I Quantum theory - Nature Paper 18 Sept

[stevendaryl]

OK, there's a bit I don't get, I think. So the final state is:

$|final\rangle = \frac{1}{\sqrt{3}} |\overline{h}\rangle |-\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |\frac{1}{2}\rangle + \frac{1}{\sqrt{3}} |\overline{t}\rangle |-\frac{1}{2}\rangle$

Expressed in the ok/fail-basis of $\overline{W}$, this is:

$|final\rangle = \frac{2}{\sqrt{6}}|\overline{fail}\rangle|-\frac{1}{2}\rangle + \frac{1}{\sqrt{6}}|\overline{fail}\rangle|\frac{1}{2}\rangle - \frac{1}{\sqrt{6}}|\overline{ok}\rangle|\frac{1}{2}\rangle$

After $\overline{W}$ measures and obtains the $\overline{ok}$-outcome, only the term $|\overline{ok}\rangle|\frac{1}{2}\rangle$ survives. If we express that again in the $\{|\overline{h}\rangle,|\overline{t}\rangle\}$-basis, we get:

$|\overline{w}=\overline{ok}\rangle=\frac{1}{\sqrt{2}}(|\overline{h}\rangle|\frac{1}{2}\rangle - |\overline{t}\rangle|\frac{1}{2}\rangle)$

But this is not a state in which we can claim that $\overline{F}$ predicts that W observes 'fail', as either outcome is possible. Consequently, if $\overline{F}$ applies quantum mechanics to themselves, they should rather reason that if $\overline{W}$ applies their measurement and observes the $\overline{ok}$-outcome, then either measurement outcome of W's measurement is possible, so no contradiction arises. Alternatively, $\overline{W}$ is wrong to believe that their inference from the measurement outcome still holds after the measurement has been performed, since that inference depends on the structure of the pre-measurement state.

The only way of making this seem reasonable, it looks to me, is if $\overline{F}$ supposes that their measurement (of the coin) 'collapses' the state to 'tails'; but that's just the same as the original Wigner's Friend-thought experiment, where if the friend were to make that assumption, they'd predict (wrongly) that a suitable experiment involving the entire lab would show no interference. So if F supposes that W observes 'fail', that just seems to me to be a misapplication of quantum mechanics in the same way as Wigner's Friend's prediction of no interference would be.

I think you're right. The paradox just boils down to: noncommuting operators can't all be said to have definite values at the same time.

But as I summarized in one of the earlier posts:

1. $\overline{W}$ can conclude: "If I measure $\overline{ok}$, then $F$ must measure $+1/2$.
2. $F$ can conclude: "If I measure $+1/2$, then that implies that $\overline{F}$ measured $\overline{t}$"
3. $\overline{F}$ can conclude: "If I measure $\overline{t}$, then $W$ will measure $fail$"

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

 

[msumm21]

Sorry if I'm re-stating what people have already said earlier in this thread, but isn't there a basic error in the analysis. The author assumes Fbar measures R (the "coin" heads or tails) and subsequently acts on that result, ... but later assumes the state of R was unaffected (back in the init state) when Wbar measures. That's not QM is it? QM says R is in the state pure heads OR pure tails, not the init superposition, right?

Correcting for these mistakes, the point of the paper doesn't pan out, right? E.g. the claim that OKbar implies S is spin up wouldn't hold, so the main conclusion wouldn't hold.

The explanation by stevendaryl earlier (#14) in this thread much appreciated, very clear & concise.

 

[vanhees71]

I think you're right. The paradox just boils down to: noncommuting operators can't all be said to have definite values at the same time.

But as I summarized in one of the earlier posts:

1. $\overline{W}$ can conclude: "If I measure $\overline{ok}$, then $F$ must measure $+1/2$.
2. $F$ can conclude: "If I measure $+1/2$, then that implies that $\overline{F}$ measured $\overline{t}$"
3. $\overline{F}$ can conclude: "If I measure $\overline{t}$, then $W$ will measure $fail$"

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

So to make a long story short: Much ado about nothing! Just check all such "philosophical claims" within the minimal interpretation, i.e., first through out the unobservable balast and then check what to be expected in physics experiments. I think it simply boils down to the suspicion I had after first reading the paper: The assumption of the various systems being isolated from each other but nevertheless measured by each other is simply an oxymoron. The very point of QT is that you cannot neglect the influence of measurements on microscopic systems and thus also in general you are able to prepare states such that incompatible observables have determined values (although there are exceptions, e.g., if preparing the angular momenum of a system in the state $j=0$, all three components of angular momentum (or thus any component of angular momentum) take the determined value $m=0$).

 

[DarMM]

I was thinking about this a bit more, probably doing something dumb, but considering agent $F$, if they get the result $z = +\frac{1}{2}$ they can conclude that $\bar{F}$ got $r = \bar{t}$. Fine.

Now if they think of themselves from $\bar{F}$'s reasoning and apply unitary evolution without any collapse to themselves they get that the state of their lab is:
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|+\frac{1}{2}\rangle_L + |-\frac{1}{2}\rangle_L\right)$$
which is $W$'s $|fail\rangle$ state. Thus $W$ must get $fail$.

