A A Realization of a Basic Wigner's Friend Type Experiment

[DarMM]

I am just saying that most people who've had some basic but not too deep exposure to QM

Ah yes, agreed. Funny in a sense since even Bohr wouldn't have held to this sort of "absolute collapse at all scales".

Chapter 11 of Richard Healey's book "The Quantum Revolution in Philosophy" has a nice account of how Copenhagen approaches Wigner's friend. Similar expositions can be found in the papers of Jeffrey Bub and this paper https://arxiv.org/abs/1901.11274

 

[kimbyd]

This only shows interference is increasingly suppressed as the atom-photon entanglement gets stronger. It does not tell us anything about if or when a nonunitary collapse occurs. Loss of interference (explained by decoherence) is not the same thing as collapse to a definite outcome/eigenstate (not explained by decoherence).

What it does say is that non-unitary collapse is fundamentally unmeasurable. Decoherence occurs at a very small scale, and it should be possible to construct an experiment which demonstrates the stated inequality on a small scale, and that the inequality disappears as you increase the complexity of the system being measured (as in this paper). Measuring that collapse without any measurement interpreted by a conscious observer disproves the notion that consciousness is required for collapse.

Sure, you can imagine all you like that there's a second collapse that happens sometime later after consciousness gets involved, but then you're engaging in speculation that not only has no evidence behind it, but the problem itself is defined in such a way that it is fundamentally impossible to obtain any supporting evidence.

But yes, loss of interference is exactly collapse to a definite outcome. With the a two-slit experiment (or analog, in this case), the "definite outcome" is which slit the particle traveled through.

 

[charters]

But yes, loss of interference is exactly collapse to a definite outcome. With the a two-slit experiment (or analog, in this case), the "definite outcome" is which slit the particle traveled through.

This isn't right. Loss of interference (due to entanglement with an apparatus) yields the improper mixture of passing through one or the other slit, which is not a definite outcome state. Accounting for definite outcomes requires additional interpretive work.

This paper, especially section 1.2.3 is a very clear and concise explanation of this: http://philsci-archive.pitt.edu/5439/

 

[kimbyd]

This isn't right. Loss of interference (due to entanglement with an apparatus) yields the improper mixture of passing through one or the other slit, which is not a definite outcome state. Accounting for definite outcomes requires additional interpretive work.

This paper, especially section 1.2.3 is a very clear and concise explanation of this: http://philsci-archive.pitt.edu/5439/

I don't think that's a valid critique. Interference is caused by superposition, specifically superposition in a basis determined by the experimental apparatus. The elimination of interference implies the system is no longer oscillating (in space or time) in a coherent fashion, i.e. that its components are evolving largely independently of one another.

This section just lays out mathematically what kinds of superpositions interfere and which don't. The pure state is in a different basis from the state determined by the system that would observe interference. The other states, the ones that are not pure states, can be interpreted as the superposition being about our ignorance of the measurement result. In these systems, the particles are definitively in the $|\uparrow\rangle$ or $|\downarrow\rangle$ states before the measurement occurred, and the measurement only let's us know about a collapse that already happened, rather than causing a collapse as in the pure state.

The mathematics of this is quite confusing mostly because a "pure state" depends upon what basis you are talking about. Measurements to observe interference generally depend upon their particles being in a pure state in one basis, but having the experimental apparatus cause components of the wavefunction to evolve differently in time or space in another basis.

 

[charters]

In these systems, the particles are definitively in the |↑⟩|↑⟩|\uparrow\rangle or |downarrow⟩|downarrow⟩|downarrow\rangle states before the measurement occurred, and the measurement only let's us know about a collapse that already happened, rather than causing a collapse as in the pure state.

This is an objective collapse interpretation. It is not equivalent to standard quantum theory, as it denies the possibility (in principle) of unitary reversals despite prior interactions with/measurements by macroscopic devices or people. The purpose of Wigner's friend is to consider exactly quantum theories, which do allow such reversals, as discussed on pg 3 of the topic paper.

