So I have this thought experiment here involving the double-slit setup, but with a twist. Normally, in the double-slit experiment, you send a bunch of electrons or photons through two slits and observe an interference pattern on a detector screen, suggesting wave-like behavior. However, if you try to detect which slit each particle goes through, the interference pattern disappears, and you get a particle-like pattern instead.
In this scenario, there's a stream of photos (I think you meant photons, not photos) being sent through one of the slits, but the detector is located 1 light minute away. That means it takes 1 minute for the light to travel from the slits to the detector. So, if I send an electron through the slits, I won't know which slit it passed through until 1 minute later when the detection happens.
Wait, actually, the problem says "a stream of photos is sent across one of the slits," but then it says "send one electron through the slits." I think there might be a confusion in the wording. Let me try to interpret this.
Perhaps it means that there are photons being sent through one of the slits to act as a which-path detector. In standard double-slit experiments, if you have a way to determine which slit the electron went through, the interference pattern collapses. Here, since the detector is 1 light minute away, the information about which slit the electron passed through isn't available immediately; it takes 1 minute to get that information.
But in the setup described, it says "send one electron through the slits. Wait for the detection. Then send another electron, wait for detection, etc." So, for each electron, you're waiting for the detection event before sending the next one.
Wait, but the detection is of the electron itself, right? The problem says "wait for the detection," which I assume means waiting for the electron to be detected on the screen. But then it mentions that the detector is 1 light minute away, which is confusing because in standard double-slit experiments, the detector screen is usually close enough that the travel time is negligible.
Wait, perhaps the key point is that the which-path information is delayed because the photons that could reveal which slit the electron went through take 1 minute to reach the detector.
Let me try to clarify the setup:
- There are two slits.
- Electrons are sent through the slits one at a time.
- Additionally, there is a stream of photons being sent through one of the slits, presumably to interact with the electron if it goes through that slit, thereby providing which-path information.
- However, the detector that would register these photons (and thus provide the which-path information) is located 1 light minute away. So, the information about which slit the electron went through isn't available until 1 minute after the electron has passed through the slits.
- But in the experiment, for each electron, you send it through, wait for the detection (of the electron on the screen), and then send the next electron.
Wait, but the detection of the electron on the screen is presumably almost instantaneous, or at least the travel time is negligible compared to the 1 minute delay for the photons. Wait, actually, the problem says "the detector is located 1 light minute away," but it's not specified whether this detector is for the electrons or for the photons.
Wait, let's look back at the problem statement: "A stream of photos is sent across one of the slits but the detector is located 1 light minute away."
I think "the detector" refers to the detector for the photons, not for the electrons. So, the setup is:
- Electrons are sent through the double slits and detected on a screen, presumably with negligible delay.
- Additionally, there are photons sent through one of the slits, and these photons, if they interact with the electron, could provide which-path information, but the detector for these photons is 1 light minute away, so the which-path information is delayed by 1 minute.
However, in the standard quantum mechanics interpretation, the key point is whether the which-path information is available in principle, not necessarily when it becomes available.
But in this case, since the experiment involves sending one electron, waiting for its detection on the screen, and then sending the next one, and so on, the question is what pattern will be observed on the screen over many such electrons.
Now, for each electron, when it passes through the slits, the which-path information isn't available until 1 minute later, but by the time you send the next electron, you might have that information, depending on how long you wait.
Wait, actually, the problem says "wait for the detection," but it's ambiguous. If "wait for the detection" means waiting for the electron to be detected on the screen, which presumably happens almost immediately, then you would send the next electron right after that, before the 1 minute has passed. But if "wait for the detection" includes waiting for the photon detection, which takes 1 minute, then you would wait 1 minute before sending the next electron.
However, the problem says "wait for the detection," and in the context, it's likely referring to the detection of the electron on the screen, not the photon detection, because the photon detection is separate and delayed.
Moreover, in standard double-slit experiments, the pattern is built up by many particles, and the interference pattern emerges regardless of the timing between particles, as long as the which-path information isn't available.
But in this case, since there is a mechanism to obtain which-path information, even if it's delayed, does that affect the pattern?
