Sean Carroll podcast on many worlds interpretation

[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.

 

[PeterDonis]

theoretically, we do need the entire wave function

Not if all you are doing is predicting further measurement results on a single decohered branch. And that's what you were talking about in the post of yours that I responded to: "development of a single branch". You don't need to know the entire wave function to calculate that. You only need to know that particular branch.

 

[Heikki Tuuri]

Not if all you are doing is predicting further measurement results on a single decohered branch.

Decoherence is never perfect. The idea is that one degree of freedom interacts with a large number of other degrees of freedom. For example, a single photon changes the state of a large number of silver and bromine atoms in a photographic film.

At which point the scientist inside the lab would be allowed to discard part of the wave function? The scientist himself may be a particle which is used in a double slit experiment. There is always a minuscule chance that the scientist will interfere with another version of himself who took a different route but arrived on the screen in the same state.

 

[PeterDonis]

Decoherence is never perfect.

It's perfect enough for us to make accurate predictions.

At which point the scientist inside the lab would be allowed to discard part of the wave function?

At the point when he can make accurate predictions by doing so.

The scientist himself may be a particle which is used in a double slit experiment.

No, he can't. The scientist has many orders of magnitude too many degrees of freedom which cannot be kept coherent for such an experiment.

 

[Minnesota Joe]

Like the GRW and de Broglie-Bohm people, in Something Deeply Hidden Sean Carroll writes that he seeks a "complete, unambiguous, realistic" theory but is discouraged by the difficulties of extending the theory once you add something in addition to Schrodinger equation. (pg 31-32).

He writes, "But we should also admit that the whole picture might be wrong, and something very different is required" page 40 and "I am defending one particular view of that reality...This shouldn't be taken to imply that the Everettian view is unquestionably right." pg 42. So I take him to be undogmatically defending his favorite.

At least some of the meaning of the statements he makes in his podcast are clearer. He reinterprets the solutions to the Schrodinger equation so of course all the other interpretations have "worlds" from that point of view, but that doesn't at all change my position that the claim is question-begging and he should stop using it.

I can see how the minimalism is attractive but on the flip side it means that if your interpretation is incorrect, you just carry the incompleteness of quantum mechanics forward.

Another attractive feature of MWI apparently is locality. Can someone please explain to me in what senses MWI is local if so? People sometimes conflate the various senses of 'local' and this caused all manner of confusion for me when I started reading quantum foundations. In particular, is it fair to say the violations of Bell's inequality are merely apparent under MWI? Or does it just mean Lorentz invariant? (I could be botching things myself I freely admit.)

 

[pinball1970]

Like the GRW and de Broglie-Bohm people, in Something Deeply Hidden Sean Carroll writes that he seeks a "complete, unambiguous, realistic" theory but is discouraged by the difficulties of extending the theory once you add something in addition to Schrodinger equation. (pg 31-32).

He writes, "But we should also admit that the whole picture might be wrong, and something very different is required" page 40 and "I am defending one particular view of that reality...This shouldn't be taken to imply that the Everettian view is unquestionably right." pg 42. So I take him to be undogmatically defending his favorite.

At least some of the meaning of the statements he makes in his podcast are clearer. He reinterprets the solutions to the Schrodinger equation so of course all the other interpretations have "worlds" from that point of view, but that doesn't at all change my position that the claim is question-begging and he should stop using it.

I can see how the minimalism is attractive but on the flip side it means that if your interpretation is incorrect, you just carry the incompleteness of quantum mechanics forward.

Another attractive feature of MWI apparently is locality. Can someone please explain to me in what senses MWI is local if so? People sometimes conflate the various senses of 'local' and this caused all manner of confusion for me when I started reading quantum foundations. In particular, is it fair to say the violations of Bell's inequality are merely apparent under MWI? Or does it just mean Lorentz invariant? (I could be botching things myself I freely admit.)

You should have put a spoiler on this post, I got the hard back yesterday. I am going to read it and possibly post a review on pf if that is allowed. This is a pop Science book after all.
He is doing real physics in this area so published paper references may let this through.
That's if I understand enough of it to review.

 

[Heikki Tuuri]

@Minnesota Joe ,

in the EPR experiment, Copenhagen people think that the measurement apparatuses at both ends "collapse" into definite classical states.

They kind of discard large parts of the wave function of the whole system, which includes also the measurement apparatuses.

In MWI there is never any collapse. When a scientist compares the results from the both ends in his mind, it is local operation.

The wave function in the Schrödinger equation develops in a local manner, and the hidden variables in the Bohm model develop locally.

But the Schrödinger equation is not relativistic. Locality is more a thing of Special relativity. We would need a relativistic wave function and a relativistic Bohm model.

 

[Minnesota Joe]

You should have put a spoiler on this post, I got the hard back yesterday.

Yes, my apologies, I'll try to remember that in the future, thank you.

 

[Minnesota Joe]

in the EPR experiment, Copenhagen people think that the measurement apparatuses at both ends "collapse" into a definite classical states.

They kind of discard large parts of the wave function of the whole system, which includes also the measurement apparatuses.

