Notion of Absolute Clock Synchronization in SR
in [Relativity]
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From: Sue... on 30 Mar 2010 13:42 On Mar 30, 12:44 pm, va...(a)icmf.inf.cu wrote: [...] > In the HIS view, I identify what 1905 Einstein name moving system > with a lower hierarchy HIS considered a single body belonging to the > higher hierarchy stationary system HIS. It is nothing better than a > well-known real world example to clear ideas. In the Solar System (SS) > HIS, The Earth-Moon (EM) one is considered a single body belonging to > the SS body set (modelled by a material point that is running the > ecliptic). At the same time, the ECI HIS and the Moon one (maybe with > it own GPS in the future) are moving around the EM centre of mass. > As you see, the NOT uniform Earth movements in higher hierarchy HIS > dont contradict at all the inertial character of the ECI with a > centre of mass considered at rest, supported by a huge experimental > evidence. Can you understand now why I beg you to put special > attention to the following point: the REAL inertial systems that I am > talking about are NOT the IMAGINARY ones of the 1907 Minkovski view?. That sort of hierarchy follows naturally when systems are coupled by mutual induction. http://en.wikipedia.org/wiki/Induced_gravity Sue... > > RVHG (Rafael Valls Hidalgo-Gato)
From: GSS on 31 Mar 2010 12:46 On Mar 30, 1:57 am, "Paul B. Andersen" <some...(a)somewhere.no> wrote: > On 29.03.2010 11:17, GSS wrote: > >> On Mar 25, 10:42 pm, Tom Roberts<tjroberts...(a)sbcglobal.net> wrote: >>> GSS wrote: >>> ... >>>> At any instant, when TAI time is t1, if each one of the two 'ideal' >>>> clocks A and B show the same time t1, shouldn't we call them >>>> 'mutually' synchronized, irrespective of the reference frame in which >>>> we may consider them to be located at that instant? > >>> Clock synchronization is INHERENTLY frame dependent. That is, a given pair of >>> clocks can be synchronized in one AND ONLY one inertial frame; they are not >>> synchronized in any other inertial frame. > >> Agreed that a given pair of precision atomic clocks A and B (separated >> by constant distance S) can be synchronized in ONE AND ONLY ONE >> inertial reference frame. But is there any restriction on the choice >> of THAT inertial reference frame? Specifically, can we practically >> (not through gedankens) synchronize two clocks A and B in an inertial >> reference frame in which they are known to be in uniform MOTION (and >> not at rest)? > Kindly make it clear whether we can practically (not through gedankens) synchronize two clocks A and B in an inertial reference frame in which they are known to be in uniform MOTION (and not at rest)? This is important because as per SR, (for a stationary observer) time in a moving reference frame is 'supposed' to be position and velocity dependent (and hence different at two points A and B spatially separated in the direction of motion). >> Let us consider four identical precision atomic clocks A,B, and C,D, >> located on earth geoid such that A and C are positioned side by side >> while B and D are also positioned side by side as shown below. > >> A..............................................B >> <-----------------S----------------------------> >> C..............................................D > >> Let us set their 'initial times' or their timing offsets by using the >> GPS service such that when the GPS time is t1 (UTC), all of the four >> clocks A, B, C and D read t1 (within the limits of timing resolution >> as available with current cutting-edge technology). Now, using the >> term 'synchronized' as approved in 'SR' standards, can you say that >> the clock pairs (A,B), (C,D), (A,C), and (B,D) are mutually >> *synchronized* in ECI frame, even though these clocks are not at rest >> in ECI and are moving with non-uniform velocity in the ECI frame? > > Yes. Clocks showing UTC (or GPS-time which is the same but for > a known offset) are synchronized in the non rotating ECI-frame. > That means that they are all simultaneously showing the same time > _in the non rotating ECI-frame_. > > Be however aware that the ECI-frame - Earth Centred Inertial frame > is a misnomer in this context. It is no inertial frame because > space-time is curved, and the curvature is essential. So you cannot > use Einstein's synchronization method to define simultaneity > (except for between clocks on the same gravitational potential). > You could say that simultaneity is defined by the Schwarzschild > time coordinate. Since clocks on the geoid, using the SI definition > of a second, are running slow compared to Schwarzschild time > by a factor of (1.0 - 6.9692842E-10), UTC and GPS-time is defined > such that simultaneity is defined (at least in effect) by > the Schwarzschild time coordinate, but all clocks should run > slow by the factor above relative to Schwarzschild time. > Whether all the four clocks under consideration are slow or fast relative to Schwarzschild time, is not relevant here. Kindly confirm whether the clock pairs (A,B), (C,D), (A,C), and (B,D), showing the same UTC, are also mutually *synchronized* in their local or lab frame? If not, why not? >> Let us now consider 'the' pair of clocks C and D as 'in motion' in >> BCRF. Without using any gedanken, kindly explain how will you mutually >> synchronize the clocks C and D in BCRF in practical terms? > > The same way as clocks on the geoid are synced to the UTC/GPS, > that is by compensating for what is called the 'Sagnac effect.' > Basically this is to use the difference between the speed of light > in the 'reference frame' and the speed of the clocks in same. > That is the same as considering the speed of light to be > c +/- v in the 'ground frame', where v is the speed of the clocks > in the 'reference frame'. > The speed of the Earth in the BCRF is ~ 3E4m/s. You would of course > have to consider Earth's rotation, the relative position of > the clocks compared to their velocity in the BCRF etc. > > But it could be done. > Due to the rotation of the Earth the clocks wouldn't stay in > sync in the BCFR for long, though. > How long? Can they stay in mutual synchronization in BCRF at least for one day? >> Will you >> physically