Notion of Absolute Clock Synchronization in SR
in [Relativity]
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From: GSS on 11 Mar 2010 10:35 As per Newtonian notion of absolute space and time, clocks can be synchronized in absolute terms such that identical precision atomic clocks located anywhere within the solar system and in any state of motion, will read the same time t1 when a standard master clock reads t1. This notion of absolute clock synchronization implies the notion of absolute simultaneity. However, as per SR, spatial distance and time measurements have been rendered 'relative' and cannot be the same value for different observers in different states of motion. As per SR the notion of global 'absolute simultaneity' is fundamentally invalid for different observers in different states of motion. Therefore, the notion of global 'absolute clock synchronization' (in contrast to e- synchronization) is no longer valid in SR. Since the term 'absolute clock synchronization' is often used in discussions, I would like to request some Relativity experts to kindly clarify the precise definition of absolute clock synchronization in SR. Kindly illustrate the procedure, through some 'thought experiment' or 'gedanken', to achieve absolute clock synchronization for all observers in different states of motion within our solar system. Further, I also need some expert opinion on the following situation, involving clock synchronization. Two identical precision atomic clocks are positioned side by side at point A on the surface of earth and mutually synchronized to ensure that (a) their clock rates or frequencies are exactly matched or synchronized (b) their instantaneous timing offsets are eliminated to ensure that a common trigger pulse yields the same timing reading t1 from both clocks. Assuming the inherent drift of the two atomic clocks is identical and well within 100 ps per day, it can be demonstrated that while the two clocks remain side by side, their synchronization, after a period of one day, is retained at well within one ns accuracy. Let us shift one of the synchronized atomic clocks to a position B such that distance AB is about 30 km. As per Newtonian notion of absolute space and time, the mutual synchronization of the two clocks, positioned at points A and B, will be retained in tact and this synchronization can be referred as 'absolute synchronization'. But according to SR, the mutual synchronization of the two clocks will 'breakdown' during the shifting of one of the clocks from point A to point B. Since 'after' shifting of one clock to point B on the surface of earth, there is no relative motion between the two clocks, their time rates or frequencies will again 'become' synchronized. Therefore, the only persisting effect of the 'synchronization breakdown' during shifting or repositioning of the two clocks, will be a motion induced constant time offset, say dT, in the instantaneous readings of the two clocks. My question to the learned Relativity experts is: What is the order of magnitude of this 'relative motion induced' timing offset dT between the two clocks? Can it be precisely calculated in SR? Is it likely to be within a few nanoseconds or less? Suppose we now shift the clock at point B to bring it back to point A, (with an identical speed and acceleration profile), will this timing offset dT now increase to 2.dT or reduce to zero? I shall be thankful to the Relativity experts for their valuable opinions and clarifications. GSS
From: Tom Roberts on 11 Mar 2010 12:07 GSS wrote: > As per Newtonian notion of absolute space and time, clocks can be > synchronized in absolute terms such that identical precision atomic > clocks located anywhere within the solar system and in any state of > motion, will read the same time t1 when a standard master clock reads > t1. This notion of absolute clock synchronization implies the notion > of absolute simultaneity. But it conflicts with actual observations of the world we inhabit. Atomic clocks on earth and in satellites do not remain synchronized. Effective clocks intrinsic to elementary particles vary widely (factors of 10,000 or more in rate) with their speed relative to the lab. > the notion of > global 'absolute clock synchronization' (in contrast to e- > synchronization) is no longer valid in SR. Yes. > I would like to request some Relativity experts to kindly > clarify the precise definition of absolute clock synchronization in > SR. There is no such definition, as "absolute clock synchronization" does not exist, either in SR or in the world we inhabit. > Two identical precision atomic clocks are positioned side by side at > point A on the surface of earth and mutually synchronized to ensure > that > (a) their clock rates or frequencies are exactly matched or > synchronized > (b) their instantaneous timing offsets are eliminated to ensure that a > common trigger pulse yields the same timing reading t1 from both > clocks. > > Assuming the inherent drift of the two atomic clocks is identical and > well within 100 ps per day, it can be demonstrated that while the two > clocks remain side by side, their synchronization, after a period of > one day, is retained at well within one ns accuracy. OK. Note that to achieve that accuracy requires multiple atomic