Interference pattern in a moving train

[Adel Makram]

Here is a thought experiment which is a modified version of a one I posted 4 years ago.
A moving train, where there are two slits at an equal distance from a photon source along the direction of motion open for a short period of time to allow the entry of photons from the source. The source emits one photon at a time. The two slit are closed before and after the photon approaching them.

For the train observer, an interference pattern will form.

However, for the ground observer, the sequence as follows; the rear slit opens and closes then the near slit opens and closes. Now, for the ground observer, the photon will only see one slit opens which mandates an outcome to be the same as a single slit experiment with no formation of any interference pattern.
I posted a similar thread in 2012 https://www.physicsforums.com/threads/interference-pattern-versus-sr.567738/page-7. At the end, I was convinced that what matters, is the coincidence of paths of two photons at the screen no matter whether the two slits open at the same time or no. But here, only one photon is emitted at a time, so there is no paths to coincide on the screen. What makes the interference pattern is the two wave-functions of the photon. but the wave-function possesses no physical reality and no such thing like a path of a wave-function which means no physical coincidence happen on the screen.

 

[Dale]

Now, for the ground observer, the photon will only see one slit opens which mandates an outcome to be the same as a single slit experiment with no formation of any interference pattern.

I will give you the same advice I did last time: work through the math. You will find that this claim is wrong, it is not what is predicted by QFT.

Hint: what do you know about commutation? Is there any known theorem about commutation of spacelike separated measurements?

 

[Heinera]

However, for the ground observer, the sequence as follows; the rear slit opens and closes then the near slit opens and closes. Now, for the ground observer, the photon will only see one slit opens which mandates an outcome to be the same as a single slit experiment with no formation of any interference pattern.

Firstly, there is nothing specific quantum about this "paradox", you can just as well use classical EM to make the same claim. The resolution is that for the ground observer, the wavefront will not reach the slits at the same time. It will first reach the rear slit, and then the near slit. This corresponds exactly to the times the respective slits are open. So the wavefront will in fact go through both slits.

In the path integral QED version of this, the ground observer will find that the photon paths to the rear slit are on average shorter than the paths to the near slit, with the same consequence as in the previous paragraph.

 

[Adel Makram]

I will give you the same advice I did last time: work through the math. You will find that this claim is wrong, it is not what is predicted by QFT.

Hint: what do you know about commutation? Is there any known theorem about commutation of spacelike separated measurements?

What is the cummutation of measurements (space-like)?

 

[Adel Makram]

Firstly, there is nothing specific quantum about this "paradox", you can just as well use classical EM to make the same claim. The resolution is that for the ground observer, the wavefront will not reach the slits at the same time. It will first reach the rear slit, and then the near slit. This corresponds exactly to the times the respective slits are open. So the wavefront will in fact go through both slits.

In the path integral QED version of this, the ground observer will find that the photon paths to the rear slit are on average shorter than the paths to the near slit, with the same consequence as in the previous paragraph.

Consider a standard double slits experiment in one single frame of reference but with one modification, other than the emission of photons one at a time, that the two slits are never open at the same time as one of them is always closed when the other is opened. Will the interference pattern form then?

 

[Heinera]

Consider a standard double slits experiment with nothing moving but with one modification, other than the emission of photons one at a time, that the two slits are never open at the same time as one of them is always closed when the other is opened. Will the interference pattern form then?

If both slits are positioned at the same distance from the source, then there will be no interference pattern.

 

[Adel Makram]

If both slits are positioned at the same distance from the source, then there will be no interference pattern.

Now, can I conclude that relative to the ground observer in my original post where the two slits are never open at the same time, that no interference pattern form?

 

[Heinera]

Now, can I conclude that relative to the ground observer in my original post where the two slits are never open at the same time, that no interference pattern form?

No, because relative to the ground observer, the two slits are not positioned at the same distance from the source (the position of the source being the position at the time of emission of the photon).

 

[Adel Makram]

No, because relative to the ground observer, the two slits are not positioned at the same distance from the source (the position of the source being the position at the time of emission of the photon).

How come? LT is a linear transformation from one space to another, so the relative distance between points should be maintained?

 

[Heinera]

How come? LT is a linear transformation from one space to another, so the relative distance between points should be maintained?

No, relative distances need not be conserved with Lorentz transformations. E.g., think of an equilateral triangle that becomes Lorentz contracted along some direction. It is no longer equilateral.

 

[Adel Makram]

No, relative distances need not be conserved with Lorentz transformations. E.g., think of an equilateral triangle that becomes Lorentz contracted along some direction. It is no longer equilateral.

I think this is true if the triangle is moving in the direction of one side of those are equal. But if it is moving, for example, in the direction of a third side, the two equal sides should remain equal too to any other observer.
Sorry, I was confused, I thought you were talking about isosceles triangle. But any way, the relative distances along the direction of motion should be the same!

 

[Heinera]

I think this is true if the triangle is moving in the direction of one side of those are equal. But if it is moving, for example, in the direction of a third side, the two equal sides should remain equal too to any other observer.

Here is the situation as seen from the ground observer: He first registers an emission event from the source. Then the photon travels at the speed of light in his frame, towards the slits. But when the photon reaches the slits, the slits are in a completely different position relative to the original position of the source (at the time of emission), due to the moving train. In particular, the photon will reach the rear slit first.

 

[Dale]

What is the cummutation of measurements (space-like)?

See section 3.2 here:

http://www.hep.manchester.ac.uk/u/dasgupta/teaching/Dasgupta-08-Intro-to-QFT.pdf

Once you have learned this aspect of QFT you will understand the resolution of your quandary. Until then I am going to close this thread to give you time to digest the material.