PeroK said:You could create "non-interacting" branches in a classical probability tree.
DarMM said:There's a purely classical model called Spekkens toy model where you have interfering probabilities, but where a form of tracing causes the interference terms to die off. As @PeroK said above in classical probability theory you have non-interacting branches, but Spekkens model is even closer to QM in that you have interacting branches but coarse grained branches become non-interacting (i.e. have a form of decoherence).
Well the analogue of Schrodinger's equation in a classical model would be the Stochastic evolution equations. They will naturally "branch" as time goes in. For example set up the statistical mechanics of some gas + detector. There you will get branching under Liouville evolution.Minnesota Joe said:Yes, something about PeroK's statement caught my eye-- it sounded like it was hinting at another approach. How does that work with Schrodinger equation though?
Very interesting. This is another independent interpretation?DarMM said:Well the analogue of Schrodinger's equation in a classical model would be the Stochastic evolution equations. They will naturally "branch" as time goes in. For example set up the statistical mechanics of some gas + detector. There you will get branching under Liouville evolution.
What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?Minnesota Joe said:Very interesting. This is another independent interpretation?
Earlier I was talking about the many world people's commitment to use only the Schrodinger equation. This is one of the superficial things in its favor (because it is easily generalized to modern physics, is simple, etc.). But that means that decoherence has to come from the SE as well. I wasn't sure where you were going with the classical analog of the Schrodinger equation or the Spekkens model.DarMM said:What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?
Just that Spekkens model is classical model that contains virtually all the features used to motivate Many Worlds and that branching isn't something unique to QM, but occurs in probability theories in general.Minnesota Joe said:Earlier I was talking about the many world people's commitment to use only the Schrodinger equation. This is one of the superficial things in its favor (because it is easily generalized to modern physics, is simple, etc.). But that means that decoherence has to come from the SE as well. I wasn't sure where you were going with the classical analog of the Schrodinger equation or the Spekkens model.
I take it that here you are using "branching" more generally than MWI does? I ask because I've in talking about many worlds I've strictly used branching to refer to the result of decoherence, so I guess there is an ambiguity here I have to watch out for.DarMM said:Just that Spekkens model is classical model that contains virtually all the features used to motivate Many Worlds and that branching isn't something unique to QM, but occurs in probability theories in general.
Actually in a way no it is not more general. Branching is a feature of classical stochastic models and in QM we get branching from decoherence because decoherence is precisely the process that converts classical probabilities into quantum probabilities.Minnesota Joe said:I take it that here you are using "branching" more generally than MWI does? I ask because I've in talking about many worlds I've strictly used branching to refer to the result of decoherence, so I guess there is an ambiguity here I have to watch out for.
As an aside question does Everett's relative-state interpretation require decoherence?DarMM said:... in QM we get branching from decoherence because decoherence is precisely the process that converts classical probabilities into quantum probabilities.
I haven't given classical theories much thought; I just don't find it compelling. But if there is no rule about when to apply which form of evolution, then I don't see how one can make predictions. There must be some other information that's implicitly used to make that choice.DarMM said:So you similarly can't make sense of classical statistical mechanics and Wiener processes or other Stochastic processes as they similarly have no rule* for when to apply Bayesian updating?
*Although I would say the do, i.e. when you make an observation and obtain a result.
I think it's confused by there really being two Born rules. One is the measure on Hilbert space, which is needed for decoherence, to be able to say two parts of ##\psi## evolve independently. I think Vaidman is also assuming this. Two is connecting ##\psi## to subjective experience, which is what this quote is about.DarMM said:This introduces "worlds" directly into the basic postulates of the theory even though "worlds" only really emerge after decoherence. How does decoherence work in such a picture exactly?
According to Sean Carroll's book and Adam Becker's book, Everett original idea didn't involve decoherence and he wasn't familiar with it. It seems to him the central idea is just superpositions of macroscopic objects that entangle with microscopic objects. So this is a step before decoherence if I understand this correctly. Sean Carroll does claim he thought of them as "worlds", but I put that in quotes intentionally, because I don't know for sure.timmdeeg said:As an aside question does Everett's relative-state interpretation require decoherence?
