How Can I Design an Experiment to Ensure Simultaneous Light Arrival?

[Ibix]

@AlMetis - you still seem to be confused between the difference between two frames' description of one experiment and two separate experiments. I thought Minkowski diagrams might help.

If we synchronise clocks in the platform's rest frame, we get the following Minkowski diagram:

This is drawn in the platform's rest frame. Three points on the platform are marked in red - each end and the middle. Th ends and middle of the train are also marked in blue. As the ends of the train pass the ends of the platform they emit yellow light pulses. You can see that the pulses meet at the middle red line (the middle of the platform), but cross the middle blue line (the middle of the train) at different times.

In this frame, then, we describe the experiment as the pulses being emitted simultaneously and arriving at the middle of the platform simultaneously, while the middle of the train moves towards one of the flashes and away from the other.

Now let's draw the same situation in the frame where the train is stationary:

This is the same experiment, but it's described in a different way. The ends of the platform do not pass the ends of the train simultaneously, so the flashes are not simultaneous. Thus they do not arrive at the middle of the train simultaneously. The train, on the other hand, is moving to the left in such a way that the earlier pulse catches up to it just as it rushes into the later pulse and the arrivals are simultaneous.

These two diagrams are diagrams of the same experiment. They are just different descriptions. It's much like you and I sitting on opposite sides of a table and watching an ant walk across it. I say the ant is moving right to left, you say it is moving left to right. We're talking about the same ant doing the same thing, just in different reference frames.

There is another experiment you can do. In this case, we synchronise the emission of the lights in the train's rest frame. The Minkowski diagram in the train's rest frame looks like this:

Note that the flashes can't be triggered when the ends of the platform pass the ends of the train because the train is longer than the platform in this frame.

With this synchronisation convention the pulses arrive at the (blue) train middle simultaneously, and separately at the (red) middle of the platform. We would explain this as being due to the platform moving left, so the pulse from the left has less distance to travel while the pulse on the right has more distance.

Once again we can draw this same experiment in another frame, in this case the platform's rest frame:

Using this frame we describe the pulses as being emitted at different times, so they arrive at the platform center at different times. However the train middle is moving to the right at just the right speed that the earlier pulse from behind it catches up with it just as it meets the later pulse from in front.

To recap, there are four diagrams of two experiments here. You seem mostly to have been talking about trying to do the first experiment, sometimes understood as the first diagram and sometimes as the second. However, it's not clear to me that you understand that the second experiment is different (albeit very similar).

 

[AlMetis]

My question should be more clear in the way I have phrased it in the next post to Ibix.

 

[AlMetis]

Dale, my question should be more clear in the way I have phrased it in the next post to Ibix.

 

[AlMetis]

You seem mostly to have been talking about trying to do the first experiment, sometimes understood as the first diagram and sometimes as the second. However, it's not clear to me that you understand that the second experiment is different (albeit very similar).

Thank you Ibix that all makes sense.

I am not confused about the difference between two descriptions of one experiment and the descriptions of two different experiments. But I have described two different experiments to point out what I am confused about.

If I use Einstein’s assumption that the flashes at A and B are simultaneous if/because the light from them arrive simultaneously at the midpoint between them, how do I construct a real version of his experiment.

I will use the laser tape method to find the distance from A to B is 2x.
I send a light signal to A and B that tells them to synchronize their clocks by setting them to t+x/c. (Where t=emission of the signal at the midpoint between A and B local time.)
I arrange to have them flash at a specific time.
The light from their flashes meet 6mm off center toward B.

What have I done wrong, how do I fix it?

 

[Dale]

Dale, my question should be more clear in the way I have phrased it in the next post to Ibix.

The question isn’t unclear. What is unclear is why you are still asking it. You already answered it for yourself with your very clear and thoughtful analysis. Now that you have the answer, and you worked so hard and carefully to get it, why are you still asking the question, and why have you gone back to sloppy descriptions?

What have I done wrong, how do I fix it?

You know what to do: describe everything carefully and in the same detail as previously. Which frame is the laser tape at rest in? Which frame are the flashes synchronized? Which frame measures the off center?