Undergrad Sean Carroll podcast on many worlds interpretation

[Minnesota Joe]

It depends what you mean by physics. If you mean objective reality then consciousness is irrelevant. If you mean what's measurable then it depends how subjective experience emerges. We have a rough idea how this works in day to day life, but things get hairy when you consider the experience of Wigner's friend or other circumstances when subjective experience differs greatly from two different viewpoints. Maybe Wallace was on the right path when we tried to derive the Born rule from decision theory, though he only considered one aspect of experience.

Really I just wanted to make sure Carroll wasn't characterized incorrectly--there are already people accusing him of engaging in woo--because as far as I know consciousness doesn't enter at all into what he is trying to do.

 

[DarMM]

We have zillions of real-lab measurement devices described by PVMs. Recently we had the debate of POVMs, and I still have not a single example for a real-lab apparatus and its description by a POVM

Really? They're incredibly common. See here:
https://arxiv.org/abs/1501.05096
He even lists the device explicitly. This is just one of several such papers. Very common in anything associated with quantum information. POVMs are decades old, I find the discussions on this forum as if they were some weird esoteric idea very odd.

I'm also not sure what POVMs have to do with "quantization of a classical quantity" or not. The observable algebra cannot be derived from classical physics of course. One has to rely on mathematical arguments like symmetry principles. Then you build a model and check, whether it describes real-world phenomena correctly. An example for an observable which for sure is not derivable by some "quantization of a classical quantity" is spin

That's not really what I mean. Spin is still connected to angular momentum and there is a classical notion of spin in terms of spinor bundles. I mean some POVMs are even more non-classical than that. The quantum observable algebra of PVMs is often connected to some classical observable algebra via a process we call quantization, but POVMs are more general than this.

I think to make physical sense of POVMs you need no more and no less than the standard postulates and the minimal interpretation including Born's rule for the measurement in the usual PVM sense

Some POVMs are not reducible to PVMs though. The rule for POVM detection event probabilities has Born's rule as a special case.

 

[vanhees71]

So is the "theorem" proven in Pere's book wrong?

Also, don't get me wrong. I've nothing against POVMs, why should I? But where do you need them for the discussion on foundations?

 

[DarMM]

So is the "theorem" proven in Pere's book wrong?

Also, don't get me wrong. I've nothing against POVMs, why should I? But where do you need them for the discussion on foundations?

I assume you mean Neumark's theorem. No that is a correct. As Peres himself says though it doesn't mean every POVM is a PVM. It means for non-QFT systems it is possible to realize a POVM as a PVM on the system + ancilla.

As for where they are needed, this is why Peres includes discussion of them in his book and many of his papers, because they give a very different picture of what a quantum measurement is. So different that many (including Peres in his monograph) propose to rename them quantum tests. This is related to what I mentioned about them and classical quantities above. See here for example:
https://arxiv.org/abs/quant-ph/0207020

 

[Minnesota Joe]

This is never answered by any of these dogmatic Everettians

I'm not an MWI proponent, but I don't get the sense that Carroll is dogmatic. On Mindscape and elsewhere he interviews way too many people with directly opposing viewpoints and really allows them to have their say for me to label him dogmatic. Go listen to the David Albert interview where Albert pinpoints for Carroll what is wrong with the probability interpretation in MWI for example. Carroll is trying to overcome those objections so he listens to people and acknowledges he might fail.

Contrast his behavior with some of the physicists linked to in this thread if you dare. You could do a simple experiment and count the ad hominem attacks and other statements irrelevant to the truth or falsehood of their claims in what they write. They are obviously smart and have good ideas, but so do lots of people and I don't like wading through the terrible to get to the good stuff. I'll take Carroll's attitude any day.

 

[atyy]

I assume you mean Neumark's theorem. No that is a correct. As Peres himself says though it doesn't mean every POVM is a PVM. It means for non-QFT systems it is possible to realize a POVM as a PVM on the system + ancilla.

Does it not hold for QFT systems because of the type III algebras that don't have have pure states?

 

[Demystifier]

But where do you need them for the discussion on foundations?

One example would be measurement of time, given that there is no time observable.

 

[Demystifier]

It means for non-QFT systems it is possible to realize a POVM as a PVM on the system + ancilla.

Whenever someone tells that something which is true for QM is not necessarily true for QFT, my first instinctive gut reaction is - that's because something in QFT is not mathematically well defined due to the infinite number of degrees of freedom, implying that it is really true for physical QFT as well, provided that one finds a way to define it precisely in a physically sensible way. And in 99% cases my first instinctive gut reaction turns out to be right.

 

[DarMM]

Does it not hold for QFT systems because of the type III algebras that don't have have pure states?

Yes exactly.

 

[DarMM]

Whenever someone tells that something which is true for QM is not necessarily true for QFT, my first instinctive gut reaction is - that's because something in QFT is not mathematically well defined due to the infinite number of degrees of freedom, implying that it is really true for physical QFT as well, provided that one finds a way to define it precisely in a physically sensible way. And in 99% cases my first instinctive gut reaction turns out to be right.

