As David points out, the notion of the collapse of wavefunction is the essential notion of the Copenhagen interpretation, not Heisenberg’s uncertainty relation.

Heisenberg’s uncertainty relation (in its simplest form) says that the more determined the location of a particle, the less determined its momentum: there’s a maximum degree of compatibility between those two observables.

A wavefunction collapse due to observation (in the Copenhagen interpretation) is one way to have a highly determined observable (e.g., position, momentum) but isn’t necessarily the only way.

The Copenhagen interpretation is one way to make sense of measurement & uncertainty in physical laws; The many-worlds interpretation is another. The Heisenberg uncertaintly relation is really a theorem about the way certain mathematical operators (which correspond to state measurements) interact with one another.

I’m sure this is clear as mud for most people, but maybe it helps clear things up for a few who stumble across this page?

In terms of that analogy, I find it a little unconvincing. :-) Also, that’s more of a Schrodinger’s cat effect than the Heisenberg Principle.

One, perhaps silly, addition: There’s some sort of analogy between BoxedAnyArray and the Heisenberg principle. The array will in effect keep an undetermined element state until somebody tries to make an observation about it. Then it will snap into whatever was requested by that observation and keep this representation thereafter.