Double slit experiment on a moving train

[m_robertson]

So I asked this question in another thread but thought the question was probably best asked here in this forum to at least understand part of the experiment. My idea follows the traditional train and platform analogy that is used in many thought experiments to explain the issue of simultaneity, however this time I wish to include the double slit experiment. Since we know that the speed of light remains the same for all observers at rest and speeds of constant velocity, I was curious to know if performing the double slit experiment under these conditions would present some problems and perhaps even contradictions in results.

Now as I mentioned elsewhere I'm not educated in QM nor SR so please excuse me if there's any errors in my logic or flaws in the structure of my experiment, if there is please point them out and I'd love to understand this idea in more detail, even if my conclusions are wrong.

- John is standing on the platform
- Emma is standing on the moving train
- On the train Emma has the apparatus for the double slit experiment
- At a specific moment in time as the train passes through the station, both observers witness a particle of light which is fired down the line of the train towards the two slits

- There are other variables we can consider later in the description of the experiment, such as the presence and location of detectors which verify which slit the photon went through

My idea is this. Since the speed of light is the same for all observers, the single photon which is fired down the line towards the double slits will be at different positions of space relative to the train for each observer. For Emma the particle of light will travel towards the apparatus at the speed of light, it will pass through the slits and will hit the detector at a specific time. For John, since the train is moving down the tracks, the particle of light will travel at the speed of light however will always remain slightly behind the particle which Emma observes. The time in which the photon passes through the slits and hits the back plate will not be simultaneous in both frames of reference.

Am I right here? I don't want to go any further yet as I did in the other thread as thinking on it there are other things to consider, such as time dilation and length contraction. Could either of these factors allow the particle to hit the back plate simultaneously in both frames of reference? My idea is that perhaps with the inclusion of a detector, not only would the times in which the photon passes through the slits not be simultaneous, but also the time in which the wave function collapses as its path is verified by the presence of a detector.

 

[tiny-tim]

hi m_robertson!

… the single photon which is fired down the line towards the double slits will be at different positions of space relative to the train for each observer. For Emma the particle of light will travel towards the apparatus at the speed of light, it will pass through the slits and will hit the detector at a specific time. For John, since the train is moving down the tracks, the particle of light will travel at the speed of light however will always remain slightly behind the particle which Emma observes. The time in which the photon passes through the slits and hits the back plate will not be simultaneous in both frames of reference.

… Could either of these factors allow the particle to hit the back plate simultaneously in both frames of reference?

"simultaneous" has no meaning between different observers

two events can be simultaneous as viewed by one observer

it is meaningless to ask whether one event is simultaneous as viewed by two observers

 

[m_robertson]

hi m_robertson!


"simultaneous" has no meaning between different observers

two events can be simultaneous as viewed by one observer

it is meaningless to ask whether one event is simultaneous as viewed by two observers

Hi! So should my question be rephrased? Do I have the right idea? Or do I have this wrong to begin with? I will admit my source material might be questionable and I appreciate any help in addressing my misunderstandings. I'm using this as the basis of my argument, although I'm getting the idea that what's presented in the opening of this video isn't actually a fact of nature, but an issue which has been resolved?



I feel like I'm taking this out of context and that length contraction resolves this issue.

 

[dauto]

I don't see what's the question here. What's simultaneous for one observer may not be simultaneous for another. What's not clear is why do you think that should affect the result of the double slit experiment.

 

[tiny-tim]

hi m_robertson!

in your diagram there are two detectors, and each detects a ray of light

one observer says those two events are simultaneous with each other

the other observer says those two events are not simultaneous with each other

in each case, one observer makes a statement about two events​

 

[dauto]

The video is an accurate description of a fact of nature confirmed by multiple experiments and observations

 

[Dale]

I am also not sure what the question is, however, if you have a wave of light moving at c in one frame then it transforms into a wave of light moving at c in all other frames also. In addition, the phase of the wave at any given event is a relativistic invariant. So all measurement results which are based on the phase will be the same in all frames. This includes two slit interference fringes.

 

[m_robertson]

Okay, so take the picture I posted above. The yellow arrows points to what would represent the double slit apparatus, the red line is the particle of light which is fired towards the apparatus. What I'm wondering is, since light travels at the same speed for each observer, then wouldn't the particle of light exist in two states at once since there is no simultaneity? Looking from Einstein's perspective, the particle of light hasn't reached the detector and it's path hasn't been determined as it is yet to pass through either slit, however from Lorentz's perspective the particle has reached the detector and it's path has been determined as it has already passed through one of the slits.

