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

[Adel Makram]

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

 

[Dale]

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.

 

[Adel Makram]

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.

 

[Dale]

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"

 

[Mentz114]

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.

 

[Adel Makram]

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]

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?

 

[Mentz114]

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.

 

[Adel Makram]

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 ?

 

[Adel Makram]

Where is the screen that both beams are projecting onto?

In the ground

 

[Adel Makram]

( 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]

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.

 

[yuiop]

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]

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?

 

[Adel Makram]

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

 

[Adel Makram]

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

 

[Adel Makram]

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]

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?

 

[Adel Makram]

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?

 

[Dale]

Yes. But simultaneity is not.

 

[Adel Makram]

Yes. But simultaneity is not.

I Know that simultaneity part, but Would u please explain the " yes"?

 

[Dale]

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.

 

[Adel Makram]

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

 

[Mentz114]

I know the statement, I want the proof

I found this fairly convincing. If you have any questions, please ask.

 

[Dale]

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.

 

[Adel Makram]

I found this fairly convincing. If you have any questions, please ask.

The ratio ΔL/λ is a direction-sensitive and uses a relativistic Doppler effect which depends on whether u apply it to slit A or B and naturally, the Lorentz factor cancels each other out. But for the train observer, the phase is a location sensitive which depends merely on the location of the source relative for the slits. For example, if I displace the location of the source by an amount = 1/2λ, of course i need to change the velocity of train for the 2 wave fronts to appear at the same time, still the phase is the same for him, but for the train one it differed by 1/2λ

Your calculation does not describe the whole picture

 

[Adel Makram]

One more thing, I think the pattern will not form any way in this particular set up. Although the phase is always equal at Slits A and B relative to the ground observer because the arrival of the wave front at the same time, yet the Doppler shift at slits makes the interaction of those waves of different wave length after leaving the slits not possible.
Still my concern not about the pattern but about the relative phase at A and B for the train observer!

 

[Mentz114]

The ratio ΔL/λ is a direction-sensitive and uses a relativistic Doppler effect which depends on whether u apply it to slit A or B and naturally, the Lorentz factor cancels each other out. But for the train observer, the phase is a location sensitive which depends merely on the location of the source relative for the slits. For example, if I displace the location of the source by an amount = 1/2λ, of course i need to change the velocity of train for the 2 wave fronts to appear at the same time, still ΔL/λ will not change, and the phase is the same for him, but for the train one it differed by 1/2λ

Your calculation does not describe the whole picture

I have no idea what you're talking about or what your problem is. I don't think you understand the concept of Lorentz invariance and I suggest you go and do some learning before you make ridiculous claims.

One thing we can be certain about is that if any observer sees a certain phase relationship ( like an interference pattern ) then all observers will see it.

[DaleSpam's proof is showing that the amplitude of a plane-wave at any point in spacetime ( i.e. phase) is an invariant.]

 

[Dale]

the Doppler shift at slits makes the interaction of those waves of different wave length after leaving the slits not possible.

The Doppler shift at the slits is not the only Doppler shift. There is also a Doppler shift at the source, at the mirror (you are probably including this one with the slit), and at the screen.

Still my concern not about the pattern but about the relative phase at A and B for the train observer!

Suppose that we set up a pair of clocks at each slit. Suppose further that one clock reads 12:00:00 when the phase is 0 at one slit and the other clock reads 12:00:01 when the phase is π at the other slit. Then, in all reference frames when the first clock reads 12:00:00 the phase is 0 at the first slit and when the other clock reads 12:00:01 the phase is π at the other slit. This is what it means for the phase to be a relativistic invariant.

 

[Adel Makram]

I have no idea what you're talking about or what your problem is. I don't think you understand the concept of Lorentz invariance and I suggest you go and do some learning before you make ridiculous claims.

One thing we can be certain about is that if any observer sees a certain phase relationship ( like an interference pattern ) then all observers will see it.

[DaleSpam's proof is showing that the amplitude of a plane-wave at any point in spacetime ( i.e. phase) is an invariant.]

You should think of the experiment set up in a more close up instead of doing general math not particularily applicable for every case. I Was not talking about the pattern at all, so stop reiterating it over and over

 

[Adel Makram]

The Doppler shift at the slits is not the only Doppler shift. There is also a Doppler shift at the source, at the mirror (you are probably including this one with the slit), and at the screen.

Suppose that we set up a pair of clocks at each slit. Suppose further that one clock reads 12:00:00 when the phase is 0 at one slit and the other clock reads 12:00:01 when the phase is π at the other slit. Then, in all reference frames when the first clock reads 12:00:00 the phase is 0 at the first slit and when the other clock reads 12:00:01 the phase is π at the other slit. This is what it means for the phase to be a relativistic invariant.

Ok, so the n phase shift at the other clock may depend on the relative path taken by the light to travel from the source toward the clock. But for that particular location of the source relative to the train, there is a velocity that an external observer can see the train with the 2 wave fronts arrive simultaneously with no n- shift!

 

[Dale]

the n phase shift

I am talking about phase, not phase shifts.

 

[Adel Makram]

I am talking about phase, not phase shifts.

The world lines of meeting between the light and the slits are invariant, so do the phase values and the phase shift ( or difference)!. So how the n read by one clock still be so on another FOR which should detect it as 0

 

[Dale]

Worldlines are usually not considered invariant. Worldlines transform as vectors, not scalars.

Note above, I am talking about phase, not phase shift. A phase shift is a difference between two phases, for example the difference between the phase at the emitter and the phase at the slit at the same time. Phase differences may not be invariant, particularly if the difference is defined using notions of simultaneity.

 

[Adel Makram]

Also, what if I change the color of the laser I use but keeping the location of the source,,, so for the ground observer, he still sees both wavefront arising simultaneously with a phase value of n for both waves,,, but the train one should see different phase value depending on the ratio between the lengths of the two paths/ λ

The detection of the wave front that defining the phase relative to the ground observer is always the same so long as he sees them simultaneously, though with different Doppler shift, but not the case for the train which the phase depends on the location of the source and the λ used