Is the concept of "wave function collapse" obsolete?

[Demystifier]

The subsequent object-subject correlation is the collapse.

No, the correlation cannot be the collapse. The collapse is associated with a single observation outcome, while correlation is associated with a large ensemble of observation outcomes.

 

[Michael Price]

No, the correlation cannot be the collapse. The collapse is associated with a single observation outcome, while correlation is associated with a large ensemble of observation outcomes.

I should have been more explicit. Each element in the superposition, after the induced correlation, stops 'seeing' the other elements. So the collapse seems to have occurred.

 

[DarMM]

What does "each element stops seeing the other elements" mean in a non-MWI reading?

 

[Michael Price]

What does "each element stops seeing the other elements" mean in a non-MWI reading?

It means, once correlated, they time-evolve independently of each other.

 

[akvadrako]

What does "each element stops seeing the other elements" mean in a non-MWI reading?

Good question. I think it’s about an outside observer and how they would calculate the evolution of psi. Even in non-MW readings, that calculation looks like a MW one until they’ve made their measurement.

 

[DarMM]

So the Schrodinger evolution separates into channels, but that doesn't tell me that I can remove components. Modes of the electromagnetic field evolve like this as well, but we don't remove them. What I need beyond this is to view QM statistically which I'll never get out of just unitary evolution and this decomposition.

 

[Michael Price]

So the Schrodinger evolution separates into channels, but that doesn't tell me that I can remove components. Modes of the electromagnetic field evolve like this as well, but we don't remove them. What I need beyond this is to view QM statistically which I'll never get out of just unitary evolution and this decomposition.

All you need is the linear nature of the Hilbert space and thus of the Schrödinger equation, or whatever unitary dynamics you are using, and has nothing to do with interpretations and/or Born statistics.

 

[vanhees71]

So the Schrodinger evolution separates into channels, but that doesn't tell me that I can remove components. Modes of the electromagnetic field evolve like this as well, but we don't remove them. What I need beyond this is to view QM statistically which I'll never get out of just unitary evolution and this decomposition.

To remove modes of an elctromagnetic field you don't need Hilbert spaces and operators therein but simply some matter blocking out the unwanted radiation ;-))) SCNR.

 

[DarMM]

All you need is the linear nature of the Hilbert space and thus of the Schrödinger equation, or whatever unitary dynamics you are using, and has nothing to do with interpretations and/or Born statistics.

That will only, under a certain system-device-environment decomposition, give separation of components of the wave-function in the system-device subsystem. That's still not collapse. To even demonstrate it you have to trace out the environment which involves the Born rule.

 

[vanhees71]

Could you enlighten me to which purpose you need a collapse to begin with? I've never understood this obsession about a collapse. Why can't you live with the working interpretation that a state (pure or mixed) is just the formal description of a preparation procedure (or more precisely an equivalence class of preparation procedures) with the usual probabilistic physical meaning given by the usual generalized Born rule? That's all that's needed to unambiguously describe what's observed (at least so far, including all tough tests of the the theory concerning all the "quantum weirdness", including entanglement)?

 

[Demystifier]

Could you enlighten me to which purpose you need a collapse to begin with? I've never understood this obsession about a collapse. Why can't you live with the working interpretation that a state (pure or mixed) is just the formal description of a preparation procedure (or more precisely an equivalence class of preparation procedures) with the usual probabilistic physical meaning given by the usual generalized Born rule? That's all that's needed to unambiguously describe what's observed ...

Engineers (you said I can call you en engineer) are satisfied by having a description of what is observed, but most physicists are not engineers. They want also to understand what is going on behind the curtains. Philosophers are not the only ones who want to understand what is going on behind the curtains, scientists want that too.

 

[vanhees71]

Well, of course, physicists try hard to lift "the curtains", but what if the overwhelming evidence tells you that you look for curtains, where none are to be seen?

 

[A. Neumaier]

Could you enlighten me to which purpose you need a collapse to begin with? I've never understood this obsession about a collapse. Why can't you live with the working interpretation that a state (pure or mixed) is just the formal description of a preparation procedure (or more precisely an equivalence class of preparation procedures) with the usual probabilistic physical meaning given by the usual generalized Born rule? That's all that's needed to unambiguously describe what's observed (at least so far, including all tough tests of the the theory concerning all the "quantum weirdness", including entanglement)?

Collapse is needed to be able to predict which state a given preparation procedure (e.g., blocking one of the two beams in a Stern-Gerlach experiment) will produce.

 

[Demystifier]

I should have been more explicit. Each element in the superposition, after the induced correlation, stops 'seeing' the other elements. So the collapse seems to have occurred.

That's fine if one takes a perspective from a single branch of the wave function. But without MWI, it is not clear why should one take a perspective from a single branch of the wave function to begin with.

 

[vanhees71]

No, the preparation procedure tells you how to choose a good description for the state! There are no Hilberst-space vectors, self-adjoint operators and all that in the lab but just particles, atoms, molecules, condensed matter etc.

 

[A. Neumaier]

There are no Hilberst-space vectors, self-adjoint operators and all that in the lab but just particles, atoms, molecules, condensed matter etc.

Neither are particles, atoms, molecules in the lab but just equipment producing beams, currents, and pictures.

 

[Demystifier]

Well, of course, physicists try hard to lift "the curtains", but what if the overwhelming evidence tells you that you look for curtains, where none are to be seen?

Sure, some evidence points to the conclusion that there may be nothing behind the curtains, but there is no proof of that. So it's reasonable to assume that the stuff behind the curtain might be there but well hidden, which motivates some people to keep searching.

 

[Lord Jestocost]

That's all that's needed to unambiguously describe what's observed...

