The article feels incomplete. I don’t feel like I have a better understanding of what’s going on during wave function collapse, rather I just know QTT is a thing and people are experimenting with it and it’s yielded promising results when using more sophisticated measurement apparatus to observe an “atom”, like reversing a quantum jump mid-flight by injecting feedback into the system as it’s being measured.
I barely understand any article on quantum mechanics, but now I know that QTT is a thing and people are experimenting with it. That's why I personally upvoted the article but I admit I was on the fence about it. I'm hoping someone knowledgeable will comment on the article and I might gain just a little more understanding. Maybe.
Quantum trajectories more or less have the usual Copenhagen interpretation built in, so they don't really solve the old interpretation problems any more than decoherence does. Although they can be a nice way to understand some experiments, in particular how conditional probabilities of a set of measurement results obtained in sequence occur, I'm not sure if it's good to present it as some fundamental insight in popular articles.
This seems to be the opposite of what the article is saying, or implying. I read it as saying that there is no need for an interpretation, because there is no wave function collapse; the particle can be described in precise terms.
> But what exactly is this trajectory? One thing is clear: It’s not like a classical trajectory, meaning a path taken in space. It’s more like the path taken through the abstract space of possible states the system might have, which is called Hilbert space.
QTT is not a definite prediction of classical physical trajectory.
To be fair in both everettian and de broglie bohm interpretations there is no physical wave function collapse. Even in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.
QBism has a cool name, but I think it's not as revolutionary as it may seem at first sight.
There are two kinds of uncertainty about a quantum system: the "classical" ignorance about what is the true quantum state and the non-determinism of the outcome of measurements even if the quantum state is perfectly known (note that only in this case the system can be described using a wave function).
"Up to an overall unitary ‘readjustment’ of one’s final probabilistic beliefs [...] quantum collapse is precisely Bayesian conditionalization."
I'd say that this 'readjustment' is the collapse with another name.
"Quantum measurement is nothing more, and nothing less, than a refinement and a readjustment of one’s initial state of belief. [...] Let us look at two limiting cases of efficient measurements. In the first, we imagine an observer whose initial belief structure ρ = |ψ⟩⟨ψ| is a maximally sharp state of belief. By this account, no measurement whatsoever can refine it. [...] The only state change that can come about from a measurement must be purely of the mental-readjustment sort: We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance."
Ok, so when you do a measurement on a pure state (i.e. when the knowledge about the quantum state is maximal and cannot be refined by Bayesian updating):
instead of the "wave function collapse" of “standard” QM (the wave function changes to the eigenstate corresponding to the outcome of the measurement)
you have a "mental-readjustment" (because as a side effect of the measurement now you describe the system using the same wave function as in standard QM).
What are the problems with the "wave function collapse" that are solved by calling it "mental readjustment"?
I think the first thing to say is that the mathematics of quantum theory is the same no matter what interpretation you adhere to (with a small caveat for things like gravity-induced collapse). So, yes, collapse is unavoidable as a mathematical operation which we apply when making predictions about future events.
Where interpretations differ is in the physical content they assign to mathematical objects and operations. In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future".
If you adhere to the former case, then either collapse is merely apparent (ie. many-worlds) or it's a real mechanical thing that is going on in the outside world. If you adhere to the latter case then the collapse process is merely an act of updating beliefs.
Now, if collapse is a real physical process then you run into the measurement problem and "Wigner's friend" style problems. At what point does collapse occur and what induces it? Why is quantum evolution reversible right up until the point of collapse? Is there a combined wave function describing both the observer and the system, and does that wave function collapse? etc... In QBism these issues do not arise because it makes perfect classical sense for, say, an observer of an observer to have beliefs about what that other observer believes.
> In some interpretations the wave function is "really objectively out there", but in others the wave function is "just a good way to store my beliefs about the future".
Those “beliefs about the future” may or may not be correct. If you describe a system with a wave function you claim that you know the quantum state perfectly and there is no margin for error.
How do you think QBism helps in the following scenario?
We have spins prepared in some state, say |up>. We agree that the wave function |up> gives a complete description of the quantum states. That’s our shared belief, if you will.
While you are not looking, I do perform some operations and the corresponding mental readjustments change my beliefs: now I describe the spins with the wave function |down>. You keep your original beliefs.
