Our understanding of wave function collapse uses the language of "standard analysis," which is not a good language for talking about existence-- which is the problem here. Instead of a "limit", which necessarily involve statements about numbers on a real number line-- which therefore say that before the"Limit" can exist, there must first exist this number line stretching in front of and in back of me who is, on the number line, performing this algorithm for "limit". The pre existing number line goes into the vanishing points on both horizons.
This kind of language doesn't help me to see "what exists" in that imagined point on a number line of time, along which travels the wave function.
So when the wave function "collapses," I am stuck with the language of standard analysis and therefore "limits" on pre-existing "number lines," to say, first, "what existed," and so "what collapsed."
Rather, the language of nonstandard analysis give me something that exists at the imagined "limit"-- "the monad." On which, one can build a mathematical game, called "the Born Infomorphism." Possibilities exist in the "nonstandard future" part of the monad. The scoreboard exists in the nonstandard past. It is just David Bohm's model of the computer guided ship guided by radio waves to its slip upriver. In nonstandard proper time-- "properTime = (now, properTime)"-- one player is the radio antenna, who places possibilities in the nonstandard future. In the standard present instant at the core of the monad, the other player in the game-- the quantum particle-- chooses where to move. After the move, the quantum particle finds whether or not the radio tower in the game wanted the quantum particle to move to that configuration, or not. And that information is placed in the scoreboard, which exists in the nonstandard past. Since after each move the radio tower lets the quantum particle know where it would have liked the quantum particle to have moved, whether it did so or not-- the probability with which the radio tower selects a possibility will match the probability with which the particle chooses that possibility. It's an old laboratory finding called "probability learning," which is explained by regret....
In each monad, a play of this game of existence is a "collapse" of the wave function. The particle jumps from trajectory to trajectory in those computer generated graphics in Bohm and Hiley's book. When it happens to hit the detection screen, who knows what trajectory it would have been following? The distribution follows the Schrodinger equation.
In language involving nonstandard analysis, non-wellfounded sets, mathematical games and "infomorphisms", the phrase "wave function collapse" means something else.