My question is this, would it be possible to quickly turn off the detector that determines which slit the particle goes through and cause contradiction in which position the particle lands? Because when the detector is off, the photon behaves as a wave and interferes with itself on the other side of the slits, causing a more broad landing site for the particle on the other side. However when the detector is on, the photon acts as a particle and doesn't interfere with its self, having a more narrow landing site directly behind both slits. Since the photon is both in front of and behind the slits at time t, isn't there a possibility for contradiction here?

 

[dauto]

No, that's complete nonsense. You cannot say that from Lorentz perspective anything happens before, after, or at the same time as Einstein's perspective because they are different perspectives. They use separate time coordinates. You are still trying to see both perspectives from a single point of view - say God's perspective. God's perspective does not exist.

 

[tiny-tim]

Since the photon is both in front of and behind the slits at time t …

sorry, but this is complete rubbish

you have taken no notice of what i said before

(what dauto says is of course entirely correct)

 

[Dale]

wouldn't the particle of light exist in two states at once since there is no simultaneity?

This scenario is completely classical, there is no need to think of light as a particle here. It is just a wave.

There is no possibility of a contradiction. The Lorentz transform preserves the temporal order of events which are timelike or null separated (I.e. Events where something can go between them at the speed of light or less)

 

[m_robertson]

This scenario is completely classical, there is no need to think of light as a particle here. It is just a wave.

There is no possibility of a contradiction. The Lorentz transform preserves the temporal order of events which are timelike or null separated (I.e. Events where something can go between them at the speed of light or less)

How can you just consider the particle as a wave when the apparatus causes the wave function to collapse and makes it behave like a particle? The action of knowing which slit the "wave" went through prevents it from interfering with itself on the other side of the slits and thus no interference pattern. Surely this experiment doesn't change that just for the sake of remaining classical?

So what would actually happen in this experiment? Can someone give me a description in the same method I've used? I understand there's no single frame of reference and I'm not intentionally trying to think in this manner, I clearly don't understand the implications of SR quite well enough. I know I don't get this, so if people can help me understand where I'm going wrong it's much appreciated! I was just interested by the thought of this experiment and wanted to understand it properly.

What interests me is the fact that we're relying on a single unit of light which travels at different speeds relative to the train depending on your frame of reference. The significance in the double slit experiment here, at least to me (I'm probably wrong), is the fact that the single particle is capable of changing its behaviour depending on its position and time relative to the apparatus. So not only is the single particle of light activating a detector showing the curiosities of simultaneity as in the above video, but the unit of light also changes its behaviour and potential position depending on the nature of the experiment.

 

[Dale]

How can you just consider the particle as a wave when the apparatus causes the wave function to collapse and makes it behave like a particle?

The collapse of wavefunctions is not in any way essential for understanding interference. The interference fringes of light in the two-slit experiment was known in the early 1800's (about a century before quantum mechanics) and it is fully described by Maxwell's equations.

The action of knowing which slit the "wave" went through prevents it from interfering with itself on the other side of the slits and thus no interference pattern. Surely this experiment doesn't change that just for the sake of remaining classical?

My point is that you are mixing up two unrelated topics and unnecessarily adding to your confusion. One topic is the treatment of a double-slit interference experiment in different reference frames. The other topic is the loss of the interference fringes in a "which way" two slit experiment. The two topics are independent.

If you want to learn, then simplify. Don't deliberately add unnecessary complexity. You will only confuse yourself and make your own learning more difficult. Please decide which topic you want to discuss. The first belongs here (which is why I assumed that was the question you actually wanted to discuss), and the second would be better in the QM forum. But you shouldn't try to discuss both at the same time.

 

[bahamagreen]

I agree, start with the fundamentals first.

Regarding the mirror clocks with the bouncing photons... some things to consider and watch out for:

First, it is common to read an analogy of these clocks posed as a boy on a moving bicycle dribbling a basketball. To the boy on the bike going 8 feet per second, the ball is bouncing up and down, say three feet, and he is bouncing it one cycle up and down every 8 feet.
To someone standing by on the sidewalk, they also see the ball bouncing up and down three feet, but they also see the bike going by a 8 feet per second, so the ball goes up three feet as the bike goes 4 feet and down three feet as the bike goes 4 feet... so by Pythagoras' theorem the ball will be going 5 feet per half second, or ten feet per second alternating 5 foot long zigs and zags at up and down angles (simplified to exclude the parabolic curves, accelerations, etc.).
The observer may also decide to measure the horizontal component of the ball and that will be 8 feet per second. Even if the kid could dribble the ball 40 bounces per second the net horizontal speed would still be four feet per second, although the "zig zag path traveled" speed would be about 240 feet per second.