Now we measure the spins along that axis. I predict a negative outcome with 100% probability, you predict a positive outcome with 100% probability. I get it right every time, you get it wrong every time.
If the |down> quantum state is not "really objectively out there", how do you explain these results?
I imagine a QBist would say that when you performed your additional secret operations you gained more information and therefore you were able to develop more accurate beliefs.
Is your issue that a belief can be completely wrong, or rather that two people can hold diametrically opposing beliefs?
I quoted above Fuchs, the main proponent of QBism, saying that in that example "We learn nothing new; we just change what we can predict as a consequence of the side effects of our experimental intervention. That is to say, there is a sense in which the measurement is solely disturbance." So it is not about refining our knowledge of the physical state as it was, it is about changing the physical state and learning what the new state happens to be.
Different people can have different beliefs (different descriptions of the physical state) but not all the beliefs are equally valid. We can in principle check how well they fit with the (shared, objective) reality. In general this is possible only statistically (comparing realized frequencies with calculated probabilities) but in the example above it can be done from a single event: if something impossible according to your beliefs does happen, your beliefs were incompatible with reality and therefore untenable.
I think I'm with you but I don't understand how this is a criticism of QBism (if that's indeed what it is). It's possible for one's beliefs to turn out to be completely wrong because of some secret actions which you were not aware of. This is just as true classically as in the quantum regime. I don't see that this requires more of an explanation than we've already given it.
This is not a criticism of QBism. It's an explanation of what QBism says, as far as I understand, and how (at least in this case) it's no different from the standard QM description: the system of interest is initially in a known quantum state described by one wave function, we perform a measurement, the quantum state is now the eigenstate corresponding to the outcome of the measurement and described by a different wave function. In standard quantum mechanics the change in the quantum state is called "collapse of the wave function", in QBism it may be called "mental readjustment" but I fail to see any substantial difference if that "mental readjustment" comes together with an actual physical change in the system ("the measurement is solely disturbance").
I just find that it's misleading to say that
> in neo-Copenhagen interpretations like QBism the apparent collapse is merely a reflection of an agent's belief update process.
or
> in some interpretations the wave function is "really objectively out there", but in others [presumably including QBism] the wave function is "just a good way to store my beliefs about the future".
Ah, I think I have a clearer understanding of what you're getting at now.
I think your first objection is to the idea that nothing physical is actually happening during the collapse of the wave function. On this I completely agree and I apologise for having used very poor phrasing. When I said "merely a reflection" I didn't intend to mean that nothing physical is occurring. I meant that (according to QBism) there is not a real objective quantum system whose real objective quantum state irreversibly collapses into a single real objective pure state. Rather, an agent has a physical interaction (a "kick") with the real world, which incurs a particular outcome, after which the agent updates their beliefs about the outcomes of future interactions in a manner analogous to Bayesian updating. The fact that this update process happens to be conveniently described by a mathematical operation we call "collapse" is neither here nor there to a QBist.
I think your second objection is something like this: some beliefs are better than others. In many situations there appears to be one belief which is "the best". Therefore whichever belief is "the best" is essentially an objective description of the world. Therefore the quantum state of a system is real and objective.
Is that a fair assessment?
Whether or not this objection holds water, I must retain the claim that in QBism the wave function is not "really objectively out there". It is clear that in QBism a quantum state represents an agent's beliefs (or in weaker interpretations, an agent's information) regarding a system, not something objective about the system. Fuchs, Schack, Caves and others have said this again and again. For example:
> Contrary to those desires, quantum theory does not
describe physical reality. What it does
is provide an algorithm for computing
probabilities for the macroscopic
events (“detector clicks”) that are the
consequences of our experimental
interventions.
> In other words, Fuchs argued, the wave function does not describe the world—it describes the observer. “Quantum mechanics,” he says, “is a law of thought.” Quantum Bayesianism, or QBism as Fuchs now calls it, solves many of quantum theory’s deepest mysteries. Take, for instance, the infamous “collapse of the wave function,” wherein the quantum system inexplicably transitions from multiple simultaneous states to a single actuality. According to QBism, the wave function’s “collapse” is simply the observer updating his or her beliefs after making a measurement.
