Is the concept of "wave function collapse" obsolete?

[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.

 

[Michael Price]

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.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.

Overlaps do not require the Born rule. I am out of here.

 

[vanhees71]

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.

Where is the collapse? The key mistake is your assumption "ignoring that spin isn't classical". You have to forget about the classical assumption that observables take a determined value and completely get used to the thinking in terms of quantum theory, according to which it depends on the state the system is prepared in (or is observed to be in) whether any specific observable takes a determined value or not.

If you have prepared your particle's spin with determined $S_z=1/2$ value, this implies that $S_x$ does not take a determined value. In this case your spin state is the pure state $|S_z=1/2 \rangle \langle S_z=1/2|$, which implies that the probability to find $S_x=\pm 1/2$ is 50% for each value.

If you now make a filter measurement of $S_x$ filtering out $S_x=-1/2$, then you get indeed a subensemble, where $S_x=-1/2$ is determined, but this again implies that $S_z$ is indetermined now taking with 50% probability either of the two posible values $S_x=\pm 1/2$.

Of course the filtering involves some interactions (e.g., using the Stern-Gerlach setup the particles are going in and adequately chosen magnetic field separating the praticles with the wanted spin values, leading to an entanglement between position and spin-component). Then looking you are simply looking at the subensemble with the wanted $S_x=-1/2$ values. This implies that $S_z$ is now indetermined.

Indeed, you cannot understand this in any classical way, but you have to think following the laws collected in QT!

 

[vanhees71]

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”.

What do you think, don't we know? The success of QT in its minimal interpretation in describing what's objectively observed in nature proves this claim wrong. We indeed do know very well, how to apply QT to real-world phenomena. Otherwise it couldn't be such a successful theory.

"Collapse" is just a sloppy abbreviating word for the simple fact that in preparing a particle such that some given observable takes a determined (or pretty well determined) value we just select those we want. This can be a complicated technical task, but it's nothing mysterios. The devices created for such state preparations can be very complex (e.g., the entire LHC to prepare (bunches of) protons and heavy ions at a given high and well-determined momentum), but it's construction is just possible by making use the known natural laws as formally described by QT in approximation sufficient for the task of construction (in the case of accelerator physics most can be understood using the classical motion of charged particles in electromagnetic fields or, at higher space charges, in terms of continuum mechanics to describe the bunches).

One must not forget that behind all the abstract math of Hilbert spaces and all that there's the real world and the manipulations and observations of experimentalists, which also make up the interpretation of QT, and that's the relevant part of the interpretation, and that's the minimal statistical interpretation. Maybe that doesn't suit our prejudices due to our intuition, which is built from the first day of our experiencing the world in terms of macroscopic many-body systems which don't show much quantum effects (though the very fact that there's a stable macroscopic world around is already is only understandable with QT rather than classical physics).

 

[A. Neumaier]

The success of QT in its minimal interpretation in describing what's objectively observed in nature proves this claim wrong. We indeed do know very well, how to apply QT to real-world phenomena. Otherwise it couldn't be such a successful theory.

We know very well how to apply QT to the statistics of real-world phenomena, averaged over many microscopic quantum systems. This fully explains its successes.

But many want to know more, in the era where one can do high precision experiments with single microscopic quantum systems.

Nothing in either theory or practice forbids that this is possible. That it is impossible is just your (and some others') conviction, not more.

"Collapse" is just a sloppy abbreviating word for the simple fact that in preparing a particle such that some given observable takes a determined (or pretty well determined) value we just select those we want.

Please give a simple derivation, based on first principles without using collapse, why blocking one of the two beams in a Stern-Gerlach experiment prepares a state with definite spin. This is not possible without making ad hoc assumptions that are equivalent to assuming collapse!

 

[DarMM]

Overlaps do not require the Born rule. I am out of here.

I never said overlaps require the Born Rule, they obviously don't. Can you show how what you are talking about leads to collapse. It's strange to be arguing for textbook stuff here. The points I'm making are referenced by Zurek:
Zurek, W. (2010). Quantum Jumps, Born’s Rule, and Objective Reality. In: S. Saunders et al, ed., Many Worlds? Everett, Quantum Theory, and Reality, 1st ed. Oxford University Press, pp. 409-432.

 

[DarMM]

The key mistake is your assumption "ignoring that spin isn't classical". You have to forget about the classical assumption that observables take a determined value and completely get used to the thinking in terms of quantum theory, according to which it depends on the state the system is prepared in (or is observed to be in) whether any specific observable takes a determined value or not

That's not an assumption, spin isn't classical. My point was the difference between QM and Classical preparations, the "spin isn't classical" just referred to the fact that the observable I was using doesn't occur in classical mechanics.

