Variant on the double slit experiment

[Linguofreak]

I've been wondering lately what would happen if we took the double slit experiment and, instead of trying to measure *which* path the particle takes, rather measuring whether it takes one path or both.

For example, we set up a pair of detectors at either slit, and wire them to an XOR gate. We fire a particle at the slits and observe a count on the screen behind the slits. There are then two possibilities for what we see at the output of our XOR gate just before we observe the count on the screen:

1) One of the detectors observes the particle, and the other doesn't (or the two detectors are in a superposition of detection/no detection such that their outputs are opposite of each other), which causes the output of the XOR gate to emit a count (per the truth table for XOR), so we know that the particle took a single path, but *we don't know which path it took* (unlike the usual formulation of the double slit experiment where we detect which path the particle took).

2) The two detectors both make the same observation, and the XOR gate stays low. We can't actually tell from just that whether either detector detected a particle or not, or was in a superposition of detection/no detection, but we know that we fired a particle and got a count at the screen but no count from the XOR gate, so we know that the particle traveled from the source to the screen, and that it did not a single path (or we'd get a count from the XOR gate), thus we can say that it took both paths.

If we place another pair of detectors immediately behind the ones wired to the XOR gate, but the second set are set up to give us "which path" information, we'll obviously see the following results:

1) We'll observe no interference pattern at the screen, just as in the usual double slit experiment.

2) We'll see a 50/50 distribution of detections at the left and right slits for both the "one path" and "two path" cases, as well as for the total number of detections. (Unless the source is off-center, in which case it will no longer be 50/50, but will still be the same for "one path" and "two path").

3) We'll see the same distribution of XOR gate counts for both left slit and right slit detections.

But if we *don't* have the left/right detectors there, what will we see? Will we still get an interference pattern overall? If we look at where "one path" and "two path" counts end up on the screen will we still observe an interference pattern in either or both distributions?

Finally am I right in thinking that |one path> and |two path> are related to |left> and |right> such that:

|two path> = (|left> + |right>) / sqrt (2), and |one path> = (|left> - |right>) / sqrt (2) ?

 

[Col_Klonk]

This experiment assumes that it is the same particle that we fired at the slits, that ended up on the other side. :idea:

 

[Linguofreak]

This experiment assumes that it is the same particle that we fired at the slits, that ended up on the other side. :idea:

Well, that is an assumption of the double slit experiment in general.

 

[statickid]

I don't know it sounds like trying to defeat the particle with a battle if wits! :lol:

My gut instinct says the particles would just carry on as if their path is being detected. I feel like it doesn't matter how the path is detected just that it's been detected.
I mean, obviously it's just speculation...
But hey that's what experiments are for!!

 

[MaverickSawyer]

I strongly suspect that you would get the same result as if you were to perform the test in the "classical" method.

 

[martins]

I would argue that it is essentially still the original experiment. The two detectors are the observers in this case, whether or not they share their observation with you directly or via an xor gate. Putting in the xor gate simply means that you don't want to know, so you remove some of the available information. The equivalent would be to leave out the xor gate, but then not looking at the measurements from the detectors. The interference pattern would still be destroyed.

 

[jedidia]

I would argue that it is essentially still the original experiment.

I had pretty much the same impression, but I wasn't sure I was understanding the question correctly.

Observation doesn't imply sharing of knowledge. It's not like there is something magical about humans that would make reality behave in a different way because it wants to fool us. Observation is observation, the nature of the observer seems rather irrelevant.

 

[RisingFury]

Observation pretty much boils down to an interaction with something. Anything.

 

[Thorsten]

The two detectors are the observers in this case, whether or not they share their observation with you directly or via an xor gate

Surprisingly not necessarily (even a detector can be in a quantum superposition of states, that's the whole point of Schroedinger's cat). I recall that there was an experiment in which the setup was such that they could determine a measurement was made but not what the outcome was, and then the outcome was erased by some means - and as a result, the full quantum interference pattern was back. So the mere fact that the detector registered something was not sufficient to destroy the pattern - you actually had to know what it registered to do that.

Sadly, I can't recall the details of the particular experiment, but conceptually a detector isn't necessarily an observer, of that I am quite sure.

QFT is more weird than usually given credit.

 

[Col_Klonk]

Well, that is an assumption of the double slit experiment in general.

I see Thorsten beat me to it.. anyway, I thought you were going the quantum route.. Sorry.. jumped the gun.. no pun jump intended

 

[Linguofreak]

Surprisingly not necessarily (even a detector can be in a quantum superposition of states, that's the whole point of Schroedinger's cat).

Well, the whole point of Schroedinger's cat was to say "but this is all absurd, if we allow an atom to be in a superposition of states, then we have to let a detector be in a superposition, and then we have to let a gun set off by the detector be in a superposition, and a cat whose brain may or may not be splattered by the gun be in a superposition, and it gets more and more absurd as we go up the chain".

