Danger for the Many-Worlds Interpretation?

[Minnesota Joe]

That's what I'm referring to ultimately as well. Though for decoherence you can't just use wave functions you need density matrices. In it's most general form that the probability for some event represented by a POVM element $E$ is $Tr(\rho E)$ with $\rho$ the state.

No, that smuggles in probability unnecessarily. That's what I'm saying. It assumes textbook quantum mechanics most likely.

The Schrodinger equation is a wave equation, right? Including waves involving multiple waves (particles) like that make up macroscopic systems. Wave equations in general exhibit properties like coherence and decoherence. For example you get decoherence when you have many sources with different phase relationships. You get coherence in the ripple tank with a double-slit because both slits are emitting waves from a single source and therefore have a well-defined phase relationship (so you get constructive and destructive interference). No Born Rule required.

But Born interpreted the square of the wave function as the probability distribution and that works. So interpretations that have real waves, that don't just assume the wave function is related to probability, have to explain why this works.

 

[vanhees71]

I would say it doesn't say "how" the outcome of a measurement comes about. Why you update your probabilities is obvious, i.e. because that's the outcome you witnessed.

But isn't this a mute argument? Physics never answers "why" and "how" questions like this.

Why in Newtonian or SRT mechanics is it that there exists an inertial frame of reference? Filling this with the details about how space and time is described is all you need to do mechanics, but why this basic assumption works, is not answered. It's just used as an empirical fact to describe as many other observables using it as an input for mathematical deduction.

In QT it's the same with the probabilities. It's the (imho) so far only consistent interpretation of Schrödinger's wave function, and how the heuristics towards the Schrödinger wave function was, is well known, leading from Planck and Einstein right away to de Broglie's idea and then the somewhat ironic remark by Debye (a pupil of Sommerfeld by the way) to Schrödinger that, when you talk about waves you'd better should have a wave equation. At the next meeting Schrödinger presented one ;-)) with no clear idea about its physical meaning. Then Born happily used it to attack the problem of scattering and came to the idea with the probability interpretation (with a missing square first, but Einstein told him to put it in right away ;-)).

So, what I never understood is the obsession to "deriving" Born's rule from something else. Isn't it simply one of the basic empirical facts entering the theory like axioms are used to build a mathematical theory?

 

[DarMM]

So, what I never understood is the obsession to "deriving" Born's rule from something else. Isn't it simply one of the basic empirical facts entering the theory like axioms are used to build a mathematical theory?

Personally I would say yes it is a basic empirical fact entering the theory. Like you the only view of the quantum state that makes much sense to me and conforms with practice is a probabilistic one. I'm simply conveying the "problem" as far as MWI proponents see it.

 

[DarMM]

Wave equations in general exhibit properties like coherence and decoherence

To demonstrate decoherence you need the Born rule. Even MWI people recognise this which is why Zurek is working on Quantum Darwinism, an attempt to derive decoherence without using the Born rule.

Show me a textbook where decoherence is derived without the Born rule.

 

[PeroK]

Okay, maybe we are victims of physics jargon. What Born Rule are you talking about?

ETA: I'm specifically referring to Max Born's 1926 probabilistic interpretation of the wave function.

Even in MWI, you must have probabilities for the following reason:

You can repeatedly carry out an experiment with two outcomes where one outcome occurs, say, 90% of the time. There are lots of examples of this.

If, in MWI, there is one branch for the first outcome and one branch for the second outcome, then why do we end up 90% of the time in the world corresponding to the first outcome?

As has been pointed out several times on this thread, MWI has no good answer to this.

 

[Minnesota Joe]

To demonstrate decoherence you need the Born rule. Even MWI people recognise this which is why Zurek is working on Quantum Darwinism, an attempt to derive decoherence without using the Born rule.

Show me a textbook where decoherence is derived without the Born rule.

Okay, I agree with you on this I think: it appears they haven't derived decoherence without assuming the Born Rule in a way that is generally accepted. At the very least this is a deeper issue than I gave it credit. It appears that so far they are only motivated by having a wave equation. So that is two problems: derive decoherence without the Born Rule and derive the Born Rule after decoherence. Carroll really glosses over some important stuff on this issue. For example, he derives the Born Rule after the decoherence, but that would be viciously circular if it is impossible to derive quantum decoherence without assuming the Born Rule! Irritating. At the very least he should have mentioned this when he wrote about decoherence, because it is very important to what he says later.

