If I shoot an electron through a substance, is it theoretically possible to plot its path through said substance?
Has this been experimentally done?
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If you try to watch it then you just find out how watched electrons move. Or as dmckee reminds us, the quantum zeno effect might even stop them from having a chance to move.
If you don't watch it then you don't see it so you don't know how they moved or whether they even just appear where you see them.
You can try so called weak measurements to try a bit of both, but it's not really what you want, but I could be wrong. Study weak measurements if you think it's good to study, maybe it is what you want.
Another option is to make a detailed theory about the probability of it being different places. Done. And then make a detailed theory about the probability flow. Done. And then when you do a measurement of position at one time you can mathematically compute the streamline that ended there and retrodict that it followed that streamline.
The biggest problems are firstly that it is pointless (retrodictions make no predictions) so not much effort it devoted to it and secondly that the probability is based on entire configurations of every particle and we don't observe all the particles. Therefore, if you only measure one or two particles or so then there are still lots of streamlines through the space of all configurations.
Timaeus
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