Ok... let me give you some background to make you appreciate my assumption about what should happen in this experiment.
The main motivation for looking for such experiments is that there is a phenomenon in this world that Physics has nothing to say about. That is consciousness. What we know at this moment is that consciousness appears in relations to objects called brains. For people who read a little philosophy of mind and reflected upon the problem, it is clear that it is not a computer program or chemical reactions and what have you. The main feature of consciousness is Meaning. Consciousness is Meaning (or Understanding). Also, given the nature of meaning, most probably consciousness exists together with free will. So this is the phenomenology.
Then there is Physics' attempt to discover new physics in order to explain phenomena like dark matter or the masses of particles, etc. The approach that Physics is taking today is to search for an explanation in 2 extreme conditions. One is at colliders where they hope that by pushing the boundaries of energy, they can uncover new physics. The other part of the spectrum is building huge telescopes and looking far into space and time. They are nice attempts, but the problem is that Physics seems to neglect (intentionally or not) another place where trully new physics is going on: our brains. Probably they think that there are only atoms in the brain, obeying already known laws of physics and that's it. Which of course is not true. There is trully new physics in our brain. The most amazing physics that can be. So the question is: What's happening in our brains beyond mere atoms interactions ? And this needs to be answered. Where can you search realistically for an answer ? The problem with consciousness is that it is ontologically subjective. How can you highlight consciousness using ontologically objective explanations ? Is an ameoba conscious ? How can you show this ? Even if you look in the brain of a human, what objective phenomenon should you look for that can tell you for sure that there is consciousness associated with that brain ? I think that this approach of looking in the brain, is at the moment impossible. We have no idea what to look for.
Then what other chances do we have ? Maybe consciousness doesn't only influence the behavior of atoms in the brain (by using free will). Perhaps the relationships between brain and consciousness is not only restricted to our heads. Maybe the relations are more subtle and they are not only relations of the kind: "visual cortex active => qualia of colors". Maybe consciousness somehow leaks out. One aspect of consciousness is knowledge. At first, knowledge seems to be a phenomenon that exists only in consciousness. But since quantum mechanics, if you adopt the interpretation of the collapse of the wavefunction produced by the observer, then it appears that knowledge is not isolated only to our heads. But there exists subtle relations between knowledge as a phenomenon in consciousness and certain phenomena in quantum mechanics. The simplest example is the double-slit experiment. In this case, the interference pattern would not be caused by the particles passing through both slits at the same time, but rather by our failure to acquire knowledge about the slits through which the particle is passing. So the interference pattern is rather the answer of Nature to the question: "Through which slit did the particle pass ?" And Nature answers that question by producing an interference pattern which means: "You don't know." If you put a detector at one of the slits, then you don't get an interference pattern anymore, this actually being the answer of Nature telling you that this time you found out the slit through which the particle passed.
Now we are getting to the experiment that I'm proposing. What we see that happens when we put a detector at slit2 and it detects only 1 particle, is that we have no idea through which slit the second particle passed. So we are basically asking Nature: "Through which slit did the second particle pass ?". And since the answer is "You don't know.", Nature will provide you this answer by displaying an interference pattern between slits1&3.
If this result will really show up when the experiment is performed, we will be finally starting to encounter consciousness and try to create a scientific theory for it. Therefore, I consider this experiment to be of a great importance for the future of all science and understanding what kind of beings we are.
