A Quora question asks: “How does quantum physics know that if a system were not measured it would be in multiple possible states (without measuring it), and that when measuring it collapses into one definite state?”
Quantum theory doesn’t “know” anything. All it does is describe what we know and makes predictions about what we may find out in future. What we call the “state” of a system is just a summary of what we know about it, and a system on which we can gain no new information without losing some of what we already have is said to be in a “pure” state.
An example is the case of a single electron whose position we are ignoring (so it can be considered fixed) and whose only measurable property is the direction of its spin. If we first measure the spin component in the vertical direction (say that of the z-axis), then we will always find that the spin is pointing straight up or straight down; and if we repeat that measurement we will see that the direction is unchanged. But if we then follow that with a measurement in any perpendicular direction then we have a 50% chance of finding that the spin is now pointing in that new direction and 50% chance of its opposite. And if we now return to the original direction we find equal chances for pointing up or down.
Here, the spin up state is a pure state because we cannot determine the sideways component without losing information about the vertical component, but being in the up state is not the same as being in both left and right states at the same time, and it is also not the same as being in a statistical mixture (ie in one or other of those two states but we just don’t know which).
P.S. In either quantum or classical physics, a system that is not measured or which we have only measured incompletely may be in any one of several pure states with different probabilities, and we call the resulting state a statistical mixture; but that is not the same as being in multiple pure states at once.