Is Relative Simultaneity Real?

[ghwellsjr]

Also, simultaneity is not an appearance. You cannot determine simultaneity of distant events simply by observing. That's one of the things I tried to point out in my previous post: No matter what frame you use to depict a scenario, all appearances remain the same even though the simultaneity of distant events has changed enormously.

Consider my last two diagrams: the order of the two colocations is different but nobody can tell, can they, just by looking? And in the first two diagrams where the two events are simultaneous in the rest frame of the platform but not in the rest frame of the train, observers on the platform or on the train still cannot determine the simultaneity of those two events. Everything appears identically to each of them no matter what frame we use to describe the scenario.

When you get a chance, please study those diagram, they could help you get over some of your misconceptions.

EDIT: I guess I'm going to have to make some more diagrams showing how observers on the platform or on the train can establish simultaneity in their own rest frames.

Remember, we are taking darkhorror's scenario from post #18:

How about look at it simply, take 4 clocks, 2 in a stationary FOR, 2 in a moving FOR. Let's put these clocks on a train and a platform. One on left side of train one on right, one on left side of platform, one on right. In the platform's FOR, the train and the platform are the same length, the clock distance is also the same. So in the platform's FOR when the left two clocks are at the same point, the right two clocks are also at the same point.
...
So if the left clocks read 0 when they line up, and the right clocks also read 0 when they align. In the train's frame of reference when the left clocks both read 0, the right clocks can't also read 0 since they aren't aligned.

I already drew two diagrams in post #47, the first one for the rest frame of the platform where each pair of clocks are colocated and display their Proper Times of zero at the Coordinate Time of zero:

...and the second one transformed to the rest frame of train where none of the colocated clocks displaying Proper Times of zero are aligned with the Coordinate Time of zero:

Now I want to pick up in the rest frame of the train where I will drawn in outgoing radar signals from the Red and Black observers at either end of the train and the reflections off of a couple objects to show how they can establish which remote events are simultaneous to the events of the Proper Times on their own clocks.

It's important to realize that an observer is constantly and continually sending out radar signals but we don't want to draw every one of them in our diagrams because it would be far too cluttered. Instead, I'm just going to draw in a few that will illustrate how the observer establishes simultaneity of distant events to events at his own local clock. The observer has to wait for the radar signals coded with his sent time to bounce off an object and return an echo signal, along with an image of the object identifying a specific event. In our case, we will use the Proper Time on a particular remote clock. Please realize that we are not concerned with the actual Proper Time on the remote clock, only with the fact that it identifies separate events at the location of the remote clock. When the observer receives an echo along with the image of the remote event, he logs the coded sent time, the received time and the time he sees on the remote clock. After he collects a lot of data, he goes back and looks at his logs, makes an assumption based on Einstein's second postulate and does some calculations to establish the simultaneous events. Hopefully, this will make sense as we work through the examples.

We'll start with the Red observer at the rear of the train sending radar signals to the Blue clock at the left end of the platform:

Even though the first radar signal he sent out was at his Proper Time of -14 nsec, he doesn't detect the echo until his Proper Time of -3.5 nsec. Here is his log of the data going from his Proper Time of -3.5 nsec to his Proper Time of -1 nsec:

Sent	Rcvd	Blue's
Time	Time	Time
-14	-3.5	-7
-12	-3	-6
-10	-2.5	-5
-8	-2	-4
-6	-1.5	-3
-4	-1	-2

His next step is to average the Sent Time and the Received Time and make a new column which identifies the established time of the measurement. This process is applying Einstein's convention that the radar signal takes the same amount of time to get to a target as the echo signal takes to get back. So here is a new table with Red's Time added that he established for each radar sent/received signal:

Sent	Rcvd	Blue's	Red's
Time	Time	Time	Time
-14	-3.5	-7	-8.75
-12	-3	-6	-7.5
-10	-2.5	-5	-6.25
-8	-2	-4	-5
-6	-1.5	-3	-3.75
-4	-1	-2	-2.5

Now he's got a list of simultaneous events according to his established rest frame in the last two columns. For example, the event of his own clock displaying -8.75 is simultaneous with the event of Blue's clock displaying -7. And if you look at the above diagram, you can see that they both have the Coordinate Time of -5.75 nsecs in the train's rest frame. But note that the Red observer has no awareness of the Coordinate Time, he is basing this on his own Proper Time.

OK, does this all make sense? Now let's show another diagram where the Red observer is sending radar signals to the Black clock at the front end of the train. You should be aware that he is sending both sets of signals at the same time (the ones shown in the previous diagram and this one) but we're just showing them on two separate diagrams to avoid clutter:

And here is his completed list including his calculated average for his established time of the measurements:

Sent	Rcvd	Black's	Red's
Time	Time	Time	Time
-16	4	0	-6
-15	5	1	-5
-14	6	2	-4
-13	7	3	-3
-12	8	4	-2

Now what the Red observer can do is look in both lists and find examples where a time in the last column from one list matches the time in the last column of the other list and that will allow him to identify two remote events for different objects that are simultaneous. Keep in mind that in a real situation, his list would be vastly longer and include matches for every row but in our very sparse example, we can identify one example where the Red's Time of -5 is simultaneous with Blue's Time of -4 and Black's Time of 1.

Now we can combine the important signals from the above two diagrams and show how the Red observer establishes the simultaneity of those three events:

As a side note, we can also show how the Red observer establishes that Black's Time of zero is not simultaneous with his own time of zero because that remote event occurred at his time of -6 based on the information from the previous list.

Next I want to illustrate a very important characteristic of simultaneous events: all inertial observers at rest with each other will establish the same set of simultaneous events no matter how their individual clocks are set (or even if their own clocks tick at different rates, which I will not show). In other words, simultaneity, as established by an observer, has nothing to do with the synchronization of clocks or even with the existence of any clocks beyond his own individual clock.

I'm going to now do a similar thing with the Black observer to show the radar measurements he makes to establish the same set of simultaneous events that the Red observer established since they are mutually at rest. We start with the same rest frame of the train but with radar signals emitted by the Black observer to reflect off the Red clock:

And here is his list:

Sent	Rcvd	Red's	Black's
Time	Time	Time	Time
-10	10	-6	0
-9	11	-5	1
-8	12	-4	2
-7	13	-3	3
-6	14	-2	4

Another diagram showing the Black observer's signals bouncing off the Blue clock:

And the corresponding list:

Sent	Rcvd	Blue's	Black's
Time	Time	Time	Time
-8	0	-8	-4
-7	4	-6	-1.5
-6	8	-4	1
-5	12	-2	3.5

By comparing both lists, we see that Black's Time of 1 is simultaneous with Red's Time of -5 and Blue's Time of -4, the same as Red established.

And here is a diagram showing just the significant radar signals the Black sends and receives:

I hope this shows in a clear and understandable way how simultaneity is established by an inertial observer and that it takes far more than simply observations. It takes sending and receiving radar signals, logging their times, the assumption of Einstein's second postulate when calculating average times and the comparison of results.