If I take two identical "colliding" particles -- e.g., electrons -- which repel one another, then in the center-of-mass coordinate system the two particles can approach one another at any angle, including head-on. They may or may not actually "meet", because the repelling force eventually becomes large enough to cause them to bounce away from one another. Since the particles approaching head-on are identical, I can't really tell whether both particles bounced or simply went straight through. The angles after a "collision" are smoothly/continuously related to the angles prior to the collision. Are there any examples of real particles where this isn't so? It wouldn't necessarily violate conservation of energy or momentum, would it? For example, suppose two identical particles approached one another head-on, but instead of bouncing back or going straight through, they shot off at right angles to the original direction, but in equal & opposite directions & with the same energies as before. In 2D, this is well-defined, but in 3D the particles would somehow have to "choose" an arbitrary direction, and then agree on it. So perhaps such a physics might only work for 2D? Clearly, such a 3D physics would violate the conservation of information (it couldn't be reversed), but quantum physics would seem to do this all the time, so that can't be a show-stopper.