Double slit experiment question.

In this scenario, the key factor determining whether an interference pattern or a particle-like behavior will be observed lies in how the information about which slit each electron passes through is handled. Let's break down the situation:

1. **Single Electron at a Time**: You are sending one electron through the slits and waiting for its detection before sending another. This method ensures that there are no simultaneous electrons interfering with each other, which simplifies the analysis since we don’t have to consider interactions between multiple particles.

2. **Delayed Detection Information**: The detector is located 1 light minute away from the slits. This means it takes at least 1 minute for any information (i.e., which slit the electron went through) to reach you after the electron has been detected. Until that time, there is no way to know which slit the electron passed through.

3. **Quantum Mechanical Consideration**: According to quantum mechanics, until a measurement or observation is made, the electron exists in a superposition of states, meaning it could have gone through either slit. The act of detection (which happens 1 minute after the electron has already passed through the slits) collapses this superposition into one specific state.

Given these points:
- **Before Detection**: While each electron is traveling from the source to the detector screen, it behaves as a wave and can interfere with itself if both paths (through either slit) are available. This would lead to an interference pattern on the detection screen.

- **After Detection**: Once you receive the information about which slit the electron passed through (after 1 minute), this is retrospective knowledge. The act of detection itself does not affect the behavior of the electrons that have already been detected; it only provides post hoc data.

Therefore, if you observe the pattern on the screen in real-time as each electron arrives, before you know which slit it passed through, you would see an interference pattern characteristic of wave-like behavior. This is because the electrons are exhibiting quantum coherence until they are actually detected, allowing for self-interference to occur. Once the detection information is received 1 minute later, that information confirms where on the screen each electron was found, but does not change the fact that while in transit, the electrons were behaving as waves capable of producing an interference pattern.

In summary, under these conditions, you would observe an interference pattern if looking at the real-time detections, indicating wave-like behavior, even though later (1 minute after each detection) you can retrospectively determine which slit each electron went through.

In this scenario, we're dealing with a delayed-choice quantum eraser experiment of sorts, where the information about which slit each electron passes through is not available until 1 light minute after it has gone through the slits.

Here's how it works:

1. **Delayed Knowledge**: Since the detector is 1 light minute away, you won't know which slit the electron went through for 1 minute after it has passed through the slits.

2. **Wave-Particle Duality**: Quantum mechanics tells us that if we do not observe which slit an electron passes through (i.e., if we don't have which-path information), the electron behaves as a wave and can interfere with itself, leading to an interference pattern on the screen. Conversely, if we do know which slit it passed through, the electron behaves more like a particle, and no interference pattern is observed.

3. **Delayed Choice**: The key insight here is that the act of observation (or lack thereof) determines whether the electron behaves as a wave or a particle, even if this decision is made after the electron has already passed through the slits. This principle is known as Wheeler's delayed-choice experiment.

### What Pattern Is Observed?

- **If You Wait to Collect All Data Before Analysis**: If you wait for 1 light minute before analyzing the data (i.e., waiting to see which slit each electron went through), and then use this information to sort the electrons, you will find that:
- Electrons for which you know the path (which slit they passed through) will form a particle-like pattern.
- Electrons for which you do not have this information (if you choose to erase or ignore it) will contribute to an interference pattern.

- **If You Send One Electron at a Time and Wait for Detection**: If you send one electron, wait for the detection signal, and then decide whether to use that information:
- If you use the which-path information after each detection, the electrons will collectively form a particle-like distribution.
- However, if you choose not to use this information (i.e., you don't record or consider it), the electrons will collectively form an interference pattern.

### Conclusion

In your specific setup where you send one electron at a time and wait for the detection signal before sending the next:

- **If you use the which-path information** (record which slit each electron went through) after each detection, you will observe a particle-like distribution.
- **If you do not use this information** (ignore or erase it), you will observe an interference pattern.

The choice of whether to use the which-path information is made after the electron has already passed through the slits, but it still determines the final observed pattern. This demonstrates the profound and non-intuitive nature of quantum mechanics, where future measurements can influence past events in a certain sense.

To answer this question, let's break it down step by step and consider what happens when we send electrons through the slits one at a time.

1. **Single Electron Experiment**: In a single-electron experiment using the double slit setup, each electron is fired individually towards the two slits. The key point here is that electrons are emitted one at a time in discrete packets known as "wave packets" or simply "quanta."

