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The observable difference is that a particle's properties have been observed.

An uncollapsed state is a placeholder - constrained by statistics, but with no definite value. A collapsed state has a definite value along some measurement basis.

Entanglement is a different phenomenon.

Uncollapsed entangled pairs remain unmeasured by anyone. Either Alice or Bob can collapse the state of an entangled pair by measuring one item in the pair. This constrains the possible results the other person can find when they measure the other object (if that's a word that even applies in QM...) in the pair.

The correlation isn't obvious unless the results are compared, so neither experimenter can see it on their own.

But there has to be collapse - or decoherence, or a measurement, or some kind of interaction - for the correlations to become observable at all.

Copenhagen interpretation is not that easy to debunk. It is not backed by any additional math beyond all of the quantum physics math that is solid but backs multiple interpretations.

In physics if something doesn't have its own math then it is just an opinion. You can't prove it, you can't debunk it, you can have different one. Ultimately it doesn't matter.

For me Copenhagen interpretation becomes absurd from the moment it states that observer matters. Each observer is just lots of particles and the fact that they arranged to have eyes and brain can't possibly matter for the basic laws of physics.

Copenhagen interpretation does not imply human or conscious observer. That's called quantum mystism that usually uses Copenhagen interpretation as a starting point.

What Heisenberg and others assumed was that that there exists so called 'Heisenberg cut' between somewhere between quantum and macroscopic phenomenon.

That's not obvious to everybody. Even in this post there is mention that Shrodinger's cat is somehow different from Shrodinger's scientist.

And I've seen serious physicist lecturers claim that even recorded measurement didn't cause collapse because recording was not seen by anyone.

This is completely bonkers and misticism is the right word for it.

People who invented the thing are to blame. Why call something 'observation' if you mean interaction with macroscopic object.

And why make the fuss about Shrodinger's cat?

You don't need eyes and a brain to observe, a photon can be an observer.

That's not obvious to everybody. Even in this post there is mention that Shrodinger's cat is somehow different from Shrodinger's scientist.

> There is no observable difference between a particle whose wave function has collapsed and one that isn't.

Don't you think that there is an observable difference between a particle that has been already observed (i.e the wave function has collapsed) and a particle that has not been observed yet (i.e. the wave function has not collapsed)?

The observed one has just narrower wave function. That narrow that we can be pretty sure that next measurement of the same thing will fall close to the first one.

If we measure, say, the spin of an electron along the z-axis the only possible outcomes are UP and DOWN.

If we measure UP, the next measurement of the same thing can only be UP. The system has a narrow wave function indeed.

(On the other hand, if the system was originally prepared in a pure state along a perpendicular axis and has not been observed yet the probability of measuring UP or DOWN is 50/50. The difference between these scenarios is quite observable.)

Yes. Spin UP and DOWN are so "far" from each other that detector that can tell them apart reshapes the probability so much that from that point on this detector will always register UP.

Think about location. If you send electron through half-mirror and put a screen behind it and see electron hitting the screen then you cut down your wave function to at most half of the size. You'll never see this photon in front of the mirror because that small interaction with the screen narrowed down the possibilities.

You'll say that after it hit the screen it must go on in straight line and will hit any subsequent screen as if it was small ball just flying through space and screens.

But imagine instead of the screen just a detector made from solenoid that will notice passing electron but not exactly where it is. This way location is still uncertain. Probability wave is not that narrow. The only thing your detection did is reshaping the wave so you no longer have any possibility of finding electron in front of a mirror.

My point is that there's no difference in math between moving ball hitting things on the way and probability wave evolving in space time and exchanging momentum and energy with other waves and getting reshaped during these exchanges.

We know equations that govern this evolution, we know what rules the exchanges obey and how the waves change shape when they interact.

So why even have little balls cluttering our imagination if they are not needed to explain anything?

I think what you call "reshaping" is what the standard interpretation calls "collapse".

Maybe you will find it easier if instead of thinking about it as "something unlocalized becoming a point", you think about it as "the observable we measure is represented by an operator and after the measurement the wave-function will be the eigen-function of the operator correspoding to the eigen-value that we obtained as outcome of the measurement." This new wave-function is not necessarily "localized".

By the way, the wave-function is not a probability wave evolving in space time. It is a (complex-valued) mathematical function "evolving" in parameter space.

> I think what you call "reshaping" is what the standard interpretation calls "collapse".

