MWI and the entangled photon experiment

[kered rettop]

That's precisely what I don't understand about the MWI interpretation. On the one hand they say there is this branching, but on the other we have definite outcomes when we are doing the experiments. So what does this branching then mean from an experimental/observational point of view?

And there lies the problem. We don't have definite outcomes when we do the experiments. We have definite apparent outcomes. They do not reflect the global superposition: the definiteness is an artifact of the branching.

 

[DrChinese]

1. That's precisely what I don't understand about the MWI interpretation. On the one hand they say there is this branching, but on the other we have definite outcomes when we are doing the experiments. So what does this branching then mean from an experimental/observational point of view?

2. I don't think so, because the perfect correlations are properties of the entangled state. E.g., if you have a polarization-singlet state of two photons, when finding photon 1 H-polarized then the other photon will be found V-polarized with probability 1 and vice versa. Which of these to possible outcomes of the measurements on the two photons is of course completely random, but the 100% correlation is always (with 100% probability) occuring.

3. That means according to MWI there are two branches when making this measurement: photon 1 H and photon 2 V and another with photon 1 V and photon 2 H polarized.

1. None of my comments in this post should be taken as disagreement with you. Every time I examine what MWI says about the details, I get squirmy answers (in sources supporting MWI) to the obvious tough questions. So let's examine your 2. and 3. in a very specific MWI example.

---

We have a straight Type I PDC setup outputting a pair of entangled photons in the |HH> + |VV> Bell basis. The inputs are single photons oriented diagonal at 45 degrees (which could also be considered an equal superposition of |H> + |V>). Each entangled output pair is sent to linear polarization detector setups far distant from each other, and are measured at the same angle - but at an angle randomly selected mid-flight and outside the light cone of the photons at time of selection. Here are the questions I have:

i. The output pairs must not yet have a specific definite polarization, correct? Because we need them to match at whatever angle they are to be detected at, and that has not been selected yet. So they must still be in a superposition (due to their "preparation" as you call it).

ii. The selected angle by some RNG is 120 degrees. Alice measures first (say), and gets result V. When exactly does that branching occur? We know in some other MWI branch the outcome was definitely H, right? The polarization detection setup itself consists of 3 components: the polarizing beam splitter (PBS) and the 2 avalanche detectors (one H, and one V). The branching occurs at one or more of these spots: a) the PBS; b) the V detector; and/or c) the H detector (which didn't fire in our branch). And in fact, the relative time of fire of the V and H detectors can be adjusted (by distance of placement after the PBS) so that they are clearly separated. Where/when does the branching occur? a)? Of course, this is a point at which the action is still reversible. b)? Of course, there has certainly been branching by this point in our particular branch, because we measured the V outcome. c)? The H detector did not fire in our branch, but we are certain it did in the other branch. But that outcome presumably came later in that branch, right?

iii. Here's the hard part: how does the branching from ii. above affect the photon Bob is getting ready to detect? That photon is far away. How does the branching action over by Alice affect Bob? Because we presumably determined Bob's photon was still in superposition as a result of i. above, right? Some of us here suspect that something "nonlocal" might be occurring. Even Vaidman seems to acknowledge something along this line. To quote, and note that there were no answers to any of my questions in his paper (and certainly no answers in his "next" section):

"But there are connections between different parts of the Universe, the wave function of the Universe is entangled. Entanglement is the essence of the nonlocality of the Universe. “Worlds” correspond to sets of well localized objects all over in space, so, in this sense, worlds are nonlocal entities. Quantum measurements performed on entangled particles lead to splitting of worlds with different local descriptions. Frequently such measurements lead to quantum paradoxes which will be discussed in the next section."

But in his parlance, whatever "nonlocal" occurs cannot quality as "action at a distance". I don't have a particular objection to this characterization, but I would not call it "spot on" either.

iv. And finally, this little gem of a question which is often overlooked with Type I PDC. We may say MWI is deterministic, but this leads to something of a paradox. Type I PDC consists of 2 thin orthogonal crystals placed face to face. One has an input of H and produces |VV>, while the other takes an input of V and produces output of |HH>. Neither of those are entangled outputs! So how does the entanglement occur? The answer is that the diagonal input to the pair of crystals takes an indistinguishable path, and the particular spot where down conversion occurs is indeterminate. So for the MWI explanation to make sense, we need to assert that NO branching occurs as the input photon splits into 2 entangled photons. What? So branching occurs everywhere else BUT the very spot where/when there's a choice of paths through the PDC setup. Huh?

