRon HatchNavCom Technology, Inc 20780 Madrona AvenueTorrance, CA 90744Recent claims that ether drag is compatible with stellar aberrationare falsified using independentexperimental data regarding clock behavior There is substantialevidence

2、 that clock velocity andclock position in a gravitational potential affect the clockreadings by causing biases in clocks thatare separated in a moving frame These clock biases cause theapparent speed of light in the frameto be isotropic and equal to c even though the true speed of lightis not affect

3、ed by the motion andis anisotropic relative to the moving frame These clock biases areverified by comparison withmillisecond pulsars Thus alternative explanations for the isotropyof the speed of light, such asSpecial Relativity Theory or ether drag, are thereby falsified.assumption.) Now let s put t

4、he two clocks on the earth, IntroductionEther drag has often been proposed as an explanation which we assume to bemoving with a velocity, V, in afor the results of the Miche1son-Morley and the Kennedy-straight line withrespect to the sun. Further assume Thorndyke experiments This position has beenhe

5、ld by a temporarily that the earth is not rotating and that there is number ofprominent modern physicists, e. g Petr no gravitational potential effect uponthe two clocks Now Beckmann Ll, the founder of Galilean Electrodynamics, weslowly, at velocity, v, move one of the clocks to theeven though it ha

6、d been ruled out by eighteenth and front of the moving earth,i e. farthest in the direction of nineteenth century physicists as beingincompatible with the velocity vector; and we move the second clock, at stellaraberration. In my book, Escape from Einstein, I also velocity, v, to the rear ofthe movi

7、ng earth Once the espoused the same view. However, the late CharlesM clocks have been moved to these two locations we know Hill challenged myposition on the basis of stellar that they are syntonized, i e. running at thesame rate, aberration and would not let me off the hook without a because theyare

8、 located in the same inertial frame, which detailed explanation. I could notgenerate a satisfactory is moving at a constant speed relative to the sun. Nowexplanation and had to revert to a fixed absolute assuming the speed of light isisotropic and given by c in Lorentzian ether to satisfy both the M

9、ichelson-Morleyand the sun s frame, what would be the measured speed of stellar aberrationphenomena light in each direction, if we could send a beam throughHowever, recently I have come across a number of the earth between the twoclocks?papers (and people) who believe that stellar aberration is From

10、 our assumptionswe know that the true speed of compatible with ether drag Typical of these isthe paper, light between the two clocks would be (c- V) and (c+V). StellarAberration and the Unjustified Denial of Ether,nHowever, we also know thatmovement at any velocity 2 in which Carel van der Togt argu

11、es that ether dragand with respect to our absolute ether causes clocks to tick at a stellar aberrationare compatible It is my intent in this slower rate, in this case given by:paper to show that all such arguments are patently false on22, fW, vvthe basis of clock behavior on and near the earth (1) 2

12、22Ironically,comparison of clock behavior with millisecond f2cc2c pulsars, as described by thesame Charles Hill 3, The first of the three terms on the right side of thisconstitutes a significant verification that ether drag does equation isindependent of the slow movement and affects not exist the f

13、requency and clocktime identically in each direction. Clocks and the one-way speed of light It canbe calibrated out or absorbed as part of the definition Let s assume we have acouple of identically of the frequency of the clock The last of the three termsconstructed atomic clocks which keep perfect

14、time Put can be made negligibleby moving the clock slow enough these two clocks adjacent to one another,synchronize The effect of the middle term on the clock reading over the them toread the same time, and syntonize them to run at time it takes to move the twoclocks apart is given by: the same rate

15、 Let us also assume, for the moment,that thesun is at rest in an absolute ether (This is not a criticalthird term of equation (2) into our calibration of the clockVdxVx, t, dt, (2) frequencysince we can no longer make it arbitrarily 22,cdtcsmal1 Thus we see that a stationary clock on the spinning wh

16、ere the velocity,v, is replaced by its definition as dx/dt earth will generate a cyclic clockbias that willThus, the temporary movement separating the two automatically keep theapparent velocity of light isotropic clocks will cause a clock bias to be generatedbetween the in the earths frame A third,

17、 arbitrarily small, velocity vtwo clocks The clock moved to the front of the earth will can then be addedto the spin velocity to account for the temporarily run slower caused by thecomposite velocity additional separation of clocks obtained by moving them whilethe clock moved to the back will tempor