clocks and a good algorithm to construct a so-called "paper clock". > Let us shift one of the synchronized atomic clocks to a position B > such that distance AB is about 30 km. As per Newtonian notion of > absolute space and time, the mutual synchronization of the two clocks, > positioned at points A and B, will be retained in tact and this > synchronization can be referred as 'absolute synchronization'. But > according to SR, the mutual synchronization of the two clocks will > 'breakdown' during the shifting of one of the clocks from point A to > point B. Since 'after' shifting of one clock to point B on the surface > of earth, there is no relative motion between the two clocks, their > time rates or frequencies will again 'become' synchronized. Therefore, > the only persisting effect of the 'synchronization breakdown' during > shifting or repositioning of the two clocks, will be a motion induced > constant time offset, say dT, in the instantaneous readings of the two > clocks. It is NOT true that "there is no relative motion between the two clocks" -- that is valid ONLY relative to the rotating earth, which is not an inertial frame. It is invariably wrong to attempt to make conclusions based on non-inertial frames without careful considerations of the implications of their non-inertialness. Relative to any inertial frame, these two clocks do have different velocities. The effect of their separation on their relative timing depends IN DETAIL on how they were moved, what their relative positions are, and how they are compared. No general conclusion can be made without specifying at least those details. > What is the order of magnitude of this 'relative motion induced' > timing offset dT between the two clocks? As I said above, it depends on details you did not give. But for a mere 30 km separation, assuming it is horizontal and not vertical, I would not expect it to be large. > Can it be precisely calculated in SR? Is it likely to be within a few > nanoseconds or less? Given sufficient information, it can be computed using GR. The gravitation of the earth can be important here, in which case SR is inadequate. But if one stipulates the two clocks both remain on earth's geoid, or at equal altitudes from it, then gravitation can be neglected and SR is sufficient. With that stipulation, and assuming the 30 km transport is at automobile speeds or less, I would not expect the clocks to differ by as much as a nanosecond. IIRC actual tests of atomic clocks in automobiles showed about a nanosecond difference after a full day at highway speeds. Certainly several hours sitting at the top of a mountain can exceed that difference relative to a clock in the valley. http://leapsecond.com/great2005/tour/ (a small mountain only 5400 ft high, ~20 ns for a weekend) > Suppose we now shift the clock at point B to bring it back to point A, > (with an identical speed and acceleration profile), will this timing > offset dT now increase to 2.dT or reduce to zero? As I said, the details matter. It is also impossible to specify what dT is when they are separated without specifying how the ambiguities of the comparison are handled, and there is no unique and definitive way to do that. But upon re-joining, the difference does not go to zero. Tom Roberts
From: kenseto on 11 Mar 2010 12:26 On Mar 11, 10:35 am, GSS <gurcharn_san...(a)yahoo.com> wrote: > As per Newtonian notion of absolute space and time, clocks can be > synchronized in absolute terms such that identical precision atomic > clocks located anywhere within the solar system and in any state of > motion, will read the same time t1 when a standard master clock reads > t1. This notion of absolute clock synchronization implies the notion > of absolute simultaneity. > > However, as per SR, spatial distance and time measurements have been > rendered 'relative' and cannot be the same value for different > observers in different states of motion. As per SR the notion of > global 'absolute simultaneity' is fundamentally invalid for different > observers in different states of motion. Therefore, the notion of > global 'absolute clock synchronization' (in contrast to e- > synchronization) is no longer valid in SR. > > Since the term 'absolute clock synchronization' is often used in > discussions, I would like to request some Relativity experts to kindly > clarify the precise definition of absolute clock synchronization in > SR. Kindly illustrate the procedure, through some 'thought experiment' > or 'gedanken', to achieve absolute clock synchronization for all > observers in different states of motion within our solar system. > > Further, I also need some expert opinion on the following situation, > involving clock synchronization. > > Two identical precision atomic clocks are positioned side by side at > point A on the surface of earth and mutually synchronized to ensure > that > (a) their clock rates or frequencies are exactly matched or > synchronized > (b) their instantaneous timing offsets are eliminated to ensure that a > common trigger pulse yields the same timing reading t1 from both > clocks. > > Assuming the inherent drift of the two atomic clocks is identical and > well within 100 ps per day, it can be demonstrated that while the two > clocks remain side by side, their synchronization, after