How can we explain the behavior of interference patterns in different frames?

[Adel Makram]

This is incorrect. For the train observer there is a fixed pattern that the ground is moving under. Obviously a pattern which is fixed relative to the train observer is not fixed relative to the ground observer. You cannot use the non-existence of a fixed pattern in one frame to show the non-existence of a fixed pattern in another frame since the property of being fixed or not is frame variant.

Fixed is fixed to the ground. What i meant by fixed is the isocenter of the pattern corresponds to a mid-point of the train at the time rays exiting slits relative to the ground observer. So I am not interested in a pattern that spread across a long distance in the direction of the train

 

[Dale]

Fixed is fixed to the ground. What i meant by fixed is the isocenter of the pattern corresponds to a mid-point of the train at the time rays exiting slits relative to the ground observer. So I am not interested in a pattern that spread across a long distance in the direction of the train

You need to learn to be more clear, talking with you is an exercise in frustration.

OK, there is no fixed pattern in either frame, using your meaning of fixed. There is, however, an interference pattern in both frames. In one frame the pattern is stationary and the ground is moving, in the other frame the ground is stationary and the pattern is moving. The pattern is there whether or not you are interested in it.

 

[Dale]

Let`s modify the experiment according to the last suggestion

I am not interested in analyzing new experiments for you. You have been given enough input and instruction that it is now time for you to take responsibility for your own analysis. If you get stuck at some point then please post your work up to that point, and if you want me to check your work I will be glad to. Once you gain some skill in working these problems then you will be able to answer many of your own questions, and hopefully those of other people.

However, you need to know one thing in advance. The behavior of interference patterns are completely governed by Maxwell's equations, and Maxwell's equations are invariant under the Lorentz transform. Therefore, you will never find a situation where interference in one frame is not interference in another frame.