[saspinski (OP)]

Suppose there is an atom clock in alpha centauri, syncronized to the earth. An observer there could detect now, signals sent from here in jan 2014, considering 4 light years of distance.

A spaceship coming from earth at 0.5c, crosses alpha centauri when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t - vx = t - 0,5 * 4 = jan 2016. An observer in the ship could detect signals sent from here in jan 2012.

A spaceship with the opposite velocity, flying to earth at 0.5c, crosses alpha centauri also when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t + vx = t + 0,5 * 4 = jan 2020. An observer in the ship could detect signals sent from here in jan 2016.

If it is right, there is any intuitive way to realize how that gap of 4 years between the available signals for the ships should happen?  I am always unconsciouly dealing with light speed as a normal material speed, instead of a constant, when I try an intuitive explanation.

[Bill S]

Saspinski. I'm certainly not the best person to deal with mathematical calculations, but the first thing that comes to mind when reading your post is that you might not have taken the RFs of the different observers into account. 

Hopefully someone better able will come up with an answer, but failing that, I'll see if I can trace my notes from a few years ago, when I wrestled with a similar problem.  Time's limited, though, so don't hold your breath. 

[Janus]

Suppose there is an atom clock in alpha centauri, syncronized to the earth. An observer there could detect now, signals sent from here in jan 2014, considering 4 light years of distance.

OK

A spaceship coming from earth at 0.5c, crosses alpha centauri when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t - vx = t - 0,5 * 4 = jan 2016. An observer in the ship could detect signals sent from here in jan 2012.

No.  The light or signals arriving at AC are the same for both the Clock at AC and the ship.  They both, at the moment of passing, detect signals that left Earth in Jan 2014.   

A spaceship with the opposite velocity, flying to earth at 0.5c, crosses alpha centauri also when the clock at the star shows jan 2018. The corresponding time at earth for the ship is t' = t + vx = t + 0,5 * 4 = jan 2020. An observer in the ship could detect signals sent from here in jan 2016.

Again, this ship would be receiving the same signals from Earth at that moment as AC and the Other ship; those that left Earth in Jan 2014.  All events( such as light carrying a certain bit of information to an observer) must be consistent across all frames of reference.
Space-time diagrams might help. going from left to right we have the Earth_AC frame, the Outbound ship frame, and the inbound ship frame.   Dark Blue is the Earth's world-line, Green AC's, Red the Outbound ship's and Light blue the inbound ship's.  The yellow line is light/signal coming from Earth.

simul.png (10.64 kB . 932x394 - viewed 2668 times)

If it is right, there is any intuitive way to realize how that gap of 4 years between the available signals for the ships should happen?  I am always unconsciouly dealing with light speed as a normal material speed, instead of a constant, when I try an intuitive explanation.

Just remember, that in any frame, light will travel at c relative to that frame (this is illustrated by the fact that in all three diagrams above light is drawn at a 45 degree angle).

[jeffreyH]

In a vacuum the inertial path of the photon contains the only static anchor points. All observers will agree on its path and location at particular times. The clocks may vary but the photon does not.

[saspinski (OP)]

Just remember, that in any frame, light will travel at c relative to that frame (this is illustrated by the fact that in all three diagrams above light is drawn at a 45 degree angle).

OK, I agree. The signals from earth, recorded in 2018 by all, had being sent in 2014.

What I am trying to understand is the meaning of simultaneity: if on Jan 2016 people at earth observe another ship (lets say from the same fleet) passing by here towards AC, also with v = 0.5c, the ship that is passing by AC on 2018 will take this event as happening now.

So, for the word "now" has any meaning, some information should be recorded by the ship in AC, that was sent 4 years ago.

I believe that the croquis in annex (where only the ship going to AC is represented)  shows what happens: the dashed line is this second ship. The signal from Jan 2012 is sent from it and arrives to AC on Jan 2108, being recorded by the first ship.

[petelamana]

I'm stuck with the base supposition.  How could a clock 4-light years distant, be it atomic or anything else, be synchronised with a clock on Earth?  What would "carry" the synchronizing information to the clock in the AC system?  And do so instantly, without any loss of time in the transfer?

When clocks are synchronized there is always a variation in the "time", in most cases imperceivable, but it exists.  So, again, the two clocks would have to be out of sync by however long it takes the synchronizing information to reach the second clock.

However, if a clock could be constructed that utilizes quantum "teleportation", then I suppose two clocks separated by great distances could be synchronized.

[chiralSPO]

Forget distances of 4 light years. How can any two clocks really be synchronized? Even if they are right next to each other. The mechanism of a clock is itself about a light nanosecond across (about 3 mm), so which part tells the "true" time? Also different parts of the clock are in different frames of reference, and may experience time and space dilations relative to each other. Especially if there are any heavy atoms around, like gold or cesium, for which relativistic effects are measurably different for different parts of the atom! How can the universe actually work with all these different frames of reference and timelines?

Well, it does work, somehow. We just get ourselves confused trying to think about it. Relativity, QM, QFT, etc. all have their failings. Hopefully we will get better theories, but I think we are doing pretty well considering we're made of meat!

By the way, welcome to the forum, petelamana! Great questions, keep it up!

