The Double Slit Experiment - delayed measurement

I'm not a physicist; I'm just curious about what would happen.

According to this video "Explained ! The Double Slit Experiment" (at 2:50):

"Somebody decided to leave the detectors on but just not take any data. [...] So if it was also going to a magnetic tape - there was no magnetic tape loaded. [...] And what do you think happed? They got this. They got the diffraction pattern."

So the act of measuring (beeing concious of the data) destroys wave-form pattern?

If so lets consider these cases:

1. What if I'd throw a dice after the experiment to decide if I should look at the data or to destroy it? (e.g. look at the data if the number on dice is even)


2. What if the information about measurement would need to travel longer period of time than the particle would need to hit the wall?

To above cases: Would it mean that information travelled instantly - faster than light or that "the particle can look into the future"?

Answer

Both of the experiments that you have proposed have actually been done. The first is called the quantum eraser, and the second is called the delayed choice quantum eraser.

The answer to your question is that if information about which path the particle took is available at the time of measurement then no diffraction pattern will be seen. So, if you take data about the path and then delete it before the experiment is observed (and your apparatus is set up so that the system does not decohere) then you will still see a diffraction pattern.

One way to understand this is to notice that a diffraction pattern is equivalent to measuring the momentum of the photons (since the wavelength is related to the distance between peaks) and a measurement of the path is a position measurement. The uncertainty principle says we can't know both with arbitrary precision at the same time. So, a well constructed quantum eraser experiment guarantees that either you can know the path or you can see the diffraction pattern but never both.

Then, your question becomes "when I observe the experiment am I performing a position measurement or a momentum measurement." The answer to this question, for any quantum mechanical experiment, is that you are performing the microscopic measurement whose different results correspond to distinct macroscopic states (like a dial being in different positions). In the quantum eraser experiment the apparatus is designed so that, depending on exactly how the experiment goes, either the microscopic position or momentum measurement will correspond to distinct macroscopic states. If you can read the data about which path the photon took it is obviously the position measurement that gives you distinct macroscopic states, and if you can see the diffraction pattern it is the momentum measurement.