alter the timing offsets of the clocks C and/or D to >> *match* with the computed requirements of SR? If you do manage to >> practically 'synchronize' the clocks C and D in BCRF, obviously their >> synchronization with clocks A and B will get broken. Then we should be >> able to say that the clocks A and B are mutually synchronized in ECI >> frame while the clocks C and D are mutually synchronized in BCRF. > > Right. > Does it imply that two clocks C and D (separated by distance S) can be mutually synchronized in practical terms in any ONE inertial reference frame (ECI, or BCRF or Galactic frame), simply by *adjusting* their mutual timing offsets as dictated by relativity formulas for THAT reference frame? Say, for example the timing offset between instantaneous time readings of clocks C and D could be dT_b when these clocks are *synchronized* in BCRF and it could be dT_g when they are synchronized in Galactic reference frame. Do you agree? > >> You are requested to kindly clarify if there is any practical method >> of *checking* or verifying that clocks A and B are indeed mutually >> synchronized in *ECI reference frame* > > This 'checking' is made on a more or less continuously basis. > Look up TAI-time, and how TAI clocks are kept in sync. > >> and the clocks C and D are >> indeed mutually synchronized in *BCRF*. Will this practical method of >> *checking* the mutual synchronization of these clock pairs be frame >> dependent or common for both pairs? > > Much harder. What would you consider to be a valid 'check'? > There is difference between 'checking' to see whether the clocks are really synchronized or not; and continuously keep sending synchronization commands to effect synchronization on instant to instant basis. So kindly clarify if there is any practical method of *checking* or verifying that clocks C and D are indeed mutually synchronized in *ECI frame* or *BCRF* or *Galactic frame*. Let us assume that the instantaneous timing offset between clocks C and D is 'dT'. Further let us assume that the time taken by a laser pulse to propagate from C to D is T_cd as measured from the clock readings and that the time taken by another laser pulse to propagate from D to C is T_dc as measured from the clock readings. Then it can be easily shown that in a stationary reference frame (as defined by Einstein), T_cd - T_dc = 2.dT ..... (1) As per Einstein's convention, offset dT in equation (1) must be set to zero in order to synchronize the two clocks in a stationary reference frame in which these clocks are at rest. However, as seen above, the value of this time offset will have to be specifically *adjusted* to match the relativity requirements. If we find the required value of this offset for synchronizing the two clocks in BCRF is dT_b, then, T_cd - T_dc = 2.dT_b ..... (2) Hence equation (2) could be used to *check* whether the clocks C and D under consideration, are *synchronized* in BCRF or not. Do you agree? GSS
From: Sue... on 31 Mar 2010 13:41 On Mar 31, 12:46 pm, GSS <gurcharn_san...(a)yahoo.com> wrote: ------------- > > Kindly make it clear whether we can practically (not through > gedankens) synchronize two clocks A and B in an inertial reference > frame in which they are known to be in uniform MOTION (and not at > rest)? This is important because as per SR [1905] , (for a stationary http://en.wikipedia.org/wiki/Lorentz_ether_theory > observer) time in a moving reference frame is 'supposed' to be > position and velocity dependent (and hence different at two points A > and B spatially separated in the direction of motion). > >
From: Inertial on 31 Mar 2010 19:18 "Sue..." <suzysewnshow(a)yahoo.com.au> wrote in message news:8cb82e7e-6260-47ed-b655-079880225d6f(a)8g2000yqz.googlegroups.com... > On Mar 31, 12:46 pm, GSS <gurcharn_san...(a)yahoo.com> wrote: > > ------------- >> >> Kindly make it clear whether we can practically (not through >> gedankens) synchronize two clocks A and B in an inertial reference >> frame in which they are known to be in uniform MOTION (and not at >> rest)? This is important because as per > > SR [1905] , (for a stationary > > http://en.wikipedia.org/wiki/Lorentz_ether_theory We're talking SR .. not LET. Try to keep up Sue
From: Tom Roberts on 31 Mar 2010 22:15
GSS wrote: > On Mar 25, 10:42 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> Clock synchronization is INHERENTLY frame dependent. That is, a given pair of >> clocks can be synchronized in one AND ONLY one inertial frame; they are not >> synchronized in any other inertial frame. > > Agreed that a given pair of precision atomic clocks A and B (separated > by constant distance S) can be synchronized in ONE AND ONLY ONE > inertial reference frame. But is there any restriction on the choice > of THAT inertial reference frame? No. But it is most natural and easiest to synchronize them in the frame in which they are at rest. Note that except for certain special cases the two clocks must be at rest in THE SAME inertial frame. The rotating earth is such a special case, for synchronization in the ECI frame. > Specifically, can we practically > (not through gedankens) synchronize two clocks A and B in an inertial > reference frame in which they are known to be in uniform MOTION (and > not at rest)? Yes. The GPS does something similar. > [... synchronize in the BCRF] Synchronizing two earthbound clocks in the BCRF can be done in exactly the same manner as they can be synchronized in the ECI. But there are difficulties: A) There is no surface corresponding to earth's geoid, so you must specify precisely where a standard clock displays the correct time. Normally earth's geoid is used, even though it is moving in a rather complex manner relative to the BCRF. B) Gravitation of planets is important (the GPS can treat the sun, moon, and planets as minuscule error terms; for the BCRF they are considerably larger, and the fact that earth's geoid is rather low in earth's gravity complicated matters). C) There are no orbiting clocks to assist you (as the GPS satellites do for the ECI). D) The volume over which synchronization can be achieved is not obvious to me; it surely extends to Pluto, and probably beyond, but cannot possibly extend to the nearest star. Tom Roberts |