Actually, in quantum mechanics, the key is whether the which-path information is obtainable in principle from the experimental setup, not when it becomes available. If the setup allows for the which-path information to be determined, even if it's after the fact, the interference pattern should not appear.
Wait, but there's a subtlety here. In delayed-choice experiments, like Wheeler's delayed-choice experiment, the decision to measure which-path information can be made after the particle has passed through the slits, and it still affects the pattern retroactively, in a sense.
However, in those experiments, the choice is made before the detection, even if after the particle has passed through the slits.
In this scenario, the which-path information is always available, but just delayed. So, for each electron, after 1 minute, you can know which slit it went through by checking the photon detector.
But when you detect the electron on the screen, at that moment, the which-path information isn't yet available, since it takes 1 minute for the photons to reach their detector.
Nevertheless, since the experimental setup includes a way to determine which path each electron took, even if the information is delayed, the standard quantum mechanical prediction is that there should be no interference pattern.
Wait, is that accurate? Actually, I think there's a distinction. If the which-path information is entangled with another system, and that information can be retrieved, then the interference pattern disappears. In this case, the photons that pass through one slit could interact with the electron if it goes through that slit, and then be detected later, providing which-path information.
So, if the electron goes through the slit with the photons, it might interact with them, and the state of those photons would be correlated with the path the electron took. Then, when those photons are detected 1 minute later, you could in principle determine which slit the electron went through.
Therefore, since there is a way to obtain which-path information, the interference pattern should not be observed. Instead, you should see a particle-like pattern, as if each electron went through one slit or the other.
Wait, but let's think carefully. In the standard double-slit experiment with which-path detection, if you have a detector at each slit that can determine which slit the particle went through, then the interference pattern disappears. Here, the setup is similar, but the detection is delayed.
However, in quantum mechanics, the timing of when the information becomes available doesn't matter; what matters is whether the information is available in principle. Since the photons that can provide which-path information are part of the system, and their state is entangled with the path of the electron, the coherence between the two paths is lost, and thus no interference pattern should be observed.
To put it another way, the electron's wave function becomes entangled with the photons' state, and when you trace over the photons' degrees of freedom (since you're not measuring them at the time of electron detection), you get a mixed state for the electron, which doesn't exhibit interference.
So, even though the which-path information isn't available until 1 minute later, the fact that it will be available means that the interference pattern shouldn't appear.
But wait, there's another way to think about it. Suppose that for each electron, you send it through, detect it on the screen, and then, after 1 minute, you get the which-path information from the photon detector. But since you're building up the pattern on the screen over many electrons, and for each electron, at the time of its detection, the which-path information isn't yet known, but it will be known later.
However, in quantum mechanics, the pattern observed is determined by the state of the system at the time of measurement. Since the electron's path is entangled with the photons, which are not measured until later, but the electron is measured first, the pattern should still be the one corresponding to no interference, because the entanglement decoheres the electron's wave function.
Alternatively, perhaps I can think of it in terms of the overall experimental procedure. If, after collecting all the data, you can go back and, for each electron detection event, determine which slit it went through by looking at the photon detection 1 minute later, then you could in principle sort the electron detections based on which slit they went through, and each subset would show a single-slit pattern, not an interference pattern.
Therefore, when you look at the overall pattern without sorting, it would be the sum of the two single-slit patterns, which is a particle-like pattern, not an interference pattern.
So, in this case, the observed pattern should be the particle pattern, not the interference pattern.
Wait, but let's consider if there's any loophole or if the delay changes anything. For example, if you were to somehow prevent the which-path information from being obtained, say by destroying the photon detector before the photons arrive, then perhaps the interference pattern could be restored. But in the setup as described, the photon detector is there, and the information is obtained, even if delayed.
Moreover, in quantum mechanics, the act of measurement or the availability of information is what collapses the wave function, but in this case, since the photons are part of the system and their state is correlated with the electron's path, the interference is already lost at the time the electron passes through the slits.
So, I believe that the pattern observed will be the particle pattern, not the interference pattern.