a period of > one day, is retained at well within one ns accuracy. > > Let us shift one of the synchronized atomic clocks to a position B > such that distance AB is about 30 km. As per Newtonian notion of > absolute space and time, the mutual synchronization of the two clocks, > positioned at points A and B, will be retained in tact and this > synchronization can be referred as 'absolute synchronization'. But > according to SR, the mutual synchronization of the two clocks will > 'breakdown' during the shifting of one of the clocks from point A to > point B. Since 'after' shifting of one clock to point B on the surface > of earth, there is no relative motion between the two clocks, their > time rates or frequencies will again 'become' synchronized. Therefore, > the only persisting effect of the 'synchronization breakdown' during > shifting or repositioning of the two clocks, will be a motion induced > constant time offset, say dT, in the instantaneous readings of the two > clocks. Let's assume that when the B clock stop at 30 km away from A the A clock shows a time interval of Delta(tA). Therefore Delta(tB) is calculated as follows: Delta(tB)=Delta(tA)/gamma_A What this mean is that the B clock will lag behind the A clock by a factor of Delta(tB) when it is stopped 30 km from A. > > My question to the learned Relativity experts is: > What is the order of magnitude of this 'relative motion induced' > timing offset dT between the two clocks? > Can it be precisely calculated in SR? Is it likely to be within a few > nanoseconds or less? > > Suppose we now shift the clock at point B to bring it back to point A, > (with an identical speed and acceleration profile), will this timing > offset dT now increase to 2.dT or reduce to zero? The B clock will lag behind the A clock by a factor of 2.dT. Ken Seto > > I shall be thankful to the Relativity experts for their valuable > opinions and clarifications. > > GSS
From: PD on 11 Mar 2010 12:58 On Mar 11, 9:35 am, GSS <gurcharn_san...(a)yahoo.com> wrote: > As per Newtonian notion of absolute space and time, clocks can be > synchronized in absolute terms such that identical precision atomic > clocks located anywhere within the solar system and in any state of > motion, will read the same time t1 when a standard master clock reads > t1. This notion of absolute clock synchronization implies the notion > of absolute simultaneity. > > However, as per SR, spatial distance and time measurements have been > rendered 'relative' and cannot be the same value for different > observers in different states of motion. As per SR the notion of > global 'absolute simultaneity' is fundamentally invalid for different > observers in different states of motion. Therefore, the notion of > global 'absolute clock synchronization' (in contrast to e- > synchronization) is no longer valid in SR. > > Since the term 'absolute clock synchronization' is often used in > discussions, I would like to request some Relativity experts to kindly > clarify the precise definition of absolute clock synchronization in > SR. Sure. One such procedure is as follows. 1. Start at clock A and note the time T1. 2. Proceed to clock B by any method of travel that is guaranteed to be at constant speed. 3. At arrival at clock B, note the time T2. 4. Proceed back to clock A by the same method of travel, and at the same speed. 5. At arrival at clock A, note the time T3. 6. If T3-T2 = T2 - T1, then the clocks are synchronized. If T3-T2 > T2- T1, then clock B is running slow and should be set forward by half the difference noted. If T3-T2 < T2-T1, then clock B is running fast and should be set back by half the difference noted. > Kindly illustrate the procedure, through some 'thought experiment' > or 'gedanken', to achieve absolute clock synchronization for all > observers in different states of motion within our solar system. This cannot be done, given what we know about the laws of physics. > > Further, I also need some expert opinion on the following situation, > involving clock synchronization. > > Two identical precision atomic clocks are positioned side by side at > point A on the surface of earth and mutually synchronized to ensure > that > (a) their clock rates or frequencies are exactly matched or > synchronized > (b) their instantaneous timing offsets are eliminated to ensure that a > common trigger pulse yields the same timing reading t1 from both > clocks. > > Assuming the inherent drift of the two atomic clocks is identical and > well within 100 ps per day, it can be demonstrated that while the two > clocks remain side by side, their synchronization, after a period of > one day, is retained at well within one ns accuracy. > > Let us shift one of the synchronized atomic clocks to a position B > such that distance AB is about 30 km. As per Newtonian notion of > absolute space and time, the mutual synchronization of the two clocks, > positioned at points A and B, will be retained in tact and this > synchronization can be referred as 'absolute synchronization'. But > according to SR, the mutual synchronization of the two clocks will > 'breakdown' during the shifting of one of the clocks from point A to > point B. No, this is not what SR says. The clocks are still synchronized in the frame in which they are at