2. **Interference Pattern Formation**: When you send individual electrons through the slits and observe where they land on the detection screen, an interesting pattern emerges. This pattern consists of alternating bright (constructive interference) and dark (destructive interference) bands. This is a classic demonstration of quantum mechanical behavior, specifically wave-particle duality. The formation of this pattern can only be explained by considering electrons as both particles and waves simultaneously – a phenomenon known as wave-particle duality.

3. **Time Delay**: In your scenario, the detector is placed far away (1 light minute) such that when an electron reaches it, you do not know which slit it passed through. This setup essentially averages out the interference pattern because each electron's position on the detection screen corresponds to both slits being open simultaneously due to the time delay.

4. **Observation**: If you were able to detect the path of each individual electron (which is impossible with current technology), you would observe that an electron either goes through one slit or the other, not both. However, when observing many electrons collectively, they display a pattern indicative of interference, which suggests that while individually they take definite paths, their collective behavior shows wave-like properties leading to the formation of an interference pattern.

5. **Conclusion**: The observation of an interference pattern in this context is consistent with the principles of quantum mechanics and demonstrates the probabilistic nature of electron behavior. This experiment illustrates how particles can exhibit characteristics traditionally associated with waves when observed collectively or over time, which contrasts with classical particle motion where each particle follows a definite path.

In summary, the pattern observed in such an experiment is an interference pattern, not because electrons are simultaneously passing through both slits (which is impossible due to their wave-like nature), but rather because of their probabilistic behavior as particles and waves combined.

The pattern observed will be an interference pattern.
Here's why:
The fact that you won't know which slit the electron passed through for 1 minute after it has already gone through the slits is crucial. The wave function of the electron passes through both slits simultaneously. The interference occurs at the slits and continues as the wave propagates towards the detector.
The act of "knowing" which slit the electron went through (measurement) is what collapses the wave function and forces the electron to behave like a particle, resulting in two distinct bands on the detector screen.
In this scenario, even though you will eventually know the path of each individual electron, that knowledge comes after the interference has already taken place. Each electron, individually, contributes to the interference pattern on the detector. Over time, as you send many electrons, the characteristic bright and dark fringes of an interference pattern will build up.
In summary: The delay in knowing the information doesn't change the fundamental principle of the double-slit experiment. As long as there is no measurement or interaction that determines the electron's path before or as it goes through the slits, it will behave as a wave and create an interference pattern.

The pattern observed will be the interference pattern.
Here's why:
The key factor in determining whether an interference pattern or a particle pattern is observed in the double-slit experiment is whether there is a measurement made to determine which slit the electron passes through before or as it passes through the slits.
In this scenario, even though the information about which slit the electron passed through is available at the source after 1 minute, this information does not affect the electron's behavior as it travels from the slits to the detector.
From the electron's perspective, no measurement is being made on its path between the slits and the detector. It behaves as a wave and passes through both slits simultaneously, leading to interference. The detection at the screen is the final interaction of the electron, and it is here that the pattern is formed.
The delayed knowledge of the slit does not retroactively change the wave-like behavior of the electron as it traveled. The electron doesn't "know" that its path will be determined later.
This is consistent with the principles of quantum mechanics, particularly the idea that observation (measurement) plays a crucial role in determining the behavior of quantum particles. Without a measurement of the electron's path at or before the slits, interference will occur.
Think of it this way: the pattern on the detector screen is formed by the accumulation of many individual electron detections. Each electron, individually, behaves as a wave and interferes with itself. The delayed information about the slit does not change the behavior of each individual electron as it travels and is detected.
Therefore, over time, the accumulation of these detections will reveal the characteristic interference pattern of the double-slit experiment.

This is an interesting variation of the double-slit experiment, which is a cornerstone of quantum mechanics. Let’s break it down step-by-step to determine what pattern you’d observe.

In the standard double-slit experiment, when electrons (or photons) are fired one at a time through two slits and detected on a screen, an interference pattern emerges over time. This pattern—alternating bands of high and low intensity—suggests that each electron behaves as a wave, passing through both slits simultaneously and interfering with itself. However, if you measure which slit the electron passes through (e.g., by placing a detector at one slit), the interference pattern disappears, and you instead see a particle-like pattern: two distinct clusters of detections corresponding to each slit.