We must have the entangled pair exit in a superposition for the rest of the MWI magic to occur. And yet, we need there to be branching by the time Alice and Bob read and record their respective results. But aren't we capable of establishing a consistent rule as to when branching occurs that doesn't appear ad hoc? Because I say that according to the MWI concept of definite deterministic outcomes: the diagonal input photon split at either the H PDC crystal (in our branch) or the V PDC crystal (in the other branch, or vice versa) - and would NOT have led to an entangled state if either of those things occurred. They would instead exit as VV or HH, and there would not be perfect correlations when later measured at 120 degrees (as selected by the RNG).

---

Making sense of this kind of setup causes me all kinds of confusion, and yet this is precisely the kind of experiment that a viable interpretation should explain today. I am *not* trying to support or reject MWI by any of my comments, I am just trying to understand the rules MWI plays by. Every interpretation seems to have some consistency issues at some level, and I believe MWI does too.

Cheers,

-DrC

 

[kered rettop]

Starting an answer in an existing thread with "I still don't understand ..." risks to annoy the other participants in that thread. If there is something which you don't understand, why don't you ask that as a separate question in a new thread? On the other hand, if you really want to give an answer in an existing thread, then requesting you to find a reputable reference in case your answer causes confusion or disagreement seems reasonable.

I appreciate your explanation of how PF works. I was reluctant to start a new thread because, of course, it loses the context. In any case, Peter Donis has said that I need to work through the literature (which I did several years ago anyway) so I think that starting a new thread would be tempting fate.

However, sometimes even slight hints that somebody might be trying to promote personal research seem to get him banned. Jarek Duda is certainly not a crank, and his research is often creative, novel and impactful. I guess he had received warnings before about which parts of his behavior won't be tolerated. And I guess that quoting poor references was not part of it.

That's very encouraging, thanks.

That said, I would be curious about your simple solution. But not in this or any other existing thread. I also would prefer if you do some research for references first (and tell us if you found nothing related), so that I as reader am at least spared the effort to research whether your solution is completely new, or not.

I am 100% certain there's nothing new about it. But it is not universally accepted and I don't know why not. It's simple enough. If you're happy to look at the matter very briefly, I can PM you.

 

[gentzen]

If you're happy to look at the matter very briefly, I can PM you.

I am certainly also happy if you just PM me your simple solution.

 

[kered rettop]

I am certainly also happy if you just PM me your simple solution.

Will do. Thanks.

 

[PeterDonis]

Our fundamental notion from a MWI perspective is that a branching of worlds occurs. This leads to multiple instances of ourself experienceing different single outcomes.

Yes, and that implies that all outcomes occur, each one in its own branch. I left out the "each one in its own branch" part, yes.

"the worlds of all instances are equally real" and "every instance experiences only a single outcome".

What does "instance" mean here? Introducing a new undefined term isn't likely to help matters.

 

[PeterDonis]

We don't have definite outcomes when we do the experiments. We have definite apparent outcomes. They do not reflect the global superposition: the definiteness is an artifact of the branching.

This is indeed a sticking point for many MWI skeptics (I'm sympathetic to it myself): ordinarily when a quantum system is in an entangled superposition, we say it doesn't have any definite state at all. We don't say each individual term in the superposition is a "branch" or a "world" in which the system has a definite state.

MWI proponents, however, simply refuse to accept this criticism, and maintain that what you call "definite apparent outcomes" are "real" definite outcomes. (Some of them even go so far as to describe, for example, quantum computing experiments as involving multiple "worlds", when what they actually mean is having systems of multiple qubits in entangled superpositions, when no decoherence has taken place anywhere and so even according to the modern version of the MWI, where "branching" happens when decoherence happens, there aren't multiple "worlds".)