My understanding of how modern physics tends to view it is that as more and more particles are involved at higher and higher temperatures and lower and lower densities, the likelihood that a randomly selected superposition out of all of the possible quantum states of a large system looks like a familiar classical state increases, such that a state that was truly ambiguous between a cat being "alive" and "dead" would be destroyed by thermal noise in the cat and its environment in less than an eyeblink, unless the cat were chilled to near absolute zero (killing it), or compressed to the point of fermion degeneracy (also killing it). The cat is in a superposition of states at all times, but each of the superpositions it ends up in can unambiguously be identified as "alive" or "dead"

Anyways, the point of the detectors and XOR gate in my example is to give an idea of the measurement I want to make on the particle. Actual non-ideal detectors hooked up to a non-ideal XOR gate might well introduce enough entropy to destroy the interference pattern, but the real question I'm asking is "what happens in the double slit experiment if we measure in a basis such that the two possible outcomes are superpositions of |left> With |right>?

 

[Thorsten]

My understanding of how modern physics tends to view it is that as more and more particles are involved at higher and higher temperatures and lower and lower densities, the likelihood that a randomly selected superposition out of all of the possible quantum states of a large system looks like a familiar classical state increases, such that a state that was truly ambiguous between a cat being "alive" and "dead" would be destroyed by thermal noise in the cat and its environment in less than an eyeblink,

Otherwise known as 'decoherence' which is one interpretation of what happens ('many worlds' and 'collapse of wave function' being others) - the problem with decoherence is that it has a 'magic' step - there's a quantum system linked to a classical environment, but such a classical environment doesn't emerge from quantum theory itself. Or, put another way, decoherence doesn't explain where the one branch of the world which was the original superposition disappears to, it's just 'gone'.

Like the other interpretations, all of this isn't really compelling if you think it through in detail.

---------- Post added at 01:17 PM ---------- Previous post was at 06:20 AM ----------

With regard to the original question, I believe what you'll see is the following:

1) since measuring two particles in two detectors for firing one particle at the setup isn't a classically possible outcome, the total count of particles measured per try will always come out as one

2) provided the information of the two detectors is sufficiently 'erased' such that the information which path was taken is truly not recoverable, the normal interference pattern will be seen once enough statistics has accumulated

3) provided the information on the path is not sufficiently erased such that it is recoverable (but you just don't recover it), a superposition of two independent probability distributions will be observed without interference

 

[Linguofreak]

1) since measuring two particles in two detectors for firing one particle at the setup isn't a classically possible outcome, the total count of particles measured per try will always come out as one

Note, however, that the setup is arranged so that the classical information that we actually observe is the presence or absence of a single pulse from the XOR gate before the particle hits the screen, with a pulse meaning "dissimilar inputs to the XOR gate", from which we infer "one way" and no pulse meaning "similar inputs to the XOR gate", from which we infer "two ways", or perhaps better "not one way".

 

[Thorsten]

I'm sure you have an idea in mind why that changes something, but I really can't see it.

 

[Linguofreak]

Well, the idea is that you're making a measurement of the state of the particle when it passes through the slits, but the basis for the measurement is rotated away from the right slit vs. left slit measurement from the usual formulation of the experiment, so the two states that the measurement might put the particle into are different, so the result when those states propagate to the screen should be different.

But actually, I just realized something: I'm not sure that the experiment as I've just described it doesn't measure the state of the particle in a basis where one of the possible outcomes of the measurement lines up with its existing state as it passes the slits, in which case we'd just always get that state: in other words, the XOR gate never fires before we observe a count on the screen, so we always find the state to be "not one path".

 

[statickid]

This is exactly what I meant in my comment: the particle is detected by the detector, the logic gate is simply a form of data processing.

---------- Post added at 12:17 PM ---------- Previous post was at 12:13 PM ----------

I can set up a gorilla detector in my yard but it's not going to cause gorillas appear for the sake of being detected.

 

[Thorsten]

Well, the idea is that you're making a measurement of the state of the particle when it passes through the slits, but the basis for the measurement is rotated away from the right slit vs. left slit measurement from the usual formulation of the experiment, so the two states that the measurement might put the particle into are different, so the result when those states propagate to the screen should be different.

I fail how you could realize this setup without asking for a position eigenstate at the location of the slits. And this will inevitably yield the observation that each particle passed through one slit only.

 

[perseus]

I propose that at the exit of the door XOR to 1
  Open a gate in a box containing a mouse that will feed Schrödinger's cat, which will be alive only if the electrons pass through grid B.

A matter of life or death, or the cat dies of hunger because the mouse does not come out, and the mouse dies locked or the cat dies and the mouse leaves when the electron passes through the slot A or the cat lives and the mouse dies Shakespearean tragedy, in which the protagonists die, to be or not to be, hehe hehe

At the end of the day, if you do not look inside a box with an animal, you will never know if it is alive or dead.
Superposition of states. If you look at it you will know, but it will destroy the probabilities of one state or another.

The persistence of a probality in time, forms a reality, (pattern of interference)-

This is exactly what I meant in my comment: the particle is detected by the detector, the logic gate is simply a form of data processing.



I can set up a gorilla detector in my yard but it's not going to cause gorillas appear for the sake of being detected.

You must have a gorilla generator near your yard and throw them through the fence in your yard.

 

[Col_Klonk]

It's simple really..
In the wave diagram.. the energy transits the medium to appear on the other side - this is the biggest clue

It would be no different for the theoretical photon particles

 

[Thunder Chicken]

Probably old news, but I quite like the visual intuition that this video delivers on the double slit experiment per deBroglie's pilot wave theory.