The problem with this analogy is that the ball has momentum initially from the motion of the boy and bike.

When the switch is made to considering the light clock, one reads Einstein's words, translated from German to English, where it says that "the velocity of light is independent of the motion of the source" or something to that effect... the poorly translated word is "velocity".

The word should have been translated as simply "speed". Velocity has a direction, and if you interpret the speed and direction of light to be independent of the source motion, you run into some problems.

First, the light pointed vertically at the upper light clock mirror would miss the mirror as the mirror moved because the light would have no horizontal component of motion - because its direction from the source point would be independent of that source point's motion - the light would be "left behind" unless the light clock just happened to be in a special reference frame... which leads to the second problem.

Second, if the light's direction was independent of the source motion, the vertical path of the light would indicate the absolute rest component for the horizontal travel direction, and a few tests later one would be able to establish the remaining coordinates of an inertial frame of absolute rest.

So, light does take its direction from the motion of the source, but not its speed; that is what underlies the geometry of the light clocks. Absolute rest cannot be revealed by light because it does take the motion of the source into account for direction only, and only its speed is independent of the source motion.

Sometimes when you hear that "moving clocks show slower time" one can be confused because it is only the vertical dimension that is accounting for the time; the speed of the light to the stand by observer is still the same as always, c, but the zig zag angle is composed of two components, only the vertical one being the "time" of the clock... it is the path of the zig or zag that is always c.

 

[m_robertson]

I understand the conflicting approach here and I guess that's part and reason for me asking about it, as I have no idea how one would approach this experiment. In a more broad term what I'm asking, or what I'm trying to find out, is what each observer would witness when performing this QM experiment under SR circumstances. You're not just sitting in a room performing the double slit experiment, you're asking what is happening to this particle of light in two different frames of reference.

So, in the video above, what exactly do they agree and disagree on? The position of light? I understand it's like explaining SR to a dummy and I apologize for generating confusion.

 

[Dale]

In a more broad term what I'm asking, or what I'm trying to find out, is what each observer would witness when performing this QM experiment under SR circumstances.

I know that is what you are asking, and I am telling you not to ask that until you already understand QM and SR separately. Until you do, we can give you the answer, but it will be useless to you because you don't have the foundation required to understand it.

What would you do if someone who didn't understand logarithms and didn't understand integration asked a question about the integration of a logarithm?

 

[BruceW]

emma finds that the light pulse takes time $t$ to pass through the slit, and john finds that the light pulse takes time $t'$ to pass through the slit.

ok, all fine so far. So what is the problem that you are thinking is happening here? If emma places detectors at the slits, then we get a wavefunction collapse at time $t$ according to emma and time $t'$ according to john.

Now, if emma takes away the detectors before time $t$, then we won't get the collapse. But according to john, she only needs to take away the detectors before time $t'$ (and $t'$ is greater than $t$). But, there is no contradiction, because according to john, the photon has further to travel. Therefore it makes sense that according to john, there is more time before the photon goes through the slit.

edit: also, you might think it is weird that according to john, emma has more time to take away the detectors before the photon reaches the slit. But according to john, emma will also move slower, and her brain will think slower, and she will age slower. So as long as you think about it carefully, every reference frame is 'correct', and every reference frame agrees on things that are absolutes (for example, what spacetime events happen in the same place and time).

 

[Dale]

we can give you the answer, but it will be useless to you

Incidentally, the answer would be something along the lines of this: The wavefunction evolves in each frame according to the Shrodinger equation. The phase is a relativistic invariant and the phase is what governs the interference fringes. For each photon, the wavefunction collapse, whether it is at the screen or at the "which way" detector, is at the same event in every frame. The collapsed wavefunction in each frame then continues to evolve according to the Schrodinger equation in each frame. As no information is transmitted due to a wavefunction collapse, there is no contradiction in any frame.

 

[BruceW]

yeah, as long as we make sure that we don't accidentally allow information to be transmitted due to wavefunction collapse, then everything should be fine. (or that's my understanding of it, anyway. I'm not very knowledgeable about this kind of stuff really).