 

[PeroK]

Okay, I agree with you on this I think: it appears they haven't derived decoherence without assuming the Born Rule in a way that is generally accepted. At the very least this is a deeper issue than I gave it credit. It appears that so far they are only motivated by having a wave equation. So that is two problems: derive decoherence without the Born Rule and derive the Born Rule after decoherence. Carroll really glosses over some important stuff on this issue. For example, he derives the Born Rule after the decoherence, but that would be viciously circular if it is impossible to derive quantum decoherence without assuming the Born Rule! Irritating. At the very least he should have mentioned this when he wrote about decoherence, because it is very important to what he says later.

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.

 

[DarMM]

derive decoherence without the Born Rule and derive the Born Rule after decoherence.

Exactly. That is what people like Zurek are trying to do. However it hasn't worked out yet. Ruth Kastner and others have pointed out that there is circularity even in the Quantum Darwinist program as it is. See her paper here:
https://arxiv.org/abs/1406.4126

Carroll really glosses over some important stuff on this issue.

I would say so yes.

 

[akvadrako]

'm simply conveying the "problem" as far as MWI proponents see it.

I don’t think most MWI proponents consider it a problem. I think it’s mostly a focus of critics.

 

[DarMM]

I don’t think most MWI proponents consider it a problem. I think it’s mostly a focus of critics.

What do you mean? It is one of the more commonly cited issues with Copenhagen.

 

[akvadrako]

What do you mean?

I think many MWI proponents think that it's possible to derive the Born rule from unitary evolution and considered that an advantage of the theory. But that's not why they are proponents, so if it can't be derived it's not a problem. Vaidman is the most clear on this point.

Others like Carroll seem to consider the existing derivations sufficient. They do require some assumptions, which perhaps are just ways of rephrasing the Born rule, but they find them acceptable.

I think the most relevant point is that most Born rule derivations seem to be just as relevant to all interpretations and don't really have anything to do with MWI. Either it's a redundant (perhaps approximate) assumption or it must be postulated, but MWI has no advantage in this aspect.

The only really relevant point is in MWI there isn't objective collapse — so the Born rule needs to be interpreted differently.

 

[DarMM]

I think many MWI proponents think that it's possible to derive the Born rule from unitary evolution and considered that an advantage of the theory. But that's not why they are proponents, so if it can't be derived it's not a problem.

I wasn't talking about derivations of the Born rule in MWI in that post, I was talking about Copenhagen.

 

[akvadrako]

I wasn't talking about derivations of the Born rule in MWI in that post, I was talking about Copenhagen.

I see; then I would say (perhaps more in reply to vanhess's concern) the issue many worlders have with the Born rule in Copenhagen isn't the lack of derivation, but that non-unitary evolution (collapse) is incompatible with unitary evolution.

 

[PeroK]

I see; then I would say (perhaps more in reply to vanhess's concern) the issue many worlders have with the Born rule in Copenhagen isn't the lack of derivation, but that non-unitary evolution (collapse) is incompatible with unitary evolution.

Even the Copenhagen-ers have that issue with Copenhagen!

 

[DarMM]

I see; then I would say (perhaps more in reply to vanhess's concern) the issue many worlders have with the Born rule in Copenhagen isn't the lack of derivation, but that non-unitary evolution (collapse) is incompatible with unitary evolution.

Why is that a problem exactly? In Stochastic theories in general Bayesian updating is not "compatible" with the general Stochastic evolution operator.

 

[DarMM]

The only really relevant point is in MWI there isn't objective collapse — so the Born rule needs to be interpreted differently.

What's an example of one of these interpretations of the Born rule?

 

[akvadrako]

Why is that a problem exactly? In Stochastic theories in general Bayesian updating is not "compatible" with the general Stochastic evolution operator.

That seems like a problem of any theory to me. If you only apply one form of evolution at a time you need a rule about which to apply. If QM is assumed complete then there can't be any rule like that.

 

[DarMM]

That seems like a problem of any theory to me. If you only apply one form of evolution at a time you need a rule about which to apply. If QM is assumed complete then there can't be any rule like that.

What I'm saying is that in an probabilistic theory in physics or elsewhere one applies Bayesian updating after an observation and this cannot be derived from the dynamical laws that apply otherwise. Why can't there be a rule like that. Unless you essentially mean a fundamental theory cannot be probabilistic.

 

[akvadrako]

What's an example of one of these interpretations of the Born rule?

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.

 

[akvadrako]

What I'm saying is that in an probabilistic theory in physics or elsewhere one applies Bayesian updating after an observation and this cannot be derived from the dynamical laws that apply otherwise. Why can't there be a rule like that. Unless you essentially mean a fundamental theory cannot be probabilistic.

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.

 

[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?