Double Slit Question: Path Information & Observer's Experiences

[Gerinski]

May I ask about this configuration:

Let's say we install detectors on the slits so the detection at the screen will be 2 dots, one coming from slit A and one coming from slit B. No interference pattern.

We also set up the experiment so that there is not 1 observer but 2.

Observer A' is placed so that he can only see half of the screen, the half that gets hit when the particle goes through slit A. If the particle goes through slit A he will see a dot on the part of the screen he can see and he can write it down. If it goes through slit B he will see nothing, he doesn't even know if a particle has been fired at all.

Conversely, observer B' is placed so that he can only see the half of the screen which gets hit when the particle goes through slit B. If the particle goes through slit B he will see a dot on the part of the screen he can see and he can write it down. If it goes through slit A he will see nothing, he doesn't even know if a particle has been fired at all.

Moreover, none of the observers is aware that there is another observer who can see the half of the screen they can not see. In fact they don't even know they are only seeing half of the screen. All they can tell is that they are requested to write down their letter whenever they see a dot in the screen they can see.

So if we run the experiment firing a shower of electrons at once, each observer will write down that they see a bright focused spot on their screen, no lines.

If we run the experiment firing electrons one by one, say 1000 electrons, observer A' will write down that he saw 500 dots appearing in the screen, and observer B' will write down that he saw 500 dots appearing in the screen, all of them, focused around one point on each screen, no lines.

Now we remove the detectors at the slits.

What will they see if we fire a shower of electrons at once. Interference lines in their half of the screen?

And what will they see if we fire 1000 electrons one by one? Will they always see a dot on the half of the screen they can see? Or only half of the time (500 each)? And will those dots be concentrated on one point, or will they gradually form interference lines?

The reason I'm asking is, most interpretations say that it boils down to whether we generate path information or not. According to each observer, every time they see a dot in their screen there is path information: 'yes, an electron has passed through my slit. I'm sure of that'. They do not know about any other observer watching the experiment.

But taken in combination, if both saw always a dot, 1000 times each, even when they think there is path information, there is none, the total combined information just says that they all passed through both slits.

And going to more extreme scenarios, what if after the experiment we kill both observers and look at their papers? (not that I want to put that in practice lol).

Or, kill only one of the observers and burn down his paper before looking at it, and look only at the other observer's paper?

 

[Nugatory]

According to each observer, every time they see a dot in their screen there is path information: 'yes, an electron has passed through my slit. I'm sure of that'.

The appearance of a dot on the screen does not itself generate any which-path information; you still need the detectors at the slits to do that. If there are no detectors in the slits the probability of a particle landing on any point in A's half of the screen will include contributions from the paths through both slits, so when A sees a dot appear he cannot conclude that the particle went through his slit.

They do not know about any other observer watching the experiment.

The presence or absence of the observers is irrelevant to the outcome of the experiment. If there are no detectors at the slit there will be no which-path information and an interference pattern will form whether there's anyone to see it or not. If there are detectors at the slit there will be which-path information and bright spots will form behind each slit, whether there's anyone to see them or not.

 

[Gerinski]

when A sees a dot appear he cannot conclude that the particle went through his slit.
.

It's easy for you to say that because you are aware of a bigger picture that observer A' is not aware of.
For observer A', if he sees a dot, it means that an electron went through his slit. Full stop.
He may wonder that perhaps it also went through some other slit he is not aware of as well, but that would be just speculation from his side, wouldn't it?
If we follow that, we could as well think that what we are seeing is just because there is some grander picture we are not aware of. Perhaps that would be hidden variables and I'm aware that that possibility was ruled out by Bell, but how could our isolated observer A' come to that conclusion (that his observation does not actually imply any path information)?

 

[Strilanc]

It's easy for you to say that because you are aware of a bigger picture that observer A' is not aware of.
For observer A', if he sees a dot, it means that an electron went through his slit. Full stop.

Observer A's ignorance or lack thereof will have no effect on the outcome of the experiment. What matters is the presence of the detectors, not the presence of the people. If you read a pop science book or video that suggested otherwise then it was either wrong, or an oversimplification that misled you.