> The world may be full of stuff and things
of all kinds, but among all the stuff and all the things,
there is no unique, observer-independent, quantum-state
kind of stuff
> Specifically, there can be no such thing as a
right and true quantum state, if such is thought of as defined by criteria external to the agent making the assignment: Quantum states must instead be like personalist,
Bayesian probabilities
BTW, have you heard of the PBR theorem? It made me do a lot of thinking about what it could possibly mean for the quantum state to be a physical fact vs simply information about an underlying state. If these sorts of ideas are interesting to you, you might enjoy a write-up of the theorem by Matt Leifer: https://arxiv.org/pdf/1409.1570.pdf
I am aware of PBR and I find it quite convincing. Regarding QBism it's not clear to me what's the point.
There is the "information processing" aspect. You have a model of physical system based on the available information (in the form of probabilities over a space of states). If you acquire more information (without changing the state of system!) you can refine your description. That's "Bayesian updating" part. If you change the system, you also get a new description. But that is not merely an update of your beliefs about the unchanged state of the system based on new information, and Fuchs distinguishes this "readjustment" from the Bayesian conditionalization.
I don't think the mechanism discussed in the previous paragraph is controversial. In standard QM you can also have imperfect information about a quantum state. Then you do not have a wave function at all. You may have a density matrix, which can be used to compute the probabilities of potential measurements, but you don't know what is the underlying state. And the underlying state exists only if you have a proper mixture, but if you're looking at a subsystem of a larger system in a non-separable state you have an improper mixture and even if you had perfect information about the composite system there is no wave function describing the subsystem.
Then there is the "quantum state is not a description of physical reality" aspect [1]. But you can have the Bayesian description of our knowledge of quantum states without breaking the link between quantum states and physical states (and I'd say that according to PBR if you have perfect knowledge of the quantum state, i.e. you have a wave function, then it does correspond to a physical state).
We could also apply the same treatment to Classical Mechanics:
The states of the system correspond to points in a phase space. The "information processing" aspect looks reasonable: we can describe our knowledge about the state as a probability distribution over the phase space, refining our knowledge means getting a more concentrated distribution as we incorporate additional information. We can also interact with the system, so we get a new description that is not simply a refinement of the previous distribution but incorporates the physical change effected. In the case when we have perfect knowledge (our description is a point in the phase space) we know how this point will evolve and no information can be gained at all. But we still can perturb the system to a different point in the phase space (this is what Fuchs would call a "readjustment").
The "state is not description of physical reality" aspect do not look so reasonable. We can say that states do not exist. Those points in phase space do not describe physical reality, they describe only the observer. There is not such a thing as a right and true state of the system, if such is thought of as defined by criteria external to the agent making the assignment. States must instead be like personalist, Bayesian probabilities. We can say all that, but what is the point?
I don't say that there are not issues with QM, but I don't see how QBism does solve them. Whatever the problems may be with the "quantum-states-are-physical-states" approach, the "quantum-states-are-not-physical-states/physical-states-are-something-else" approach may get rid of some of them but that's not exactly solving them and introduces new issues in defining what is the relation between "quantum states" and "physical states" (hopefully there is some, if we're doing physics).
[1]: which is controversial, here QBism is closest to the “hardcore” Copenhagen view (the wave funciton is a mathematical device used to calculate in the context of an experimetal setting) than to the "standard" QM theory which is based on the state of a physical system being described by its wave function.
So... quantum interpretations can broadly be categorised thus.
1) Psi-ontic: the wave function is a real objective property of a system. This splits further depending on what is said to happen during collapse:
1a) Collapse is real (I don't know if this interpretation has a name but I think a lot of practising physicists think in these terms): this leads to the measurement and Wigner's friends problems I alluded to above
1b) Collapse is apparent (many worlds, de broglie-bohm): this is somewhat more satisfactory but usually raises other issues (e.g. the emergence of the Born rule).
2) Psi-epistemic: the wave function is a representation of some subjective state regarding a system and an agent. This splits further depending on how subjective you're prepared to go.
2a) Weakly psi-epistemic: the wave function represents an agent's state of information/ignorance regarding some true underlying objective ontic state of the system. This type of interpretation is (more or less) demolished by PBR.
2b) Strongly psi-epistemic (QBism): denies the existence of an underlying objective ontic state of a system. The wave function merely represents an agent's beliefs regarding the outcome of future interactions with the system.
I agree QBism is pretty controversial and that it lacks a certain satisfying explanatory mechanism. However I don't think you can deny that it is more than simply "standard QM", or that there are some good reasons for preferring it.