The problem is it's not "evolution" in a mechanical sense. Collapse is just Bayesian updating. Bayesian updating has a clear rule for when it is applied, i.e. when you make an observation. I don't really understand what the issue is or how this is "not predictive". Clearly these theories are predictive.akvadrako said:I haven't given classical theories much thought; I just don't find it compelling. But if there is no rule about when to apply which form of evolution, then I don't see how one can make predictions. There must be some other information that's implicitly used to make that choice
Oh, hey, this might solve a mystery for me. I was really puzzled why Carroll thought it permissible to derive the Born rule from epistemic probability after decoherence if decoherence requires the Born rule. Maybe this is motivation?akvadrako said:I think it's confused by there really being two Born rules. One is the measure on Hilbert space, which is needed for decoherence, to be able to say two parts of ##\psi## evolve independently. I think Vaidman is also assuming this. Two is connecting ##\psi## to subjective experience, which is what this quote is about.
DarMM said:The problem is it's not "evolution" in a mechanical sense. Collapse is just Bayesian updating. Bayesian updating has a clear rule for when it is applied, i.e. when you make an observation. I don't really understand what the issue is or how this is "not predictive". Clearly these theories are predictive.
Surely you find regular statistics or statistical mechanics "compelling"?
Do you mean "Why is statistical mechanics compelling"?akvadrako said:Why? And why do you think Bayesian updating isn't evolution? It changes the state — that seems like evolution.
Yes, that's what I thought. So this seems to make the difference if one compares Everett's relative states with MWI's branches. In contrast to the former the latter requires decoherence. But how is that justified?Minnesota Joe said:According to Sean Carroll's book and Adam Becker's book, Everett original idea didn't involve decoherence and he wasn't familiar with it. It seems to him the central idea is just superpositions of macroscopic objects that entangle with microscopic objects. So this is a step before decoherence if I understand this correctly.
Minnesota Joe said:Oh, hey, this might solve a mystery for me. I was really puzzled why Carroll thought it permissible to derive the Born rule from epistemic probability after decoherence if decoherence requires the Born rule. Maybe this is motivation?
DarMM said:Do you mean "Why is statistical mechanics compelling"?
I don't really care too much about whether evolution is the correct word. Obviously the state changes but it's not meant to be a physical process. My point is more why is Bayesian updating a problem in QM and not in classical statistics or theories that use it?
I think you are correct that it makes a difference. But we could also flip it around and ask how Everett was justified in thinking that the terms in his branches are worlds. Decoherence provides the mechanism for considering them to be approximately "separate" in some sense, like two perpendicular vectors. And it isn't just many world's that finds this idea useful, it is used in other contexts and interpretations too.timmdeeg said:Yes, that's what I thought. So this seems to make the difference if one compares Everett's relative states with MWI's branches. In contrast to the former the latter requires decoherence. But how is that justified?
That alone is very enlightening, thanks! It's why I was asking @DarMM about details around the decoherence calculation. I was wondering if it involved amplitudes (perhaps squared), but not probabilities, necessarily. According to Carroll in that thread it doesn't involve probabilities and off diagonal elements are "small". Whether or not that is true, he believes it, so it makes his project make more sense.akvadrako said:I think so. He's really trying to derive probability and you don't need probability to get decoherence. Look at his conversation with Eric in the comments from the link below. Maybe he's improved his argument since then.
http://www.preposterousuniverse.com...hanics-is-given-by-the-wave-function-squared/
What issue do you mean? If it's about the "problem" of collapse most consider this to be the resolution. I'm the opposite, I don't see how it doesn't instantly resolve this whole "two evolutions" problem. Collapse is mathematically just a generalization of Bayesian conditioning. I don't really see the "issue" as such.akvadrako said:That's what I mean; I really have never given it much thought and I don't see how it'll shed much light on this issue.
Decoherence requires probabilities and thus the Born rule. Carroll's argument in that link makes little sense to me. "Magically" decoherence happens, then we get branches, then we get probabilties.Minnesota Joe said:That alone is very enlightening, thanks! It's why I was asking @DarMM about details around the decoherence calculation. I was wondering if it involved amplitudes (perhaps squared), but not probabilities, necessarily. According to Carroll in that thread it doesn't involve probabilities and off diagonal elements are "small". Whether or not that is true, he believes it, so it makes his project make more sense.
