Well... no.

The usual statement is that entanglement can not be used to exchange information between spatially separated observers, right? I totally agree with that. But what about the wave function? If the wave function is spatially extended, then the change of the wave function has to propagate through space if one assumes that the change is caused by a local measurement. And the wave function contains the information that fully describes the state of the system but one can not learn the wave function in general because some operators are not commutative. Nonetheless a change of the wave function means a change of the information describing the system whether an observer can detect that change or not. That are of course two different things, the information describing the state of the system and the information an observer can learn about the state of the system, but I see no conflict here.

No, you can't. You're using colloquial English to reason about physics. This is wrong. Physicists have a very specific definition for "information" (as I already said, and you ignored). And in this case, no information is exchanged.

If I measure a spin without prior knowledge of its state, I obtain one bit of information, I guess that is the sense in which you want to understand information, right? If I repeat the experiment with identical preparation over and over again, then I can learn the wave function, maybe 30 % up, 70 % down. If Alice and Bob do this with their entangled cards, then Bob can decide between the case that Alice saw a red card in which case he will always see his card blue and the case that Alice did not look at her card in which case he will see his card as randomly red or blue. When Alice looks at her card she must of course perform a post selection to get rid of the pairs where she saw her card as blue.

I hope you notice that I am not trying to argue that you are wrong, I am just trying to understand what you say, especially why one would consider the result of a measurement as information but not consider the wave function as information.

Looking at the wave function changes nothing. It's all the same physics, and all the same concepts. You can't get different behavior from the physical system by "looking at the wave function" instead of looking at the particles.

> If the wave function is spatially extended, then the change of the wave function has to propagate through space

... via real particles. Which can't go faster than the speed of light.

> And the wave function contains the information that fully describes the state of the system but one can not learn the wave function in general because some operators are not commutative.

That... doesn't make any sense from a physics point of view.

You're trying to understand which is good. But you're mangling the concepts.

> If I measure a spin without prior knowledge of its state, I obtain one bit of information, I guess that is the sense in which you want to understand information, right? If I repeat the experiment with identical preparation over and over again, then I can learn the wave function, maybe 30 % up, 70 % down

No. You're learning the probability distribution of the wave function. i.e the statistical distribution of the wave function, taken over many measurements.

> If Alice and Bob do this with their entangled cards,

... they learn that 50% of the cards are blue, and 50% of the cards are red. Which they already knew.

> ... Bob can decide between the case that Alice saw a red card in which case he will always see his card blue and the case that Alice did not look at her card in which case he will see his card as randomly red or blue

I'm not even sure what that means. It's based on a misunderstanding of the underlying concepts, so the sentence doesn't really make sense to me.

> I am just trying to understand what you say, especially why one would consider the result of a measurement as information but not consider the wave function as information.

I never said that.

The wave function is a probability distribution.

Information is exchanged via real particles.

You can learn new information through measurements... but not when the underlying measurements are random. i.e. with entangled particles, all you measure is that (in this case) half of the cards are red, and half are blue. Which you already knew.

Since you already knew that half of the cards are red and half are blue, the measurements give you no new information.

The concepts are really quite simple, once you throw away your "common sense" understanding of what is going on.

Alice hands Bob a particle that is either spin up or a superposition of spin up and spin down. Bob can not distinguish those two cases with a measurement. But if Bob would know the wave function he could tell the difference and Bob could learn the wave function be repeating the experiment many times. So there is a difference between looking at the outcome of a measurement and looking at the wave function.

... via real particles. Which can't go faster than the speed of light.

If Alice measures her particle of an entangled pair the wave function of Bobs particle will change without any particle transporting any information from Alice to Bob. Bob is unable to detect that change with a local measurement but the wave function changed and no particle has been exchanged.

That... doesn't make any sense from a physics point of view. You're trying to understand which is good. But you're mangling the concepts.

What is wrong with that? The wave function fully describes the state of a system but you can not learn that state in general because you would have to perform several different measurements and those measurements do not commute in general and change the state to an eigenstate of the measured observable. Only in an experimental setup with repeated measurements on identically prepared systems can you learn the wave function of the system.

No. You're learning the probability distribution of the wave function. i.e the statistical distribution of the wave function, taken over many measurements.

No, I said identically prepared systems, so the wave functions are identical in every run of the experiment. I then obtain a distribution of the eigenstates of the operator by repeating the experiment and that determines the wave function up to the phase.

I'm not even sure what that means. It's based on a misunderstanding of the underlying concepts, so the sentence doesn't really make sense to me.

Alice prepares a set of entangled particle pairs. On two thirds of the sets she measures her particle and sorts them by outcome. Now Alice has three sets, unmeasured, measured up and measured down. Bob can determine which set is which by measuring his particles, he gets 50/50 up and down, 100 % down and 100 % up respectively.

I never said that.