However if they think of themselves from what they see in their own lab then either $z = -\frac{1}{2}$ or $z = +\frac{1}{2}$ results correspond to a superposition in the $\{|okay\rangle,|fail\rangle\}$ basis. Thus they would reason that $W$ could get $okay$.

So isn't there already a contradiction with just three observers?

$F$ will reach one conclusion about $W$'s result if he just considers his own experiences in his lab and another conclusion if he considers himself from $\bar{F}$'s model of him as a unitarily evolving superposition without decoherence.

 

[DarMM]

For anybody interested Renato Renner's argument has three forms. The form in the original paper from 2016 (explained in standard language by Bub here: https://arxiv.org/abs/1804.03267), the form from the nature article we have been discussing and a third form due to Luis Masanes.

It is harder to pinpoint errors of this third form in my opinion. Expositions of it are found in section 4 of this paper by Richard Healey:
https://arxiv.org/abs/1807.00421

And also this talk by Matthew Pusey (18:35):


And this lecture by Matthew Leifer (39:44):

 

[Fra]

Nice thread which i largely missed and haven't had time to engage in!

whether quantum theory can, in principle, have universal validity.The idea is that, if the answer was yes, it must be possible to employ quantum theory to model complex systems that include agents who are themselves using quantum theory.

This is a good key question about the consistency of reasoning.

To summarize my opnion I think as quantum theory stands clearly isn't meant to have this universal validity. But this should be no news, is I read things this was implicit already in Bohrs views. Quantum mechanics is essentially _formulated_ with respect to a classical measurement device. Where the classical divide for example means that intercommunication in principle commute. But what happes if two different independent classical measurement devices, perform measurements on the same quantum system is a different thing. And if the two classical devices exchange quantum information then the cut is changed. So I think the contradictions that may emerge are only due to invalid inferences in the chain of reasoning, when mixing different premises in a random way.

But there is a rational incentive for asking questions that current quantum theory doesn't allow. For example how should "quantum theory" in terms of cosmological perspectives understood, if the observer is a system on earth? Asking how an observers in principle should infer and produce expectations of the process of other observers making measurements on each other, is a key way to explore this logic.

This paper to me is an argument for the need to keep working on the foundations of quantum theory to harmonize with different complexity scales, but does not contain any suggetsions. But interpretations isn't the problem, its i think that we need a revised theory. All we know is that this theory should reproduce quantum theory in the small system; dominant large observer limit. Essentially when we look at the scattering matrix. I think most agrees that talking about Scattering matrix for complex systems that are larger than the observer or even cosmologies from the perspective of Earth makes no sense, beacuse there is no way to set that experiment up. Even the gedanken experiments in this case are in my mind pathological.

/Fredrik

 

[DarMM]

If anybody wants a description of the third version of the argument.

In essence we have two observers $C, D$ and two superobservers $A, B$.
$C, D$ share a pair of spin-$\frac{1}{2}$ particles, $p_1,p_2$, in the Bell state:
$$|\psi\rangle = \frac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$$
They measure the spin at angles they choose associated with operators $\hat{C}_c, \hat{D}_d$.

Once the measurements are complete, the superobservers $A, B$ then apply a unitary to the $(C, p_1, D, p_2)$ system to reset everything to its original state and then measure their own spin angles $\hat{A}_a, \hat{B}_b$.

This is then repeated over and over again, so one builds up a joint probability distribution $\rho(a,b,c,d)$. The existence of a joint probability distribution then implies for the marginals:
$$|E(a,b) + E(b,c) + E(c,d) - E(a,d)| \leq 2$$

Which contradicts the normal properties of the Bell state which violates these inequalities.

Ultimately the third version of the FR theorem states that being able to reverse measurements on Bell states results in a contradiction with respect to their usual statistics, it would render their statistics classical. Also note that no one observer has knowledge of each outcome $a,b,c,d$.

In this version there are four* ways out:

1. There are systems that cannot be reversed to their initial states by a unitary time evolution, particularly certain measurements at least. Unitary evolution is not universally valid.
2. Multiple Worlds.
3. Quantum Mechanics is only about what can be measured by a single observer/from a single Boolean frame. Since nobody can experience all of $a,b,c,d$, the statistics of them together are meaningless.
4. One of the Marginals do not obey the quantum predictions and thus it is true that $|E(a,b) + E(b,c) + E(c,d) - E(a,d)| \leq 2$. This would be an experimental disagreement with QM. Some retrocausal theories might allow this.

*there are in the Nature version of Frauchiger-Renner as well, but it's not as obvious as they only mention three. The fourth is the one stevedaryl has mentioned

 

[DarMM]

The problem is chaining these claims together. Each of the conclusions is true under the assumption that we're starting in the state $|final\rangle$. But under a "collapse" model, after the first observation, the state collapses to something other than $|final\rangle$, so the reasoning no longer applies. If you don't assume collapse, then it's a little more complicated to reason about it, but I think that all interpretations agree that things will work out as if the state collapses upon making an observation.

