Let's first look at the experimental setup in the image below:
The light particles or photons are sent to 2 different detectors D_s and D_p which are connected with a “coincidence counter“. The photons of type "s" pass through a double slit (one at a time) before hitting detector D_s whereas photons of type "p" travel unhindered to the detector D_p. The setup is configured in such a way that the polarization of "s" photons at D_s can only be measured if the coincidence counter registers an event: a coincidence event only happens if "s" photons and their entangled twins (photons of type “p”) arrive at their detectors D_s and D_p at about the same time.
Before the "s" photons reach the detector D_s a set of 2 quarter wave plates QWP1 and QWP2 can be activated: each quarter wave plate alters the polarization of the light in a specific way, say photons travelling through the left slit are polarized vertically, the ones that go through the right slit are polarized horizontally. The detector D_s finally measures the polarization of the incoming photons so that we know which slit the photons went through.
Now let's look at the actual experiment:
Without switching on QWP1 and QWP2 we first detect the familiar interference pattern at D_S: each photon acts as a wave of probabilities. As soon as we activate QWP1 and QWP2 the wave function of the photons collapses: the interference pattern is replaced by stripes as the act of measuring the polarization at D_s, or learning the path of each photon constitutes a quantum measurement (see the second post of this series).
It has to be emphasized that without the measurement at D_s the mere act of changing the photon's polarization doesn't have the slightest effect on the creation of an interference pattern. It's the act of measuring the polarization at D_s that leads to a collapse of the wave function.
Note that in this setup the entangled photons on path "s" and "p" arrive about the same time at their respective detectors, that's why the conicidence counter allows a measurement of the "s" polarization at D_s at all.
So far, so good. Be prepared for something really bizarre ...
Now we put a plate in the path of the "p" photons that tends to block them (the plate is not displayed in the image above), the rest of the setup remains unchanged. The effect of the plate is to somewhat stop the coincidence counter from registering coincidences. As a consequence the ability to learn about the path the "s" photons took is lost as most of them don't arrive simultaneously with their "p" twins any more and so a measurement at D_s does not take place.
As a result of this altered setup we see an interference pattern again at D_s - kind of makes sense: No coincidence event -> no measurement as D_s -> information loss about which way the "s" photons travelled -> no collapse of the wave funtion -> no stripes but an interference pattern. Business as usual, one would think ...
But think again: how on earth could the "s" photons possibly know that we put the plate in the path of the "p" photons and thus behave differently?
You might say that "s" and "p" photons somehow quickly exchange information about the altered setup. After all they are entangled so maybe, as soon as the "p" photons hit the plate they sent a quantum sms to the "s" photons saying "hey partner, I'm getting blocked here, you better behave like waves now".
So, let's extend the path "p" such that "s" photons go through the double slit way before the "p" photons hit the plate, that way relevant information from "p" to "s" photons can't possibly be exchanged without going backwards in time.
Guess what: We still detect an interference pattern at D_s although all the action for "s" photons around the double slit happened before the "p" photons hit the plate which ultimately leads to the information loss described above. The "s" photons act like waves although the decision whether to behave like particles or waves at the double slit has to happen before the information loss occurs through the missing coincidence event.
This is worth being spelled out: An event that happens in the future ("p" photons hit the plate resulting in information loss) influences the way the "s" photons behave in the present (ie. acting like waves when going trough the double slit). Does that mean photons can go back in time ignoring the law of cause and effect?
Somehow the photons seem to know what we intend to measure: The "s" photons decide to act like waves as soon as we intend to destroy the ability to learn information on the way the "s" photons travel by scrambling up the coincidence events.
The shocking conclusion is that the photons seem to know our mind and act in accordance with our intention!
Meditate on this, I will ...
The experiment described above was first performed in 2002 (Physical Reviews A65, 033818) and confirmed again and again in countless variations: it seems to be the intention of the observer alone that influences the outcome of a quantum measurement. To this present day nobody succeeded in coming up with an alternative, reproducable explanation (and believe me, thousands of physicists tried very hard), which of course doesn't mean there isn't any :-)