Distance role in simultaneity measurement

[FactChecker]

Unfortunately you're mixing up all these different frames and it's only making things more hectic than they need to be. If you have two Einstein synchronized clocks at rest in an IRF and you Born rigidly accelerate them along the line separating them so that they remain at rest relative to one another then they will immediately become desynchronized as explained earlier by Peter. If you impart to the initially synchronized clocks the same proper acceleration along the line separating them then they will not be at rest relative to one another but rather will have a relative radial velocity so they will still become desynchronized except now it's because of kinematical time dilation.

Born rigid acceleration is interesting, and what I was visualizing without questioning it. So you are saying that a Born rigidly accelerating frame can see its clocks getting out of Einstein-synchronization. Sad. Nothing is simple. I see that there is no substitute for adopting better tools to analyse these things.

 

[WannabeNewton]

So you are saying that a Born rigidly accelerating frame can see its clocks getting out of Einstein-synchronization. Sad. Nothing is simple.

Well it's not so much of an issue in the case of Born rigid linear acceleration. So as long as we are willing to use non-ideal clocks, we can synchronize all the clocks permanently by using point-wise Einstein synchronization and build a global Einstein time for the Born rigidly accelerating frame. The real problem is when we considering Born rigid rotating frames. Here there is a fundamental obstruction preventing the use of point-wise Einstein synchronization to build a global Einstein time for the rotating frame i.e. one cannot achieve global synchronization by using point-wise Einstein synchronization when considering a family of corotating clocks, regardless of whether we use ideal or non-ideal clocks.

I see that there is no substitute for adopting better tools to analyse these things.

Thankfully the tools aren't sophisticated by any means, you could easily acquire them by working through standard textbooks like MTW.

 

[ghwellsjr]

But there doesn't need to be a clock at the distant event in order for the observer (who, of course, must have a clock) to establish such simultaneity. If that were true, then there is no point in discussing simultaneity at large distances where no clock has ever been such as at Andromeda and especially not one that is at rest with the two observers moving toward Andromeda.

You do realize in physics we work with theoretical constructions right? We don't actually hire a person to go out into space and place a clock at each point. Sorry but this isn't a rebuttal it's just a poor cop out.

Sorry but you were the one that said:

An inertial observer deems a distant event $q$ [a star exploding on Andromeda] to be simultaneous with an event $p$ [a reading on his clock] in his vicinity if and only if a clock in the vicinity of $q$ [a star exploding on Andromeda] synchronized with the observer's clock reads the same time as the observer's clock at $p$. Using this prescription the inertial observer can build a global time coordinate and from it a global inertial frame.

We don't want to associate Coordinate Time (the basis of simultaneity) with a bunch of clocks pervading the universe.

Obviously it's imaginary. But how else do you think coordinate time relative to an IRF is defined? It doesn't just pop up out of the blue. We construct it from first principles using synchronized clocks. Both global distance functions and global time functions relative to an IRF are constructed operationally using synchronized clocks, radar sets, and a theodolite.

You don't have to use those first principles with multiple synchronized clocks and multiple radar sets--a single inertial observer can do it all with just his one clock (synchronized to nothing else), his one radar set and his one theodolite.

EDIT: I would really recommend reading "Relativity and Geometry"-Torretti. Foundations are important, especially if one wants to avoid semantics based arguments such as this.

If you think this is just a semantics issue then you need to clarify the terms in dispute. I would rather show you how the two observers approaching Andromeda can establish the simultaneous events without any synchronized clocks.

I start with the last diagram from post #15 but I have changed the radar signals to focus in on just the ones sent out by the green observer. Keep in mind that he is continually sending out radar signals in both directions and receiving their echoes along with the images of the other objects/observers but I'm only showing the significant ones. Note that there are no synchronized clocks:

To recap what the green observer does after the scenario is over, he first looks in his log of radar sent/received times and observations of Andromeda that he saw a star explode on Andromeda at his time of 3.1 years and the radar echo that he received simultaneous with that observation was from a radar signal that was sent at 1.1 years. He averages these two numbers and establishes that the event of the star exploding was simultaneous with the event of his clock reading 2.1 years.

Then he looks in his log for the sent/received radar information related to the black observer that also averages to 2.1 years and he finds a signal that was also sent at 1.1 years and received at 3.1 years along with the image of the black's clock reading 2 years and so he establishes that the event of the black's clock reading 2 years was simultaneous with the first two simultaneous events.

Finally, he does the same thing for the Earth data and establishes the event of the Earth's clock reading 1.96 years as simultaneous with the previous three simultaneous events.

So there we have it, green established four events as being simultaneous in the Inertial Reference Frame (IRF) in which he is at rest, using his own clock as the coordinate time, even though there were no other synchronized clocks.

Now I want to repeat the whole process but this time focusing on the black observer who is also racing toward Andromeda. He is at rest in the same IRF as the green observer but since their clocks are not synchronized, he will use his clock for the coordinate time of the IRF:

He observes the star on Andromeda exploding at his time of 4 years which corresponds to a radar signal sent at 0 years so he establishes his time of 2 years as being simultaneous with the event of the star exploding. He also establishes the simultaneous events on Earth as 1.96 years and the green observer as 2.1 years.

If you compare the events that the green observer established as being simultaneous in his rest IRF with the star exploding to the events that the black observer established as being simultaneous in his IRF with the star exploding, you see that they are identical, even though they used different time coordinates based on their own unsynchronized clocks.

Next I want to show the same measurements in the mutual rest frame of the Earth/Andromeda IRF. We start with the green observer's measurements:

All of green's measurements and observations and establishments are the same as they were in his rest IRF.

And here is the same IRF showing black's measurements:

All of black's measurements and observations and establishments are the same as they were in his rest IRF.

 

[WannabeNewton]

If you think this is just a semantics issue then you need to clarify the terms in dispute. I would rather show you how the two observers approaching Andromeda can establish the simultaneous events without any synchronized clocks.

George, I feel like we're speaking past each other. I'm not disagreeing with anything you're saying; yes I agree that you don't need synchronized clocks and as always your diagrams are crystal clear in driving home the operational use of radar simultaneity. However what I am saying is that using light signals to establish simultaneity is equivalent to using light signals to synchronize distant clocks so saying they have nothing to do with each other antagonizes that equivalence, that's all; here and elsewhere the "lattice" of synchronized clocks are all conceptual. But whatever you start with, be it synchronized clocks or simultaneity, you need one or the other as a starting point before being able to construct a global time coordinate relative to an IRF (and more general frames as well)-this part still holds true. In other words the concept of a global time coordinate relative to an IRF depends on the establishment relative to the IRF of operational clock synchronization or the equivalent notion of operational simultaneity. This is all with regards to inertial observers of course. As soon as we talk about non-inertial observers the equivalence between clock synchronization and radar simultaneity is broken naturally.

 

[TrickyDicky]

I would really recommend reading "Relativity and Geometry"-Torretti. Foundations are important, especially if one wants to avoid semantics based arguments such as this.

WBN recommending a philosophy book by a notorious philosopher. Shame, shame.

 

[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 occurred.

 

[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?