 

[kimbyd]

This is an objective collapse interpretation. It is not equivalent to standard quantum theory, as it denies the possibility (in principle) of unitary reversals despite prior interactions with/measurements by macroscopic devices or people. The purpose of Wigner's friend is to consider exactly quantum theories, which do allow such reversals, as discussed on pg 3 of the topic paper.

No, I'm just pointing out that the ontological interpretation of a wavefunction which no longer interferes due to interactions is that collapse has effectively occurred.

 

[charters]

No, I'm just pointing out that the ontological interpretation of a wavefunction which no longer interferes due to interactions is that collapse has effectively occurred.

Effectively, sure, or for practical purposes. But "effectively" is not a meaningful concept in Wigner's Friend discussions, which are predicated on unitarily reversing such interactions. Either the Friend's (whether a human, AI, or machine) measurement can be unitarily reversed, in which case Friend did not cause a collapse from Wigner's perspective. Or Friend can't be reversed, in which case Wigner can't rely on unitary QT. One must make a choice here.

 

[PeterDonis]

Interference is caused by superposition, specifically superposition in a basis determined by the experimental apparatus.

This doesn't seem right, since whether or not a state is a superposition is basis dependent, but interference is an observed phenomenon so it can't be basis dependent.

a "pure state" depends upon what basis you are talking about

This doesn't seem right either. Whether or not a state is pure is basis independent.

Ordinary language is often not suitable for such discussions; it might be helpful to write down explicit math for what you mean.

 

[StevieTNZ]

Pretty sure it's refuted by the measured fact that collapse measurably occurs for systems far less complex than humans, without results being ever observed by humans.

If some want to claim that that's not "real" collapse and "real" collapse only occurs due to consciousness, then that's a pretty extraordinary claim requiring extraordinary evidence.

news to me. measurement problem resolved then?

Perhaps re-read the paper I posted and see the various claims made in there that conflict with what you posted (and I've quoted in this post).

 

[charters]

Similar expositions can be found in the papers of Jeffrey Bub

By coincidence or superdeterminism, Bub just dropped a new paper on Wigner's friend tonight (which I think is wrong in its critique of Everett): https://arxiv.org/abs/1907.06240

 

[kimbyd]

This doesn't seem right, since whether or not a state is a superposition is basis dependent, but interference is an observed phenomenon so it can't be basis dependent.

You're right, my use of language is a little bit sloppy. The difficulty is in correlating the quantum mechanics notion of a "pure state" and the plain language of a "definite state".

After collapse, the measured state of a given quantum system doesn't change in the basis which was measured (note: the state will evolve with time, but won't behave as if it had any components that weren't the value measured).

So the question is: how do we represent a system where a measurement has occurred, but we don't know what the result of that measurement is? The answer is typically an uncorrelated mixed state. Which is also the state you get after complete decoherence. Such an uncorrelated mixed state is the equivalent, therefore, of saying, "This system is definitely in one state or the other, but I don't know which."

Going back to the Wigner's friend idea, the quantum effects there should be limited by the sizes of the systems. Attempting to unitarily reverse the decoherence can only work up to a point. Any such attempt will naturally be pushing up against thermodynamics, and thus will be of limited success as the system gets more complex.

 

[PeterDonis]

After collapse, the measured state of a given quantum system doesn't change in the basis which was measured

I don't understand what this means. Collapse is a change of state--it's a change from an entangled state with multiple terms, each one a product of a particular state of the measured system and a corresponding state of the measuring apparatus ("corresponding" mean "the state of the apparatus that means the particular state of the measured system was measured"), to a state that is just one of those terms--all the other ones disappear. This change obviously has to change the state of the measured system.

how do we represent a system where a measurement has occurred, but we don't know what the result of that measurement is? The answer is typically an uncorrelated mixed state. Which is also the state you get after complete decoherence. Such an uncorrelated mixed state is the equivalent, therefore, of saying, "This system is definitely in one state or the other, but I don't know which."

