Notion of Absolute Clock Synchronization in SR
in [Relativity]
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From: Tom Roberts on 5 Apr 2010 23:13 GSS wrote: > On Apr 3, 9:12 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> By saying "inertial frame" you imply the context is SR -- in SR one could set >> the offsets of two clocks such that they are synchronized in any inertial frame >> you choose. They would be synchronized with each other in that frame, but not >> with coordinate clocks of the selected frame (these two would "tick at a >> different rate" than those coordinate clocks). >> > You have made a very important statement which I would like to repeat > with some emphasis. "In SR one could set the *offsets* of two clocks > such that they are *synchronized* in *any* inertial frame you choose. > They would be synchronized with each other in *that* frame." > > Let us extend the analogy of two clocks fixed on earth's geoid to a > million (or more) clocks fixed on earth's geoid. Let us synchronize > all these clocks in ECI frame by synchronizing their time to UTC by > using GPS service. In this state, each and every adjoining pair of > clocks can be considered as mutually synchronized with zero time > offset between them. But, of course, each pair is synchronized in the ECI frame. The concept "synchronized" is ALWAYS qualified with a frame. > Let us *adjust* the offsets of all these clocks such that they are now > synchronized in BCRF. It is not possible to make such an "adjustment". They all have essentially the same gravitational potential, but they have different speeds relative to the BCRF -- the earth both rotates and revolves around the sun. As I said before: for time-indicating devices [#] on earth's geoid to be synchronized in the BCRF, they must vary their tick rate according to observations of their locations and speeds wrt the BCRF. [#] These are not "clocks" in the usual sense of the word. > A little reflection will show that the required > offset will finally come out to be zero [...] Even ignoring the above impossibility, this cannot possibly be true: both ECI and BCRF are inertial frames (in the local sense of GR, but here "local" includes all these clocks on the geoid). If these clocks were synchronized in both inertial frames, then the two frames must be the same. But they are manifestly not the same. > [... more errors building on the above error...] Tom Roberts
From: GSS on 6 Apr 2010 13:04 On Apr 6, 8:13 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > GSS wrote: > > On Apr 3, 9:12 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >>> By saying "inertial frame" you imply the context is SR -- in SR one could set >>> the offsets of two clocks such that they are synchronized in any inertial frame >>> you choose. They would be synchronized with each other in that frame, but not >>> with coordinate clocks of the selected frame (these two would "tick at a >>> different rate" than those coordinate clocks). > >> You have made a very important statement which I would like to repeat >> with some emphasis. "In SR one could set the *offsets* of two clocks >> such that they are *synchronized* in *any* inertial frame you choose. >> They would be synchronized with each other in *that* frame." > >> Let us extend the analogy of two clocks fixed on earth's geoid to a >> million (or more) clocks fixed on earth's geoid. Let us synchronize >> all these clocks in ECI frame by synchronizing their time to UTC by >> using GPS service. In this state, each and every adjoining pair of >> clocks can be considered as mutually synchronized with zero time >> offset between them. > > But, of course, each pair is synchronized in the ECI frame. The concept > "synchronized" is ALWAYS qualified with a frame. > >> Let us *adjust* the offsets of all these clocks such that they are now >> synchronized in BCRF. > > It is not possible to make such an "adjustment". They all have essentially the > same gravitational potential, but they have different speeds relative to the > BCRF -- the earth both rotates and revolves around the sun. > As per your statement above, "They would be synchronized with each other in that [BCRF] frame, but not with coordinate clocks of the selected [BCRF] frame (these two would "tick at a different rate" than those coordinate clocks)." Here we are not insisting on their *synchronization* with the *coordinate clocks*, but only on the *mutual synchronization* of all clocks located on earth's geoid. That is, all these clocks when in *mutual synchronization* will display the same instantaneous time (as UTC), but *that* time need not be the same as the *corresponding* time on the coordinate clocks in BCRF. >> A little reflection will show that the required >> offset will finally come out to be zero [...] > > Even ignoring the above impossibility, this cannot possibly be true: both ECI > and BCRF are inertial frames (in the local sense of GR, but here "local" > includes all these clocks on the geoid). If these clocks were synchronized in > both inertial frames, then the two frames must be the same. But they are > manifestly not the same. > Let me present the same problem in a slightly different form. As per Wikipedia, the coordinate times cannot be measured with real physical clocks, but only computed from the proper-time readings of real clocks