[Janus]

I'm stuck with the base supposition.  How could a clock 4-light years distant, be it atomic or anything else, be synchronised with a clock on Earth?  What would "carry" the synchronizing information to the clock in the AC system?  And do so instantly, without any loss of time in the transfer?

When clocks are synchronized there is always a variation in the "time", in most cases imperceivable, but it exists.  So, again, the two clocks would have to be out of sync by however long it takes the synchronizing information to reach the second clock.

However, if a clock could be constructed that utilizes quantum "teleportation", then I suppose two clocks separated by great distances could be synchronized.

You use the Einstein Synchronization method.   You put a light source halfway between the to clocks, It sends a synchronizing signal to both clocks which tells them to start.  This only has to be done once, as it is assumed that both clocks from then on will remain in sync in their rest frame (in thought experiments, we assume ideal clocks, in real life we would use clocks who's known limits of drift are much smaller than the effect we are attempting to measure. 
Another method is to send a signal from one clock to the other and just account for the distance the signal has to travel. If Clock 1 sends a signal to clock 2 and they are 4 light years apart, then when Clock 2 gets the signal it knows that the light left 4 years ago and can set itself accordingly to sync itself with Clock 1.  The point is that in principle it is possible to sync the clocks exactly in their rest frame and in practice it is possible to sync them close enough that the difference is insignificant to the experiment.

[guest4091]

You are measuring a time difference.
The time transformation is t'=g(t-.5x)=1.15(8-2)=6.9.
The ship time would correspond to 2016.9 earth time.
I'll just support the last post by Janus. The earth only has to poll the distant clocks to get a reading, to check for synchronization.

[petelamana]

Janus, thank you.  If I may be allowed to expound, and I mean not impertinence.

As I read the first part of your explanation,  "You use the Einstein Synchronization method.   You put a light source halfway between the to clocks, It sends a synchronizing signal to both clocks which tells them to start."  I immediately thought of Zeno's Paradoxes, specifically Dichotomy.  To refresh your memory, Zeno correctly asserts that in order for anything that is in motion from point A to point B it must first achieve the halfway point.  In order for it to make it to the halfway point it must first get to the halfway point of that, or the one-quarter (overall) point, and in order to reach that it must cross the half-way of the halfway of the half-way, or the one-eighth point, and so on.

In a similar fashion, this is the same as folding, or tearing, a piece of paper in half, and then in half again, and so on.  Can you tear the paper in half enough times to make the paper cease to exist?  Obviously, no.

So, back to the Einstein Synchronization method...

Each iteration of the halving of the distance from Earth to AC would cause a time lag.  Not in the halving, but in the fact that the signal still has to travel from one point to another.

Thank you for indulging me. - Pete

[saspinski (OP)]

The next mission to Mars could verify the lack of synchronism. After returning to earth, with an average speed of 20000 km/h, and a distance of 55 millions of kilometres, there should be a difference of 0,003 s between previously synchronized clocks. The ship clock behind that one that stayed here.

[wolfekeeper]

One interesting thing I worked out a while back, if you move a clock at a very slow speed along a moving object, then you get the same result as the Einstein synchronisation method. The overall sum of the time dilation, does not tend to zero. In fact it depends on the distance and the speed of the object. Indeed, that's where the lack of simultaneity comes from, it's just another effect of time dilation really.

[Janus]

Janus, thank you.  If I may be allowed to expound, and I mean not impertinence.

As I read the first part of your explanation,  "You use the Einstein Synchronization method.   You put a light source halfway between the to clocks, It sends a synchronizing signal to both clocks which tells them to start."  I immediately thought of Zeno's Paradoxes, specifically Dichotomy.  To refresh your memory, Zeno correctly asserts that in order for anything that is in motion from point A to point B it must first achieve the halfway point.  In order for it to make it to the halfway point it must first get to the halfway point of that, or the one-quarter (overall) point, and in order to reach that it must cross the half-way of the halfway of the half-way, or the one-eighth point, and so on.

In a similar fashion, this is the same as folding, or tearing, a piece of paper in half, and then in half again, and so on.  Can you tear the paper in half enough times to make the paper cease to exist?  Obviously, no.

So, back to the Einstein Synchronization method...

Each iteration of the halving of the distance from Earth to AC would cause a time lag.  Not in the halving, but in the fact that the signal still has to travel from one point to another.

Thank you for indulging me. - Pete

Zeno's paradox has no relevance here (besides, it fail to take into account the concept of a "limit".)

There is no series of "dividing in half" involved.  You simply have a light source that is mid way between the clocks you want to synchronize.  It does not matter how you determined the midpoint, You could have stretched a measuring tape between the light source and one clock and then between the light source and the other clock, or used some other method. 
The light then emits one flash which then starts the two clocks, The delay time between the emission of the light and its reception at the clocks is of no matter (you don't even need to know the speed of light for it to work), because it's the fact that the flashes reach both clocks at the same time that is used to synchronize the clocks.  The two clocks involved do not have to communicate with each other at all.

[petelamana]

Thank you, Janus.

I admit that I now see the synchronization of the two clocks more clearly.  For that I am very grateful.

As for Zeno, one of the saddest "non-developments" in history is that he never quite got the limit.  Imagine where the world could be if Zeno had been able to clearly define a limit, 2100 years before Leibnitz? 

Again, thank you for your illumination. - Pete