Shortest distence between two points? 0.
You can say that matter have two sides. One side is particles and the other side is the "waves", or energy. They are all the same, just different sides of the same thing. Sometimes matter act like particles, sometimes like waves.
What I have heard, though, is that information on quantom level travel at an infinate speed. Was what our teacher told us, anyway.
Quote: "You cannot chop stuff up into indefinitely small pieces. Here is a version of Zeno's most famous paradox: Imagine a greek warior sees an archer fire an arrow at him from 100m away so he turns and runs. The arrow is moving 10 times as fast as the runner. By the time the arrow has covered the distance of 100m the runner will have moved 10m. By the time the arrow has moved 10m the runner will have moved 1m. By the time the arrow has moved 1m the runner will have moved 0.1 m. By the time the arrow has moved 0.1m the runner will have moved 0.01 m and so on and so forth. So while we continue to chop things up into indefinitely smaller pieces the arrow will never hit the runner, just like those exponential graphs that get close and closer to 0 but never actually touch it. Obviously this does not work in real life. It would be more like: The arrow moves 100m. The runner moves 10. The arrow moves 100m *THWACK!* And this is why there are planck units like the planck length, the smallest measurable length. This way we can avoid stuff like greek warriors outrunning arrows or zenos original story which was of tortoises outrunning sprinters!
Or you could take my brother's theory: Science is a lie. The universe is controlled by magic and science just happens to be a very good explanation so far. Bur it's actually jusy magic.
Now remember. This stuff is bad for you, especially in excess quantities. So rather talk about your favorite FPS or something."
Well, fortunelty the universe does not care of philosophical things like that paradox. There also exist an paradox that "proves" that movement is impossible. It is like that old coin thing someone told me once that made no sense until you realized that the math in it was wrong.
And sience a lie? Nah, sience is just a way to through trial and error build up models of the universe, test it and if it fails, build new ones and do that over and over again approaching the model that works best. Sience is not static, it is just to build up models (not one, sience is not one model) of reality based on what know and so.
There is no greater virtue, then the ability to face oneself.