Yes. But traditionally collapse is from a wave into result of measurement. My point is that it actually is from wave into a wave.

> operator correspoding to the eigen-value

This suspiciously for me sounds like a single value and something of different nature than operator you mentioned earlier.

> It is a (complex-valued) mathematical function "evolving" in parameter space.

I know. I called it probability function because its squared modulus can give you probability of getting measurement of given value.

Traditional collapse is from wave-function to wave-function. The result of the measurement is something different (but related).

The result of the measurement is one of the eigen-values of the observable operator (that's the essence of quantum mechanics, the set of outcomes is "quantized").

If the eigen-value observed is non-degenerate there is only one wave-function that corresponds to that pure state (i.e. the corresponding eigen-function). Immediately after the measurement, that will be the wave-function describing the system (and then will evolve according to Schroedinger's equation). In the general degenerate case, it will be the projection of the wavefunction before the measurement on the corresponding subspace.

Depending on what you measure the probability density corresponding to the after-measurement wave-function may or may not be concentrated at some point. It will happen if you measure the position (you know where it is know!). But if you measure the momentum, the location becomes completely undetermined.

That's great. So, pretty much I have correct intuitive understanding of quantum mechanics (except with that degenerate thing which I never encounterd before).

Thank you for your comments. At least now I can be now at peace when I read pop-sci articles about quantum knowing that they are just using extreme simplification (to the point of being wrong) but the actual current understanding is same as I believe and I'm in no obligation to share my insights. ;-)

Remember: "I think I can safely say that nobody understands quantum mechanics." ~ Richard Feynman

Edit: Degenerate means that the measurement doesn't completely determine the state of the system. In that case the state before the measurement is projected onto the subspace of states compatible with the measurement, I think this may be more or less what you meant by "narrowing down the possibilities".

More precisely (Quantum Mechanics, McIntyre):

"Postulate 5 (projection postulate): After a measurement of A that yields the result a_n, the quantum system is in a new state that is the normalized projection of the original system ket onto the ket (or kets) corresponding to the result of the measurement: ∣ψ′⟩ = P_n ∣ψ⟩ / sqrt( ⟨ψ∣ P_n ∣ψ⟩ )"

I agree that there are reasons to prefer waves to idealized point-like particles as the more fundamental description (singularities are always difficult to handle). But that's essentially unrelated to the single-world / many-worlds debate, I think.

This sounds much more like something I imagine.

Before collapse you have a system which evolution is governed by some equations, then interaction happens, then you get new system that is a transformation of old system into something dependent on result of interaction (measurement) but what we get in the end is still of the same nature and still evolves according to same equations as initial system.

That's QM in a nutshell. Of course, it's not completely clear why two different regimes are needed and when should one or the other be used. But as John Bell wrote in his "Against 'measurement'" article (https://www.tau.ac.il/~quantum/Vaidman/IQM/BellAM.pdf): "ORDINARY QUANTUM MECHANICS (as far as I know) IS JUST FINE FOR ALL PRACTICAL PURPOSES".

Quoting Everett's dissertation (http://www.weylmann.com/relative_state.pdf):

We take the conventional or "external observation" formulation of quantum mechanics to be essentially the following [1]: A physical system is completely described by a state function ψ, which is an element of a Hilbert space, and which furthermore gives information only to the extent of specifying the probabilities of the results of various observations which can be made on the system by external observers. There are two fundamentally different ways in which the state function can change:

Process 1: The discontinuous change brought about by the observation of a quantity with eigenstates φ_1, φ_2, ... , in which the state ψ will be changed to the state φ_j, with probability |(ψ,φ_j)|^2.

Process 2: The continuous, deterministic change of state of an isolated system with time according to a wave equation dψ/dt = Aψ, where A is a linear operator.

This formulation describes a wealth of experience. No experimental evidence is known which contradicts it.

[1] We use the terminology and notation of J. von Neumann, Mathematical Foundations of Quantum Mechanics, translated by R.T.Beyer (Princeton University Press, Princeton, I955).

> receive either a stream of particles with collapsed wave functions, or a stream of uncollapsed ones

I don’t think there’s any way for Bob to determine whether the particle stream has been measured by Alice or not.

>> I don’t think there’s any way for Bob to determine whether the particle stream has been measured by Alice or not.

That's why I wrote: "There is no observable difference between a particle whose wave function has collapsed and one that isn't."

If there was a way to tell it would violate relativity by allowing FTL communication.