with the aid of the time dilation relationship. Let us therefore now consider a million (or more) identical atomic clocks fixed on earth's geoid. Let us *synchronize* their *proper time* with the UTC time by using GPS service. In this state, each and every adjoining pair of clocks can be considered as mutually synchronized in *proper time* with zero time offset between them. However, since the *proper time* of all these clocks cannot physically change whether we consider them located in ECI frame or BCRF or the Galactic reference frame, we can always state that these clocks are *synchronized in proper time* which remains same in all inertial reference frames. Of course for your relativity computations, you can always transform these proper times to the corresponding *coordinate times* of the selected reference frame. Do you agree? GSS
From: Tom Roberts on 6 Apr 2010 16:15 GSS wrote: > On Apr 6, 8:13 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >> GSS wrote: >>> On Apr 3, 9:12 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: >>>> By saying "inertial frame" you imply the context is SR -- in SR one could set >>>> the offsets of two clocks such that they are synchronized in any inertial frame >>>> you choose. They would be synchronized with each other in that frame, but not >>>> with coordinate clocks of the selected frame (these two would "tick at a >>>> different rate" than those coordinate clocks). >>> You have made a very important statement which I would like to repeat >>> with some emphasis. "In SR one could set the *offsets* of two clocks >>> such that they are *synchronized* in *any* inertial frame you choose. >>> They would be synchronized with each other in *that* frame." >>> Let us extend the analogy of two clocks fixed on earth's geoid to a >>> million (or more) clocks fixed on earth's geoid. Let us synchronize >>> all these clocks in ECI frame by synchronizing their time to UTC by >>> using GPS service. In this state, each and every adjoining pair of >>> clocks can be considered as mutually synchronized with zero time >>> offset between them. >> But, of course, each pair is synchronized in the ECI frame. The concept >> "synchronized" is ALWAYS qualified with a frame. >> >>> Let us *adjust* the offsets of all these clocks such that they are now >>> synchronized in BCRF. >> It is not possible to make such an "adjustment". They all have essentially the >> same gravitational potential, but they have different speeds relative to the >> BCRF -- the earth both rotates and revolves around the sun. >> > As per your statement above, "They would be synchronized with each > other in that [BCRF] frame, but not with coordinate clocks of the > selected [BCRF] frame (these two would "tick at a different rate" than > those coordinate clocks)." That was for two clocks AT REST IN SOME INERTIAL FRAME, being synchronized in some other inertial frame. Here the clocks on the geoid are NOT at rest in ANY inertial frame, and my "statement above" does not apply. Remember that the context in which statements are made is important, and you cannot take a statement from one context, apply it in a different context, and expect it to remain valid. > [...] we can always state that these clocks are > *synchronized in proper time* There is no such thing [#]. As I said before, synchronization is ALWAYS qualified with an inertial frame. You synchronized all those clocks in the ECI frame, so they cannot be synchronized in the BCRF. [#] If there were, then the "twin paradox" would not occur. It does. [This is getting overly repetitive; don't expect me to continue. You cannot reasonably expect to learn much via "20 questions". Get a good textbook and STUDY.] Tom Roberts
From: Sue... on 6 Apr 2010 16:37 On Apr 6, 4:15 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > GSS wrote: > > On Apr 6, 8:13 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > >> GSS wrote: > >>> On Apr 3, 9:12 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > >>>> By saying "inertial frame" you imply the context is SR -- in SR one could set > >>>> the offsets of two clocks such that they are synchronized in any inertial frame > >>>> you choose. They would be synchronized with each other in that frame, but not > >>>> with coordinate clocks of the selected frame (these two would "tick at a > >>>> different rate" than those coordinate clocks). > >>> You have made a very important statement which I would like to repeat > >>> with some emphasis. "In SR one could set the *offsets* of two clocks > >>> such that they are *synchronized* in *any* inertial frame you choose. > >>> They would be synchronized with each other in *that* frame." > >>> Let us extend the analogy of two clocks fixed on earth's geoid to a > >>> million (or more) clocks fixed on earth's geoid. Let us synchronize > >>> all these clocks in ECI frame by synchronizing their time to UTC by > >>> using GPS service. In this state, each and every adjoining pair of > >>> clocks can be considered as mutually synchronized with zero time > >>> offset between them. > >> But, of course, each pair is synchronized in the ECI frame. The concept > >> "synchronized" is ALWAYS qualified with a frame. > > >>> Let us *adjust* the offsets of all these clocks such that they are now > >>> synchronized in BCRF. > >> It is not possible to make such an "adjustment". They