Electrons are able to move from one relative position in spacetime to another, seemingly without traversing any physical space. This is currently explained by the particle-wave duality.
Once the math involving multidimensional space becomes more refined and accepted (inevitable), I suspect the new explanation will be the fact that these particles can move on more than just an XYZ axis.
If/when it is proven that electrons and other particles can move between higher dimensional planes (we'll need to discover first what's "inside" a particle), people will begin to realize that a silhouette of their body, in the form of pure energy, exists both "down" here and "up" there, simultaneously.