The experiment says that if I split a photon into two coherent entangled photons, one towards a double-slit, one towards a which-way detector, I can control whether
- the interference pattern appears by choosing either detecting which way the photon came through or
- destroying the information about the photon, even if the detector/destroyer is further away than the double slit screen.
Does it imply that I can know about whether the which-way information will be detected or not even before it is detected?
Suppose I have a person controlling the detector 10 ly away from the slits, and the double-slit setup immediately in front. Then just by looking at the screen, will I be able to know whether the person 10ly away decides to observe or not 10 years before he even decides it? I am quite uncomfortable with this thought.