The screen itself already distinguishes between "electron hit left" vs "electron hit right". Adding redundant detection of this information, whether it be a video camera or someone peeking into see how the experiment is going, will not affect the statistics.

 

[bhobba]

For observer A', if he sees a dot, it means that an electron went through his slit. Full stop.

If he sees a dot it means a dot was observed - end of story. To say it went through a slit you need to detect it went through the slit.

Thanks
Bill

 

[Nugatory]

He may wonder that perhaps it also went through some other slit he is not aware of as well, but that would be just speculation from his side, wouldn't it?

No. He observes that an interference pattern builds up and correctly infers from this experimental evidence that there is more than one path available to the electron.

 

[Gerinski]

Thanks to all.
I would however like to have more explicit answers to the question: What will they see and what will we see?

1. If we fire a shower of electrons, I guess you mean they will each see an interference pattern, lines in their half of the screen, even if they don't know what can it be interfering with.

2. If we fire electrons one by one, I guess you mean that each of them will see 1000 spots gradually appearing in the part of the screen they can see, building an interference pattern.

3. If we kill both observers and then look at their papers, we will see the same as in #2 i.e. each will have written down 1000 electrons and they will be forming lines (interference).

4. If we kill observer A' and burn down his paper without looking at it, we will find the paper of observer 2 showing that 1000 electrons were detected on his screen, forming lines (an interference pattern with something he is not aware of).

So in all of these configurations, the interference pattern builds up. Only by placing detectors at the slits themselves we can destroy the interference pattern, right?

 

[bhobba]

So in all of these configurations, the interference pattern builds up. Only by placing detectors at the slits themselves we can destroy the interference pattern, right?

Observers have nothing to do with anything.

Thanks
Bill

 

[Nugatory]

1. If we fire a shower of electrons, I guess you mean they will each see an interference pattern, lines in their half of the screen, even if they don't know what can it be interfering with.

Yes. This is no different than seeing a puddle of water on the ground underneath a leaking pipe even if you don't know where the leak is. If a pipe is leaking there will be a puddle of water underneath it whether you know about it or not, and if there are two paths available there will be an interference pattern whether anyone knows about it or not.

2. If we fire electrons one by one, I guess you mean that each of them will see 1000 spots gradually appearing in the part of the screen they can see, building an interference pattern.

There wil be one spot for each electron that reaches the screen, and these spots will form an interference pattern if both slits are open. The pattern will be there whether there are observers or not and whether the observers look at all of the screen or just part of it. As for how many spots each one sees... Well, they'll see all the spots they look at, so if they only look at part of the screen then they'll only see some of the spots on the screen.

If we kill both observers and then look at their papers, we will see the same as in #2 i.e. each will have written down 1000 electrons and they will be forming lines (interference).

If we look at their papers, we'll see whatever they wrote down. Isn't that what "look at" and "write down" means?

4. If we kill observer A' and burn down his paper without looking at it, we will find the paper of observer 2 showing that 1000 electrons were detected on his screen, forming lines

Yes, of course. Why on Earth would you think that what's written on paper number two might change because we burned paper number one?

(an interference pattern with something he is not aware of)

Well, as soon as he saw the interference pattern he knew that there's interference with something, just as you know that there's a leak in the pipes somewhere when you find a puddle of water on the floor.

So in all of these configurations, the interference pattern builds up. Only by placing detectors at the slits themselves we can destroy the interference pattern, right?

yes... Although given the questions you're asking above, we might need to talk about what a "detector" is.

 

[Gerinski]

Thanks

 

[Feeble Wonk]

Observers have nothing to do with anything.

Thanks
Bill

I'm aware that the significant majority of physicists would agree with this position, and will usually attribute any "collapse" that takes place to decoherence effects.

But is the situation truly as certain as your statement would imply? While they are certainly not "main stream", aren't there models consistent with existing data that posit a "participational" role for consciousness?

 

[Nugatory]

But is the situation truly as certain as your statement would imply? While they are certainly not "main stream", aren't there models consistent with existing data that posit a "participational" role for consciousness?

There are, but none of these have any bearing on OP's question nor would call into the question the answers in this thread.

As the original question has been answered, we can close this thread,