QBism doesn't seem "more" than standard QM to me, it seems "less" because it's just standard QM without pretending that the quantum state describes the physical state. There may be some reasons to throw the towel on realism and just shut up and calculate, but it's not like that's a new idea.
The operations done to establish from the available information what is the quantum state of a system and to calculate predictions are exactly the same in QBism and standard QM. All the positive-operator-valued-measures stuff works just the same, as far as I can tell, when quantum states are considered representations of reality. If our knowledge is sharp we have a wave function which describes the physical state, otherwise we have a density matrix and we ignore the precise state but we can make predictions about physics. In QBism we have the same predictions (and the same wave function / density matrix but devoid of meaning).
I don't completely understand the split 2a/2b and how 2b is more tenable. What does "the outcome of future interactions with the system" mean if there is no "true underlying objective ontic state of the system"? I understand that according to QBism quantum states do not represent reality. But does physical reality exist at all or not? Is there a "physical state of the system", even though it cannot be described using QM? If there is no state of the system, what does "system" mean? How is the "outcome of the interactions with the system" determined?
This thread is getting a lot longer and more involved than I anticipated. Apologies but for the sake of my own free time and sanity I may have to slow down and make more use of citations. The main point I was trying to get across was that QBism does say these things about quantum theory, regardless of whether or not you find it tenable.
As I say the mathematics is invariant across interpretations, therefore the Born rule and POVMs have a use to an Everettian just as they do a QBist. The difference is what they think of the physical meaning of such a thing. [0][1]
Interpreting quantum theory with a radical, personalist Bayesian perspective of the quantum state is novel, although it has historical precedents starting with Bohr and continuing with Jaynes, Wheeler. [2]
QBists broadly speaking tend to assume a pragmatist view of realism, at least in relation to quantum theory. Fuchs describes it as "participatory realism". There is a physical reality but we are ourselves entwined with it and cannot assume that the models we construct are objective and observer-independent. I think Fuchs has argued that the measurement problem, Wigner's friend, Bell's theorem and Kochen-Specker all point us irrevocably towards a radical Bayesian perspective of the quantum state. The task remaining is to disentangle the subjective from the objective:
> The professed goal is to strip away all those elements of quantum theory that can be interpreted in subjective, agent-dependent terms. The hope is that whatever remains will hint at something essential and objective about nature. [3]
I don't deny that QBism says things, but they don't seem so interesting to me. At least not as much as I expected when I approached the subject some time ago. I'm a fan of Jaynes and his work on information theory and statistical mechanics and I very much like the Bayesian angle here but it can be applied exactly the same (even better, I'd say) in a "realist" setting.
I think the problems in QM may not be problems after all if we could understand the physics better. Standard QM also consists in doing "as if" the quantum state represented physical reality: we (should) know that QM cannot be right and it's just an approximation to something else (QFT or whatever unification with GR) and even the way we apply QM cannot be right because it's also full of approximations (isolated systems do not exist, etc.). The "problems" that QBism "solves" may be artifacts due to those approximations and not fundamental problems. I find that all the (highly-speculative) physical theories trying to explain why things are "as if" QM was true are more promising than the metaphysical proposals of QBism or MWI (and as much as the MWI is metaphysical at least it seems better defined!).
I lack the time and patience to read the thousands of pages that Fuchs has written on the subject and I don't expect you to explain them to me either. So long, and thanks for all the fish^H^H^H^H discussion.
I recently read a book by a cosmologist Max Tegmark in which he brought up another theory - that the function wave function doesn't really collapse, it's just that the moment of measurement lets us determine our location in the multiverse. I think this is related:
> “Quantum trajectory theory makes predictions that are impossible to make with the standard formulation,” Devoret said.
That is bullshit. If it were true, the predictions made by QTT would be tested and if they came out as predicted it would be the biggest news in physics since the Aspect experiment.
What is "going on" during wave function "collapse" has been known for decades: entanglement and decoherence. That's all.
I am really getting sick and tired of these sensationalistic headlines.
(I'm also not entirely sober. It is the Fourth of July after all.)
> What is "going on" during wave function "collapse" has been known for decades: entanglement and decoherence. That's all.
Wasn't it a famous physicist who said "If you think you understand Quantum Mechanics then you don't understand Quantum Mechanics"?