Unfortunately, this is the kind of dispute that can't be resolved, at least not while all we have is our current theory of QM and the MWI as an interpretation of it. Someone will have to come up with an actual different theory based on the MWI that makes different predictions in at least some experiment.

 

[PeterDonis]

how does the branching from ii. above affect the photon Bob is getting ready to detect?

Through the wave function. I already showed the math for this in some detail. The wave function is nonlocal, so this effect is also nonlocal.

whatever "nonlocal" occurs cannot quality as "action at a distance"

Yes, because this nonlocality doesn't violate the no signaling theorem and doesn't allow FTL communication. But it's still nonlocality: it still produces Bell inequality violations and still rules out the kinds of models that Bell's theorem and other similar theorems are based on. Which leaves us with no intuitively satisfying model of what is going on "behind the scenes".

for the MWI explanation to make sense, we need to assert that NO branching occurs as the input photon splits into 2 entangled photons.

As far as I know, this process does not involve decoherence, so no, there would not be any branching.

branching occurs everywhere else BUT the very spot where/when there's a choice of paths through the PDC setup.

I don't see where this is coming from. Where is the "everywhere else" where branching is occurring? Branching only occurs when there is decoherence.

aren't we capable of establishing a consistent rule as to when branching occurs that doesn't appear ad hoc?

Yes, I've stated it multiple times above--and indeed multiple times previously in this thread. Branching occurs when there is decoherence.

The original MWI proponents, Everett and DeWitt (among others), came before decoherence theory was developed, so their accounts of when branching happened were unavoidably vague and hand-waving. But now we have decoherence theory and that vagueness and hand-waving is no longer necessary.

 

[kith]

What does "instance" mean here? Introducing a new undefined term isn't likely to help matters.

I don't see how we can do without it.

If I prepare the single particle state $|\uparrow\rangle + |\!\downarrow\rangle$ and perform the corresponding spin measurement, branching occurs. Have I measured spin up or spin down? On the one hand, we have to say "There's a world where I have measured spin up and a world where I have measured spin down. But looking at the needle of my apparatus I see it pointing upwards and conclude "I have measured spin up".

So either we have a contradiction or the "I"s in the previous two sentences don't refer to the same thing. The "I" in the second sentence is what I would call something like an "instance", "version", etc. of the generic "I" of the first sentence.

 

[PeterDonis]

If I prepare the single particle state $|\uparrow\rangle + |\!\downarrow\rangle$ and perform the corresponding spin measurement, branching occurs. Have I measured spin up or spin down?

Both. The "you" in the "measured spin up" branch has measured spin up. The "you" in the "measured spin down" branch has measured spin down.

On the one hand, we have to say "There's a world where I have measured spin up and a world where I have measured spin down.

Yes.

But looking at the needle of my apparatus I see it pointing upwards and conclude "I have measured spin up".

No. You can't state this as a unique fact, because it isn't. It only applies to the "you" in the "measured spin up" branch. There is also a "you" in the "measured spin down" branch who sees the needle pointing down.

The MWI is difficult to discuss because ordinary language has built-in assumptions that the MWI violates, like the assumption that pronouns like "you" have unique referents. In the MWI, they don't; there is one referent in each branch. If you use those pronouns, you have to realize that and take it into account. Otherwise you're simply not talking about the MWI, you're talking about some straw man version you've made up.

So either we have a contradiction or the "I"s in the previous two sentences don't refer to the same thing.

False dichotomy. The "I"'s do refer to the same thing in the sense that they refer to the same quantum degrees of freedom. They only differ in whether those degrees of freedom are entangled. See further comments below.

The "I" in the second sentence is what I would call something like an "instance", "version", etc. of the generic "I" of the first sentence.

You're misdescribing again. The "I" before the measurement is not "generic". "I" refers to the same quantum degrees of freedom before and after the measurement. The difference is that, before the measurement, those degrees of freedom are not entangled with the particle whose spin is being measured or the spin measuring apparatus. After the measurement, they are, and the entangled state decoheres.

