Genady

... to become inadequate.

This analogy is plain wrong. Quantum mechanics is much (!!!) deeper than this.

Thank you. My pipes are buried in the ground around the pool, but not under the concrete. Still, before digging and messing up a big area I'd like to narrow it down as much as possible.

The motor pendulum, classically, has probability 1 to be where it is and probability 0 to be anywhere else. It is not so in quantum mechanics, and it makes a big difference for electron. Probability amplitude - Wikipedia

It has a probability amplitude to be there.

Unlike the motor, electron does not take up that space.

Only in one day, the effect is clear enough. I've modified the test from the original idea. Instead of covering all the inlets and outlets, I plugged only the outlets, i.e., the main drain, the skimmer, and the vacuum. The lowering of the water level has slowed down to about the evaporation rate. Thus, the leak is not in the body of the pool, but in the plumbing between the pool and the filter. This is good news. Now, how do I pinpoint the leak? The suspected three lines are mostly buried.

It is not the same thing at all. One is a region of space, correct, the other is a position of an electron, incorrect.

No, electrons in atoms do not have definite positions.

No, they do not. Electrons in atoms do not have orbits.

This is good, but my pool is a fresh water one. OTOH, I am sure it is a leak, as discussed earlier with @TheVat. I'm going to check 'pool vs. lines' following this idea:

I do not have such equipment. I will keep this possibility in mind, but it will take time to get them to do this check. And cost. There are four lines: from the skimmer, from the main drain, from the vacuum, and the return. Not the first option on my list. Thank you anyway. This was one of the first things I did myself (I am a former SCUBA instructor.) I've just thought of a very simple way to check if the leak is in the pool or in the pipes. I can cover all the inlets and outlets in the pool and see if the leaking stops.

I cannot cover the pool. I can experiment with 'buckets' of different sizes and shapes. I don't think the difference would be so dramatic. If any, I'd expect that relatively shallow buckets heat up and evaporate faster than the much deeper pool. Plus... Buckets have the same or more exposure to the sun. The pool is located on the property in such a way that it is protected from winds. Plus... I am sure that in the last several months I need to add water to the pool about weekly rather than bi-weekly as it used to be for the last 20 years. This was how the project started.

I measure it quite 'scientifically'. I put a backet of water on the pool side and mark the water level in the backet and in the pool. Later, I compare the change of the level between the two. The pool level goes down about twice faster.

I've inspected it on SCUBA vary closely and meticulously. I doubt that I've missed it.

It does. Fresh water is not cheap in Bonaire. It is produced from sea water by reverse osmosis, and we pay by cubic meters consumed. It is pure concrete.

I let it go down to the bottom of the skimmer, with no effect. I don't want it to get any lower.

OK. How do I find / check this?

It's concrete pool, partially in-ground. I SCUBA dove in it to look for cracks. Didn't find any. Not a very fast leak, about 2cm down of the water level a week. This is about twice of a normal evaporation.

Let's start this simple and I will fill in details as needed.

It is an old and well-known problem. What is in it to be discussed here?

One does not need to deal with GR or QM to have meaningful and useful non-commuting operations. They are everywhere. For example, rotations in Euclidean 3D space do not commute.

Knowing this, one can calculate the gas temperature.

What do you mean, temperature of the Sun?

A short Internet search returns many sites explaining how to calculate Jeans length. Just plug in the numbers.