I got confused about SR after trying to reply to another

[learning]

So let us say that there are 3 separate alien species that somehow speak and write the same language. Let us say that 2 of these have always lived and died in their spaceships/asteriod ... going at speeds close to that of light.
Alien species 3. A3 leaves behind a message saying that at time t0 after passing this message observe the other alien races clock.
assumption1:
A1 and A2 observe themselves passing the message simultaneously.
than A1 would observe A2 moving away and so at t0 would observe that the clock of A2 was behind. A2 would also think the same of A1.
However if A1 is correct than when A2 observes A1, the clock of A1 should be ahead of t0. This is also true viceversa.
As such it could only be that the assumption was wrong. However if these Alien races knew special relativity than could they not calculate the correct time difference Tx? They would know that there was time dilation
t' = t*root(1 - (v/c)^2)
A1 could think:
so if A2 is tf at t0 then it should measure t0 + (t0 - tf)/(root(1 - (v/c)^2) ) instead of tf. Eventually A1 would be able to calculate Tx and A2 would calculate the same number for A1. If they measure again at the next t0 however than they would still have a paradox as otherwise, they should be able to figure out who was going faster which would break relativity. So I am confused as there seems to be an inconsistency either way.

 

[Ibix]

So, I think you have two ships passing each other that zero their clocks as they pass, and then at time $t_0$ they look at the other's clock?

Things you need to get into the habit of specifying when you think about relativity problems: who is measuring what? Do you mean that each ship, when its own clock reads $t_0$ should check the other's clock? Or is it one ship's clock that does the specifying? Second, do you actually mean "what does each ship see on the other's clock", or do you expect them to correct for the travel time of light?

I'm guessing you meant for each ship to check the other's clock when its own reads $t_0$. Both ships will agree that what they directly see on the other's clock is some time before $t_0$, because they are aware of the finite speed of light and know their information is out of date. If they correct for the travel time they will still agree that the other's clock show some time before $t_0$. If this seems paradoxical to you, you should probably Google for "relativity of simultaneity". The point is that what one ship calls "at the same time as my clock reads $t_0$" is not the same slice of spacetime as what the other ship calls "at the same time as my clock reads $t_0$".

In summary, time dilation is not the whole story. I'd say it's not even the important part of the story. The important part is the relativity of simultaneity - the idea that "at the same time" is just as frame-dependent as "in the same place" is.

 

[learning]

So, I think you have two ships passing each other that zero their clocks as they pass, and then at time $t_0$ they look at the other's clock?

Things you need to get into the habit of specifying when you think about relativity problems: who is measuring what? Do you mean that each ship, when its own clock reads $t_0$ should check the other's clock? Or is it one ship's clock that does the specifying? Second, do you actually mean "what does each ship see on the other's clock", or do you expect them to correct for the travel time of light?

I'm guessing you meant for each ship to check the other's clock when its own reads $t_0$. Both ships will agree that what they directly see on the other's clock is some time before $t_0$, because they are aware of the finite speed of light and know their information is out of date. If they correct for the travel time they will still agree that the other's clock show some time before $t_0$. If this seems paradoxical to you, you should probably Google for "relativity of simultaneity". The point is that what one ship calls "at the same time as my clock reads $t_0$" is not the same slice of spacetime as what the other ship calls "at the same time as my clock reads $t_0$".

In summary, time dilation is not the whole story. I'd say it's not even the important part of the story. The important part is the relativity of simultaneity - the idea that "at the same time" is just as frame-dependent as "in the same place" is.

Oh thank you. I can see how things of this nature need very specific details.

So what I mean is:
The ship's after their own clock measures t0. Check the other ship's clock.
So for A1:
When A1 sees that the clock on his ship is t0. He observes the clock on A2.
A1 knows the time it would take for light to reach it from A2 and includes that in his calculation to calculate the time that the clock in A2 is really at.
After which A1 uses his understanding of special relativity to calculate what A2 should see when A2 observes A1's clock. A1 than uses this to calculate the initial difference in the time of synchronization. Accounting for this difference A1 again checks the time of A2's clock at 2*t0. If it was as he expected it to be or if he could use any information to truly calculate the difference in time of synchronization then he would be able to tell who is moving or not. Which is in my understanding against relativity. If he couldn't do it however than there would be the paradox of A1's version of reality requiring A2 to measure A1's clock to be ahead of t0 and A2 is not doing that. As the same is true for A2. Both versions are not true.

 

[Ibix]

So what I mean is:
The ship's after their own clock measures t0. Check the other ship's clock.
So for A1:
When A1 sees that the clock on his ship is t0. He observes the clock on A2.
A1 knows the time it would take for light to reach it from A2 and includes that in his calculation to calculate the time that the clock in A2 is really at.

There is no "really" here. That's the point. Different frames will have different opinions on what time it is "now" at some other location. You can subtract out the light travel time using a chosen frame's definition of distance and get the time the clock shows now according to that frame. Or you can use a different frame's definition of distance and get a different answer.

After which A1 uses his understanding of special relativity to calculate what A2 should see when A2 observes A1's clock. A1 than uses this to calculate the initial difference in the time of synchronization. Accounting for this difference A1 again checks the time of A2's clock at 2*t0. If it was as he expected it to be or if he could use any information to truly calculate the difference in time of synchronization then he would be able to tell who is moving or not. Which is in my understanding against relativity. If he couldn't do it however than there would be the paradox of A1's version of reality requiring A2 to measure A1's clock to be ahead of t0 and A2 is not doing that. As the same is true for A2. Both versions are not true.

I have no idea what calculations you think you are doing here. The relevant ones are the Lorentz transforms, and they will produce a consistent result. In this case, since both ships are doing the same thing, both ships will run through the same calculation and get the same result (the other's clock reads $t_0/\gamma$) because both can consider themselves at rest and the other to be moving.

 

[learning]

There is no "really" here. That's the point. Different frames will have different opinions on what time it is "now" at some other location. You can subtract out the light travel time using a chosen frame's definition of distance and get the time the clock shows now according to that frame. Or you can use a different frame's definition of distance and get a different answer.
I have no idea what calculations you think you are doing here. The relevant ones are the Lorentz transforms, and they will produce a consistent result. In this case, since both ships are doing the same thing, both ships will run through the same calculation and get the same result (the other's clock reads $t_0/\gamma$) because both can consider themselves at rest and the other to be moving.

Thank you. I figured it out. They will be able to calculate the difference in times that they set the clock to 0. However each will believe themselves to be the faster. Using the synchronization difference make it so that in their world view the other measures them to be at the time that they do actually measure them at.