I've a read a good few papers discussing the result now. What the result actually shows is an inconsistency with multi-agent reasoning when considering subjective collapse. Subjective collapse being that a (sealed) observer can use collapse to update their state, but it is still valid for superobservers outside of the observers' labs to use superposition.

So either you have objective collapse (as you discussed above) and superobservers should model other observers post-measurement via mixed states. Or there is no collapse and in some scenarios one is wrong to consider oneself collapsed. Or one simply rejects standard methods of reasoning between agents in QM, i.e. modal logic cannot be applied consistently and you shouldn't consider other agent's conclusions in QM, essentially because QM is about what one observer should expect, not objective reality.

The result however is not philosophy in my opinion. It does show a situation where, under the assumption QM is about objective reality in some sense, relative state formulations like Bohmian Mechanics and Many-Worlds will give different predictions to models with objective collapse. This means Bohmian Mechanics and Many-Worlds are not just interpretations of the same theory as those of objective collapse views like the minimal statistical view and Ballentine (if I understand them correctly). It means there are two quantum formalisms and we now have a scenario with a predicted difference in their results.

Objective collapse and no-collapse give different results in the Frauchiger-Renner case. Subjective collapse gives contradictory results unless you confine QM to being a single-user theory. I do think this is a significant find for this reason (currently anyway until somebody updates my probability of this with a convincing argument! )

For more on this exposition of the Frauchiger-Renner result see here:
https://arxiv.org/abs/1611.01111
https://arxiv.org/abs/1710.07212

 

[kith]

While looking for something else I just stumbled upon the following answer to Frauchiger-Renner which claims that decoherence resolves the alleged problems:
https://arxiv.org/abs/1810.07065

I don't have time to read it right now but it may be of interest for the discussion here. A quick look on the other papers of the author gives him enough initial credibility to take him serious (he has published in the field of decoherence).

 

[DarMM]

While looking for something else I just stumbled upon the following answer to Frauchiger-Renner which claims that decoherence resolves the alleged problems:
https://arxiv.org/abs/1810.07065

I don't have time to read it right now but it may be of interest for the discussion here. A quick look on the other papers of the author gives him enough initial credibility to take him serious (he has published in the field of decoherence).

Unless I'm mistaken he's saying some of the observers can't reach their conclusions because they don't know if mixtures they receive are proper or improper.

I think that's the point of agreeing on the experimental layout in advance.

 

[stevendaryl]

The result however is not philosophy in my opinion. It does show a situation where, under the assumption QM is about objective reality in some sense, relative state formulations like Bohmian Mechanics and Many-Worlds will give different predictions to models with objective collapse. This means Bohmian Mechanics and Many-Worlds are not just interpretations of the same theory as those of objective collapse views like the minimal statistical view and Ballentine (if I understand them correctly). It means there are two quantum formalisms and we now have a scenario with a predicted difference in their results.

I agree with that. People often say that Many-Worlds, Bohmian mechanics and Copenhagen are different interpretations of the same theory, and so by definition, they can't be distinguished by experiment. To me, they are slightly different theories, not different interpretations of the same theory. So they potentially could be distinguished by experiment. However, the circumstances where they might make different predictions happen to be circumstances where it is infeasible to make precise predictions (circumstances involving huge numbers of particles interacting), so in practice, they don't make different predictions, even though in principle they do.

 

[akvadrako]

so in practice, they don't make different predictions, even though in principle they do.

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work. It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

 

[Demystifier]

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work.

If someone survives thousand times in a row, one can explain it without MWI by using the anthropic argument: "If I haven't survived I woldn't be there to observe it." Do you find this argument vague?

 

[Demystifier]

It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

Why no adherent of MWI has actually performed that experiment?

 

[DarMM]

The one major exception to this might be quantum immortality, though there are some vague arguments why it might not work. It's an experiment you can only perform for yourself and gaining confidence in the results will take a long time, but it certainly has practical consequences.

Related to the Pusey-Leifer theorem and other recent work in Foundations, assuming no fine tuning they (i.e. Realist interpretations like MWI, Bohmian, Transactional) should also show up in deviations from "regular" QM in the early universe, e.g. CMB or similar.

 

[atyy]

Why no adherent of MWI has actually performed that experiment?

They have. Many times. In other worlds.

 

[mfb]

Why no adherent of MWI has actually performed that experiment?

They want to stay alive in many worlds, not just one.

 

[stevendaryl]

so in practice, they don't make different predictions, even though in principle they do.

There is some famous saying along the lines of

In principle, there is no difference between 'in principle' and 'in practice'. In practice, there is.

 

[akvadrako]

If someone survives thousand times in a row, one can explain it without MWI by using the anthropic argument: "If I haven't survived I woldn't be there to observe it." Do you find this argument vague?

I would say anthropic reasoning is totally invalid for future events, assuming there is only a single world. Sure, after the fact you can use it and it wouldn't tell you much.

