Can we know the future with quantum mechanics? I have created a test scenario.
Please see the image below. Two men working on this test, Erdal and Kervan.
Erdal is in the world, but kervan is 10 light seconds far from the world.
The light source throws a photon once per 10 seconds, And kervan randomly places or removes the mirror 5 seconds after the light source throws the photon.
As I understand from the Delayed-choice quantum eraser if we measure the way of the photon DX will detect the photon as particle form. But if we don't measure the way of the photon DX will detect the photon as a waveform.
So, If this test scenario works, can Erdal know Kervan's decision before he does?

 A: You have misunderstood the quantum eraser. I also misunderstood it for a long time because it is often explained in a way that sounds cool, but is misleading (e.g. PBS Space Time on YouTube). What is not emphasized is that at detector D X, it doesn't matter what Kervan does, D X sees no interference on his screen. That is because as soon as the crystal at BBO splits the photon into two entangled photons, there cannot be any interference anymore.
Where the interference "appears" is that if, after the whole experiment is done, Kervan tells Erdal which photons hit detector 1 vs which ones hit detector 2, then if Erdal looks only at the subset of his sample which went into Kervan's detector 1, he will see an interference pattern. And by sampling only the photons from Kervan's detector 2 you also see an interference pattern, offset by one half wavelength. Summing those two patterns together creates the no-interference pattern seen by Erdal, which he sees regardless of whatever Kervan decides to do with his photons. So you only see interference after the fact, by choosing which photons to look at.
A good source to understand the quantum eraser is Sean Carroll's blog (here).