In MWI there is never any collapse. When a scientist compares the results from the both ends in his mind, it is local operation.

If I understand what you wrote correctly, that is what I meant by the violations being only apparent. Because we only see the set of statistics in our branch. Do you agree?

The wave function in the Schrödinger equation develops in a local manner, and the hidden variables in the Bohm model develop locally.

But the Schrödinger equation is not relativistic. Locality is more a thing of Special relativity. We would need a relativistic wave function and a relativistic Bohm model.

So do we prefer to use 'locality' to mean relativistic? What word do we use for instantaneous influence at large distances? Or, rather, the idea discussed long before Einstein that you ought not be able to influence a system without propagating some signal to where that system is? (Implying both finite time and intervening causes.)

 

[OCR]

You should have put a spoiler on this post. . .

Lol. . . ah, c'mon now pinball.

Spoiler: 👀

You would have looked, anyway. . . .

.

 

[pinball1970]

Lol. . . ah, c'mon now pinball.

Spoiler: 👀

You would have looked, anyway. . . .

.

Yes I still looked.
I saw a quote from page 32 on post #94 and I was barely through the introduction. My spoiler post was half in jest, it's not like @Minnesota Joe gave away the end of House season 4 or anything.

 

[romsofia]

The conclusion from the FANTASTIC lecture notes by Robert Geroch some 44 years ago called "Geometrical Quantum Mechanics".
There is a lot more information in these notes than what i quote, so go check out the lecture notes, very well written!

In short, the Everett interpretation asks that one take quantum mechanics, as is, very seriously, and learns to live with the resulting picture. One gives up the notion of certain classical possibilities being realized in favor of the introduction of certain regions of configuration space in which the wave function is small. One carries out the same calculations, and transmits the same information, but in slightly different language. One obtains precisely the same description of the Universe that would be obtained by some external observer O. This O, however, would do nothing except look on with satisfaction as the wave function of Universe evolves. We might as well dispense with him. One does not need a classical framework in which to anchor quantum mechanics: one can just let quantum mechanics drift on its own.

Finally, one might object: “All this seems awfully philosophical and rather pointless.” Imagine yourself in the following situation. You wake up one morning to discover that people always talk to each other by saying “In the region of configuration space corresponding to ... the wave function is small.” That’s just the way they always talk. You put up with this very confusing situation for a few days, and finally can’t stand it anymore. You ask a friend to come into see you. You say to him: “I want to reformulate quantum mechanics in such a way that classical possibilities actually occur in the Universe. I want to introduce smaller quantum systems, and observables, and breaks in the chain of instruments, on one side of which classical possibilities are actually realized. I want to modify, along these lines, the interface between quantum mechanics and what human beings actually observe. It is true that, in this program, I cannot provide details of the internal workings of people, but this feature is also common in other areas of physics.” After a pause, your friend replies: “All this seems awfully philosophical and rather pointless.”

 

[Minnesota Joe]

The conclusion from the FANTASTIC lecture notes by Robert Geroch some 44 years ago called "Geometrical Quantum Mechanics".
There is a lot more information in these notes than what i quote, so go check out the lecture notes, very well written!

"In short, the Everett interpretation asks that one take quantum mechanics, as is, very seriously, and learns to live with the resulting picture. "

Which I guess I understand now means just use the Schrodinger equation and reinterpret it. It is that reinterpretation that is difficult to believe.

My spoiler post was half in jest, it's not like @Minnesota Joe gave away the end of House season 4 or anything.

Sean Bean dies. Oops.

 

[pinball1970]

Which I guess I understand now means just use the Schrodinger equation and reinterpret it. It is that reinterpretation that is difficult to believe.Sean Bean dies. Oops.

Yes but he is also alive in one of the many other episodes in one of the other MW

 

[Heikki Tuuri]

@Minnesota Joe ,

https://en.wikipedia.org/wiki/Bell's_theorem

Bell's theorem says that we cannot assume local hidden variables which would determine the measurement result at the ends of the EPR experiment setup.

Quantum mechanics says that Bell's theorem is true. It has been empirically demonstrated many times.

MWI, of course, satisfies Bell's theorem, just like other interpretations. I never remember which way John Bell wrote the inequality. I assume QM breaks the inequality? And hidden variables would uphold the inequality?

Einstein protested the "spooky action at a distance" in the EPR experiment. In MWI, there is no spooky action at a distance for the simple reason that all data processing happens in the head of a single scientist, and there are no great distances inside a single head.

Note that Bell's theorem is just a special case of a general rule: you cannot discard parts of the wave function if you want to calculate correctly. Hidden variables would mean that we discard the relevant wave function immediately after we have prepared the two particles in the EPR experiment.

A classical analogue: if you want to calculate the route of a toy boat on waves of water, you need to know the full wave pattern. You cannot discard the information about the waves and calculate from the location of the boat alone.

 

[DarMM]

Well Copenhagen views takes the formalism "as is" as well. It's just that they read it differently, i.e. that $\psi$ is a generalized probability distribution rather than a physical degree of freedom.