Assuming that collapse occurs, yes. But this uncorrelated mixed state is a mixture of product states--states that are each just one product of a measured state of the quantum system and the corresponding state of the measuring apparatus. It is not a mixture of entangled states.

the quantum effects there should be limited by the sizes of the systems. Attempting to unitarily reverse the decoherence can only work up to a point. Any such attempt will naturally be pushing up against thermodynamics, and thus will be of limited success as the system gets more complex.

In a practical sense, of course this is true. But there seem to be many physicists who are not willing to extend "in a practical sense" to "even in principle". Only by being so unwilling can they talk about Wigner's friend type experiments in which humans are treated as quantum systems that can be unitarily transformed at will just like qubits can.

 

[kimbyd]

I don't understand what this means. Collapse is a change of state--it's a change from an entangled state with multiple terms, each one a product of a particular state of the measured system and a corresponding state of the measuring apparatus ("corresponding" mean "the state of the apparatus that means the particular state of the measured system was measured"), to a state that is just one of those terms--all the other ones disappear. This change obviously has to change the state of the measured system.

That definition of collapse only works if you only talk about collapse when you have observed the result of the experiment. How do you represent the state of a system that has been measured, but you don't have any access to the result of said measurement?

The paper charters links above talks about this in section 1.2.3:
http://philsci-archive.pitt.edu/5439/

In a practical sense, of course this is true. But there seem to be many physicists who are not willing to extend "in a practical sense" to "even in principle". Only by being so unwilling can they talk about Wigner's friend type experiments in which humans are treated as quantum systems that can be unitarily transformed at will just like qubits can.

Right. My point is that the Wigner's friend type experiment is likely to not show any quantum effects if humans are the observers closest to the observed system. Decoherence will almost certainly eliminate any such quantum effects. But it shouldn't be hard to design a Wigner's friend-type experiment at a much smaller scale with an experimental apparatus playing the part of an "observer" even though it has nothing like consciousness. And it should also be possible to cause the quantum effects to disappear by making the low-level "observer" further from the quantum regime (possibilities include increasing its temperature or increasing its interactions with its local environment, for example).

I'm quite sure that humans are quantum systems, and are subject to this kind of experiment in principle. But it's highly unlikely to be measurable in practice because decoherence will be so complete by the time the experimental system is entangled with a human.

 

[PeterDonis]

How do you represent the state of a system that has been measured, but you don't have any access to the result of said measurement?

Just like you said--with an uncorrelated mixed state. And using such a state implicitly assumes that a collapse occurred when the measurement took place, so the only uncertainty left is our classical uncertainty about which result was measured.

If you don't assume that collapse occurs when a measurement happens, then you are using an interpretation like the MWI, and you would represent the state of the system as an entangled pure state--the entanglement is between the measured system and the measurement apparatus. If you don't have any access to the results of the measurement, that just means you haven't yet interacted with the measured system and/or measurement apparatus, so the overall pure state is a product of your state and the entangled system-apparatus state. Then your gaining access to the measurement result is a further interaction that entangles you with the system-apparatus.

 

[PeterDonis]

I'm quite sure that humans are quantum systems, and are subject to this kind of experiment in principle. But it's highly unlikely to be measurable in practice because decoherence will be so complete by the time the experimental system is entangled with a human.

In other words, you're quite sure that in principle humans could have unitary "quantum eraser" operators applied to them, even though you also think it's highly unlikely to be possible in practice.

To me, this viewpoint shows a huge overconfidence in exact unitary quantum mechanics. If you had just made your statement conditional--if exact unitary QM is true, then in principle humans could be quantum erased--that would be one thing. But you say you're "quite sure" that exact unitary QM is true, even though you admit there is no experimental evidence that it's true for humans (or even objects much smaller and less complex than humans--very small rocks, say) and it is highly unlikely that there ever will be such evidence.

I understand that this viewpoint is not just yours--many physicists seem to hold it. I still think it's huge overconfidence. In Bayesian terms, I see no reason at present to assign basically all of the probability mass to the hypothesis that exact unitary QM is true. I think any prudent Bayesian would retain a significant probability mass for the hypothesis that there is other physics involved that we don't yet understand that keeps exact unitary QM from scaling up all the way to rocks and humans.