The fact that QFT has type-III C*-algebras is rigorously established.

 

[Demystifier]

The fact that QFT has type-III C*-algebras is rigorously established.

I don't see how is that related to physics. Can you give example of a physical measurement described by QFT where it would imply POVM that cannot be reduced to PVM?

 

[Quanundrum]

I'm not an MWI proponent, but I don't get the sense that Carroll is dogmatic. On Mindscape and elsewhere he interviews way too many people with directly opposing viewpoints and really allows them to have their say for me to label him dogmatic. Go listen to the David Albert interview where Albert pinpoints for Carroll what is wrong with the probability interpretation in MWI for example. Carroll is trying to overcome those objections so he listens to people and acknowledges he might fail.

I still maintain that his attitude is dogmatic. He is on record repeatedly saying that the state of Quantum Foundations is "embarrassing" for not having solved the measurement problem in a century, and then concludes every time that one should naturally choose Everett. He's not as straightforward as David Deutsch in his insistence, but sometime around 2010 he started insisting on Everettian QM.

The reason he has people like David Albert on his podcast and treats them respectfully is tied to the fact that these people have contemplated and published on the topic of Everett since before Carroll graduated. However, in all his blog posts over the past ~9 years, all the interviews and recently published book he insists that Everett is simply "taking the physics seriously", echoing the arrogant sentiment from the Oxford camp over the past 20 years. That is dogma.

You have Saunders, Deutsch and Wallace in the Decision Theoretic camp, you have Sean Carroll and Lev Vaidman in the Self-Location Uncertainty camp, but Vaidman rejects Carroll and Sebens 'proof' of derivation of the Born Rule. Similarly you have Wallace and Timpson in the State Space camp versus Carroll and Singh in their Mad Dogg Everettian camp. Add to this the Splitting vs Divergence. And then finally add to this the whole extravaganza of "Multiverse = Many Worlds" that Susskind, Tegmark and sometimes Carroll espouse. The Everettian program is littered in unanswered questions and indicators that it is far from as simple as "taking the math/physics" seriously. If he had acknowledged this, I'd respect him a lot more. Instead he feels comfortable dogmatically going into interviews and proclaiming that Everett is "just QM taken seriously" and then extrapolating claims from there, even though the myriad of different Everettian readings wildly disagree on those claims...

 

[DarMM]

I don't see how is that related to physics. Can you give example of a physical measurement described by QFT where it would imply POVM that cannot be reduced to PVM?

QFT implies it for all POVMs, such as the one given in the paper above in #62

 

[Demystifier]

QFT implies it for all POVMs, such as the one given in the paper above in #62

How can that be rigorous in general, given that interacting QFT itself is not rigorous in general?

 

[DarMM]

How can that be rigorous in general, given that interacting QFT itself is not rigorous in general?

The existence of type-III algebras requires the existence of the continuum limit. For 4D Yang-Mills Balaban has established enough to show Type-III algebras hold.

 

[atyy]

@DarMM, at the non-rigorous physics level there are also arguments against associating pure states with local subsystems, eg. https://arxiv.org/abs/1406.7304 and https://arxiv.org/abs/1601.04744

Is this related to the Type III algebras or is it a different issue?

 

[Demystifier]

The existence of type-III algebras requires the existence of the continuum limit. For 4D Yang-Mills Balaban has established enough to show Type-III algebras hold.

OK, my gut intuition then tells me that there should be some kind of weak equivalence between POVM's and PVM's. Perhaps something like - there is no PVM that is exactly equivalent to the POVM, but the POVM can be approximated arbitrarily well with a PVM, with a suitable definition of "approximated arbitrarily well". Could something like that be true?

 

[bhobba]

I'm not sure what you mean by QM not needing collapse. I mean after an observation you update the state, right?

If that's what you man by collapse the yes, but some include things like the state instantaneously changing. I am not going to argue one way or the other on that - its similar to when you throw a dice the outcome is 1-6 - is that collapse? Just something to think about, I am not taking any side.

Thanks
Bill

 

[DarMM]

If that's what you man by collapse the yes, but some include things like the state instantaneously changing. I am not going to argue one way or the other on that - its similar to when you throw a dice the outcome is 1-6 - is that collapse? Just something to think about, I am not taking any side.

I just meant state reduction, usually that's what people mean by collapse. I was just checking what you meant.

That state reduction is like bayesian updating, such as in your dice example, is a well known aspect of viewing QM as a generalization of probability theory.

 

[vanhees71]

State reduction and collapse is usually used synonymous. If you interpret as a Bayesian updating, it's no problem. The problem arises, and this made obviously a big part of the debate beween Einstein and Bohr, when one assumes that the collapse is a physical process acting instantaneously on the entire universe. This is neither a necessary assumption to use QT to describe observations (state preparation and measurements) nor is it consistent with the mathematical features built in the usual local relativistic QFTs, according to which space-like separated events cannot be causally connected since the Hamilton density commutes by construction with all local operators with space-like separated arguments.