I'm not defending this article, but I was under the impression that the proper interpretation of quantum mechanics / QFT is far from a settled matter among physicists.
> Wasn't it a famous physicist who said "If you think you understand Quantum Mechanics then you don't understand Quantum Mechanics"?
No. That's an apocryphal quote. Richard Feynman said in 1965, " I think I can safely say that nobody understands quantum mechanics." It turns out it wasn't true even when Feynman said it, and it's certainly not true today.
Feynman's problem is that he was committed to the idea that particles are real. They aren't [1].
There are a lot of arguments over the proper interpretation of QM but it turns out that when you get to the bottom of things they are all saying the same things using different terminology.
It's not so much that it is settled as everybody knows that it isn't a useful topic of conversation. All the various interpretations have the same math behind them, give the same prediction, and have the same observable behavior. Since there isn't anything to distinguish them, they are all equally valid.
In practice, things tend to go with the "Shut up and calculate"[1] philosophy.
I've heard that idiom, and I'm sure it has its use. I don't think we should stop calculating, by any means. However, there are individuals in the field who think new insights are possible through continued attempts to improve our interpretations (in addition to continued development of the theory as expressed through robust math). I don't have a source handy, but I've heard the physicist Sean Carroll express this idea on his podcast, Mindscape.
Numbers by themselves don't mean anything (for humans at least). The meaning is found in how the numbers relate to the concepts that we make use of.
It is legitimate to ask how our everyday perceptions can be so radically and fundamentally different from what the math appears to say about the nature of reality. "Shut up and calculate" is not a legitimate answer.
(For the record, the phrase "Shut up and calculate" was coined by David Mermin as a pejorative characterization of the Copenhagen interpretation, which actually says simply that we cannot know anything more than what the math says, and that's just the way it is, and any attempt at further inquiry is doomed to fail and therefore should not be attempted. It's a deeply unscientific attitude.)
I read statements from Feynman that I interpreted as very similar. He said things like: the question "what is the underlying reality behind all this" probably "has no meaning." I never understood what he was trying to say.
So, I am not quite up to date on the latest views on QM in general, but how do entanglement and decoherence explain, for instance, doing a double-slit experiment, sending a particle through, and getting a dot on the screen? What goes on there?
That's kind of like saying that Maxwell's equations solve the luminiferous aether problem only if you subscribe to relativity (or something equivalent).
More like solving the hard problem of consciousness via appeals to a world soul: It requires commitment to certain unfalsifiable metaphysical assumptions.
> It requires commitment to certain unfalsifiable metaphysical assumptions.
Like what? "Multiple worlds" does not require a commitment to the reality of multiple worlds (the misleading rhetoric notwithstanding). (Everett never called it "multiple worlds", he called it "relative state", which is IMHO much less misleading.)
Everett never called it "multiple worlds", he called it "relative state", which is IMHO much less misleading
Also note that Everett's dissertation was titled The Theory of the Universal Wave Function, which puts a different emphasis on the thing as well.
He did believe in quantum immortality, though, and assumed the alternate 'worlds' were real. That's the standard interpretation of MWI: While there's just a single wave function, it factors into 'branches' entangling measurement results and states of consciousness, with all the different versions of yourself coexisting in a realist sense. However, as these branches tend to no longer interact, that's an unfalsifiable claim.
> as these branches tend to no longer interact, that's an unfalsifiable claim.
The key word there is "tend". The branches can interact (via interference) it's just the the technological challenges of demonstrating this become more pronounced as you add degrees of freedom. The limits of falsifiability here are technological, not limits in principle. To be considered unfalsifiable (in the Popperian sense), a theory has to be unfalsifiable in principle, not just in practice.
In fact, interference has already been experimentally demonstrated on some very large systems, and work on quantum computing is progressing rapidly enough that post-quantum cryptography is a serious concern. The falsifiability of the universal wave function is at a similar stage as the falsifiability of gravity waves was a few decades ago.
My mistake: I should have said can't. Schrödinger time evolution is linear and unitary, ie once you split off branches that have factors living in different eigenspaces, they can no longer interact.
It is true that branches may in principle join again - however, that cannot be detected by nature of the process.
> once you split off branches that have factors living in different eigenspaces
And how exactly does that happen?