 

[kimbyd]

Just like you said--with an uncorrelated mixed state. And using such a state implicitly assumes that a collapse occurred when the measurement took place, so the only uncertainty left is our classical uncertainty about which result was measured.

If you don't assume that collapse occurs when a measurement happens, then you are using an interpretation like the MWI, and you would represent the state of the system as an entangled pure state--the entanglement is between the measured system and the measurement apparatus. If you don't have any access to the results of the measurement, that just means you haven't yet interacted with the measured system and/or measurement apparatus, so the overall pure state is a product of your state and the entangled system-apparatus state. Then your gaining access to the measurement result is a further interaction that entangles you with the system-apparatus.

Right, but the thing is that decoherence will still cause the appearance of collapse in any interpretation. Decoherence is not a phenomenon that is restricted only to MWI. It's a physical process that is an inevitable consequence of the wavefunction dynamics and is independent of any interpretation. Decoherence is a process which requires no assumption beyond quantum wavefunctions evolving over time according to the relevant equations.

If you really thought that the Copenhagen interpretation was correct, and did your math carefully, you'd have to conclude that the wavefunction of the primary observer in a Wigner's Friend-type experiment would have the appearance of having collapsed long before the secondary observer checked on them, assuming the observers are humans or as complex as humans. That's why in order to test this sort of thing, you'd have to use small-scale "observers" who are sufficiently isolated from the environments so as to avoid decoherence that renders the quantum nature of the system unmeasurable.

In principle it's possible for an alternative interpretation to cause collapse other than that caused by decoherence, so it could in principle result in collapse before that predicted by MWI. But it could never cause measurable collapse that occurs later, because decoherence renders any such collapse unmeasurable.

So, yeah, if anybody could successfully develop a sentient computer that was tiny enough to avoid decoherence when measuring a system, then we'd have a direct test of whether consciousness causes collapse.

I just don't see the point of that because I find the idea that consciousness matters one whit when it comes to the behavior of the universe to be ludicrous.

 

[PeterDonis]

Decoherence is not a phenomenon that is restricted only to MWI.

Yes, agreed.

If you really thought that the Copenhagen interpretation was correct, and did your math carefully, you'd have to conclude that the wavefunction of the primary observer in a Wigner's Friend-type experiment would have the appearance of having collapsed long before the secondary observer checked on them, assuming the observers are humans or as complex as humans.

Agreed. But also, if you really thought the MWI was correct, you'd still have to conclude that the unitary "eraser" operations described in the Wigner's Friend-type experiment as being performed on human observers are impossible, because you can only perform them on systems that haven't decohered yet.

 

[kimbyd]

In other words, you're quite sure that in principle humans could have unitary "quantum eraser" operators applied to them, even though you also think it's highly unlikely to be possible in practice.

To me, this viewpoint shows a huge overconfidence in exact unitary quantum mechanics. If you had just made your statement conditional--if exact unitary QM is true, then in principle humans could be quantum erased--that would be one thing. But you say you're "quite sure" that exact unitary QM is true, even though you admit there is no experimental evidence that it's true for humans (or even objects much smaller and less complex than humans--very small rocks, say) and it is highly unlikely that there ever will be such evidence.

I understand that this viewpoint is not just yours--many physicists seem to hold it. I still think it's huge overconfidence. In Bayesian terms, I see no reason at present to assign basically all of the probability mass to the hypothesis that exact unitary QM is true. I think any prudent Bayesian would retain a significant probability mass for the hypothesis that there is other physics involved that we don't yet understand that keeps exact unitary QM from scaling up all the way to rocks and humans.

When you're talking about systems that are so far separated from the quantum realm that it's effectively impossible to ever measure their quantum behavior, what is the point in asserting that something different is happening?

Quantum mechanics predicts Newtonian behavior in the macroscopic world we inhabit. Just as General Relativity predicts Newtonian behavior for most Solar System observations.

I see no reason to explicitly state that I'm failing to assume that some fundamentally unmeasurable process happens between the quantum realm and the world we are more familiar with when the equations predict the same outcome in either event, just as I see no reason to explicitly state that I don't think General Relativity suddenly stops describing gravity near the surface of the Earth.

