Interference pattern again!

A train is moving from the left to the right direction. There is a light source emitting 2 beams of lights toward 2 slits A and B at both ends of the train. The source is put near the slit A Than B.

A ground observer is watching the scene and sees that the 2 light rays reaching A and B simultaneously and in-phase to form a pattern.
However, the train observer sees that the light toward A takes a shorter path than light toward B which makes the ratio between those 2distance and the wave length of the light not necessarily the same in order that the 2 beams arrive in phase!
So how the phase become a physical invariant value?
https://www.physicsforums.com/attachment.php?attachmentid=46226&stc=1&d=1334428798

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Dale
Mentor
A ground observer is watching the scene and sees that the 2 light rays reaching A and B simultaneously and in-phase to form a pattern.
You don't get any interference pattern unless you recombine the beams somewhere.

You don't get any interference pattern unless you recombine the beams somewhere.
The ground obs, does not need to recombine any thing as long as he sees the 2beams reaching at 2 slits simultaneously and in phase.

For the interference pattern to form, the rays must also reach in phase.
( from the PDF)
Not true. Changing the phase of one of the interfering beams just shifts the pattern. And you need to combine two sources to get interference, as DaleSpam has pointed out.

He does if he wants an interference pattern.

http://en.wikipedia.org/wiki/Interference_(wave_propagation)

"interference is a phenomenon in which two waves superimpose to form a resultant wave of greater or lower amplitude"

The interference pattern needs 2 waves of same phases exits 2 slits and projecting onto a screen, all those cretieria are met for the ground observer!

Dale
Mentor
The interference pattern needs 2 waves of same phases exits 2 slits and projecting onto a screen, all those cretieria are met for the ground observer!
Where is the screen that both beams are projecting onto?

The interference pattern needs 2 waves of same phases exits 2 slits and projecting onto a screen, all those cretieria are met for the ground observer!
Not true ! Will you stop talking nonsense, please. The waves going through interference slits do not have to be in phase ! And you don't have any slits in any case.

Not true ! Will you stop talking nonsense, please. The waves going through interference slits do not have to be in phase ! And you don't have any slits in any case.
Before u accusing my words of being nonsense, you should ask more details about the experiment set up in order to understand it if it woes not clear from the first instance,,,,,, what do u mean by not having slits in any cases! The wave leaving slits must be in the same phase (wave anrounds or the ground FOR , no matter what will be the superposition on the ground screen,,, What appears on ground screen is a superposition of two waves of different phases, only on the screen, because of the relative difference between the two light paths,,, this is not my topic, my topic is clear from the first post! Will be the phase when leaving slits an invariant physical quantity ?

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Where is the screen that both beams are projecting onto?
In the ground

( from the PDF)
Not true. Changing the phase of one of the interfering beams just shifts the pattern. And you need to combine two sources to get interference, as DaleSpam has pointed out.
What I meant by "reach" is reaching slits not screen of course

Dale
Mentor
In the ground
Can you draw it, because it is not at all clear from your drawing. In fact, the ground isn't shown in your drawing. I don't know if this picture is looking from the side, the top, or the front. Also, the only way I can think to combine the beams given your arrangement is more like a mirror than like a slit, so I am not sure how that is going to work. You do understand that slits diffract, not reflect, right?

Also, Mentz114 is correct. It is not required that the two waves be in phase, merely that they be coherent. See the first paragraph of the Wikipedia link I posted earlier.

my topic is clear from the first post!
No, it wasn't. If it were we wouldn't be at post 12 still with no idea how there can even be interference here.

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For the sake of discussion here is a suggested set up which I think is in the spirit that the O.P. intended. At each end of the rocket we have a mirror at 45 degrees that deflect the light rays towards the ground. After reflecting off the mirrors, the light rays are passed through their respective slits in the lower side of the rocket. The ground is the screen. In the rest frame of the rocket the source is exactly one half wavelength forward of the centre of the rocket. In the rest frame of the rocket it does not matter that the ground is moving relative to the rocket as far as the interference pattern is concerned as it will appear exactly the same as if it was projected onto a co-moving screen.

Some complications to consider:

1)Doppler shift.
In the ground rest frame, light going to the rear of the rocket is red shifted and light going forward is blue shifted. If these were reflected straight back to the source the Doppler shifts would cancel out as the source and mirrors are co-moving, but when the rays are deflected at right angles there will probably be Doppler effects measured in the ground rest frame. The frequencies at the light rays pass through the slits should however be equal when measured in the rocket rest frame.

2)Aberration.
When light reflects of relativistic mirrors, the angle of the incident ray is not equal to the reflected ray relative to the norm of the mirror measured in the ground frame. Neither is the angle of the mirrors as seen in the ground frame the same as seen in the rocket frame. These effects are not too difficult to calculate. To transform the light paths as seen in the rocket frame to the ground frame, we only have to take relativistic aberration into account.