18、arily run apart on the spinning earth faster The time difference between the two clocks is given The oneway speedof light on an orbiting earth by equation (2) where x is the final separationdistance Two additional constraints need to be removed.In the The time difference between the two clocks is ex

19、actly abovedevelopment it was assumed that there was no effect the amount which causes theapparent speed of light to be of theof the sun, and the earth was measured asif speed of light is (c-V) and (c+V) in the twodirections.constraints are removed? For illustrative purposes, a illustrate this, thea

20、pparent time of flight in the upwind circular orbit is assumed (An eccentricorbit complicates direction is obtained by dividing the distance, x, (as theanalysis but is reasonably easy to deal with 4.) measured in the moving system)by the true speed of light Clearly, clocks on the earth and in the Gl

21、obal (c-V),Positioning System (GPS) do not appear to be affected bythe sun s gravitational potentia1 Yet we know that clocksVx(l, )are affected by the earth* s gravitational potentia1. Clocks xxWxc (3) ,(1, ), , utrun faster when they are moved to a position farther away 22, V(c,V)cccfrom the center

22、 of the earth The effect of the earth s c(1,)2cgravitationalpotential is verified by two phenomena associated with the GPS system. First,identical atomic where the subscript u is used to designate the upwind clockslocated at sea level anywhere on the surface of the elapsed time and the subscriptt is

23、 used to designate the earth run at the same rate The clocks run slowerthe lower average of the two-way elapsed time their latitude because of theincreased spin velocity at Because of length contraction and time slowing in thelower latitudes However, that same spin causes an moving earthfs frame, th

24、etrue two-way speed of light 22equatorial bulge from centrifugal force, and thehigher relative to the frame, c(1-V/c) or c is measured as if it gravitationalpotential at the lower latitudes exactly has the same unchanged value of c in thesun s frame.counteracts the spin-induced clock slowing Also, t

25、he GPS Now it is apparentgravitational potentialin each direction, eventhough the true assumed to travel in a straightline path. What happensTo thesethat the clock bias (caused by moving satellite clocks are affected by the earth*s gravitational the two clocks apart) given in equation (2) will cance

26、l outpotentia1. Since the orbits have a small eccentricity, they the extra travel timein the upwind direction, so that the move up and down in the earth * s gravitationalpotentia1. upwind elapsed time is measured as the average of the When the GPSsatellites are near perigee, they move faster two-way

27、 elapsed time Thedownwind result is obtained and are at a lower potentia1 The higher velocityand the easily as the parallel to this result lower potential cause the clocksto slow equally, causing This is a very important result What has been shownthe total effect to be twice the individual effects A

28、t apogee is that, in anabsolute ether system, where clocks are the clocks run faster due to both lowervelocity and higher slowed by their movement with respect to that ether andgravitational potential, lengths are contracted by movement, the natural resultof So why doesn t the sun s gravitational po

29、tential also separating clocks inthat moving frame is to induce a clock cause the clocks to run at different rateswhen on and near bias that will cause the measured speed of light to appear theearth? Banesh Hoffmann 5 has proposed an unchanged In other words, the speedof light will appear explanatio

30、n. It is an interesting proposa1 He says that,to be isotropic and equal to c with respect to the moving since the velocityaround the sun is slower at noon than the frame velocity around the sun at midnight,the difference in the The one-way speed of light on a spinning earth velocity willexactly canc

31、el out the difference in the sun s In our example above we assumedthe earth itself was gravitational potential at noon and at midnight He is notspinning What modifications do we need to make if actually correctif we causethe inertial frame of the earth the earth is allowed to spin? If we let the val

32、ue,v, in the to rotate once per year Now clearly the earth* s inertial abovedevelopment to be equal to the spin velocity of the frame does not rotate onceper year Neither do the orbital earth, the only change we have to make is toabsorb the planes of the GPS satellite rotate once per year一yet there

33、is noapparent effect of the sun s gravitational potential gradient of thegravitational potential, which is the upon the GPS satellite clocks gravitational force But it is that same gravitational forceHowever, let us presume for the moment that which causes the direction of motionof the earth to chan

34、ge Hoffmann is correct Assume that the inertial frameof the Thus, per equation (8) the gravitational potential of the earth does rotateonce per orbit This would lead to a sun causes a one-year cyclic variation inclocks on the cancellation of the sun s gravitational potential effect upon earthThis cy

