This article reminded me of one of the strange features of the standard wave equation from basic physics.  The wave equation describes an infinitely long vibrating string.  Like point masses from Newtonian physics each bit of string has a position and velocity.  If you know the position and velocity of the entire string at one moment of time, you can predict the position and momentum of any bit of string at any time in the past or present.  It seems natural to think in those terms because we predict the motion of things around us all the time.

The reason this works is that the wave equation lets us solve for the time evolution of the system based on the current state.  For the case of a string, the time and position variables are symmetric, and knowing the position and velocity of the string at one point for all time is just as good as knowing about all space at one time.  Philosophically this is a nice feature.  It means that nothing in this world can escape you, all you have to do is sit in one place and everything either has passed you by or will pass you by, nothing can avoid you forever.

In higher dimensions things are similar, but just a little different.  For a 3 dimensional space time (2 spacial dimensions and 1 time) knowing the position and velocity for all space at an instant of time is what you need to make predictions.  Instead of sitting in 1 place and being able to keep track of everything, you need to monitor a single line that divides the world in half.  Knowing everything that crosses that line for all time lets you know everything in that space.  In our 3 dimensional spacial world, you have to monitor an entire infinite plane.

That works because signals on this string travel in one direction with one speed, they never turn around or stop.  That is completely unlike particle dynamics where things move independently.  This would be just an interesting feature of these wave equations, but basic quantum mechanics  is a wave theory, and the same rules apply.