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

[Dale]

I am concerned about a fixed pattern on a ground

Then I would recommend modifying your chart to say "no fixed pattern" (which is correct) rather than just "no pattern" (which may not be correct).

 

[Dale]

I don't understand step 2 and 4. What I understood were step 1 and 3. Doppler effect occurs at the receiver who is moving relative to a source. In step 2, you mentioned that the slits receives the light red shifted relative to the external observer, does the external observer emitts any thing? In step 4 the screen is at rest relative to the external observer, so there is no relative velocity plus no emission of lights from the external observer!

No, the external observer is just the hypothetical observer who measures the frequency of each light pulse in the given reference frame. He never emits anything, and he samples everything without interrupting it. Here are the Doppler related questions:

What is the frequency of:
1) the light from source to A according to the source?
2) the light from source to A according to the frame?
3) the light from source to A according to A?
4) the light from A to ground according to A?
5) the light from A to ground according to the frame?
6) the light from A to ground according to the ground?

 

[Adel Makram]

No, the external observer is just the hypothetical observer who measures the frequency of each light pulse in the given reference frame. He never emits anything, and he samples everything without interrupting it. Here are the Doppler related questions:

What is the frequency of:
1) the light from source to A according to the source?
2) the light from source to A according to the frame?
3) the light from source to A according to A?
4) the light from A to ground according to A?
5) the light from A to ground according to the frame?
6) the light from A to ground according to the ground?

1) no shift because A and the source are at rest relative to each other
3) no shift either
4) red shifted
6) red shifted

I don't understand what do you mean by frame?

 

[Dale]

Reference frame is short hand for the inertial coordinate system associated with some object or observer.

 

[Adel Makram]

Reference frame is short hand for the inertial coordinate system associated with some object or observer.

I know the meaning of the word in physics but I don't know which frame you mean, the train or the ground ?

 

[Dale]

The frame that the drawing in post 16 represents. I don't know how you want to name that frame. I guess it is probably the ground frame.

 

[Dale]

BTW, here is how I would answer those questions I posed above

What is the frequency of:
1) the light from source to A according to the source? =F
2) the light from source to A according to the frame? >F
3) the light from source to A according to A? =F
4) the light from A to ground according to A? =F
5) the light from A to ground according to the frame? <F
6) the light from A to ground according to the ground? <F

 

[Adel Makram]

BTW, here is how I would answer those questions I posed above

What is the frequency of:
1) the light from source to A according to the source? =F
2) the light from source to A according to the frame? >F
3) the light from source to A according to A? =F
4) the light from A to ground according to A? =F
5) the light from A to ground according to the frame? <F
6) the light from A to ground according to the ground? <F

The frequency (f) from the source to a hypothetical external observer >f and from that observer to A < f so they canceled each other out. What remains is only from A to the screen according to the screen which is <f. This is the same as my first suggestion that the effective Doppler shifts is only from slits. So any way, we have now light from A <f and light from B>f, and they are traveling the same paths to the a mid-screen point ( concern about a fixed pattern). This makes the formation of a pattern not possible.

That would be the same conclusion according to the train observer. He sees different paths from A and B, with the same f from A and B, to a point on the screen which makes the pattern not possible ( i don`t think that Doppler effect at the screen relative to the screen will affect the case because the light rays have already reached it and interacted, so the different in D-shifts at the point of screen will not count!)

 

[Adel Makram]

Let`s modify the experiment according to the last suggestion ( which is: no pattern will form)
Think of 2 trains moving in the opposite directions toward each other. That will be our train with velocity v to the right direction and another one with -v to the left direction. The first train has slits; A and B and the second one has; C and D as shown in the diagram. Their mid-points will coincide at a corresponding point in a ground screen when rays leaving slits ( we can make them very thin trains with slits from them at 2 sides are so closed together)
This will make the D-shift from A matchs that from C and B with D,,, ultimately the pattern will form! ( the color of lines in the diagram indicates the Doppler shift)
If so:
1) will the 2 trains move in opposite directions With their sources moving altogether is equivalent to the classical pattern where There is only one fixed source relative to the ground and nothing moving?
2) According to QM, there would be no pattern if more than 2 slits are there and we got 4 slits now! ( forget this point for a while as the number of slits should be in one direction)
https://www.physicsforums.com/attachment.php?attachmentid=46357&stc=1&d=1334750489

 

[Dale]

The frequency (f) from the source to a hypothetical external observer >f and from that observer to A < f so they canceled each other out. What remains is only from A to the screen according to the screen which is <f. This is the same as my first suggestion that the effective Doppler shifts is only from slits. So any way, we have now light from A <f and light from B>f, and they are traveling the same paths to the a mid-screen point ( concern about a fixed pattern). This makes the formation of a fixed pattern not possible.

Yes. Note the clarification I added here and below.

That would be the same conclusion according to the train observer. He sees different paths from A and B, with the same f from A and B, to a point on the screen which makes the fixed pattern not possible ( i don`t think that Doppler effect at the screen relative to the screen will affect the case because the light rays have already reached it and interacted, so the different in D-shifts at the point of screen will not count!)

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.

 

[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.