rest. However, they are not synchronized in any frame where the two clocks are moving. > Since 'after' shifting of one clock to point B on the surface > of earth, there is no relative motion between the two clocks, their > time rates or frequencies will again 'become' synchronized. Therefore, > the only persisting effect of the 'synchronization breakdown' during > shifting or repositioning of the two clocks, will be a motion induced > constant time offset, say dT, in the instantaneous readings of the two > clocks. > > My question to the learned Relativity experts is: > What is the order of magnitude of this 'relative motion induced' > timing offset dT between the two clocks? > Can it be precisely calculated in SR? Is it likely to be within a few > nanoseconds or less? > > Suppose we now shift the clock at point B to bring it back to point A, > (with an identical speed and acceleration profile), will this timing > offset dT now increase to 2.dT or reduce to zero? > > I shall be thankful to the Relativity experts for their valuable > opinions and clarifications. > > GSS
From: kenseto on 11 Mar 2010 13:12
On Mar 11, 12:26 pm, kenseto <kens...(a)erinet.com> wrote: > On Mar 11, 10:35 am, GSS <gurcharn_san...(a)yahoo.com> wrote: > > > > > > > As per Newtonian notion of absolute space and time, clocks can be > > synchronized in absolute terms such that identical precision atomic > > clocks located anywhere within the solar system and in any state of > > motion, will read the same time t1 when a standard master clock reads > > t1. This notion of absolute clock synchronization implies the notion > > of absolute simultaneity. > > > However, as per SR, spatial distance and time measurements have been > > rendered 'relative' and cannot be the same value for different > > observers in different states of motion. As per SR the notion of > > global 'absolute simultaneity' is fundamentally invalid for different > > observers in different states of motion. Therefore, the notion of > > global 'absolute clock synchronization' (in contrast to e- > > synchronization) is no longer valid in SR. > > > Since the term 'absolute clock synchronization' is often used in > > discussions, I would like to request some Relativity experts to kindly > > clarify the precise definition of absolute clock synchronization in > > SR. Kindly illustrate the procedure, through some 'thought experiment' > > or 'gedanken', to achieve absolute clock synchronization for all > > observers in different states of motion within our solar system. > > > Further, I also need some expert opinion on the following situation, > > involving clock synchronization. > > > Two identical precision atomic clocks are positioned side by side at > > point A on the surface of earth and mutually synchronized to ensure > > that > > (a) their clock rates or frequencies are exactly matched or > > synchronized > > (b) their instantaneous timing offsets are eliminated to ensure that a > > common trigger pulse yields the same timing reading t1 from both > > clocks. > > > Assuming the inherent drift of the two atomic clocks is identical and > > well within 100 ps per day, it can be demonstrated that while the two > > clocks remain side by side, their synchronization, after a period of > > one day, is retained at well within one ns accuracy. > > > Let us shift one of the synchronized atomic clocks to a position B > > such that distance AB is about 30 km. As per Newtonian notion of > > absolute space and time, the mutual synchronization of the two clocks, > > positioned at points A and B, will be retained in tact and this > > synchronization can be referred as 'absolute synchronization'. But > > according to SR, the mutual synchronization of the two clocks will > > 'breakdown' during the shifting of one of the clocks from point A to > > point B. Since 'after' shifting of one clock to point B on the surface > > of earth, there is no relative motion between the two clocks, their > > time rates or frequencies will again 'become' synchronized. Therefore, > > the only persisting effect of the 'synchronization breakdown' during > > shifting or repositioning of the two clocks, will be a motion induced > > constant time offset, say dT, in the instantaneous readings of the two > > clocks. > > Let's assume that when the B clock stop at 30 km away from A the A > clock shows a time interval of Delta(tA). Therefore Delta(tB) is > calculated as follows: > Delta(tB)=Delta(tA)/gamma_A > What this mean is that the B clock will lag behind the A clock by a > factor of Delta(tB) when it is stopped 30 km from A. Sorry the B clock will lag behind the A clock by a factor of: [Delta(tA)-Delta(tB)] > > > > > My question to the learned Relativity experts is: > > What is the order of magnitude of this 'relative motion induced' > > timing offset dT between the two clocks? > > Can it be precisely calculated in SR? Is it likely to be within a few > > nanoseconds or less? > > > Suppose we now shift the clock at point B to bring it back to point A, > > (with an identical speed and acceleration profile), will this timing > > offset dT now increase to 2.dT or reduce to zero? > > The B clock will lag behind the A clock by a factor of 2.dT. Sorry the B clock will lag behind the A clock by a factor of: 2[Delta(tA)-Delta(tB)] Ken Seto |