Knowing which-path information by calculating distance time?

[Vloodz]

In many experiments that show quantum effects particles are given the option to take different paths/routes. This is done using devices that act as mirrors/splitters/joiners/etc. Probably the most famous of these type of experiments is the Delayed Choice Quantum Eraser, but there are many others.

These experiments always show us that if it is impossible to know which route the particle has taken (aka the which-path information) the result of the experiment itself will be different. These different routes however have different distances. Sometimes the different distances are obvious and visible via the experiment's diagram. Even if the difference is not obvious I'm assuming it's still there as it seems impossible to me to physically design different routes with the exact same distance, down to the last Angstrom.

Now, since the distances are different this also means the time it takes the particle to reach its destination(usually some kind of a detector) will be different, and if this is true, the which-path information is not actually lost. Sure, we might be talking about a very small time difference, such as picoseconds, nevertheless though, a difference is a difference, and with very accurate equipment we should even be able to detect/calculate it ourselves. We can potentially even force the issue by intentionally making some paths much longer than the others, resulting in bigger time differences between the different routes.

 

[Swamp Thing]

We need to be able to time the arrival closely enough to tell "which path". This implies a certain degree of localization of the wavefunction. When you have a localized wavefunction, two things could happen : first, the wavelength gets smeared out and this results in washing out the interference -- you end up with the scalar sum of the two individual patterns. The other thing is that the waves may no longer overlap at the detector at all, temporally speaking. If the two paths reach the detector at different times with no overlap then again you have no interference.

In other words, you need non-overlapping arrivals to distinguish the path without ambiguity, but that then implies no interference. In a sense this is a rather trivial example of path-distinguishability being incompatible with interference.

 

[bhobba]

Now, since the distances are different this also means the time it takes the particle to reach its destination(usually some kind of a detector) will be different, and if this is true, the which-path information is not actually lost. Sure, we might be talking about a very small time difference, such as picoseconds, nevertheless though, a difference is a difference, and with very accurate equipment we should even be able to detect/calculate it ourselves. We can potentially even force the issue by intentionally making some paths much longer than the others, resulting in bigger time differences between the different routes.

Do you have a detailed, and I emphasise detailed, set-up to exploit this to investigate some QM effect?

With such it can be analysed to see what QM would predict.

Thanks
Bill

 

[Vloodz]

Do you have a detailed, and I emphasise detailed, set-up to exploit this to investigate some QM effect?

With such it can be analysed to see what QM would predict.

No I do not.

However, I am willing to come up with one. I first need to know though, what exactly do you mean by a detailed set-up?
Does this count as a detailed set-up?

 

[bhobba]

Does this count as a detailed set-up?

Yes.

Thanks
Bill

 

[Vloodz]

Alright, here's an example of how this experiment might work.

Step 1
https://dl.dropboxusercontent.com/u/21029539/quantum/setup2/step1a.png
We create 2 paths for a particle to go through. We put a barrier at the bottom path so we know for sure the particle went through the top path once it hits the detector. We then proceed to firing our particle in this setup and record the exact time it was shot. If the particle didn't hit the detector we assume it went through the bottom slit and simply fire again until eventually the particle reaches the detector. Once the particle does reach the detector we record the time of arrival. At this point we can calculate the time it took the particle to reach the detector from the moment we shot it using simple subtraction. We repeat this process a bunch of times, say 100, and save all the results.

In an ideal scenario we will get the exact same result every time. In the real world however, due to equipment inaccuracies(and possibly other factors?) we will probably get a slightly different result each time. The best thing we can do is keep the result range, aka the min and max results and assume the particle cannot exceed this range when it goes through the top path. So for example we will now know it takes the particle between 6.26-6.35 ns to reach its destination (these are just random numbers).

https://dl.dropboxusercontent.com/u/21029539/quantum/setup2/step1b.png
Once finished we repeat everything but this time we block only the upper path. We now know also know the time range of the bottom path. The 2 ranges should be at least slightly different in order for us to get meaningful results in the next step.

Step 2
https://dl.dropboxusercontent.com/u/21029539/quantum/setup2/step2.png
We remove the barrier completely and start firing particles again. At this point the we should be getting an interference pattern at the detector as the particle should be in a superposition of taking both paths and interfere with itself. This is nothing new, but what is interesting to me is calculating how long it took the particle to reach the detector. Will it match the upper path range? Will it match the lower path range? Will it have a new range which lies somewhere in the middle?Step 3
https://dl.dropboxusercontent.com/u/21029539/quantum/setup2/step3.png
We move the upper mirror, causing the upper path to be much longer. We also add a barrier at the lower path again and recalculate the time it takes the particle to reach the detector using the upper path.

Step 4
https://dl.dropboxusercontent.com/u/21029539/quantum/setup2/step4.png
We remove the barrier and run the experiment again. What kind of results will be getting now?
Will we still see an interference pattern at the detector?
Will the particle's travel time match the upper path? Will it match the lower path? Will it match neither?

At this point, we can start repeating steps 3 and 4 as many times as we'd like using different distances and see how they effect the results. Sometimes we may move the top mirror only slightly, and sometimes go for more radical changes.

Notes:
* The barriers can be put at the slits instead of at a later part of the path. I'm assuming this won't make much difference.
* After we set up everything in step one all the equipment must stay in place from that moment on till the end of experiment. Any slight movement to any instrument might effect the path length, thus changing the particle's travel time. The only exception to this rule is the barrier, which we are allowed to move freely, and the upper mirror during step 3, which we move intentionally.Similar setup
As I'm new to quantum physics I wasn't sure how important it is for the particle to reach the detector at the same angle, regardless of which path it took. Here's a very similar setup that will fix this issue if indeed it makes a difference:
https://dl.dropboxusercontent.com/u/21029539/quantum/setup1/step2.png

https://dl.dropboxusercontent.com/u/21029539/quantum/setup1/step4.png

 

[Nugatory]

We then proceed to firing our particle in this setup and record the exact time it was shot.

How exactly do you determine this exact time which you're going to record? That's an important detail that you've left out.

Once you've worked that out, this setup will be covered by SwampThing's answer in #2 of the thread.

 

[Gaz]

Isn't the difference in distance the whole point of the DELAYED choice experiment?
I was under the impression that the difference in distance was what the delayed was all about and the fact that the results still came out regardless of the delay.

 

[bhobba]

Isn't the difference in distance the whole point of the DELAYED choice experiment?

Actually, while most articles on it don't emphasise it, the whole point really is that decoherence in simple cases can be undone. Once you realize that it becomes quite trivial.

I see a lot of posts about this interesting experiment, but none, in specific set-up's, exactly how decoherence is undone.

Thanks
Bill

 

[Nugatory]

Isn't the difference in distance the whole point of the DELAYED choice experiment?
I was under the impression that the difference in distance was what the delayed was all about and the fact that the results still came out regardless of the delay.

You're talking about something different. The different distance that you refer to is used to delay the availability of "which path" information without disturbing the paths by which interference will be generated (two paths contribute to pattern) or not (one path contributes to pattern).

Here Vloodz is varying the paths by which interference is generated. Not surprisingly, if he varies them so much that only one path can contribute, he gets no pattern.

 

[georgir]

In order for there to be interference, you need to have waves on both paths. So the differences in distance can not be significant. Differences on the order of the wavelength are essentially differences in wave phase, and determine if the interference is constructive or destructive. Larger differences just break the interference completely.

EDIT: And especially when you want to recombine the two paths and "erase" the first splitter, you have to match distances extremely precisely. Otherwise instead of recombining them into a single known direction, it just acts as yet another splitter.