[hamdani yusuf (OP)]

Thanks to our understanding of relativity, it works very well.

Which means they can be synchronized. It's not impossible.

[hamdani yusuf (OP)]

I have a clock and a watch, both radio-controlled. Immediately after the radio sync phase, if I'm standing still, they can remain mutually synchronised because Δx = 0.If I move, so Δx ≠ 0, I will have accelerated  the wristwatch and imposed a relative velocity, so I can't expect them to remain synchronised.

What if both accelerated equally in opposite direction?

[alancalverd]

Then each would see the other as running slow.

[alancalverd]

Which means they can be synchronized. It's not impossible.

Not at all. We know the relativistic offsets and can either adjust each clock so that the time signals received at a reference point on Earth appear synchronised, or apply the relativistic correction to the time stamp of each received signal.

[hamdani yusuf (OP)]

Which means they can be synchronized. It's not impossible.

Not at all. We know the relativistic offsets and can either adjust each clock so that the time signals received at a reference point on Earth appear synchronised, or apply the relativistic correction to the time stamp of each received signal.

Which then makes them synchronized.

[pzkpfw]

Which means they can be synchronized. It's not impossible.

Not at all. We know the relativistic offsets and can either adjust each clock so that the time signals received at a reference point on Earth appear synchronised, or apply the relativistic correction to the time stamp of each received signal.

Which then makes them synchronized.

What exactly do you think synchronised means with respect to two clocks?

[hamdani yusuf (OP)]

What exactly do you think synchronised means with respect to two clocks?

When they can show the same value at one time, and still show the same value at later time.

[pzkpfw]

What exactly do you think synchronised means with respect to two clocks?

When they can show the same value at one time, and still show the same value at later time.

(Ignoring for now who is deciding (and how) the times they are compared ...)

If the two clocks are in relative movement (the distance between them is changing), will they tick at the same rate (and according to whom)?

[hamdani yusuf (OP)]

If the two clocks are in relative movement (the distance between them is changing), will they tick at the same rate (and according to whom)?

According to relativity principle, an observers who keep their position right between those clocks should see them synchronized, based on symmetry.

[pzkpfw]

If the two clocks are in relative movement (the distance between them is changing), will they tick at the same rate (and according to whom)?

According to relativity principle, an observers who keep their position right between those clocks should see them synchronized, based on symmetry.

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

And this is not quite what you earlier said:

They can also be achieved when relative position=zero to the observer.

And ... how does this apply to GPS?

[alancalverd]

This discussion has turned into an argument about the meaning of "synchronised".

It resolves very simply if you compare observation with relativistic prediction (so far, no discrepancy) and accept that relativity applies for all values of v_rel including zero.

[hamdani yusuf (OP)]

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

Thinking otherwise would lead to contradiction.

[hamdani yusuf (OP)]

And ... how does this apply to GPS?

Send a spacecraft to geostationarily float near the orbit of a GPS satellite. Set the clock the same as the satellite is passing by. Wait until the satellite return to the same spot. Compare the results. Make adjustments as needed.

[alancalverd]

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

Thinking otherwise would lead to contradiction.

The why would each clock appear to be running slow when viewed from the other?  And wouldn't they both appear slow to the midpoint observer with an identical clock?

What your midpoint observer sees is two clocks, equally wrong.

Send a spacecraft to geostationarily float near the orbit of a GPS satellite.

Bit of a problem there. GPS satellites orbit every 12 hours, at about 20,000 km altitude. Geostationary orbit doesn't move, at 36 ,000 km altitude.

But the Haefle-Keating experiment demonstrated the effect to most people's satisfaction, just using an aeroplane.

[pzkpfw]

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

Thinking otherwise would lead to contradiction.

WHAT contradiction? (Are you a dentist?)

And, doesn't this basically mean any two clocks are synchronised? What's even the point then of specifying that clocks are synchronised or not?

[hamdani yusuf (OP)]

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

Thinking otherwise would lead to contradiction.

WHAT contradiction? (Are you a dentist?)

And, doesn't this basically mean any two clocks are synchronised? What's even the point then of specifying that clocks are synchronised or not?

You seem to forget about the requirement that the observer keeps his position right between those two clocks.