But if you make your predictions beforehand I think you can use bayesian reasoning. If MWI is true, I expect to survive an event with certainty, $p_\text{MW} = 1$. If it's false, it's $p_\text{1W} < 1$. So survival of an event is evidence of multiple worlds. Not much evidence, but if I'm still around in a million years it's either incredible luck (which has a very low prior) or there's a force of nature that makes it more likely than you would expect based on classical reasoning. To make it more clear, if you survive an infinite number of events, the odds that it's due to lucky quantum outcomes is 0.

Why no adherent of MWI has actually performed that experiment?

You wouldn't see evidence of others performing it. You have to perform it yourself and I would say we all are doing it right now just by living.

 

[StevieTNZ]

A link to a presentation by one of the authors, made on this thought experiment if anyone is interested:
https://www.video.ethz.ch/speakers/...oExmHKbHOT7fw62pctqqZJlz3Q9ZReWi89TiqKAO1UQzk

 

[akvadrako]

Related to the Pusey-Leifer theorem and other recent work in Foundations, assuming no fine tuning they (i.e. Realist interpretations like MWI, Bohmian, Transactional) should also show up in deviations from "regular" QM in the early universe, e.g. CMB or similar.

This is in regards to the lack of operational time symmetry, right? Since I’ve seen you mention this a few times, I wanted to understand it a bit myself. It seems to me P&L are premature in claiming WMI doesn’t have operational time symmetry. In their paper they only seem to consider the complete final state, but in a real experiment you won’t be able to measure that as you’ll only have access to one of the resulting branches.

To look for operational aspects it’s more appropriate to post-select on the result of your measurements. It seems TSVF is an appropriate way to view operational aspects in WMI; the backwards evolving state can be used as an index to which branch you find yourself in. P&L explicitly mention TSVF as satisfying their assumption and since both formalisms make the same predictions for branching observers, they should have equal operational qualities.

The paper Measurement and collapse within the two-state vector formalism (2014) shows “how macroscopic time reversibility is attained, at the level of a single branch of the wavefunction”.

 

[DarMM]

This is in regards to the lack of operational time symmetry, right? Since I’ve seen you mention this a few times, I wanted to understand it a bit myself. It seems to me P&L are premature in claiming WMI doesn’t have operational time symmetry. In their paper they only seem to consider the complete final state, but in a real experiment you won’t be able to measure that as you’ll only have access to one of the resulting branches.

To look for operational aspects it’s more appropriate to post-select on the result of your measurements. It seems TSVF is an appropriate way to view operational aspects in WMI; the backwards evolving state can be used as an index to which branch you find yourself in. P&L explicitly mention TSVF as satisfying their assumption and since both formalisms make the same predictions for branching observers, they should have equal operational qualities.

The paper Measurement and collapse within the two-state vector formalism (2014) shows “how macroscopic time reversibility is attained, at the level of a single branch of the wavefunction”.

That paper is explicitly not a Many-Worlds theory:

It will inherit the advantages of the MWI without assuming multiple realities

It's a retrocausal fine-tuned (as they mention when discussing the future boundary conditions, they just think the tunings are of a reasonable class) model, as one would expect from the Pusey-Leifer theorem.

 

[vanhees71]

Related to the Pusey-Leifer theorem and other recent work in Foundations, assuming no fine tuning they (i.e. Realist interpretations like MWI, Bohmian, Transactional) should also show up in deviations from "regular" QM in the early universe, e.g. CMB or similar.

How can Bohmian QM and MWI be both "realistic". I thought, "realistic", is for a sharp physicists' interpretation synomymous for "deterministic". Then BM is "realistic", while MWI is not, or how do you define "realistic"? I think the word "realistic" is "burnt" in a sense by the philosophers, because everybody seems to have a slightly different definition for its meaning. So one has always to mention which definition one follows.

 

[akvadrako]

That paper is explicitly not a Many-Worlds theory:

That's true, but it's a fine distinction. They are assuming the backwards wave function is ontic, but you can also take it as epistemic, in which case it's just a way to analyse a single branch, which is what's relevant for operational concerns. Anyway, my main point is that P&L did not actually analyse MWI and find that it violates operational time symmetry, so their claim is invalid.

It's a retrocausal fine-tuned (as they mention when discussing the future boundary conditions, they just think the tunings are of a reasonable class) model, as one would expect from the Pusey-Leifer theorem.

You can say it's fine-tuned, but the nature of the fine tuning is what I'm after. In this case, the fine-tuning means "like a classical world".

 

[akvadrako]

How can Bohmian QM and MWI be both "realistic". I thought, "realistic", is for a sharp physicists' interpretation synomymous for "deterministic". Then BM is "realistic", while MWI is not, or how do you define "realistic"? I think the word "realistic" is "burnt" in a sense by the philosophers, because everybody seems to have a slightly different definition for its meaning. So one has always to mention which definition one follows.

Realistic is more clear in philosophy, and it means that there is some objective state. Realists believe there is something like that; anti-realists think everything is subjective. The MWI is realistic, because the wave function is real. In Bohmian QM, it's that plus a world-particle, to pick out the world you are in.

