The trigger is when the front or mid of the train hits some position. In this location,delays in the triggering mechanism will cause the train midpoint to align exactly with the station when the flashes occur in train frame of reference.
??
I thought the trigger was to be the timers or sidetrack arms…?
Either way there are two triggers, one for each flasher.
I already said that two triggers won’t work because you can’t align front and rear simultaneously in station and train frames.
The midpoint of station and train can be aligned at least theoretically.
Oh. I misunderstood what you meant.
The timers are in sync and the distance Xs is identical on both sides of the center clock, for both perspectives. How can they not be centered from both perspectives?
Actually at this point, we can state the paradox in another way;
Assuming that the station clock does not stop;
Thought A
The station knows that the timers were put in sync
And that nothing happened to get them out of sync
Therefore, they are still in sync.
Thought B
The station perceives them out of sync
Therefore the station knows that they are out of sync.
The paradox is that thought A denies thought B and B denies A.
Assuming that the train clock does not stop;
Thought A
The train perceives them out of sync,
Therefore they are out of sync
Thought B
The train knows that the timers were put in sync
And that nothing happened to get them out of sync
Therefore, they are still in sync.
Again, the paradox is that thought A denies thought B and B denies A.
You can measure out Xs in both frames, but so what. They don’t match across frames of reference.
In the station frame, you can’t trigger both front and rear because the front and rear of the train don’t cross +Xs and -Xs at the same time.
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They don’t have to. The clocks must merely be centered between the timers. It doesn’t matter if Xs is different for each frame.
The timers don’t care about Xs.
So now you only have timers? No +Xs and-Xs triggers?
The logic will work out the same either way.
I stated it for the timers, but the same is true for the Xs distance.
Assuming that the station clock does not stop;
Thought A
The station knows that the acceleration was identical
And that nothing happened to change the distance Xs
Therefore, Xs is still the same.
Thought B
The station perceives Xs as different.
Therefore the station knows Xs is different.
The paradox is that thought A denies thought B and B denies A.
Assuming that the train clock does not stop;
Thought A
The train perceives Xs as different
Therefore Xs is different.
Thought B
The train knows that the acceleration was identical
And that nothing happened to change Xs
Therefore, Xs is the same.
Again, the paradox is that thought A denies thought B and B denies A.
If you only have timers and you calculated the precise time to set off the flashes in the train such that the midpoints of train and station line up … the station will still detect the flashes at different times.
We have already stated that… several times.
Remember it doesn’t matter if the flashers are moving with the train or moving with the station. They both trigger at “Tf” even if Tf is different between the station and the train (exactly like Xs). If I had said that the timers were affixed to the track and also the train had the arms to trigger the flashers, your mind would feel more certain that it is the train clock that would perceive the flashes at different times. But the logic would really be the same although reversed;
That’s because you keep saying the same thing over and over again. I figure that’s how you want to communicate. In fact, you repeated the same Thought A and Thought B several times. :-"
Of course it matters. 
Finally you are getting it. The flashes are simultaneous in the frame where they are created. Progress. ( expect for the plural ‘arms to trigger’ which suggest that you can force simultaneity in another frame)
You seem to be conveniently leaving out a Thought;
I’m not leaving it out without good reasons.
SR doesn’t handle accelerating frames. Who knows what happening there, but it doesn’t seem to matter because when acceleration stops there will be specific distances between clocks.
Xs looks shrunk to both observers looking at the other object. IOW it’s not the same.
Thought A therefore does not carry much weight.
You conveniently ignore length compression and the complications that it produces.
You think acceleration is Newtonian.
SR doesn’t need to “handle accelerating frames”. All it has to handle (and it definitely must handle) is the fact that equal treatment was given to equal entities and thus equal results are mandated. If SR didn’t accept that, then ALL SR equations would be totally pointless, along with all other scientific thought.
Note that the scenario does not require numbers, merely concepts. And the concept that it most certainly must maintain is that when the same treatment is given to two identical entities, the result will be the same for each. Without that, no prediction is possible at all, with or without relativity. Each application of an equation or theory is another incident of the “identical treatment of an identical entity to yield an identical result”.
Thought A is MORE fundamental than thought B, and cannot be denied without making thought B completely pointless to conclude.
It does yield identical results… simultaneous events in one frame are not simultaneous in the other. Accelerations will match for the center of each mass.
Show me how you get unsimultaneous results in either frame by treating each engine identically?
How does either Xs or Tf get altered between two identical flashers being treated identically?
You don’t have to use acceleration equations. Use any equation, as long as you apply it to both entities.
You just said that the scenario does not require numbers. And we have been giving you arguments for 6 pages now.
Okay, you have this theory. So now you can show us that your calculations place the front, rear and midpoint of the trains in proper simultaneous alignment when the flashes occur. Once you do that , you can proceed to show that your calculation match experimental results.
Need help getting started?
In the station frame you have a distance Xs. It matches the length of the train which you allowed to stretch so that the station sees a compressed length of Xs. Easy.
Now in the train, there is an elongated distance of Xstretched between front and rear. When the train passes the station, it sees the markers for Xs but they are compressed so that they look like Xshortened. Therefore, when the midpoint of train and station line up, the Xs markers are not at the position of the front and rear of the train.
Explain and show your work.
What’s the problem? When the front of the train reaches the Xs marker, the mid and rear don’t line up with the mid of the station of the rear Xs marker. They will individually line up at other times.
You have not been giving me arguments. You have been making an assertion, with no argument other than "The Holy Physble says…" I have explained in two ways how what you assert cannot be true. And in reality, your Holy Physble doesn’t really say any different, but you think it does, so I am not going to argue with what you believe your holy documents to be saying (I tried arguing Physble interpretations with Carleas and it took some 800 posts before he merely saw that he had to be wrong even though he still couldn’t see what was right).
No. YOU have a theory. I gave an explanation that did not involve any theory at all, but rather simple step by step logic.
I can’t argue with an equation that you think you have if you don’t show me the equation that you are using to come to the conclusion that you are asserting.
And that is not what I proposed.
I have three engines separated by distance Xs.
I need to know what makes you think that distance shrank.
I gave you the reasons why it could not have.
That isn’t a “theory”. It is simple logic.
So with which of those 3 steps do you disagree; a, b, or c?
The speed of light won’t be measured as a constant unless a moving object contracts in the direction of motion.
I thought you might have heard about it and that it was not in question.