Genady

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?

Why would I read a Scientific American Blog?

Yes, this is my message.

Exactly. Just like we can't measure the number \(\pi\).

\(\pi\)

Immediate:

When we measure, we could only measure one value. The question of "collapse" is how it causes the multiple simultaneous states to become a definite state corresponding to the measured value.

Not necessarily. Blind people know shapes and sizes of new items by themselves, using hands, sticks, etc., without having somebody telling them.

So, in the assertion that "we do receive a shape of an item thanks to a colour", the blind people are not included in the WE?

So, contrary to the assertion that "we do receive a shape of an item thanks to a colour", blind from birth people receive a shape of an item NOT thanks to a color.

Blind from birth people - what colors?

The point is that all this is obtained without colors.

What memory? They are blind from birth. What concepts?

This is incorrect. Blind people know shapes.

There is nothing special about color in this respect. The same holds for shape, motion, smell, taste, touch, etc.

You should also be aware that the situation is not necessarily binary, i.e., pattern or no-pattern. Depending on the interaction, the result can be any of the continuous set of possibilities between a clear interference pattern and no signs of any interference at all. Let's take an extreme scenario of a detector that can be in three states: 0 - default, L - the particle went through the left slit, R - the particle went through the right slit. Let' assume that the detector is perfect, i.e., starting from the state 0 it always changes to either L or R depending on the interaction with the particle. Immediately after going to the L or to the R state, the detector self-destructs. Then, another such detector interacts with the next particle. And so on. There will be no interference pattern in this scenario.

How Googlers cracked OpenAI's ChatGPT with a single word (sfgate.com)