You did or at least I understood it that way. You say that information is what an observer can learn about the state of a system by performing measurements but there is also the information describing the state of the system, the wave function, which is not necessarily accessible to an observer.

The wave function is a probability distribution.

It is not, it is a description of the state of the system. You can obtain a probability distribution of eigenstates by repeatedly performing measurements on identical wave functions and that distribution is determined by the magnitude of the amplitude of the wave function but the wave function itself is not a probability distribution.

You can learn new information through measurements... but not when the underlying measurements are random. i.e. with entangled particles, all you measure is that (in this case) half of the cards are red, and half are blue. Which you already knew.

Since you already knew that half of the cards are red and half are blue, the measurements give you no new information.

I did not dispute that, observers obtain information about the state of a system by performing measurements, but that is not the same as the information describing the state of the system. The later is the truth, the former is what an observer knows about the truth.

You're using colloquial English to reason about physics. This is wrong. Physicists have very specific definitions of the terms they use. Which are sort of similar to the common ones, but differ in key points. Those key points are what you're getting hung up on. And it's difficult to explain the differences without explaining all pf physics.

On top of that, you've disagreed with the common definitions used by physicists "I'm not sure that's correct". Well, it is. If you think that's wrong, you either think you're smarter than all physicists alive, or you're wrong. Pick one.

> ... But if Bob would know the wave function he could tell the difference ...

No. No. A thousand times no.

It just doesn't work like that.

> If Alice measures her particle of an entangled pair the wave function of Bobs particle will change without any particle transporting any information from Alice to Bob. Bob is unable to detect that change with a local measurement but the wave function changed and no particle has been exchanged.

That is a bunch of pseudo-physics words put together in a sentence.

>> You're trying to understand which is good. But you're mangling the concepts. > What is wrong with that?

Everything. If you're not using the correct terms in the correct way, you might as well be putting random words together in a sentence.

>> No. You're learning the probability distribution of the wave function. i.e the statistical distribution of the wave function, taken over many measurements. > No, I said identically prepared systems, so the wave functions are identical in every run of the experiment.

So... you know better than the nuclear physicist.

This should set off alarm bells that you either don't understand the topic, or you don't care to understand it.

> You did or at least I understood it that way. You say that information is what an observer can learn about the state of a system by performing measurements but there is also the information describing the state of the system, the wave function, which is not necessarily accessible to an observer.

<sigh> The observer can do multiple measurements to determine the wave function.

>> The wave function is a probability distribution. > It is not, it is a description of the state of the system.

Again, you're arguing with the nuclear physicist.

The probability distribution is a description of the system.

>> Since you already knew that half of the cards are red and half are blue, the measurements give you no new information. > I did not dispute that, observers obtain information about the state of a system by performing measurements,

Yes.

> but that is not the same as the information describing the state of the system. The later is the truth, the former is what an observer knows about the truth.

<sigh> I'm trying to educate you on physics, and you're arguing pseudo-philosophical metaphysics.

Please stop. Your understanding of the terms is largely wrong. As a result, your arguments are based on falsities, and therefore also wrong.

Please go read a popular book about QM before discussing this with anyone.

And stop arguing with the nuclear physicist. This is one situation where I can appeal to authority without it being a logical fallacy. I've explained repeatedly why you're wrong. You don't seem to understand.

Wave function and probability distribution. You repeatedly insisted on precise language, that is why I objected your statement that the wave function is a probability distribution. And I still do, nuclear physicist or not. A wave function is complex-valued, a probability distribution is usually defined by a real-valued probability density function or a real-valued cumulative distribution function. The state 1/sqrt(2)(|0> + |1>) has probability amplitudes of magnitude 1/sqrt(2) for both states, the probability distribution you obtain when you repeatedly measure particles in that state has probability 1/2 for both states, the square of the magnitude of the amplitude. The wave function certainly defines a probability distribution but it is not itself one.

<sigh> I'm trying to educate you on physics, and you're arguing pseudo-philosophical metaphysics. Please stop. Your understanding of the terms is largely wrong. As a result, your arguments are based on falsities, and therefore also wrong. Please go read a popular book about QM before discussing this with anyone. And stop arguing with the nuclear physicist. This is one situation where I can appeal to authority without it being a logical fallacy. I've explained repeatedly why you're wrong. You don't seem to understand.

I haven't read everything again but most of your responses, especially in your last comment, simply state that I am wrong without pointing out why or providing a supposedly correct point of view. It is of course not you job to teach me physics, but simply stating that I am wrong is only of limited help to overcome misunderstandings. Besides that we are discussing a topic that has not been definitely settled and where there is disagreement even among professional physicists, so maybe we should not be too surprised about a certain amount of disagreement.

I would very much appreciate if we could continue this discussion a bit once I had time for a full reply - and I agree, we have to back up quite a bit, the discussion got fragmented pretty quickly - but I won't blame you if you declare me a lost case.