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Is the overall rate of particle detections you will obtain in a classic double slit experiment dependent on whether the experiment is set up to cause an interference pattern or not?

Another way of asking this is whether you can interpret the interference pattern as the ABSENCE of particles you would have ostensibly detected had their paths been defined?

The motive behind this is that in quantum eraser experiments, the initial detection pattern always appears as random noise; it's only when you filter the results based on the "erasure" of the which-path information for the entangled twins that the pattern emerges from the noise. While often presented as proof of retrocausality, one could (and IMO should) interpret the results merely as a data gathering and filtering exercise.

But of course in the classic double slit scenario, there is no correlating and filtering after the fact; the pattern emerges then and there. But does that pattern arise because the particles we wound up detecting behaved differently due to the presence or absence of path detectors, or - as in the quantum eraser - because we failed (intentionally or not) to detect the ones that would have otherwise landed between the bands? And if the detection rate is unaffected by path knowledge in the classic experiment, does this suggest a different physical mechanism is at play vs a quantum eraser?

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Is the overall rate of particle detections you will obtain in a classic double slit experiment dependent on whether the experiment is set up to cause an interference pattern or not? Another way of asking this is whether you can interpret the interference pattern as the ABSENCE of particles you would have ostensibly detected had their paths been defined?

No, regardless of whether the setup is designed to get which-way information (thereby destroying the interference pattern) or not, the same number of photons will hit the screen*. While the total number of photons is the same, however, their distributions in the interference case is of course different from the non-interference case.

While often presented as proof of retrocausality, one could (and IMO should) interpret the results merely as a data gathering and filtering exercise.

I agree with this, and at some point I was also fooled by explanations of the delayed choice double slit which didn't make this clear.

But does that pattern arise because the particles we wound up detecting behaved differently due to the presence or absence of path detectors, or - as in the quantum eraser - because we failed (intentionally or not) to detect the ones that would have otherwise landed between the bands?

The former is correct here and the latter is not.

And if the detection rate is unaffected by path knowledge in the classic experiment, does this suggest a different physical mechanism is at play vs a quantum eraser?

In the quantum eraser the detection rate at each point is still the same regardless of any path knowledge obtained afterwards. So I would see it as the same physical mechanism, unless you had a different idea in mind? In addition to this same physical mechanism, the delayed choice quantum eraser has a filtering effect, but I understand that as a separate effect which results from the entangled photons that are created.