Do we have time because we are moving?

[ghwellsjr]

maybe that's what I am trying to do...

If I had 2 synchronized clocks A&B and send B away with.9c for one year after which it decellerates and flies back. would the clocks still be synchronized? As I understand it, B would show less time has passed?

If that's correct, I would expect that in C time runs slower than in B, but from A's perspective in C time runs less slow than in B...so no...probably not...
But if it is a measurable effect with clocks there must be a solution to this?

I guess it would be too much to clarify here why speeds don't add algebraically? not sure, what to search for...

Of course there's a solution for any problem that's consistently and completely described but you have combined parameters that are inconsistent and left out other important details so that there is not a single interpretation of your scenario.

You could have said:

3 synchronized clocks, one stays at A while two are sent with B at .6c away from A.
After one year according to B's time, C gets with one of those clocks on B in a lifeboat and heads at .9c away from B relative to B in direction of A.

Then you could ask your questions like how fast is C traveling in A's rest frame and what time is on each clock in the different rest frames.

 

[Taragond]

You could have said:

3 synchronized clocks, one stays at A while two are sent with B at .6c away from A.
After one year according to B's time, C gets with one of those clocks on B in a lifeboat and heads at .9c away from B relative to B in direction of A.

Then you could ask your questions like how fast is C traveling in A's rest frame and what time is on each clock in the different rest frames.

well...that one!

I am really sorry for my lack of precision in my questions. Maybe it's because english is not my native language, maybe lack of experience in discussions on these matters. Probably a bit of both...

But what does happen if you remove the difference in rest-frames by decellerating before comparing the clocks?

 

[ghwellsjr]

You could have said:

3 synchronized clocks, one stays at A while two are sent with B at .6c away from A.
After one year according to B's time, C gets with one of those clocks on B in a lifeboat and heads at .9c away from B relative to B in direction of A.

Then you could ask your questions like how fast is C traveling in A's rest frame and what time is on each clock in the different rest frames.

well...that one!

Ok, I'm going to do it from the Inertial Reference Frame (IRF) of the B clock after it leaves the A clock at 0.6c because then I can simply specify the speed of the C clock after 1 year to be -0.9c according to the same IRF. I have made a spacetime diagram showing all the timings you asked about. Note that the dots mark off one-month intervals of Proper Time along each of the three clocks' worldlines. I have marked in some of the Proper Time values to help you determine the intervening ones. I have also annotated significant events along the way. Start at the bottom of the diagram and work your way up:

In the above diagram, there are three significant speeds:

1) All three clocks start out at -0.6c with synchronized clocks up until time zero. The A clock (blue) continues on an inertial path.

2) The B clock (red) along with the C clock accelerates to 0.6c with respect to the A clock so it comes to rest in the IRF that I am calling B's IRF (even though it is only B's IRF after time zero).

3) At B's Proper Time (which is also the Coordinate Time) of twelve months, C accelerates away from B at -0.9c toward A.

I have also annotated the Proper Times along each of the worldlines corresponding to the 1-, 2- and 3-year intervals of Coordinante Time as you requested.

Does that make perfect sense to you?

Now you were also interested in the speed of C relative to A. You had said that it would be 0.3c since C originally departed away form A at 0.6c and then returned at 0.9c. But a simple algebraic solution doesn't work. Instead, we can see the answer by using the Lorentz Transformation on the Coordinates of all the events (dots) in the original diagram to create a new diagram moving at -0.6c with respect to the first one. This now becomes the IRF in which the A clock (blue) is at rest:

We can see that the speed of the C clock (black) as it is approaching the A clock (blue) is about -0.65c. Do you know how to determine this speed from the diagram? We can also determine this speed exactly using the relativistic velocity addition formula with v=0.6 and u=-0.9:

s = (v + u)/(1 + vu) = (0.6-0.9)/(1 + (0.6)(-0.9)) = -0.3/(1-0.54) = -0.3/0.46 = -0.652

I have also marked in the Proper Times along each of the clocks' worldlines corresponding to the 1-, 2-, and 3-year intervals of Coordinate Times as per your request. Note that these Proper Times are completely different than those that were determined according to the first IRF.

Even though the Proper Times at which the Coordinate Times are different in the two IRF's, the Proper Times at which identifiable events occur along the worldlines are the same in both IRF's. For example in both diagrams:

1) the last Proper Times at which all three clocks are together is 0.

2) the Proper Times on clocks B (red) and C (black) when they separate is 12 months.

3) the Proper Times on clocks A (blue) and C (black) when they pass each other is 28.8 months for clock A and 22.46 for clock C.

I am really sorry for my lack of precision in my questions. Maybe it's because english is not my native language, maybe lack of experience in discussions on these matters. Probably a bit of both...

But what does happen if you remove the difference in rest-frames by decellerating before comparing the clocks?

Here's another example of lack of precision: are you wanting the C clock to decelerate to the same speed as the A clock when they reunite? But then what about the B clock? It just keeps on going away from the A clock. When do you want it to decelerate and to what speed in which IRF do you want this to happen?