|MadSci Network: Physics|
You ask some tough questions!
Yes, if you send electrons through a 2-slit system one at a time, they will still create an interference pattern on the other side.
No one really knows *why* this happens; no one knows *why* quantum mechanics is the way nature works. In fact, most physicists don't like to think about the question, content to know that the postulates of QM always seem to give the right answer.
But some people still ponder these questions, and the most promising line of reasoning that might someday yield an answer has to do with time symmetry.
Most of the known laws of physics are time-symmetric, and ALL of the known laws of physics are CPT-symmetric (meaning symmetric under a flipping of charge sign, mirror-image, and time-reversal). The arrow of time we observe has to do with a peculiar (low-entropy) boundary condition which lies in the past, but on a microscopic level one could argue that the arrow of time no longer exists -- everything should be symmetric. Philosopher and mathematician Huw Price argues (in his book "Time's Arrow and Archimedes' Point") that in a world where there's no arrow of time, quantum mechanics should be exactly the sort of physics we should expect! Maybe this line of reasoning will one day lead to an answer as to "why" quantum mechanics is the way it is.
As for question #2, you almost seem to be precisely describing John Cramer's transactional interpretation of quantum mechanics.
In this theory, an electron approaching a 2-slit apparatus would send out a "transactional wave" into the future. The wave would pass through both slits, arrive at the detector in the back, and then reflect *backwards in time* back through the 2-slit system, back to the original electron. The interference of the forward-in-time and backwards-in-time wave would then form a type of "guide", telling the electron where to go. The electron would follow this guide, and would arrive at the detector as IF it passed through both slits, although in reality it would only pass through one.
This theory precisely duplicates all predictions of standard quantum mechanics, and it gets rid of nasty wave/particle duality questions altogether. However, it now has waves travelling backwards in time -- something most physicists have an aversion to. Still, as argued above, perhaps one would *expect* this sort of time-symmetric behavior on a microscopic scale, so perhaps even this is an advantage. Still, these theories remain highly speculative and it's not clear how one would experimentally test them.
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