 

[kimbyd]

Agreed. But also, if you really thought the MWI was correct, you'd still have to conclude that the unitary "eraser" operations described in the Wigner's Friend-type experiment as being performed on human observers are impossible, because you can only perform them on systems that haven't decohered yet.

That conclusion is independent of interpretation. It's not restricted to MWI.

 

[PeterDonis]

When you're talking about systems that are so far separated from the quantum realm that it's effectively impossible to ever measure their quantum behavior, what is the point in asserting that something different is happening?

Because something different does happen. You can quantum erase qubits. You can't quantum erase humans.

Quantum mechanics predicts Newtonian behavior in the macroscopic world we inhabit.

More precisely, QM in a particular classical approximation that basically ignores all quantum effects predicts Newtonian behavior in the macroscopic world.

Just as General Relativity predicts Newtonian behavior for most Solar System observations.

Yes, but the approximation used here is very different from the QM one. GR predicts that the effects that depart from Newtonian behavior are too small to measure for most solar system observations. But GR is still a classical deterministic theory that predicts one result for all observations, just as Newtonian mechanics was.

The approximation that gets "Newtonian behavior" out of QM, however, has to ignore the fact that QM has a measurement problem. "Newtonian behavior" means a single deterministic trajectory. The unitary math of QM does not predict a single deterministic trajectory. It predicts a huge entangled mess of things that don't even amount to trajectories at all in ordinary 3-dimensional space: the only deterministic trajectory is in the configuration space of the system, which for a macroscopic object has something like $10^{25}$ degrees of freedom. You have to either assume that collapse occurs (Copenhagen) or assume that it makes sense to talk about a particular branch of a horribly messy entangled state as a "single trajectory" (MWI) to get Newtonian behavior.

The usual answer to the latter problem is decoherence--all the branches are decohered when we're talking about macroscopic objects, and a single trajectory is what is measured in each branch. I think this still sweeps a lot of issues under the rug, but in any case the point is that we don't need to go through any of this to get Newtonian behavior from GR.

In short, you're basically asking why you shouldn't consider QM to be a theory of everything (which is what you are doing when you ask what the point is in saying "something different is happening"). My answer is to ask why I should consider QM to be a theory of everything when it has such obvious foundational issues and I have perfectly good classical theories for things that behave classically. The viewpoint that both our best current classical theory, GR, and QM are both approximations to some other more fundamental theory that we don't have yet seems to me to be much more reasonable than the viewpoint that, well, QM just has to be the theory of everything so why not make the best of it.

 

[kimbyd]

The approximation that gets "Newtonian behavior" out of QM, however, has to ignore the fact that QM has a measurement problem. "Newtonian behavior" means a single deterministic trajectory. The unitary math of QM does not predict a single deterministic trajectory. It predicts a huge entangled mess of things that don't even amount to trajectories at all in ordinary 3-dimensional space: the only deterministic trajectory is in the configuration space of the system, which for a macroscopic object has something like $10^{25}$ degrees of freedom. You have to either assume that collapse occurs (Copenhagen) or assume that it makes sense to talk about a particular branch of a horribly messy entangled state as a "single trajectory" (MWI) to get Newtonian behavior.

This is fundamentally incorrect. You don't need a single deterministic trajectory to match observations to Newtonian mechanics. You only need the appearance of one.

And the unitary evolution of the wavefunction in QM predicts the appearance of a single deterministic trajectory in the classical limit. This fact is apparent no matter what. You can layer some assumptions about wavefunction collapse on top of that, but those assumptions are fundamentally untestable unless they result in a collapse that happens before the effective collapse that happens in any interpretation due to decoherence.

In short, you're basically asking why you shouldn't consider QM to be a theory of everything (which is what you are doing when you ask what the point is in saying "something different is happening"). My answer is to ask why I should consider QM to be a theory of everything when it has such obvious foundational issues and I have perfectly good classical theories for things that behave classically. The viewpoint that both our best current classical theory, GR, and QM are both approximations to some other more fundamental theory that we don't have yet seems to me to be much more reasonable than the viewpoint that, well, QM just has to be the theory of everything so why not make the best of it.

