Danger for the Many-Worlds Interpretation?

[DarMM]

Even in a probabilistic theory, I don't see how this is consistent. You need a rule that tells you when to apply which kind of evolution.

Statistical Mechanics is the same though. When you make an observation the Liouville distribution collapses on observation. In any stochastic theory is there a "rule" for when to apply Bayesian updating?

 

[DarMM]

As a measure of the "stuff" that makes up reality, or in a diverging view of MWI, the number of worlds. As Vaidman says it:
Probability Postulate: An observer should set his subjective probability of the outcome of a quantum experiment in proportion to the total measure of existence of all worlds with that outcome.

Why would one take this kind of view of the coefficients in Quantum Theory, but not in classical probabilistic theories like Wiener processes? What aspect of QM makes one not view the coefficients in the same way?

 

[akvadrako]

Statistical Mechanics is the same though. When you make an observation the Liouville distribution collapses on observation. In any stochastic theory is there a "rule" for when to apply Bayesian updating?

I don't think so. If there was a rule then I would consider both forms of evolution to be contained within that rule.

Why would one take this kind of view of the coefficients in Quantum Theory, but not in classical probabilistic theories like Wiener processes? What aspect of QM makes one not view the coefficients in the same way?

I am not sure. Maybe because of the assumption of completeness. If QM is incomplete and reality is non-linear, then linear evolution is just an approximation that needs periodic corrections.

 

[Minnesota Joe]

You don't need the Born rule, per se, but without probabilities you are just going to have a large number of branches, all with equal weight.

There would be no reason then to have any phenomena consistent with one thing being more likely than another. The physics we see is dependent on the most likely outcomes being favoured.

The Born rule gives a specific outcome distribution. But, you need something; otherwise you are giving equal weight to what - classically at least - would be impossible outcomes.

Are you talking about just entanglement without decoherence here?

My understanding was that MWI requires decoherence in order to get branches that are separate and non-interacting. This seems absolutely crucial because we don't observe superpositions.

Exactly. That is what people like Zurek are trying to do. However it hasn't worked out yet.

Zurek himself seems to acknowledge the circularity in earlier work.

Can you elaborate on the role the Born Rule plays in the density derivation of decoherence? What happens if you don't apply the Born Rule assumption?

 

[DarMM]

I don't think so. If there was a rule then I would consider both forms of evolution to be contained within that rule.

So really this is a problem with a fundamental theory being Stochastic? Since any Stochastic theory will have two such "evolution" processes.

 

[DarMM]

Can you elaborate on the role the Born Rule plays in the density derivation of decoherence? What happens if you don't apply the Born Rule assumption?

This is a bit of a boring answer, but basically you can't derive decoherence at all since you have no way to pass from the state of the system to the state of a subsystem.

 

[akvadrako]

So really this is a problem with a fundamental theory being Stochastic? Since any Stochastic theory will have two such "evolution" processes.

I can't make sense of such a theory unless there is a rule telling you which form of evolution to apply.

 

[DarMM]

I can't make sense of such a theory unless there is a rule telling you which form of evolution to apply.

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.

 

[DarMM]

As a measure of the "stuff" that makes up reality, or in a diverging view of MWI, the number of worlds. As Vaidman says it:
Probability Postulate: An observer should set his subjective probability of the outcome of a quantum experiment in proportion to the total measure of existence of all worlds with that outcome.

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?

 

[PeroK]

Are you talking about just entanglement without decoherence here?

My understanding was that MWI requires decoherence in order to get branches that are separate and non-interacting. This seems absolutely crucial because we don't observe superpositions.

In my view, you have misunderstood decoherence and, especially, "non-interacting". We don't observe superpositions not because for some physical reason they cannot happen; but, because (after a certain period of time evolution) the probability of a significant superposition is vanishingly small.

There is, quite fundamentally, no hard and fast physical division between branches, but an increasingly low probability of the significant superpositions between the two.

If we take the example of the infamous cat. After a period of time evolution, there is a huge number of states that are largely grouped around the concept of a "live" cat - and between them, they have a significant probability of approx 50%; and, there is another huge array of states that are grouped around the concept of a "dead" cat - and, again, the combined probability is 50%. There are at least as many states again that represent a half-live, half-dead cat, but these states combined have approx 0% probability.