This statement is misleading. Quantum theory is, as termed by Schwinger, a causal, statistically deterministic theory. That’s all. But quantum theory has nothing to say regarding the outcome of a single measurement event; there exists no connection between quantum theory and individual measurement events.

 

[vanhees71]

I can agree to everything than the last phrase. If this were true, quantum theory couldn't be the most successful theory ever. Of course, to empirically check probabilistic predictions you need an ensemble, i.e., many "individual measurements", but it must be well-defined ensemble, i.e., the preparation procedure must be describable correctly by the model to be able to define the ensemble given by individual realizations to be measured on. Each individual measurement is of course random in its outcome, but that's precisely what QT describes! It does even more, it also gives clear probability distributions (or probabilities in the discrete part of the spectra of the measured observable) for these outcomes.

Of course, Schwinger has the issue right (at least in the book compiled by Englert from his lecture notes: Quantum Mechanics, Symbolism for atomic measurements, Springer): QT is a causal probabilistic theory, which is describing the indeterminism of observable depending on the state the system is prepared in. In any state only a few independent observables have determined values, all others are indetermined and thus there's no definite outcome when properly measureing these observables (of course for those observables the state provides determined values you get a definite outcome of each individual measurement).

 

[DarMM]

Could you enlighten me to which purpose you need a collapse to begin with? I've never understood this obsession about a collapse. Why can't you live with the working interpretation that a state (pure or mixed) is just the formal description of a preparation procedure (or more precisely an equivalence class of preparation procedures) with the usual probabilistic physical meaning given by the usual generalized Born rule?

Collapse doesn't contradict this preparation based view. Ultimately you can consider collapse to be a relation between preparations which is different from the relations in a classical theory.

For example if one takes a preparation where some source (that part is unimportant for now) emits something in a $|S_{z} = +\frac{1}{2}\rangle$ state and then an $S_{x}$ measurement is performed with some device filtering out $S_{x} = -\frac{1}{2}$ cases.

In the classical case (ignoring that spin isn't classical) something like this would prepare a sub-ensemble of the $S_{z} = +\frac{1}{2}$ case, but in quantum mechanics this is not so. It must solely be considered a $S_{x} = +\frac{1}{2}$ preparation. That's all collapse is.

 

[Sophrosyne]

Well, of course, physicists try hard to lift "the curtains", but what if the overwhelming evidence tells you that you look for curtains, where none are to be seen?

There’s something funny going on with all this superposition states and wave function collapse stuff. We may not know what it is yet. But I am sure there is some intelligible explanation for why quantum mechanics behaves in the weird way that it does. Once we find out, I am sure we will smack our forehead and wonder why we didn’t think of it before. But I am sure that will also create even more questions, and that’s OK because that’s how Science usually works.

But the curtain may just be so big we don’t realize yet the whole thing is one big curtain.

But until we figure it out, I think we just have to be satisfied with Feynman’s approach of “shut up and calculate”.

 

[Michael Price]

That will only, under a certain system-device-environment decomposition, give separation of components of the wave-function in the system-device subsystem. That's still not collapse. To even demonstrate it you have to trace out the environment which involves the Born rule.

We shall have to agree to disagree, since you haven't explained why it isn't collapse.

 

[DarMM]

We shall have to agree to disagree, since you haven't explained why it isn't collapse.

You said this:

All you need is the linear nature of the Hilbert space and thus of the Schrödinger equation, or whatever unitary dynamics you are using, and has nothing to do with interpretations and/or Born statistics.

This isn't true. You don't get the evolution separating into channels like this without the Born statistics. The evolution only separates into different branches within certain subsystems given the Born statistics.

 

[Michael Price]

That's fine if one takes a perspective from a single branch of the wave function. But without MWI, it is not clear why should one take a perspective from a single branch of the wave function to begin with.

First, MWI doesn't come with a built-in perspective; everything is deduced.
Second, the way to deduce it is to consider the example where there is only one component or branch. Cleary the single branch with no companions has a perspective. In the more general case, where other elements or branches exist, each branch must have a unique perspective because the other branches, by linearity, do not affect it.

 

[DarMM]

because the other branches, by linearity, do not affect it

Not by linearity. By decoherence, which operates above a certain scale and requires the Born rule to derive.

 

[Michael Price]

Not by linearity. By decoherence, which operates above a certain scale and requires the Born rule to derive.

No, linearity. You are thinking of interference effects which I am not taking about.

 

[DarMM]

No, linearity. You are thinking of interference effects which I am not taking about.

If there is interference effects you can in no way consider collapse to have occurred. It wouldn't even qualify as "apparent collapse" in Many Worlds.

 

[Michael Price]

To DarMM:
Okay, I see why we may be disagreeing . I am thinking of decoherence being when macrostates cease overlapping, which doesn't require the Born rule. Since decoherence defines branching, in my terminology, you don't need the Born rule to define branching. Perhaps you are thinking of branching into a mixture which requires a probability measure?

 

[Michael Price]

If there is interference effects you can in no way consider collapse to have occurred. It wouldn't even qualify as "apparent collapse" in Many Worlds.

But I am not thinking of interference effects. We agree on this?

 

[DarMM]

But I am not thinking of interference effects. We agree on this?

You might not be thinking of them, but they are very relevant to collapse. If there are interference effects you don't have collapse. Linearity alone will still have interference effects and thus even in MWI people in different branches wouldn't be able to consider the other branches to have separated and so you don't have collapse.

To DarMM:
Okay, I see why we may be disagreeing . I am thinking of decoherence being when macrostates cease overlapping, which doesn't require the Born rule.

It does. The induced state on macroscopic subsystems is formed via tracing and tracing is derived as the only way of projecting onto subsystems that preserves the Born statistics. See Nielsen and Chuang, tracing and the Born rule are connected and decoherence requires tracing.