Genady

It is a subject matter for some, e.g., Karl Popper, Thomas Kuhn, among others. This is too bad. Are you sure it is irreversible?

A straightforward trial-and-error gets it on a second trial.

Why?

I don't have a definition. I refer with this word to an object of scientific studies.

It is not that it is somewhere, but we don't know where. We know that it does not have a definite position.

No, it they do not. All your references - measurements, clockwork, unexpected - refer to our use of models. They say nothing about the world.

In my understanding, world is neither. The concept of linearity is not applicable to world.

So, you mean that our models are non-linear, not our world.

If the particle is in a superposition of momentum eigenstates and its momentum is measured, then its state changes and becomes one of the momentum eigenstates (physically, a narrow range around such eigenstate). (It is after midnight here, so the follow up questions might need to wait.)

Generally, we do not. Physically, as @swansont has mentioned, momentum eigenstate is impossible. So, physically, it is always a superposition. But its range can be very narrow, concentrated very close to an eigenstate.

Superposition of states.

Yes, it is completely uncertain before and after the measurement. I call this, "does not change."

This cannot be answered. What can be said is, If a particle has a definite momentum, measuring its momentum does not change its momentum, its position, its spin, etc.

(We can call it, "particle".) Yes, if a particle has a definite momentum, measuring its momentum does not change its state. The same holds for its position.

Sure. If the state of a system is an eigenstate of the observable in question, then it does not change.

Yes, it does.

A measurement usually changes the state. Non-commuting implies that the measurement of one observable affects the measurement of the other. The two cannot be both measured independently on the same state.

Non-commuting observables.

I struggle to see how linearity or non-linearity can be applied to a world.

I think that @joigus has already explained that the latter was just a word play. I take it as "nothing more than that."

I know and understand meaning of the phrase "pushing the envelope", but I don't know what "to develop the envelope" means.

What envelope?

This is where I get lost.

As far as I can understand from the abstracts, they are scientific. However, they don't seem to have a relation to this thread's topic.

Let's take a simple case of only two possible values, e.g., electron spin. A measurement in UP/DOWN basis results in either UP or DOWN. Let's take an electron in the superposition state \( (\frac 1 {\sqrt 2}, \frac 1 {\sqrt 2}) \). Immediately after measuring say UP, its state is \( (1, 0) \). How can the limitations above explain this transformation?