I don't think the word "realistic" means anything consistent to physicists.

Also, MWI is deterministic - it has only unitary evolution so that's obvious.

 

[DarMM]

How can Bohmian QM and MWI be both "realistic". I thought, "realistic", is for a sharp physicists' interpretation synomymous for "deterministic". Then BM is "realistic", while MWI is not, or how do you define "realistic"? I think the word "realistic" is "burnt" in a sense by the philosophers, because everybody seems to have a slightly different definition for its meaning. So one has always to mention which definition one follows.

The definition used in Quantum Foundations (which I am using) is essentially the presence of a decorrelating explanation (in the sense of Reichenbach's principle). Less technically it would mean that the quantum probabilities follow in some sense from intrinsic properties of the system (in addition to those of the apparatus possibly).

It's separate to determinism. Bell's theorem (the 1976 version) is ultimately about this sense of realism as opposed to determinism.

I don't like the phrasing either, but it is standard.

 

[DrChinese]

Also, MWI is deterministic - it has only unitary evolution so that's obvious.

Not sure I see that. Why is that electron spin up rather than spin down?

 

[DarMM]

That's true, but it's a fine distinction.

Having one world versus a multiverse of $\aleph_{1}$ cardinality worlds is a fine distinction? It seems almost one of the largest conceivable distinctions possible in my mind. Unless I'm missing something.

They are assuming the backwards wave function is ontic, but you can also take it as epistemic

Could I have a reference to how this is done. The paper you linked relies on it being ontic as it has physical effects, I don't think one can simply state it can also be taken as epistemic without a proof that all relevant aspects work out the same. As results like the PBR theorem show us, you can't simply say "this can be taken epistemically" without proof when it comes to QM.

Anyway, my main point is that P&L did not actually analyse MWI and find that it violates operational time symmetry, so their claim is invalid.

To come back to this:

In their paper they only seem to consider the complete final state, but in a real experiment you won’t be able to measure that as you’ll only have access to one of the resulting branches.

To look for operational aspects it’s more appropriate to post-select on the result of your measurements. It seems TSVF is an appropriate way to view operational aspects in WMI; the backwards evolving state can be used as an index to which branch you find yourself in. P&L explicitly mention TSVF as satisfying their assumption

Only an ontic TSVF satisfies their assumption as they state.

MWI explicitly breaks Operational Time Symmetry (OTS) at the global level, one can see that immediately.

You are saying that on restriction to a single branch one gets an "effective backward time state" that is epistemic, that somehow restores OTS in a branch, even though Price's argument shows only an ontic backward state does this. I'd like to see the details as the ontic nature of the backward state is crucial to removing the need to fine-tune to restore OTS.

You can say it's fine-tuned, but the nature of the fine tuning is what I'm after. In this case, the fine-tuning means "like a classical world".

Genuine question, do you think an ontic wave traveling back in time toward the Big Bang containing precisely classical information (not approximate) distributed exactly in a Born distribution is okay and simply a fine-tuning in a pedantic irrelevant sense?

Finally note that when I say Many-Worlds, I mean only Everett's theory, not multiverse interpretations in general. The "parallel lives" interpretation for example escapes Price and Pusey-Leifer's arguments and is an interpretation with multiple worlds, it's just not a "wave-function and nothing else" multiverse like Everett. Essentially it has additional "charges".

(On a personal note, although I'm not an advocate, I find the parallel lives explanation of how nonlocal correlations don't break locality much more comprehensible than Many-Worlds, whose explanation of things like Aravind-Mermin Pentagram correlations simply seems blatantly nonlocal to me)

 

[PeterDonis]

Why is that electron spin up rather than spin down?

In the MWI, it's both: there is one branch where the electron is spin up, and all other systems, including your brain, observe it to be spin up; and there is another branch where the electron is spin down, and all other systems, including your brain, observe it to be spin down. This is what unitary evolution produces from an initial state in which the electron is in a superposition of spin up and spin down and all other systems are in "ready to measure" states.

 

[DrChinese]

In the MWI, it's both: there is one branch where the electron is spin up, and all other systems, including your brain, observe it to be spin up; and there is another branch where the electron is spin down, and all other systems, including your brain, observe it to be spin down. This is what unitary evolution produces from an initial state in which the electron is in a superposition of spin up and spin down and all other systems are in "ready to measure" states.

When it starts in superposition, there is clearly nothing that "determines" it will become spin up. One world will have one, and vice versa. How can we - in our world - claim that could have been determined in advance? It is pure chance, by design! All outcomes occur.

 

[PeterDonis]

When it starts in superposition, there is clearly nothing that "determines" it will become spin up.

That's correct; unitary evolution does not determine it will be spin up. Unitary evolution determines that it will become entangled with the measuring device, the environment, your brain, etc., so that the states of all of those things are correlated. This evolution is perfectly deterministic; it just doesn't determine that the electron will become spin up. It determines something else.

 

[PeterDonis]

How can we - in our world - claim that could have been determined in advance?