DarMM said:What issue do you mean? If it's about the "problem" of collapse most consider this to be the resolution. I'm the opposite, I don't see how it doesn't instantly resolve this whole "two evolutions" problem. Collapse is mathematically just a generalization of Bayesian conditioning. I don't really see the "issue" as such.
What issue?akvadrako said:This doesn't resolve anything; it just suggest Bayesian updating also has the same issue.
But the "shut up and calculate" perspective contradicts the MWI anyway. So I wonder what Hossenfelder's statementPeterDonis said:No. It's part of the minimal "shut up and calculate" machinery of QM. It's independent of any interpretation. You have to do it in order to make the predictions from the mathematical machinery match actual experimental data.
DarMM said:What issue?
But how is that really an issue? Several physical theories have it, classical statistics has it, QM has it. All are predictive and confirmed in every observation we have. What exactly is the issue?akvadrako said:Of two different forms of evolution.
timmdeeg said:the "shut up and calculate" perspective contradicts the MWI anyway
timmdeeg said:I wonder what Hossenfelder's statement
"The wave-function collapse, I have to emphasize, is not optional. It is an observational requirement."
clarifies in addition.
Yeah, I have to remain agnostic about whether or not it is circular, given what we discussed earlier, until I know more. I should probably read his paper, because he certainly didn't go into any detail in his book. I think he ought to have mentioned it, frankly. All I was arguing is that, given that he believes it at least I understand his project better.DarMM said:Decoherence requires probabilities and thus the Born rule. Carroll's argument in that link makes little sense to me. "Magically" decoherence happens, then we get branches, then we get probabilties.
...Constructing the reduced density matrix” is a purely mathematical process, completely well-posed whether or not you have the Born Rule. The question is what meaning we should attach to it, which is what our argument addresses. In Appendix B we address this in gruesome detail, and in the shorter paper we do the whole thing without ever using density matrices, just to assuage skepticism.
Of course, you do need to use the inner product on Hilbert space to construct the reduced density matrix. But the inner product is part of the theory, and nobody is going to make sense of quantum mechanics without assuming it."
DarMM said:But how is that really an issue? Several physical theories have it, classical statistics has it, QM has it. All are predictive and confirmed in every observation we have. What exactly is the issue?
Let me reiterate this. This two evolution issue occurs in any probabilistic theory, so this is really just a problem with probabilistic theories is it not?
You might have said it a lot but you haven't really shown the contradiction or how these theories are not predictive. Quantum Mechanics and Statistical Mechanics clearly are predictive. Could you give an example of such a contradiction in a specific scenario?akvadrako said:That's what I think I've said about 5 times now. It's not specific to QM - any theory with two forms of evolution which can't be reconciled into one seems obviously self-contradictory because you get different results depending on which form of evolution you apply. So I don't see how such theories even make predictions.
I'd have a read of the papers of Kent and Vaidman (one a critic of MWI, the other a proponent) which for similar reasons find Carroll's derivation flawed.Minnesota Joe said:Yeah, I have to remain agnostic about whether or not it is circular, given what we discussed earlier, until I know more. I should probably read his paper, because he certainly didn't go into any detail in his book. I think he ought to have mentioned it, frankly. All I was arguing is that, given that he believes it at least I understand his project better.
He claims to do it without density matrices too:
But there is no contradiction in QM: Unitary evolution applies only to isolated systems, and Born's rule (with some form of collapse) only to measured systems. The latter are clearly not isolated. Thus the two forms of evolution apply to disjoint contexts. How could they ever be contradictory?akvadrako said:It's not specific to QM - any theory with two forms of evolution which can't be reconciled into one seems obviously self-contradictory because you get different results depending on which form of evolution you apply.
A. Neumaier said:But there is no contradiction in QM: Unitary evolution applies only to isolated systems, and Born's rule (with some form of collapse) only to measured systems. The latter are clearly not isolated. Thus the two forms of evolution apply to disjoint contexts. How could they ever be contradictory?