The answer is: it doesn't. The orthogonality of different branches is an approximation. It's a very good approximation because decoherence is a phenomenally efficient process, but it's an approximation nonetheless. The universal wave function always resides in the same Hilbert space because, as you yourself pointed out, Schrödinger time evolution is linear and unitary.
Indeed very interesting, what's going on? Reading the article, the only phrase where "wave function collapse" occurred is:
> What’s more, this near-complete knowledge of how the system changes smoothly over time allows researchers to “rewind the tape” and avoid the apparently irreversible “wave function collapse” of the standard quantum formalism.
Please, answer this intriguing question, what's going on?
I think in QTT there is no collapse event, just a series of state transitions. It looks like the concept of a collapse is a product of a less complete understanding of what is going on.
That’s why the article spends so much time contrasting QTT with the view offered by Shroedingers equation. With Shroedinger there is no specific state predicted, so you have to introduce the concept of some event inducing a specific state to occur. QTT allows continuous prediction of state and even the ability to prevent or influence state transitions. At least that’s what I got out if it, although I’ll concede I think that’s a rough attempt at a summary.
Stopped reading half way through, as it felt like the author didn't understand what he was writing about. What hope do I have reading the article, then?
It took me a long time to understand two's complement arithmetic for negative numbers in binary. Read several explanations on books and magazines (this was before the internet existed), couldn't understand it. Then one day it clicked. Awesome trick. I went back to some of the explanations that hadn't helped me understand it, and I could clearly see the author didn't understand it themselves. The world is too full of that.
MWI can be differentiated from the Copenhagen Interpretation via experiment as soon as the Copenhagen Interpretation decides what a "measurement" is, when it happens, and when it doesn't.
As it is now, the Copenhagen Interpretation is an incomplete theory because it doesn't give you a formal algorithmic way to know when to apply the measurement operator. The answer is whatever it needs to be to make the answer come out right.
To answer your question more directly, MWI could be falsified in a lot of ways, but one would be if structures larger than a certain size don't self-interfere.
Yes it is. MWI's only rule is that reality evolves according the the Schrödinger equation. It's what would get if you took collapse out of the Copenhagen Interpretation.
The idea of "branching" is a human-legible metaphor for describing the resultant behavior. But the math doesn't have branching.
According to MWI, there's no special privileged operation called "measurement" like there is in the Copenhagen Interpretation. Of course there's still scientists looking at stuff, but according to MWI, the scientists and their machines are made of matter that follows the same law of physics of the matter they're studying.
You do need something more than Schroedinger’s equation to get definite outcomes and probabilities. Apparently when and how it happens are not questions so easy to answer, are they?
MWI may be what you would get if you took collapse out of the Copenhagen Interpretation, but to get the same predictions you have to put the collapse back in somehow. And the question of what is a measurement cannot be completely avoided.
OK, I guess you need Born's Rule, too. But so does every other interpretation, including the Copenhagen one. My uneducated guess is that there's some geometric reason for it that hasn't been discovered yet.
> to get the same predictions you have to put the collapse back in somehow.
This part is just not true. There's no collapse and no formal "measurement" in MWI. You seem like you might have some misconceptions about MWI. I would urge you to read more about it rather than discussing it with amateurs on HN.
> OK, I guess you need Born's Rule, too. But so does every other interpretation, including the Copenhagen one.
Sure (note that some people claim that Born's rule can be derived from other considerations but the issue remains highly controversial). And at what point do you need Born's Rule? (hint: m9t)
I've read enough about the subject to know that there is not "one" MWI but many different variants (that's of course also the case for the Copenhagen Interpretation, which is even less well-defined). DeWitt (who introduced the "many-worlds" label, by the way) seemed to believe that branches are more "real" than Everet did, for example. And I don't know where do you put the "consistent histories" formulation (some people say it's many-worlds, some people say it's neo-Copenhagen).
Anyway, you have not yet explained to me how do you get predictions about experimental outcomes.
This is what happens in standard QM:
1) You have a wave function describing the system of interest (psi), we assume it was prepared in that state.
2) You can calculate the possible outocomes of a measurement, say +1 with probability 50% and -1 with probability 50%.
3) You perform the experiment, the outcome is +1
4) Immediately after the measurment you describe the system with the wave function psi+ that is the eigentstate corresponding to the outcome +1 (for -1 it would be psi-).