No MWI advocate claims that it is determined that the electron will be spin up, so you are attacking a straw man here. As I said in my previous post just now, unitary evolution is deterministic, but "deterministic" does not mean "determines that the electron is spin up". It determines something else.

It is pure chance, by design! All outcomes occur.

These two sentences contradict each other. The second statement is correct. The first is false; a correct statement would be that it is determined that all outcomes occur. There is no chance in the MWI anywhere. It's all deterministic. It just doesn't determine what you're claiming it determines.

Please bear in mind that I am not saying I think the MWI is correct. I'm just saying that we should be clear about what it actually says.

 

[akvadrako]

Having one world versus a multiverse of $\aleph_{1}$ cardinality worlds is a fine distinction? It seems almost one of the largest conceivable distinctions possible in my mind. Unless I'm missing something.

Could I have a reference to how this is done. The paper you linked relies on it being ontic as it has physical effects,

I think it's a fine distinction because it doesn't have physical effects, so the paper could have been written without the ontic claim. I have read this (quotes below) and I think about it like this: Using just unitary evolution, we assume (or show elsewhere) that approximately classical branches emerge. One of those resulting states can be used as a boundary condition - it's where we actually end up. Then we can use the starting and ending boundaries to show the history between them, just looking at the total contribution from the other branches. It's just pre/post-selection of intermediate states; it doesn't change what those states are.

Time Symmetry and the Many-Worlds Interpretation (2009, Lev Vaidman)

My additional backwards evolving state is not of this kind (at least until I introduce a more speculative modification below). It is an explanatory concept for the inhabitants of a particular world.
...
The fundamental ontological picture remains, as in standard MWI, that of a single forwards evolving quantum state. The forwards evolving state of measuring devices defines the outcomes of measurements which, in turn, define the forwards and backwards evolving states within a world.​

The Two-State Vector Formalism (2013, Lev Vaidman)

The TSVF is equivalent to the standard quantum mechanics, but it is more convenient for analyzing the pre-and post-selected systems and allowed to see numerous surprising quantum effects. The TSVF is compatible with almost all interpretations of quantum mechanics but it fits particularly well the many-worlds interpretation. The concepts of “elements of reality” and “weak-measurement elements of reality” obtain a clear meaning in worlds with particular post-selection, while they have no ontological meaning in the scope of physical universe which incorporates all the worlds.​

You are saying that on restriction to a single branch one gets an "effective backward time state" that is epistemic, that somehow restores OTS in a branch, even though Price's argument shows only an ontic backward state does this.

Price's theorem depends on Discreteness (single outcomes, as pointed out in P&L's paper) just as P&L's depends on Assumption V.1, (Single-world) Realism.

MWI explicitly breaks Operational Time Symmetry (OTS) at the global level, one can see that immediately.

Does OTS even make sense on a global level? It's about running experiments - which can only be done on a branch level.

I wish there was more work than Vaidman's directly addressing many worlds and OTS (in terms of real experiments), but at least I don't see anyone demonstrating counter claims.

Genuine question, do you think an ontic wave traveling back in time toward the Big Bang containing precisely classical information (not approximate) distributed exactly in a Born distribution is okay and simply a fine-tuning in a pedantic irrelevant sense?

That would be true retrocausality - the past being determined from the present. My issue with retrocausality is "where did the present come from?".

Finally note that when I say Many-Worlds, I mean only Everett's theory, not multiverse interpretations in general. The "parallel lives" interpretation for example escapes Price and Pusey-Leifer's arguments and is an interpretation with multiple worlds, it's just not a "wave-function and nothing else" multiverse like Everett. Essentially it has additional "charges".

(On a personal note, although I'm not an advocate, I find the parallel lives explanation of how nonlocal correlations don't break locality much more comprehensible than Many-Worlds, whose explanation of things like Aravind-Mermin Pentagram correlations simply seems blatantly nonlocal to me)

I do mean Everett's theory, though I find the term unitary QM more clear. And I think of the Born rule as a measure of world volume. If you mean the version of parallel lives where each agent has their own copy of $\Psi$, it is more clearly local. But it seems like cheating to me - each individual $\Psi$ should also contain copies of the other agents with their own experiences and those are just as local as unitary QM.

 

[DarMM]

EDIT: Ignore this, I think I have a better approach below.

I think it's a fine distinction because it doesn't have physical effects

In their paper it does though, how does it not. Genuinely I'm not seeing it, they posit its physical effects.

One of those resulting states can be used as a boundary condition - it's where we actually end up. Then we can use the starting and ending boundaries to show the history between them, just looking at the total contribution from the other branches. It's just pre/post-selection of intermediate states

I know Vaidman's papers on this, but they are just a sketch of how it might work, is their any proof in general that it does work?

Regardless of general arguments like this, take Price's photon beam splitter experiment, can you show me how Many-Worlds replicates OTS in a branch for that (for general coefficients), it seems to me that by inspection even within a branch it does not. That's what Pusey-Leifer mean, it manifestly does not obey it. If they're wrong fine, but it seems clear to me that even observers within a branch would see OTS violated.
Their proof assumes single-world Realism, hence it can't tackle multiverse theories in general, but Many-Worlds seems to explicitly violate it as they say.