In your setup, you’re sending electrons one at a time through the slits, but the detector is 1 light-minute away (the distance light travels in 1 minute, about 18 million kilometers). You wait for each electron’s detection before sending the next one. The key question is whether the delay between emission and detection, or the act of waiting, affects the pattern observed.

### Analysis
1. **No Which-Slit Measurement**: You’ve described a setup where a “stream of photos” (likely a typo for photons or electrons) passes through one of the slits, but the detector is far away, and you’re not explicitly measuring which slit each electron goes through before it reaches the detector. Assuming the detector only records the position of each electron’s arrival (like a screen in the classic experiment), the information about "which slit" remains unmeasured. In quantum mechanics, it’s the act of measuring or knowing the path that collapses the wavefunction, not the distance to the detector or the time it takes to get there.

2. **One Electron at a Time**: Since you’re sending one electron, waiting for its detection (1 minute later), then sending the next, you’re ensuring that only one electron is in flight at a time. This mirrors the single-particle version of the double-slit experiment. In the standard case, even with one electron at a time, the interference pattern builds up over many detections because each electron’s wavefunction passes through both slits and interferes with itself.

3. **Delayed Detection**: The 1-light-minute distance introduces a delay, but this doesn’t fundamentally change the quantum behavior. The electron’s wavefunction propagates through both slits, travels to the detector, and collapses upon detection. The time it takes (1 minute) is irrelevant to the pattern formation, as quantum mechanics doesn’t depend on the classical travel time in this way—only on whether path information is obtained.

4. **Pattern Build-Up**: As you repeat this process—send an electron, wait 1 minute, detect it, send the next—you’re effectively recording the position of each electron on the detector. Over many electrons, the pattern that emerges depends on whether the "which-slit" information is available. Since your setup doesn’t include a mechanism to determine which slit each electron passes through (the detector is just recording final positions), the electrons remain in a superposition of passing through both slits until detected.

### Conclusion
You will observe an **interference pattern**. The pattern will consist of alternating bands of high and low detection probability, characteristic of wave-like behavior, building up over time as you send more electrons. The 1-minute delay and the wait between electrons don’t introduce any "which-slit" knowledge, so the wavefunction doesn’t collapse into a particle-like state prematurely. This is consistent with the standard double-slit experiment when no path information is measured.

If you *did* add a detector at one slit to determine which path each electron took, the interference pattern would vanish, and you’d see a **particle pattern** (two clusters). But based on your description, that’s not the case here.

Let’s dive into this intriguing twist on the classic double-slit experiment. The setup involves sending electrons through two slits, one at a time, with a stream of photons (assuming "photos" is a typo for "photons") passing through one of the slits, and a detector positioned 1 light minute away. We’re tasked with determining whether the pattern observed on the screen—where the electrons are detected—is the wave-like interference pattern or the particle-like pattern. Here’s how we can unravel this step by step.

### Understanding the Standard Double-Slit Experiment
First, let’s establish the baseline. In the traditional double-slit experiment with electrons:

- **No observation of slits**: When electrons pass through the slits without any attempt to determine which slit they go through, they exhibit wave-like behavior. Over many electrons, an interference pattern builds up on the screen—a series of bright and dark bands caused by the superposition of waves from both slits.
- **Which-path information available**: If a detector is placed to identify which slit each electron passes through, the interference pattern vanishes. Instead, you get a particle-like pattern—essentially two overlapping single-slit diffraction patterns, resembling what you’d expect if electrons behaved as classical particles passing through one slit or the other.

The key principle here is that the availability of "which-path" information—knowing which slit the electron traverses—destroys the quantum coherence between the two possible paths, collapsing the wave-like interference.

### Interpreting the Given Setup
Now, let’s dissect the scenario provided:

- **Electrons**: We send one electron through the slits at a time, wait for its detection, then send the next, and so on. Typically, in a double-slit setup, the detector is the screen where the electron’s position is recorded, and this detection happens almost instantaneously after passing through the slits (assuming the screen is close to the slits unless specified otherwise).
- **Stream of photons**: Photons are sent through one of the slits. These photons could interact with an electron passing through that same slit, potentially marking its path. This suggests they act as a which-path detector.
- **Detector 1 light minute away**: The problem states "the detector is located 1 light minute away," and this is tied to the photons, implying that this detector registers the photons, not the electrons. Since light travels 1 light minute in 1 minute, any information carried by the photons (e.g., whether they interacted with an electron) takes 1 minute to reach this detector.
- **Ambiguity in "wait for the detection"**: The instruction to "wait for the detection" before sending the next electron is ambiguous. Does it mean waiting for the electron to hit the screen, or waiting for the photon detection 1 minute later? In context, since we’re observing a pattern formed by electron detections on a screen, it’s reasonable to assume "detection" refers to the electron hitting the screen, which occurs with negligible delay relative to 1 minute, unless the screen itself is 1 light minute away (which isn’t specified and seems unlikely given standard setups).