As for the rest of your post, I know all the details of the quantum formalism, the point is that one's measurement of $S_x$ does not constitute a filtered subensemble of the $S_z$ case you've already prepared. That's all collapse is.

As @A. Neumaier said can you show how measuring $S_x$ on a collection of particles with $S_z = +\frac{1}{2}$ works out without using collapse.

 

[rumobritt Reference]

I see. So it's sounding to me like it's not WRONG to keep talking about wave function collapse to describe what looks to me to be a very real phenomenon. Thank you.

 

[Sophrosyne]

What do you think, don't we know? The success of QT in its minimal interpretation in describing what's objectively observed in nature proves this claim wrong. We indeed do know very well, how to apply QT to real-world phenomena. Otherwise it couldn't be such a successful theory.

"Collapse" is just a sloppy abbreviating word for the simple fact that in preparing a particle such that some given observable takes a determined (or pretty well determined) value we just select those we want. This can be a complicated technical task, but it's nothing mysterios. The devices created for such state preparations can be very complex (e.g., the entire LHC to prepare (bunches of) protons and heavy ions at a given high and well-determined momentum), but it's construction is just possible by making use the known natural laws as formally described by QT in approximation sufficient for the task of construction (in the case of accelerator physics most can be understood using the classical motion of charged particles in electromagnetic fields or, at higher space charges, in terms of continuum mechanics to describe the bunches).

One must not forget that behind all the abstract math of Hilbert spaces and all that there's the real world and the manipulations and observations of experimentalists, which also make up the interpretation of QT, and that's the relevant part of the interpretation, and that's the minimal statistical interpretation. Maybe that doesn't suit our prejudices due to our intuition, which is built from the first day of our experiencing the world in terms of macroscopic many-body systems which don't show much quantum effects (though the very fact that there's a stable macroscopic world around is already is only understandable with QT rather than classical physics).

This is a little like a 19th century chemist saying that we know that mixing acids and bases creates heat. What else is there to know and why keep asking questions on the mechanism?

But that’s just an observation, not a mechanistic explanation. If that’s all we have, then fine, it’s all we got and we have to be satisfied with it. “Shut up and calculate”, as Feynman said. But today we have more detailed explanations for that observation, based on energy levels of electrons and atomic orbitals and quantum mechanics of the Schrödinger equation to explain the heat released with mixing acids and bases- stuff the 19th century chemist never even dreamed of.

The mechanism of the wave-particle duality and wave function collapse is also similarly just an empirical observation- and one which we have learned to quantify in our equations. But that’s not a mechanistic explanation. It’s just an observation.

What I think people realize is that there is some weird stuff happening under the hood here that we don’t understand. We will accept the observation for what it is right now because we can’t do any better. But this doesn’t strike me As some fundamental, irreducible level of understanding to just be accepted.

We may never be able to figure it out. Or it may be centuries before we do. But I think theoretically at least, there is some explanation. There is always a next level of “why” or “how”. It’s turtles all the way down.

 

[vanhees71]

We know very well how to apply QT to the statistics of real-world phenomena, averaged over many microscopic quantum systems. This fully explains its successes.

But many want to know more, in the era where one can do high precision experiments with single microscopic quantum systems.

Nothing in either theory or practice forbids that this is possible. That it is impossible is just your (and some others') conviction, not more.

Please give a simple derivation, based on first principles without using collapse, why blocking one of the two beams in a Stern-Gerlach experiment prepares a state with definite spin. This is not possible without making ad hoc assumptions that are equivalent to assuming collapse!

First of all, what do you think comes out of the high-precision experiment with single microscopic quantum systems other than the predicted statistics for measurement outcomes? If there where something else observed, QT were obsolete and we'd have to look for a better theory. Do you have single example (a real experiment of course not some philosophical pseudoproblem)?

Then, what derivation do you need for the SG experiment? After a silver atom is deflected by the magnetic field to one of two clearly separated directions (that must be ensured of course by the appropriate choice of the magnetic field) you know its spin state being in one of the two pure states since through the SG apparatus position and the spin component in the direction of the magnetic field (to be more precise the large homogeneous part of the magnetic field). Now you just use the silver atoms in the spin state you want, i.e., being at the corresponding "right place" and block the silber atoms at the other place. A simple piece of matter will do that for you easily. That the magnetic field has the appropriate state-preparing features, follows from a quite simple calculation. I am still in the process of writing this up.

There's nothing more to derive. You just do the experiment ;-)).

 

[DarMM]

There's nothing more to derive. You just do the experiment

Yes, but what about the experiment where you take particles of definite $S_z$ and then perform an $S_x$ measurement? Afterward they've gone from a state with definite $S_z$ to one of definite $S_x$ in a way that cannot be described by unitary evolution.