3)Interpretation.
In the rest frame of the rocket, differences in phase at the slits results in the interference pattern shifting relative to the rocket. This is fairly easy to measure. In the ground frame the interference pattern is moving relative to the ground. Measuring the shift of pattern is is difficult in this frame as the rocket will have moved during the time interval it takes the light to travel from the slits to the ground. Finding a meaningful reference might be difficult.

There are additional difficulties regarding the feasibility of whether any interference pattern is observed or not. Some texts state that photons only interfere with themselves and individual photons pass through both slits. This will be difficult to arrange in the rocket with the slits so far apart, but might be possible with entangled photons. The visibility of an interference pattern also requires the slits to be very close together so it is debatable whether or not the pattern would be visible even if it did form in the first place.

As you can see, this seemingly simple experiment is actually quite complex and may not be possible even in principle.

ghwellsjr
Gold Member
A train is moving from the left to the right direction. There is a light source emitting 2 beams of lights toward 2 slits A and B at both ends of the train. The source is put near the slit A Than B.
Are there a total of 4 slits, 2 at A and 2 at B, or are there a total of 2 slits, 1 at A and 1 at B?

And where does the light go after it passes through the slit(s) at each end of the train?

Are there a total of 4 slits, 2 at A and 2 at B, or are there a total of 2 slits, 1 at A and 1 at B?

And where does the light go after it passes through the slit(s) at each end of the train?
There r only 2 slits, one at each end

Light goes to a ground screen

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Can you draw it, because it is not at all clear from your drawing. In fact, the ground isn't shown in your drawing. I don't know if this picture is looking from the side, the top, or the front. Also, the only way I can think to combine the beams given your arrangement is more like a mirror than like a slit, so I am not sure how that is going to work. You do understand that slits diffract, not reflect, right?

Also, Mentz114 is correct. It is not required that the two waves be in phase, merely that they be coherent. See the first paragraph of the Wikipedia link I posted earlier.

No, it wasn't. If it were we wouldn't be at post 12 still with no idea how there can even be interference here.
The blue line is the ground screen, the train moves in the right direction,,, it does not matter wether I put mirrors or the slit emission is done by diffraction

https://www.physicsforums.com/attachment.php?attachmentid=46253&stc=1&d=1334500883

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3)Interpretation.
In the rest frame of the rocket, differences in phase at the slits results in the interference pattern shifting relative to the rocket. This is fairly easy to measure. In the ground frame the interference pattern is moving relative to the ground. Measuring the shift of pattern is is difficult in this frame as the rocket will have moved during the time interval it takes the light to travel from the slits to the ground. Finding a meaningful reference might be difficult.

There are additional difficulties regarding the feasibility of whether any interference pattern is observed or not. Some texts state that photons only interfere with themselves and individual photons pass through both slits. This will be difficult to arrange in the rocket with the slits so far apart, but might be possible with entangled photons. The visibility of an interference pattern also requires the slits to be very close together so it is debatable whether or not the pattern would be visible even if it did form in the first place.
1) we can arrange the set up by making the rocket /train moves in a quite large circle ( ignoring the effect of GR) and repeat the emission of light at exactly the same point over and over again to complete the pattern, or alternatively, by making a very long train and multiple slits replicating A and B so as to complete the pattern over many cycles
2) the wavelength can be chosen To match the distance between the 2 slits

Dale
Mentor
The blue line is the ground screen, the train moves in the right direction,,, it does not matter wether I put mirrors or the slit emission is done by diffraction
Actually, you need both mirrors and slits for this configuration to work. So you could have the light go out from the source above the slits, then the mirrors reflect the light in and down to the slits, then the slits diffract it to the ground making an interference pattern.

OK, so now that I understand your scenario, what is your concern?

OK, so now that I understand your scenario, what is your concern?
will the wave- phase when light exiting slits be an invariant physical value?

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Dale
Mentor
Yes. But simultaneity is not.

Yes. But simultaneity is not.
I Know that simultaneity part, but Would u please explain the " yes"?

Dale
Mentor
Yes, the phase of a signal at any given event is a relativistic invariant. I.e. all frames agree on the phase at any event.

Yes, the phase of a signal at any given event is a relativistic invariant. I.e. all frames agree on the phase at any event.
I know the statement, I want the proof

I know the statement, I want the proof
I found this fairly convincing. If you have any questions, please ask.

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Dale
Mentor
I know the statement, I want the proof
Mentz114 has provided one proof. I prefer to simply note that (in units where c=1)

$k^{\mu}=( \omega, k_x, k_y, k_z )$ is a four-vector and
$x^{\mu}= (t,x,y,z)$ is also a four-vector. So then
$\phi=\omega t - k_x x - k_y y - k_z z = k_{\mu} x^{\mu}$ is manifestly a scalar.

But that does require previous knowledge of the wave four-vector.

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