 

[Michael Price]

The maximum entropy of one bit is $k_B \ln 2$ in the standard definition. But a qubit is not a bit. A bit can only have two values, $0$ or $1$. A qubit's wave function can have any value on the Bloch sphere. Measuring a qubit can only result in one of two values, but a single measurement on a qubit is not sufficient to tell you its exact wave function. Strictly speaking, it takes an infinite number of measurements (on an ensemble of identically prepared qubits) to do that.

That, at least, is how I understand Motl's argument, and it seems at least worth enough consideration for somebody to have written a paper on it at some point; that's why I asked if anyone knows of such a paper.

The answer is that the infinite information stored on the Bloch sphere is spread across the infinity of mutually inaccessible worlds that split off from an idealised measurement. No single world can access this infinity of information or entropy.

 

[Swamp Thing]

https://www.quora.com/How-does-the-...ding-to-the-Born-rule/answer/Michael-Price-29

How does this work when we look at a continuously distributed observable?
And in a rigorous formulation, would the term "overlap" be well defined?

 

[Michael Price]

How does this work when we look at a continuously distributed observable?
And in a rigorous formulation, would the term "overlap" be well defined?

Overlap is a well defined (and elementary) procedure for producing a complex number from two wave vectors.
The continuous case is just the limit of the discrete case - nothing fancy or controversial.

All undergrad stuff.

 

[pinball1970]

Overlap is a well defined (and elementary) procedure for producing a complex number from two wave vectors.
The continuous case is just the limit of the discrete case - nothing fancy or controversial.

All undergrad stuff.

The discussion has been above my pay grade for the most part but fascinating none the less.
Thanks for making the thread lively.
I am off to Waterstones to get the hardback and had a quick look at the reviews while I was checking if they have it in stock
Jim Al Kalili and Brian Greene gave good reviews
https://www.waterstones.com/book/something-deeply-hidden/sean-carroll/9781786076335

 

[Heikki Tuuri]

One can say that the Copenhagen interpretation is an MWI "in denial".

Think of the thought experiment which I mentioned earlier. We have a physicist performing measurements in an isolated laboratory. For outside observers, the wave function of the lab, including the physicist, develops smoothly. There is no collapse.

The wave function can be input to the Bohm model, and there we can calculate a continuum many branches in the wave function. If we consider these branches "really" existing, then we have an MWI where we have used the Bohm model to pick the branches, that is, the worlds.

If we take the ontology above, then a wave function always involves many worlds.

But is Newtonian mechanics an MWI? We initialize some particles in the system and let it develop in time. If we would have chosen different initial values, we would have had a different history. A Platonist might claim that the alternative histories do exist. We just happen to live in this particular history.

The big difference between the Newtonian model and quantum mechanics is that we need the wave function in quantum mechanics. The development of a single branch cannot be calculated from the branch alone. We need to know the wave function.

 

[vanhees71]

Think of the thought experiment which I mentioned earlier. We have a physicist performing measurements in an isolated laboratory. For outside observers, the wave function of the lab, including the physicist, develops smoothly. There is no collapse.

The problem with such statements in quantum-foundations discussions is that it is self-contradictory. If there are outside observers being able to observe anything what the physicist in his lab is doing, this physicist's lab is no longer isolated but is interacting with the outside observer. Not taking this into account easily leads to paradoxes and endless discussions.

 

[Heikki Tuuri]

The problem with such statements in quantum-foundations discussions is that it is self-contradictory. If there are outside observers being able to observe anything what the physicist in his lab is doing, this physicist's lab is no longer isolated but is interacting with the outside observer.

I am sorry. I was careless with my words. The lab is isolated. Only at a later time, an observer opens the lab. It is just like Schrödinger's cat, except that we have put a physicist inside the box.

 

[PeterDonis]

The development of a single branch cannot be calculated from the branch alone. We need to know the wave function.

This is not correct for a branch that has decohered. For a decohered branch, you can just use the term in the wave function that corresponds to that branch to predict all future measurement results in the branch. You don't need to know the entire wave function. If this were not true, MWI would not work as an interpretation.

 

[Heikki Tuuri]

This is not correct for a branch that has decohered. For a decohered branch, you can just use the term in the wave function that corresponds to that branch to predict all future measurement results in the branch. You don't need to know the entire wave function. If this were not true, MWI would not work as an interpretation.

Decoherence makes it possible to discard conflicting branches, in practice. For example, if we find Schrödinger's cat alive, we do not need to think about dead cat branches any more.

But theoretically, we do need the entire wave function. Nothing can be discarded. This assumes that the whole universe is one giant box with a single wave function.

The wave function of the universe involves philosophical as well as practical problems, though. Are we sure that a physicist living within that wave function observes things like we observe now?

 

[DarMM]

@atyy and @Demystifier , both your questions are very interesting. I want to speak to former colleagues first, as I'm not entirely sure my intuitive answers are correct and up to date. Apologies for the delay.

A difficulty with your question @Demystifier is that there simply are no local PVMs in QFT, so we need a way of characterizing "PVM-like" in a theory with no PVMs.