I don't honestly see why you have a problem with the simple fact that unitary evolution of the wavefunction leads to the appearance of wavefunction collapse.

The fact that this happens is a really trivial analysis: entanglement of a system with a complex system extends the interference time dramatically. You don't need much complexity before the interference time becomes longer than the age of our universe. And the extension of that interference time to absurdly long timescales means that thereafter, the wavefunction branches will evolve as if they were independent.

I see no way in which this simple analysis can be effectively argued against. The only question that needs to be answered on top of that is whether the apparent wavefunction collapse has the same probability properties as the Born rule. And due to the work of Davids Deutsch and Wallace (and others) over a decade ago, we now know that the Born rule drops out of the theory naturally given some very basic assumptions about observers (see here: https://arxiv.org/abs/0906.2718).

 

[PeterDonis]

You don't need a single deterministic trajectory to match observations to Newtonian mechanics. You only need the appearance of one.

If you are willing to accept the MWI, yes, I suppose this is true.

the Born rule drops out of the theory naturally given some very basic assumptions about observers

I'm personally not convinced by these arguments, but that's a subject for a different discussion (and not one that can really be had here).

 

[kimbyd]

If you are willing to accept the MWI, yes, I suppose this is true.

You don't have to accept MWI, though. Do you really think that decoherence doesn't happen if MWI isn't correct?

 

[DarMM]

You don't have to accept MWI, though. Do you really think that decoherence doesn't happen if MWI isn't correct?

Decoherence doesn't give all of collapse. It shows the event space of the device pointer states become a Boolean lattice. However it doesn't select which event occurs.

 

[kimbyd]

Decoherence doesn't give all of collapse. It shows the event space of the device pointer states become a Boolean lattice. However it doesn't select which event occurs.

Right. But if the observer is also a quantum object, then after decoherence it will look like they observed collapse, regardless of which outcome you look at.

 

[DarMM]

Right. But if the observer is also a quantum object, then after decoherence it will look like they observed collapse, regardless of which outcome you look at.

Collapse means reducing the state down to one outcome. You don't get that from decoherence. You still have all pointer states.

 

[PeterDonis]

Do you really think that decoherence doesn't happen if MWI isn't correct?

Of course not. But the whole idea of "we only need the appearance of a single trajectory" only makes sense if you believe the MWI is true.

 

[kimbyd]

Collapse means reducing the state down to one outcome. You don't get that from decoherence. You still have all pointer states.

But an observer will only observe one outcome after decoherence, even if the wavefunction still describes multiple.

I really don't understand what the confusion is here. I'm making two points:
1) Decoherence is a feature of the wavefunction dynamics of QM, and is therefore independent of interpretation.
2) After sufficient decoherence, any observer described by QM will observe what looks like collapse.

Point (2) means that if you are trying to measure something like this Wigner's friend effect, it is necessary to use very small, isolated pseudo-observers which don't have issues with decoherence. The Wigner's friend experiment might be able to unroll the effects of decoherence somewhat, but it's not likely to be by all that much.

 

[kimbyd]

Of course not. But the whole idea of "we only need the appearance of a single trajectory" only makes sense if you believe the MWI is true.

Again, this is an observational statement. It is observationally impossible to distinguish between "real" collapse and the appearance of collapse.

 

[charters]

Point (2) means that if you are trying to measure something like this Wigner's friend effect, it is necessary to use very small, isolated pseudo-observers which don't have issues with decoherence. The Wigner's friend experiment might be able to unroll the effects of decoherence somewhat, but it's not likely to be by all that much.

But this is just rejecting the premise of the thought experiment, which is that Wigner has complete control over all degrees of freedom in the closed friend/lab system, so Wigner can reverse decoherence at his leisure. Saying this is not feasible in practice is besides the point, as we are trying to assess the logical consistency of the theory under maximally extreme circumstances. Your argument is similar to saying since nobody can live inside a black hole, it doesn't matter if GR breaks down at the singularity.