[hamdani yusuf (OP)]

wouldn't they both appear slow to the midpoint observer with an identical clock?

Both slow down equally, thus they are still synchronized to each other.

[pzkpfw]

Between the clocks is one special case, yes. But does that really mean those two clocks were synchronised?

Thinking otherwise would lead to contradiction.

WHAT contradiction? (Are you a dentist?)

And, doesn't this basically mean any two clocks are synchronised? What's even the point then of specifying that clocks are synchronised or not?

You seem to forget about the requirement that the observer keeps his position right between those two clocks.

No, I am not forgetting the very thing I am responding to. You tend to throw out snippets that contradict your own previous snippets, or lead to consequences that don't make sense. This is one.

Take Alice and Bob passing each other in space, in inertial relative movement.
Alice can consider herself at rest, and Bob is passing at 100 kph.
Bob can consider himself at rest, and Alice is passing at 100 kph.
Alice has a clock that ticks at 1 second per second, but for her, Bob's clock is slow.
Bob has a clock that ticks at 1 second per second, but for him, Alice's clock is slow.
Thus, their clocks cannot be synchronised. This is basic relativity.

Well, yes, you can insert Carol who remains between Alice and Bob, for whom they are both doing 50 kph. For Carol, Alice and Bob's clocks tick at the same rate. (*1)

But does that mean Alice and Bob's clocks ARE in an absolute sense (or can be) synchronised?
Would Alice and Bob agree?
And, if that were true, doesn't that mean you could postulate a Carol for ANY two such clocks? (*2)
Do you think it matters to Alice and Bob if there is a Carol there or not?

Notes:
*1 For Carol, Alice and Bob's clocks will tick slower than hers of course, so you've also just moved the synchronisation issue one step deeper
*2 That's why I made my previous post

[Halc]

You seem to forget about the requirement that the observer keeps his position right between those two clocks.

There is no such requirement. Clocks running in sync is a function of a reference frame, not of observation, location, or even coordinate system (*).  'Clocks being in sync' is meaningless without a frame reference. If two clocks are in sync relative to frame F, that means they read the same value in frame F at all times, which is true regardless of any observer's location or motion. It has nothing whatsoever to do with observation.
In particular, it doesn't mean that any given observer sees both clocks reading the same value.

I do acknowledge that the intended purpose of an observer is often to simply hang a name tag on a frame, so 'according to Carol' becomes shorthand for 'relative to the frame in which Carol is stationary', but 1) it matters not a hoot then where Carol is in that frame, and 2) a rock with 'Carol' painted on it serves the same purpose.

Take Alice and Bob passing each other in space, in inertial relative movement.
Alice can consider herself at rest, and Bob is passing at 100 kph.
Bob can consider himself at rest, and Alice is passing at 100 kph.
Alice has a clock that ticks at 1 second per second, but for her, Bob's clock is slow.
Bob has a clock that ticks at 1 second per second, but for him, Alice's clock is slow.
Thus, their clocks cannot be synchronised. This is basic relativity.

Well, yes, you can insert Carol who remains between Alice and Bob, for whom they are both doing 50 kph. For Carol, Alice and Bob's clocks tick at the same rate.

Your scenario seems to have the clocks meet at a common event, but to generalize a bit, and to remove all unnecessary observers, consider flat spacetime containing two inertial clocks at arbitrary locations, moving at arbitrary velocities, and set to arbitrary times.
In exactly one frame C will those clocks be moving in equal and opposite velocities. There will be events EA and EB on the respective worldlines where each clock is closest in C to the other clock. If the spatial distance in C between those two events is less than the difference in time that each clock reads at those respective clocks, then there will be a set of inertial frames in which both clocks run in sync. If the time difference is not less than that limit, then in no frame will this be true.


* A coordinate system is a reference frame with the addition of specification of an origin and axis orientations, so I'm saying that the sync of clocks is not dependent on those selections, only a function of the frame selection.

[alancalverd]

Both slow down equally, thus they are still synchronized to each other.

But each appears to be running slow from the point of view of the other, and neither is in sync with the midpoint observer's clock.  So none is synchronised with any other. It just happens that, seen from the midpoint, both departing clocks are equally wrong.