There are not two cats. There is either one cat or an uncountable number of cats, depending on how you define the term "cat". And, these states are constantly evolving. But, the laws of physics - implied by QM and the Born rule, if you like - keep the two sets of states apart. For example:

Cells continue to develop in a live cat; but cells cannot be rejuvenated in a dead cat (or if they can, in such small numbers and with such a low probability that you won't notice). That's decoherence.

 

[PeterDonis]

isn't this claim not just Kopenhagen view?

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.

 

[Minnesota Joe]

In my view, you have misunderstood decoherence and, especially, "non-interacting". We don't observe superpositions not because for some physical reason they cannot happen; but, because (after a certain period of time evolution) the probability of a significant superposition is vanishingly small.

Well "non-interacting" was really short-hand for vanishing small. The way I understand this is that after decoherence each worlds is represented by a state and the states have approximately 0 overlap (your vanishingly small).

But let's back up. You wrote, "You don't need the Born rule, per se, but without probabilities you are just going to have a large number of branches, all with equal weight. "

I found that interesting. Were you talking about decoherence here or something else?

 

[PeroK]

Well "non-interacting" was really short-hand for vanishing small. The way I understand this is that after decoherence each worlds is represented by a state and the states have approximately 0 overlap (your vanishingly small).

But let's back up. You wrote, "You don't need the Born rule, per se, but without probabilities you are just going to have a large number of branches, all with equal weight. "

I found that interesting. Were you talking about decoherence here or something else?

You could create "non-interacting" branches in a classical probability tree.

 

[DarMM]

But let's back up. You wrote, "You don't need the Born rule, per se, but without probabilities you are just going to have a large number of branches, all with equal weight. "

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).

 

[entropy1]

But it seems all she really can say is you need an additional assumption to derive subjective collapse from unitary evolution.

So how about: given the current outcome of the measurement, all the other outcomes don't happen in this (subjective) world and this outcome doesn't occur on other branches? That means there is a single measurement outcome with given probability?

 

[Minnesota Joe]

You could create "non-interacting" branches in a classical probability tree.

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).

Yes, something about PeroK's statement caught my eye-- it sounded like it was hinting at another approach. How does that work with Schrödinger equation though?

 

[DarMM]

Yes, something about PeroK's statement caught my eye-- it sounded like it was hinting at another approach. How does that work with Schrödinger equation though?

Well the analogue of Schrödinger'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]

Well the analogue of Schrödinger'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.

Very interesting. This is another independent interpretation?

 

[DarMM]

Very interesting. This is another independent interpretation?

What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?

 

[Minnesota Joe]

What part? That classical stochastic equations have branching isn't an interpretation of QM. Or did you mean Spekkens model?

Earlier I was talking about the many world people's commitment to use only the Schrödinger 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 Schrödinger equation or the Spekkens model.

 

[DarMM]

Earlier I was talking about the many world people's commitment to use only the Schrödinger 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 Schrödinger equation or the 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]

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.

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]

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.

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.

 

[timmdeeg]

... in QM we get branching from decoherence because decoherence is precisely the process that converts classical probabilities into quantum probabilities.

As an aside question does Everett's relative-state interpretation require decoherence?

 

[akvadrako]

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 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.

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?

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.

Another way to think is that worlds are like points similar to Bohmian mechaincs and never split, but diverge. So what in a splitting view one might call one world is a collection of an infinite number of worlds, which will diverge sometime in the future. In this sense I don't think you need decoherence to define a world density.

 

[Minnesota Joe]

As an aside question does Everett's relative-state interpretation require decoherence?

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.

People cite H. Dieter Zeh in 1970 https://link.springer.com/article/10.1007/BF00708656 for introducing decoherence, but I don't understand how long the idea was kicking around before that, if it was. So I don't myself know if it was even possible for Everett to be familiar with the concept when he wrote his dissertation.

 

[DarMM]

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

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"?

In a normal statistical model what is the "implicit information" used to apply Bayesian updating?

 

[Minnesota Joe]

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.

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]

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"?

Why? And why do you think Bayesian updating isn't evolution? It changes the state — that seems like evolution.

 

[DarMM]

Why? And why do you think Bayesian updating isn't evolution? It changes the state — that seems like evolution.

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?