I started this thread to continue a conversation from another thread. Does HUP imply randomness? What really is the definition of randomness? I would say that HUP does not imply randomness, but just tells you the relationship between how the state vector is spread out along the basis of two non commuting operators (positions and momentum in this case). Randomness only comes in when we try to measure the value of a particular observable, that is when the state vector collapses along an eigenstate with the appropriate probability. I was under the impression that a random event was one that is uncorrelated to previous events, and this is how I would define randomness; the inability to correlate a certain event with any past events.