Genady

You are correct. Not since the Big Bang. It started accelerating only several billion years ago: Evolution of the universe - Expansion of the universe - Wikipedia

Right. I've expected a question from OP regarding this \(2\).

In other words, you have found that \(v=\sqrt {ax}\), where \(v\) is speed, \(a\) is acceleration, and \(x\) is displacement. There is a known kinematic equation for this: if a body starts moving from a rest with a constant acceleration \(a\), when it moves the distance \(x\) its speed is \(v=\sqrt {2ax}\).

and scientific concepts / models being tools to deal with the world rather than representations of the world.

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.