Wait, but to make sure, let's consider a similar scenario. Suppose you have a double-slit experiment with electrons, and you have a which-path detector that records the information about which slit each electron went through, but you don't look at that information until later. Still, the pattern on the screen will be the particle pattern, not the interference pattern, because the which-path information is available in the system.
Similarly, in this case, even though the information is delayed, it's still available, so the interference pattern shouldn't appear.
Alternatively, perhaps I can think about it in terms of quantum erasure. In quantum erasure experiments, if you have which-path information but then erase it before the final detection, the interference pattern can be restored. However, in this setup, the which-path information is not being erased; it's being detected later.
So, since the information is ultimately obtained, the interference pattern shouldn't be present.
Therefore, the pattern observed should be the particle pattern.
Wait, but let's double-check with a more precise reasoning.
Suppose we model the system quantum mechanically. Let’s say the electron can go through slit 1 or slit 2, with corresponding states |1⟩ and |2⟩. If there were no which-path detection, the state would be a superposition, say (|1⟩ + |2⟩)/√2, and upon detection, it would produce an interference pattern.
However, in this setup, there are photons sent through, say, slit 1. So, if the electron goes through slit 1, it might interact with the photons, changing their state.
For simplicity, let's assume that if the electron goes through slit 1, it interacts with the photons in such a way that the photons' state becomes |photon_interacted⟩, and if it goes through slit 2, the photons remain in their initial state |photon_no_interaction⟩.
So, the overall state after the electron passes through the slits would be:
(1/√2) [ |1⟩ |photon_interacted⟩ + |2⟩ |photon_no_interaction⟩ ]
Then, when the electron is detected on the screen, the measurement is on the electron's position, but the state is entangled with the photons.
In this case, since the photons' states are different depending on which path the electron took, the interference terms cancel out, and the pattern observed is equivalent to a classical mixture of electrons going through slit 1 and slit 2, i.e., no interference.
Even though the photons are not measured until later, the fact that they are in different states correlated with the electron's path means that the electron's wave function has effectively collapsed, and no interference is observed.
Therefore, the pattern observed should be the particle pattern.
Alternatively, if the interaction with the photons is such that it doesn't perfectly distinguish the paths, there might be some residual interference, but in the problem as stated, it seems that the stream of photons is intended to provide clear which-path information, so I think the interference pattern is destroyed.
Moreover, the fact that the detector is 1 light minute away and that you wait for the detection of each electron before sending the next one doesn't change the fundamental quantum mechanical prediction, because each electron is independent, and the pattern is built up from many individual detections.
So, in conclusion, the pattern observed should be the particle pattern, not the interference pattern.
Wait, but just to be thorough, let's consider the timing. Suppose you send an electron, it passes through the slits, and almost immediately is detected on the screen. Then, 1 minute later, the photons arrive at their detector, and you can determine which slit the electron went through. But since the electron has already been detected, and its position recorded, the pattern is already formed.
However, in quantum mechanics, the pattern is determined by the state at the time of detection, and since at that time the which-path information was entangled with the photons, the pattern should reflect that.
Alternatively, perhaps one could argue that since the which-path information isn't available until after the electron is detected, maybe the interference pattern could still be present. But I don't think that's how quantum mechanics works. The presence of the entanglement with the photons, which can later reveal the which-path information, is sufficient to destroy the interference.
In fact, this is similar to the concept in quantum information where if a system is entangled with another system, measuring the first system doesn't show interference effects, even if the second system isn't measured until later.
So, I believe the correct answer is that the particle pattern is observed.
Therefore, the final answer is the particle pattern.
Wait, but in the problem statement, it says "wait for the detection," which might imply waiting for both the electron detection and the photon detection, but I think it's more likely that it means waiting for the electron detection, as that's the primary measurement being made.
Moreover, even if you wait for the photon detection before sending the next electron, since for each electron, the which-path information is available (albeit after its detection), when you look at the overall pattern, it should still be the particle pattern, because each electron's detection is correlated with its path.
Alternatively, perhaps if you consider the entire sequence, but I think it doesn't change the conclusion.
So, to summarize:
particle pattern \boxed{\text{particle pattern}} particle pattern
Yes, I think that's the answer.