# Double slit experiment on a moving train

1. Oct 3, 2013

### 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.

Last edited: Oct 3, 2013
2. Oct 3, 2013

### tiny-tim

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

3. Oct 3, 2013

### m_robertson

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.

Last edited by a moderator: Sep 25, 2014
4. Oct 3, 2013

### 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.

5. Oct 3, 2013

### 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​

6. Oct 3, 2013

### dauto

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

7. Oct 3, 2013

### Staff: Mentor

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.

8. Oct 3, 2013

### 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 its self 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?

9. Oct 3, 2013

### 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.

10. Oct 3, 2013

### tiny-tim

sorry, but this is complete rubbish

you have taken no notice of what i said before

(what dauto says is of course entirely correct)

11. Oct 3, 2013

### Staff: Mentor

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)

12. Oct 3, 2013

### m_robertson

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 its self 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.

13. Oct 3, 2013

### Staff: Mentor

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.

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.

14. Oct 4, 2013

### bahamagreen

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.

15. Oct 4, 2013

### 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.

16. Oct 4, 2013

### Staff: Mentor

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?

17. Oct 4, 2013

### 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).

18. Oct 4, 2013

### Staff: Mentor

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.

19. Oct 4, 2013

### 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).

20. Oct 4, 2013

### m_robertson

Thanks for the answers and explanations!

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

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 wont reach the detector in time at position x and the wave function wont 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 realise 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.

Last edited: Oct 4, 2013