 

[m_robertson]

Thanks for the answers and explanations!

Incidentally, the answer would be something along the lines of this: The wavefunction evolves in each frame according to the Shrodinger equation. The phase is a relativistic invariant and the phase is what governs the interference fringes. For each photon, the wavefunction collapse, whether it is at the screen or at the "which way" detector, is at the same event in every frame. The collapsed wavefunction in each frame then continues to evolve according to the Schrodinger equation in each frame. As no information is transmitted due to a wavefunction collapse, there is no contradiction in any frame.

I'm curious, what do you mean that there is no information transmitted due to a wave function collapse?

emma finds that the light pulse takes time $t$ to pass through the slit, and john finds that the light pulse takes time $t'$ to pass through the slit.

ok, all fine so far. So what is the problem that you are thinking is happening here? If emma places detectors at the slits, then we get a wavefunction collapse at time $t$ according to emma and time $t'$ according to john.

Now, if emma takes away the detectors before time $t$, then we won't get the collapse. But according to john, she only needs to take away the detectors before time $t'$ (and $t'$ is greater than $t$). But, there is no contradiction, because according to john, the photon has further to travel. Therefore it makes sense that according to john, there is more time before the photon goes through the slit.

edit: also, you might think it is weird that according to john, emma has more time to take away the detectors before the photon reaches the slit. But according to john, emma will also move slower, and her brain will think slower, and she will age slower. So as long as you think about it carefully, every reference frame is 'correct', and every reference frame agrees on things that are absolutes (for example, what spacetime events happen in the same place and time).

The area I was curious about contradiction was if the detector was in the wrong position for John to learn which slit the light pulse went through. Instead of the time in which the detector was turned off, instead look at the position of the detector relative to the light pulse. Imagine the detector is in a fixed position x on the opposite platform to John which connects momentarily to Emma on the train as it reaches position x, however the light pulse is not in a fixed position as its speed is relative to each frame of reference. So because Emma's light pulse is moving with the train, it will reach the detector in time at position x and she will learn which slit the light pulse went through, but because John's light pulse is moving relative to him standing on the platform, it won't reach the detector in time at position x and the wave function won't collapse because the apparatus has already moved on with the train, thus providing a contradiction in which position the particle will land on the back plate of the apparatus in each frame of reference.

I realize I'm likely wrong here, I'm not trying to prove a point, I merely envisioned this experiment and am curious as to the outcome and how any issue present might be resolved.

 

[BruceW]

The area I was curious about contradiction was if the detector was in the wrong position for John to learn which slit the light pulse went through. Instead of the time in which the detector was turned off, instead look at the position of the detector relative to the light pulse. Imagine the detector is in a fixed position x on the opposite platform to John which connects momentarily to Emma on the train as it reaches position x, however the light pulse is not in a fixed position as its speed is relative to each frame of reference. So because Emma's light pulse is moving with the train, it will reach the detector in time at position x and she will learn which slit the light pulse went through, but because John's light pulse is moving relative to him standing on the platform, it won't reach the detector in time at position x and the wave function won't collapse because the apparatus has already moved on with the train, thus providing a contradiction in which position the particle will land on the back plate of the apparatus in each frame of reference.

Before, you were saying the photon is sent down the line of the train towards the two slits. So now we are talking about a different scenario, where the two slits and the detector are on the platform, and the photon is fired from the train, in a direction perpendicular to the train? (I just want to make sure that I have understood what you are describing?)

edit: If this is what you mean, then you don't need to worry about the light pulse getting to the slits in one frame but not the other. For example, if you had a dartboard on the platform, and fired the photon from the train, then if the photon hits the bullseye according to emma, then the photon will also hit the bullseye according to john. The length contraction will be exactly what it needs to be to make this happen. (and you can derive equations for length contraction, using thought-experiments like this).

 

[m_robertson]

Before, you were saying the photon is sent down the line of the train towards the two slits. So now we are talking about a different scenario, where the two slits and the detector are on the platform, and the photon is fired from the train, in a direction perpendicular to the train? (I just want to make sure that I have understood what you are describing?)