all have essentially the > >> same gravitational potential, but they have different speeds relative to the > >> BCRF -- the earth both rotates and revolves around the sun. > > > As per your statement above, "They would be synchronized with each > > other in that [BCRF] frame, but not with coordinate clocks of the > > selected [BCRF] frame (these two would "tick at a different rate" than > > those coordinate clocks)." > > That was for two clocks AT REST IN SOME INERTIAL FRAME, being synchronized in > some other inertial frame. Here the clocks on the geoid are NOT at rest in ANY > inertial frame, and my "statement above" does not apply. > > Remember that the context in which statements are made is important, and you > cannot take a statement from one context, apply it in a different context, and > expect it to remain valid. > > > [...] we can always state that these clocks are > > *synchronized in proper time* > > There is no such thing [#]. As I said before, synchronization is ALWAYS > qualified with an inertial frame. You synchronized all those clocks in the ECI > frame, so they cannot be synchronized in the BCRF. > > [#] If there were, then the "twin paradox" would not occur. > It does. > > [This is getting overly repetitive; don't expect me to continue. You cannot > reasonably expect to learn much via "20 questions". Get a good textbook and STUDY.] Gosh Tom, When half the returns for a Google search for the term "accumulated proper time" are posts by yourself or Daryl, one begins to give up looking for an adequate text on the subject. Ya can't blame folks for wanting to get it from straight from the horse's mouth. Sue... > > Tom Roberts
From: PD on 6 Apr 2010 16:51
On Apr 6, 3:37 pm, "Sue..." <suzysewns...(a)yahoo.com.au> wrote: > On Apr 6, 4:15 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > > > > GSS wrote: > > > On Apr 6, 8:13 am, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > >> GSS wrote: > > >>> On Apr 3, 9:12 pm, Tom Roberts <tjroberts...(a)sbcglobal.net> wrote: > > >>>> By saying "inertial frame" you imply the context is SR -- in SR one could set > > >>>> the offsets of two clocks such that they are synchronized in any inertial frame > > >>>> you choose. They would be synchronized with each other in that frame, but not > > >>>> with coordinate clocks of the selected frame (these two would "tick at a > > >>>> different rate" than those coordinate clocks). > > >>> You have made a very important statement which I would like to repeat > > >>> with some emphasis. "In SR one could set the *offsets* of two clocks > > >>> such that they are *synchronized* in *any* inertial frame you choose. > > >>> They would be synchronized with each other in *that* frame." > > >>> Let us extend the analogy of two clocks fixed on earth's geoid to a > > >>> million (or more) clocks fixed on earth's geoid. Let us synchronize > > >>> all these clocks in ECI frame by synchronizing their time to UTC by > > >>> using GPS service. In this state, each and every adjoining pair of > > >>> clocks can be considered as mutually synchronized with zero time > > >>> offset between them. > > >> But, of course, each pair is synchronized in the ECI frame. The concept > > >> "synchronized" is ALWAYS qualified with a frame. > > > >>> Let us *adjust* the offsets of all these clocks such that they are now > > >>> synchronized in BCRF. > > >> It is not possible to make such an "adjustment". They all have essentially the > > >> same gravitational potential, but they have different speeds relative to the > > >> BCRF -- the earth both rotates and revolves around the sun. > > > > As per your statement above, "They would be synchronized with each > > > other in that [BCRF] frame, but not with coordinate clocks of the > > > selected [BCRF] frame (these two would "tick at a different rate" than > > > those coordinate clocks)." > > > That was for two clocks AT REST IN SOME INERTIAL FRAME, being synchronized in > > some other inertial frame. Here the clocks on the geoid are NOT at rest in ANY > > inertial frame, and my "statement above" does not apply. > > > Remember that the context in which statements are made is important, and you > > cannot take a statement from one context, apply it in a different context, and > > expect it to remain valid. > > > > [...] we can always state that these clocks are > > > *synchronized in proper time* > > > There is no such thing [#]. As I said before, synchronization is ALWAYS > > qualified with an inertial frame. You synchronized all those clocks in the ECI > > frame, so they cannot be synchronized in the BCRF. > > > [#] If there were, then the "twin paradox" would not occur. > > It does. > > > [This is getting overly repetitive; don't expect me to continue. You cannot > > reasonably expect to learn much via "20 questions". Get a good textbook and STUDY.] > > Gosh Tom, > When half the returns for a Google search Tom said to get a good *textbook*, not a search return list. You do know the difference and the relative value of each, don't you? If not, then this perhaps accounts for much of your problem. > for the term "accumulated proper time" are posts by > yourself or Daryl, one begins to give up looking for an > adequate text on the subject. Ya can't blame folks for > wanting to get it from straight from the horse's mouth. > > Sue... > > > > > Tom Roberts > > |