35、clic variation subtracts from the cyclic the clocks The low velocityapproximation of the effect sidereal variation and causes a solar-day cyclicvariation in on the clock is given by: the clocks The result is that the xdirection of the clockbias in equation (2) is kept in the direction of the orbital

36、 222Vr, velocityof the earth, and the apparent speed of light fff (4) , 22remains isotropiceven as the velocity of the earth changes 2c2cdirection. where , is the rotation rate of the earth around the sun and Thesame gradient of the gravitational potential which also the rotation rate of theearth s

37、inertial frame Taking causes the clock biases to change direction isthe source of the radial gradient of this gives the relative effect on clocks theforce which causes massive bodies to change direction. as a function of theirradial distance from the sun. Therefore, it should be obvious that the eff

38、ect ofthe moon2on the earth s orbit and the effect of the galactic potential , d(f)r, (5) ,fon the motion of the sun likewise have no apparent effect 2drcupon the apparentspeed of light But for a circular orbit the orbital rotation rate can be Special RelativityTheory and the speed of light expresse

39、d as a function of the gravitationalpotentia1 This The Special Relativity Theory (SRT) has a problem gives: withthe derivation above According to SRT the speed oflight in any inertial frame automatically adjusts to be d(, f)GM(6) , fisotropic and equal to c. Thus, for SRT to be valid the 22drrcclock

40、-slowingmechanisms described above must beeliminated in order to retain the SRT magical adjustment Now a similarprocedure is used to find the effect ofEliminating the effect of the spin seems to be relatively the sun sgravitational potential upon clocks in the earth * seasy By describing the earth a

41、s resident in its own inertial vicinity The gravitational potential effect is approximatedframe, the cross-product of the orbital velocity and the spin by: velocityin equation (1) is eliminated However, there is no GMvalid way to eliminatethe effect of the sun s gravitational , f, f (7) 2potential f

42、rom affecting clockson and near the earth As a reresult the SRT is falsified Taking the radial gradient gives： Two attemptshave been made to save SRT from thiscontradiction. The one by Hoffmann has already been d(, f)GM(8) , fconsidered It is clearly invalidated because the earthfs 22drrcinertialfra

43、me clearly does not rotateelse the spin axis of which shows that indeedrotating the earthTs inertial frame the earth would rotate once per year Thefact that the would cancel out the effect of the sun1s gravitational orbital planesof the GPS satellites do not rotate is further potential, since equati

44、ons (6) and(8) are identical except proof that Hoffmann* s solution is invalid for the sign. The second attempt to save SRT from theHowever, a problem would remain. In the straight-consequences is to claim thatthe free fall of the earth in line non-orbiting model the earth * s spin causeda cyclic th

45、e gravitational field of the sun cancels out the effect of clock biasthat had a period of one sidereal day. If the the sun s gravitational potentialvia the equivalence gravitational potential of the sun is canceled, the cyclicprinciple 6 This attempt also fails, as detailed in three of clock period

46、wouldremain at one sidereal day and the my earlier papers 7-9, because the equivalenceprinciple direction of the clock bias would remain invariant in space onlyapplies at infinitesimal distances But, to keep the apparent speed of light at c on the earth, Ether drag andthe speed of light on the earth

47、 the bias needs to change direction as the orbitof the earth Like SRT the theory that the ether is dragged along by changesdirection. This is achieved by not rotating the the motion of the earth would causethe speed of light to inertial frame of the earth and allowing the gravitationalremain isotrop

48、ic and equal to c in the vicinity of the earth potential of thesun to affect the clocks In fact, as But, also like SRT, for this to be thecase, the clock biasing equation (8) shows, the clock bias is affected by themechanism must be falsified It is not sufficient to comeup with some strange mechanis

49、m to explain how stellar aberration is compatiblewith ether drag One must also come up with a mechanism that explains how clockbiases due to velocity and gravitational potentials can be eliminated一becausethose biases make the speed of light appear to be isotropic without ether dragVerification of cyclic clock biasesIt turns out that an extremely accurate independent clock rate can be obtainedfrom the radiation of millisecond pulsars Hill 3 reports on comparisons ofthe millisecond pulsar rates with atomic clocks on the surface of the earth According to him