Distance role in simultaneity measurement

[phyti]

George;
How do you explain the longevity of these observers?

 

[ghwellsjr]

George;
How do you explain the longevity of these observers?

Lorentz Transformation.

 

[FactChecker]

My statements don't disagree with the lattice of clocks

Then why is there an argument? If your results and conclusions are identical, what is your complaint?

The red flag is if someone claims that there must be a lattice of real clocks

Who said these are real? The space travelers are not real and the clocks are not real.

 

[ghwellsjr]

My statements don't disagree with the lattice of clocks

Then why is there an argument? If your results and conclusions are identical, what is your complaint?

Because the lattice of clocks is another way of saying a specific coordinate chart. The OP asked about two separated observers moving at the same speed toward Andromeda. They don't need to be using the same coordinate chart even though they are at rest in the same Inertial Reference Frame. This is what DaleSpam pointed out in his usual inimitable and definitive way in post #2 and in post #11, that they don't have to be using the same inertial coordinate chart, in other words, they do not have to have synchronized clocks or applying the same lattice of clocks. Your first statement was:

The travelers at the same rate all agree on what happened, where, and when.

But this would only be true if they were using the same inertial coordinate chart which means the same imaginary lattice of clocks. And the OP didn't ask about the two travelers agreeing on where or even when things at Andromeda happened, he only wanted to know about how two traveling observers at different distances would measure simultaneity. This does not require them to be at rest in the same inertial coordinate chart or agree on distances or times or have synchronized clocks, only that they will agree on the same set of events being simultaneous. And that's what I proceeded to demonstrate in my post #15.

The red flag is if someone claims that there must be a lattice of real clocks

Who said these are real? The space travelers are not real and the clocks are not real.

It sure sounded like that's what you meant when you said:

If we are studying "simultanious" events at a distance, the first thing we should do is Einstein-synchronize all clocks in our inertial reference frame.

But I'm glad everyone now agrees that that is not necessary.

 

[ghwellsjr]

...In my previous diagrams in post #12, I picked up the scenario in the Earth/Andromeda rest frame when the black traveler left Earth and I defined that event as the origin of both diagrams. I also assumed that the Proper Times on all three of those clocks was set to the Coordinate Time and I pointed out that the Proper Time on the green traveler was not set to the Coordinate Time of that IRF but rather to the Coordinate Time of the mutual rest frame of both travelers. However, I didn't say how that was done and as a matter of fact, as is often done in scenarios like this, we don't concern ourselves with how clocks get synchronized but there is a required process that must be performed to actually make it happen.

Now I'm going to show how the green traveler can synchronize his clock to the black traveler's clock so that they can both use the same coordinate chart to determine the distances to the event of the exploding star on Andromeda.

NOTE: I just realized that I neglected to add the "million multiplier" to all the units in my comments in post #33. Consider it done.

We start with the second diagram shown in post #15:

The green observer is continually sending radar signals to the black observer and watching for their echoes as well as watching the black observer. As soon as he sees the black observer launch from Earth, he notes the time the corresponding echo was received (1.1 million years) and when it was sent (-0.9 million years). He takes the difference in those two times (1.1+0.9 = 2.0) and divides by 2 (2/2 = 1.0 million years) and establishes how far light travels in that amount of time (1 million light-years). He takes the average of the sent and received times (0.1 million years) and determines that he should set his clock so that it would have read the same as black's clock at that time. Since he has just determined that he is 1 million light-years from black when black's clock was at 0, then he changes his clock from 1.1 million years to 1.0 million years as shown in this diagram:

The green observer also adopts the black observer's position as being at zero, making his own be at 1 million light-years. The green observer continues to send and receive radar signals. Eventually, he sees the star explode at Andromeda and determines that it occurred at the Coordinate Time of 2 million years and at a Coordinate Location of 2 million light-years, just as the black observer determined in post #15.

 

[phyti]

If we are studying "simultanious" events at a distance, the first thing we should do is Einstein-synchronize all clocks in our inertial reference frame.

This is something that would already be in place, like time zones, for practical reasons.
A remote event anywhere beyond the local inertial frame occurs independently of local events (unless you are pinging an object there with em signals).
A clock at the remote event will with a high probability be running at a rate different from the local clock, and therefore its time will be meaningless. All you get are two local time values for emission and detection of the returning signal. Using the SR simultaneous convention, you assign the remote event cordinates (ct, t). You declare the remote event to be simultaneous with t. This is physics by decree. You in fact do not know precisely where or when the event occured.

 

[WannabeNewton]

You declare the remote event to be simultaneous with t.

For the umpteenth time, this is equivalent to Einstein clock synchronization. There is no difference mathematically or conceptually between Einstein simultaneity and Einstein synchronization for inertial observers at rest with respect to one another. Only operationally do the two differ. Also, we're obviously talking about ideal clocks here. The only way for two ideal clocks at rest with respect to one another to tick at different rates is for the clocks to be non-inertial whereas we're discussing ideal inertial clocks at rest with respect to one another-in this case as already stated Einstein synchronization $\Leftrightarrow$ Einstein simultaneity trivially. It's almost a tautology.

 

[phyti]

For the umpteenth time, this is equivalent to Einstein clock synchronization. There is no difference mathematically or conceptually between Einstein simultaneity and Einstein synchronization for inertial observers at rest with respect to one another. Only operationally do the two differ. Also, we're obviously talking about ideal clocks here.

I'm not saying there is a difference.

The only way for two ideal clocks at rest with respect to one another to tick at different rates is for the clocks to be non-inertial whereas we're discussing ideal inertial clocks at rest with respect to one another-in this case as already stated Einstein synchron ization $\Leftrightarrow$ Einstein simultaneity trivially. It's almost a tautology.

If the remote ideal clock was in synch, it wouldn't remain so after a year of Earth orbit, so what's the point?

I'm just emphasizing/reminding the poster that simultaneity is analyzed using a convention based
on definitions and not physical facts that are not available.
How much significance is simultaneity worth?