This is the same scenario, the double slit apparatus is still on the train, only this time the detector which looks to see which slit the light pulse goes through is stationary on the platform opposite to John at position x. As the train passes the train station the light pulse is fired and both John and Emma look to see what it does. As the train and double slit apparatus passes position x in Emma's scenario the light pulse goes through one of the two slits, gets measured by the detector and the wave function collapses preventing it from interfering with itself on the other side. However, as I assume (probably naively), this only happens because the light pulse is moving with the train relative to Emma's frame of reference. Since in John's scenario the light pulse doesn't move consistently with the train but at the speed of light relative to his frame of reference, the double slit apparatus is not at position x when the light pulse reaches the detector and he never learns which slit the particle goes through, causing it to take all possible paths when it reaches the slits and preventing the wave function from collapsing.

As I mentioned before I assume length contraction and time dilation, or some other thing I'm not considering, prevents there from being a contradiction.

 

[BruceW]

yeah, you've got the right idea. Length contraction in the direction of the motion of the train will cause the photon to still go through the slit, and still hit the detector in john's perspective.

 

[mfb]

All observers will agree on the question whether the detectors were active at the time the photon passed the slits or not.
As a more fundamental rule: relativistic quantum mechanics is a consistent theory. You cannot construct contradictions based on this theory - that is a mathematical fact. Nature does not have to follow relativistic quantum mechanics, but that would need actual experiments (showing deviations from its predictions) to find out.

 

[BruceW]

@ m_robertson: Although, there might be one thing I think you might have confused. It is when you put a detector at each slit, this causes the interference pattern to get messed up. So as long as there are not detectors at the slits, then you will get the interference pattern.

 

[BruceW]

I'll try to explain a bit more. In the usual double-slit experiment, there are two slits, and one detector, some distance on the other side. And we get an interference pattern on the detector. This is possible because we don't know which slit the electron (or photon) went through. Now, if we put a small coil or something similar around each slit, then we can tell which slit the photon went through. But, this messes up the interference, and we no longer get an interference pattern at the detector which is some distance away. So, when I say 'detector at the slit', I mean these little coils at the slit, which allow the photon to pass, but also detect its presence at one of the slits.

 

[Dale]

I'm curious, what do you mean that there is no information transmitted due to a wave function collapse?

I mean, if you measure a particle at some event A and there is some other event B which is spacelike separated from A then there is nothing that you can do at event B which will let you know about the result of the measurement at A, even though B occurs after A in some frame and therefore the wavefunction has collapsed at B in that frame.

 

[BruceW]

yeah, in quantum mechanics, the non-unitary collapse must not be allowed to make any physical difference to the system we are modelling. So, it is kinda suspicious and is one of the forms of the 'measurement problem'.

edit: sorry that's off-topic now. But also, even if there is an objective non-unitary collapse, then you'd expect it to not violate relativity. (or there would be problems).

 

[Dale]

Yes, but this kind of stuff is only worth discussing AFTER you have a firm grasp of both SR and QM. The OP should separate the questions so he can learn the basic concepts of each first.

 

[BruceW]

yeah, the 'main' question (as far I as I can tell), was a relativity question. along the lines of 'if I emit a pulse of light and it hits a target, then does it also hit the target in another reference frame?' But I might have misinterpreted.

 

[Dale]

Yes, that was how I understood the question also, particularly given that this was posted to the relativity forum rather than the QM forum.

 

[EskWIRED]

If you want to learn, then simplify. Don't deliberately add unnecessary complexity. You will only confuse yourself and make your own learning more difficult. Please decide which topic you want to discuss. The first belongs here (which is why I assumed that was the question you actually wanted to discuss), and the second would be better in the QM forum. But you shouldn't try to discuss both at the same time.

I find that as I learn Physics, I often try do exactly what you dissuade the OP from doing. I always thought it was a good way to get a deeper understanding of both of the admixed concepts.

Fortunately or unfortunately, that is the way my mind works. I take knowledge from one area and try to see what sort of conclusions I can reach by applying the concepts to another area of study.

Of course, taking a misunderstanding in one area and applying it to another does not work. But it may well illuminate the original source of misunderstanding in stark detail.

So I think that the admixture of concepts can be very valuable, even when (especially when?) it results in the identification of misconceptions.

 

[Dale]

In my experience that type of learning is not compatible with an internet forum as the medium for learning. Similarly, the Socratic method is also an effective teaching method face-to-face, but I have never seen it work successfully here.

If you and the OP wish to learn that way then, in my experience, PF will not be able to help.

 

[EskWIRED]

Thanks for the thoughtful reply. I think that there is merit in your views.

I recently read the posting on properly formed questions that was in somebody's sig, and it offers good methods of obtaining satisfying answers.