### Constructing the Experimental Picture
Let’s assume a practical configuration:

- **Electron path**: An electron is fired through the double-slit apparatus and hits a nearby screen, where its position is recorded. This happens quickly—let’s say effectively instantaneously for simplicity, as no significant delay is mentioned for the screen.
- **Photon role**: A stream of photons passes through, say, slit 1. If an electron goes through slit 1, it might interact with these photons (e.g., scattering them), altering their state. If it goes through slit 2, the photons are unaffected. These photons then travel 1 light minute to their detector.
- **Timing**: After the electron is detected on the screen, we send the next electron. Since the screen is presumably close to the slits, this next electron is sent well before the photons from the first electron’s passage reach their detector 1 minute later.

### Quantum Mechanics at Play
In quantum mechanics, the pattern on the screen depends on the state of the electron when it’s detected. Let’s explore this:

- **Initial state**: Without the photons, the electron’s state after the slits is a superposition, like \( (|1\rangle + |2\rangle)/\sqrt{2} \), where \( |1\rangle \) and \( |2\rangle \) represent paths through slit 1 and slit 2. This leads to interference.
- **Photons as which-path markers**: With photons at slit 1, the system becomes entangled. If the electron goes through slit 1 and interacts with the photons, their state might change to \( |p_1\rangle \) (interacted); if it goes through slit 2, they remain \( |p_0\rangle \) (no interaction). The combined state becomes something like:
\[
\frac{1}{\sqrt{2}} \left( |1\rangle |p_1\rangle + |2\rangle |p_0\rangle \right)
\]
- **Electron detection**: When the electron hits the screen, we measure its position, but the photons are still en route, unmeasured for another minute. However, the electron’s state is no longer a pure superposition. Because its path is entangled with the photons’ state, the interference between paths \( |1\rangle \) and \( |2\rangle \) is lost.

### Does the Delay Matter?
Here’s the crux: the photon detector provides which-path information, but not until 1 minute after the electron passes the slits. Does this delay preserve the interference pattern since the information isn’t available when the electron hits the screen?

- **Standard quantum mechanics**: The pattern depends on whether which-path information is obtainable in principle from the experimental setup, not when it’s accessed. The photons’ entanglement with the electron’s path means that, later, one could determine which slit each electron took by checking the photon detector. This potential knowledge decoheres the electron’s wave function at the time of its detection.
- **Delayed-choice analogy**: In Wheeler’s delayed-choice experiment, choosing to measure which-path information after the particle passes the slits still eliminates interference, retroactively aligning the outcome with the measurement choice. Here, the setup inherently includes a which-path mechanism (the photons), fixed from the start, even if the data arrives later.

### The Observed Pattern
Since the photons can reveal which slit the electron passed through—albeit 1 minute later—the electron’s two paths are distinguishable in the system. When we detect the electron on the screen, we don’t see interference because:

- The electron’s state is entangled with the photons.
- Tracing over the photons’ states (since they’re not measured yet) gives a mixed state for the electron, lacking the coherence needed for interference.
- Over many electrons, the screen shows a pattern as if each electron went through one slit or the other, not both.

Thus, the result is a **particle pattern**—two single-slit diffraction patterns superimposed, without the oscillating bands of interference.

### Double-Checking
Could the 1-minute delay allow interference since the which-path information isn’t known at detection time? Quantum mechanics doesn’t work that way here. The entanglement exists from the moment the electron passes the slits, and the future availability of the information is enough to destroy interference. If we blocked the photons from reaching their detector (a quantum eraser scenario), interference might return, but the setup implies the photons are detected, sealing the particle-like outcome.

### Conclusion
The pattern observed on the screen, built up from detecting each electron after it passes the slits, is the particle pattern, not the interference pattern, due to the presence of the photon stream enabling which-path information, despite the 1-minute delay in accessing it.

So, the answer is: **particle pattern**.

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.