Let's say take the case with $x \in \mathbb{Z}_2$ and $y$ similar, classical probabilities for selection in $x$ preparation being $\frac{1}{3}, \frac{1}{2}$ in both cases. Easiest case probably being $x$ and $y$ involving preparation at different angles displaced by $\frac{\pi}{4}$.

it is more clearly local. But it seems like cheating to me

I might start a thread on Aravind-Mermin in Many-Worlds, as it seems confusing to me how each of outcomes at Alice and Bob's locations "know" that they are to pair up with worlds of the other observer in specific combinations without some nonlocality.

 

[DarMM]

I think this can be resolved much easier, directed at @akvadrako .

Firstly, do you accept Many-Worlds lacks OTS in its fundamental ontology, i.e. as a whole, not within a branch?

 

[stevendaryl]

No MWI advocate claims that it is determined that the electron will be spin up, so you are attacking a straw man here. As I said in my previous post just now, unitary evolution is deterministic, but "deterministic" does not mean "determines that the electron is spin up". It determines something else.

I think this is just about different notions of "deterministic". In MWI, the entire many-worlds ontology evolves deterministically. But for the experience of observers within that ontology, what they experience is completely nondeterministic.

 

[DrChinese]

No MWI advocate claims that it is determined that the electron will be spin up, so you are attacking a straw man here. As I said in my previous post just now, unitary evolution is deterministic, but "deterministic" does not mean "determines that the electron is spin up". It determines something else.

OK, no real disagreement, I guess it comes back to semantics. To me, Bohmian Mechanics is deterministic because knowledge of all variables would (in principle) lead to a certain outcome (even though such knowledge is not possible) for an observer. To me, MWI is not deterministic precisely because that same thing is not possible. Your prediction will always be expressed as a chance of an outcome, and there is fundamentally no amount of knowledge that would change that.

 

[PeterDonis]

To me, MWI is not deterministic precisely because that same thing is not possible.

Yes, it is. If you know the exact wave function of the entire system at one instant of time, you can predict the wave function at all future times exactly. In practice we never know the exact wave function of an entire system, but that doesn't make the MWI not deterministic, any more than our inability to know in practice the exact state of a system in Newtonian mechanics makes Newtonian mechanics not deterministic.

Your prediction will always be expressed as a chance of an outcome

In the MWI this is problematic; the question of how probabilities arise in the MWI (or, as it's more often stated, how the Born rule arises in the MWI) is one of the key issues with it, because according to the MWI taken at face value, there are no probabilities at all: everything is deterministic.

To put this another way: according to the MWI, taken at face value, if you are about to make a measurement of the spin of a qubit, say, you should not predict that you will see spin up with some probability and spin down with 1 minus that probability. You should predict that you will split into two copies, one of which sees spin up and one of which sees spin down (and each copy will be correlated with the appropriate state of the qubit). How you get from that to what we all actually predict in QM (that you will see spin up with some probability and spin down with 1 minus that probability) is, according to critics of MWI, not adequately accounted for.

 

[DrChinese]

Yes, it is. If you know the exact wave function of the entire system at one instant of time, you can predict the wave function at all future times exactly. In practice we never know the exact wave function of an entire system, but that doesn't make the MWI not deterministic, any more than our inability to know in practice the exact state of a system in Newtonian mechanics makes Newtonian mechanics not deterministic.

...

Thanks for taking the time to explain some of the nuances of MWI. Admittedly I am not sure how you get from knowing "the exact wave function of the entire system at one instant of time" to "you can predict the wave function at all future times exactly" after some series of measurements. It would seem that the Born Rule would come into play and the future wave function would no longer look the same.

Anyway, I'm satisfied.

 

[A. Neumaier]

"you can predict the wave function at all future times exactly" after some series of measurements.

In MWI, the wave function is always the wave function of the universe - that's the whole point of the ''world'' aspect. This ensures determinism. Measurements happen inside the universe (deterministically, dependent upon preparations, parameter settings, and intentions of the experimenters), in a way not precisely specified by MWI. Hence its vagueness...

 

[PeterDonis]

I am not sure how you get from knowing "the exact wave function of the entire system at one instant of time" to "you can predict the wave function at all future times exactly" after some series of measurements.

From the standpoint of the MWI, a "measurement" is just an interaction between different subsystems of the total system (which is the whole universe if we take things to their logical conclusion) that entangle the subsystems. These interactions are realized by unitary operators (basically $\exp i H t$, where $H$ is the full Hamiltonian including interaction terms), so the time evolution they induce is deterministic and reversible.

 

[DrChinese]

From the standpoint of the MWI, a "measurement" is just an interaction between different subsystems of the total system (which is the whole universe if we take things to their logical conclusion) that entangle the subsystems. These interactions are realized by unitary operators (basically $\exp i H t$, where $H$ is the full Hamiltonian including interaction terms), so the time evolution they induce is deterministic and reversible.