5) You can use the wave function psi+ to make predictions for new experiments, for example repeating the measurement before the state has time to evolve (according to Schroedinger's equation) you will get +1 again.
If you think the MWI gives the same predictions, this is my best guess of how you may think it works:
0) There is a universal wave function describing the whole UNIVERSE (PSI)
1b) Some mathemagical operations can be used to extract a wave function that describes the physical universe (the branch of the UNIVERSE that we are in, however you want to call "our world" out of "many worlds"). Let's say we decompose it as psi for the system (which in "our world" has been prepared in that state, so it's described as in the standard formulation) and psi' for the rest of our universe (not the UNIVERSE, mind you).
2) You can calculate the possible outocomes of a measurement, say +1 with probability 50% and -1 with probability 50%.
3b) You perform the experiment, but you don't really do perform an experiment because the only thing that happens is that the UNIVERSE evolves unitarily and PSI follows Schroedinger's equation in a completely deterministic fashion. However, somehow you do get a random outcome. You do also get the other outcome, but that's in another branch (or whatever). In your branch, you get an outcome with is either +1 or -1 as predicted. Remarkably, if you repeat the experiment the frequency of the different outcomes will match the predicted probabilities (unless you're unlucky, because there are other branches where you don't get the expected frequencies and your predictions will fail). Anyway, say that in your branch you got the result +1.
4b) You do the mathemagical operations of step (1b) again, but in this case to get the wave function describing your branch you don't say "in my world I have a system prepared as such and such", you say "in my world I had a system prepared as such and such and then I did a measurement and I got +1 as outcome". This gives you the wave function for your universe, that can be factored as psi+ (because you got the result +1) for the system of interest and psi'' for the rest of our universe.
5) You can use the wave function psi+ to make predictions for new experiments, for example repeating the measurement before the state has time to evolve (according to Schroedinger's equation) you will get +1 again.
As far as I can imagine, to make predictions about "your universe" you have to include the outcomes of the previous measurements to get the right description for the system (i.e. you need to recover the "collapsed" wave function psi, even though PSI doesn't collapse). That's what I mean by putting the collapse back in somehow.
I always say nothing is going on during wave function collapse. You can't tell the difference between a particle whose wave function has collapsed and one that hasn't. Since there is no change it seems nothing actually happened ;-)
> I always say nothing is going on during wave function collapse.
I don't see how that could possibly be true. In the double slit experiment collapsing the wave by observing which slit the light passed through alters the outcome. Anything that alters observable reality is by definition not "nothing".
In general QM defines an observable value as a operator, meaning in the process or observing the value you operate on (ie change) the thing you are observing. Again, that could hardly be described as "nothing".
> You can't tell the difference between a particle whose wave function has collapsed and one that hasn't.
Could you expand on this? For example, in the double slit experiment, it's easy to observe the effects of "uncollapsed" (superposition) behavior.
Perhaps you're saying that we can't observe a particle without collapse occurring (from a Copenhagen perspective), so we never directly observe an uncollapsed particle. But we can observe the distinct effects that uncollapsed particles have, which seems to undermine your claim.
How do you believe that supports the original claim that I quoted, "You can't tell the difference between a particle whose wave function has collapsed and one that hasn't"?
Even if we take that paper at face value, there's a clear distinction once a "particle" has interacted with something, like a detector screen: the particle's wave is no longer sustained, so you can indeed "tell the difference."
In any case, that paper's parallels with quantum systems are limited at best. Even in the paper itself, we find some of the caveats:
> "There is, however, a huge gap between our system and the quantum world where diffraction and interference of single particles is usually observed."
It goes on to list a number of differences which make it clear that all we're dealing with is a limited analogy, the relevance of which is dubious.
> A series of bouncing-droplet findings since 2015 has crushed this dream. The results indicate that Couder’s most striking demonstration of quantum-like phenomena, back in 2006 — “the experiment that got me hooked on this problem,” the fluid dynamicist Paul Milewski said — was in error. Repeat runs of the experiment, called the “double-slit experiment,” have contradicted Couder’s initial results and revealed the double-slit experiment to be the breaking point of both the bouncing-droplet analogy and de Broglie’s pilot-wave vision of quantum mechanics.
No matter how you look at it, this paper can't support the claim I was asking about.
The interaction in that experiment doesn't have the droplet dividing or dissolving into the wave. For the purposes of that experiment, the droplet is a quantum unit.