I can see now I have some studying to do. There are key elements of MWI I am clearly ignorant of.

 

[DarMM]

I can see now I have some studying to do. There are key elements of MWI I am clearly ignorant of.

I recommend Travis Norsen's chapter on it in his book "Foundations of Quantum Mechanics: An Exploration of the Physical Meaning of Quantum Theory"

 

[akvadrako]

I think this can be resolved much easier, directed at @akvadrako .

Firstly, do you accept Many-Worlds lacks OTS in its fundamental ontology, i.e. as a whole, not within a branch?

OTS is not part of it's ontology of course but it's ontology isn't operational, so I don't understand how it makes sense.

Just to clarify; when I say I'm using Everett's version of the theory, I don't mean his definition of world/branch, but just the objective part of the theory. I am not sure an exact definition is even possible without understanding the dynamics of an agent (or life), though the one used in the TSVF paper seems vaguely reasonable.

 

[akvadrako]

EDIT: Ignore this, I think I have a better approach below.

Let's say take the case with $x \in \mathbb{Z}_2$ and $y$ similar, classical probabilities for selection in $x$ preparation being $\frac{1}{3}, \frac{1}{2}$ in both cases. Easiest case probably being $x$ and $y$ involving preparation at different angles displaced by $\frac{\pi}{4}$.

I'll ignore the rest of the post until I see your other point, though I have one avenue to investigate still. I also want to mention that I don't know how to do my own analysis; I mostly just read papers and try to put the pieces of the puzzle together from what's already shown. For now, I find it higher priority to maintain a high-level overview of the literature. Maybe I'm slow but even on this rather specific topic that takes a fair chunk of time.

I might start a thread on Aravind-Mermin in Many-Worlds, as it seems confusing to me how each of outcomes at Alice and Bob's locations "know" that they are to pair up with worlds of the other observer in specific combinations without some nonlocality.

This would be interesting, though if someone did discover any nonlocal (hidden) effects in MWI, I would be very surprised.

 

[PeterDonis]

it seems confusing to me how each of outcomes at Alice and Bob's locations "know" that they are to pair up with worlds of the other observer in specific combinations without some nonlocality.

They don't have to "know" anything. All of the measurement interactions are local; there is nothing to "pair up". In terms of Bell's Theorem, the MWI violates one of the assumptions that underlies the theorem, namely, that measurements have single results. So the theorem does not apply to the MWI.

 

[DarMM]

They don't have to "know" anything. All of the measurement interactions are local; there is nothing to "pair up". In terms of Bell's Theorem, the MWI violates one of the assumptions that underlies the theorem, namely, that measurements have single results. So the theorem does not apply to the MWI.

I'm not sure about this, I think even in the field it is considered an open problem as to whether Many-Worlds is nonlocal in some sense, see Travis Norsen's book I mentioned above.

I know MWI violates one of the ontological framework axioms (and so escapes most results in quantum foundations) however that doesn't mean it automatically has the properties the no-go results typically prevent, e.g. just because you aren't covered by Bell's theorem doesn't necessarily mean you are local.

For example in the Aravind-Mermin case Alice's world splits locally into one of sixteen worlds, then Bob's world splits locally into sixteen worlds. This naively gives 256 possible worlds, however if Alice and Bob fly toward each other only worlds with common values for the shared vertex in the Aravind-Mermin Pentagram can meet/interact, i.e. there is only 128 worlds.

How during the initial local splittings do same vertex splittings emerge into the same world?

In some sense it wouldn't be too surprising if Many-Worlds was nonlocal as spacetime is only an illusion of a sort that exists in the quasi-classical branches that appears once an environment has emerged that a position basis can decohere against. The wavefunction naturally lives in a configuration space.

 

[DarMM]

I also want to mention that I don't know how to do my own analysis

Yeah the reason I switched is that I thought the original version would be way too long and detailed, in fact you'd probably have a paper at the end (i.e. a correction to Pusey and Leifer!)

This would be interesting, though if someone did discover any nonlocal (hidden) effects in MWI, I would be very surprised.

See the book by Travis Norsen I mentioned above to @PeterDonis . It's an open problem as to whether Many-Worlds is strictly local.

 

[DarMM]

OTS is not part of it's ontology of course but it's ontology isn't operational, so I don't understand how it makes sense.

That doesn't matter too much, remember the Pusey-Leifer theorem is about seeing if a theory has an ontological symmetry that directly reflects OTS, this is defined as Ontological Time Symmetry, see p.8

The only thing I'm asking is if you agree Many-Worlds lacks such an ontological symmetry. The definition makes sense to me when applied to Many-Worlds and I would say it violates it at a global level.

Leifer's reply to Tim Maudlin here might help:
https://arxiv.org/abs/1708.04364

The initial historical explanation part.

 

[akvadrako]

See the book by Travis Norsen I mentioned above to @PeterDonis . It's an open problem as to whether Many-Worlds is strictly local.

I will take a look. In general I agree it's an open question; the only proof of locality I'm aware of is Vindication of Quantum Locality (Deutsch, 2011), but I know it's not totally accepted.