I see no need to make up a new term, "instance", to describe this. "Branching" already describes what happens. And "instance" suggest that some kind of "copying" or "instantiation" is going on, when nothing of the sort is going on. As I have pointed out repeatedly, time evolution in the MWI is always unitary, and unitary evolution can't create or destroy anything, or "copy" or "instantiate" anything. All that happens is that quantum degrees of freedom that weren't entangled, become entangled. The number of degrees of freedom remains the same.

 

[kith]

No. You can't state this as a unique fact, because it isn't. It only applies to the "you" in the "measured spin up" branch. There is also a "you" in the "measured spin down" branch who sees the needle pointing down.

Just to get you right: You are saying that when we write down a conditional probability for the next measurement (like $P(\uparrow_x | \uparrow_z)$) and are speaking from a MWI perspective, we shouldn't say that this is the probability to measure spin up in the x-direction given that we measured spin up in z-direction (or given that the electron has spin up in the z-direction). What should we say instead?

The MWI is difficult to discuss because ordinary language has built-in assumptions that the MWI violates, like the assumption that pronouns like "you" have unique referents. In the MWI, they don't; there is one referent in each branch. If you use those pronouns, you have to realize that and take it into account.

This seems to be the crux of the matter. I need to think about it a bit. Do you have a reading recommendation which expands on what you wrote?

Otherwise you're simply not talking about the MWI, you're talking about some straw man version you've made up.

This is uncalled-for. I'm not weakening an argument in order to disprove it, I'm providing one. I'm giving my understanding of the MWI and I've used qualifiers like "I don't see" and "what I would call" to indicate this. If my argument is flawed, I'm happy to learn this and improve my understanding. In the two paragraphs above, you raise relevant points but I'm not convinced yet.

The "I" before the measurement is not "generic". [...] "instance" suggest that some kind of "copying" or "instantiation" is going on, when nothing of the sort is going on. [...]

I agree that the terminology I've used has unfortunate connotations. So thanks for improving it by mentioning degrees of freedom and referents.

 

[PeterDonis]

You are saying that when we write down a conditional probability for the next measurement (like $P(\uparrow_x | \uparrow_z)$) and are speaking from a MWI perspective, we shouldn't say that this is the probability to measure spin up in the x-direction given that we measured spin up in z-direction (or given that the electron has spin up in the z-direction). What should we say instead?

That is an open question for MWI proponents: how to make sense of the concept of "probability" when the interpretation says the dynamics are deterministic. As far as I know, MWI proponents do not have a single response to this question that all of them agree on. There are responses in the literature, but they're different and mutually inconsistent and none of them has the support of all MWI proponents.

This is uncalled-for. I'm not weakening an argument in order to disprove it, I'm providing one. I'm giving my understanding of the MWI and I've used qualifiers like "I don't see" and "what I would call" to indicate this. If my argument is flawed, I'm happy to learn this and improve my understanding. In the two paragraphs above, you raise relevant points but I'm not convinced yet.

Not convinced of what?

The MWI is very simple as far as its basic premises go: the wave function is real and contains all of reality, and the time evolution of the wave function is always unitary. Everything I have said is a simple mathematical consequence of those two basic premises. I understand that it's very counterintuitive and many people are skeptical that any such thing could possibly be true. I am one of those people. But being skeptical about whether it's true doesn't mean one can't describe what it says.

 

[PeterDonis]

Do you have a reading recommendation which expands on what you wrote?

Unfortunately, MWI proponents do not like to talk about the issues I raised in what you quoted. I suspect that this is because doing so would make the MWI look less plausible. It would also make it harder for proponents to talk about the MWI because they wouldn't be able to help themselves to ordinary language with ordinary language connotations in order to make it seem like the MWI is just describing ordinary experience. However, that is just my personal view.

As far as papers that describe what the MWI says, in its modern version, I would suggest reading the paper by Vaidman that @DrChinese referenced in post #14.

 

[Morbert]

@PeterDonis You adopted a specific convention re/pronouns, not insisted upon by the interpretation, and then cast aspersions on @kith re/ building a strawman. @kith Is not building a strawman. They are pointing out that the lab experience of performing measurement and observing a unique outcome is not immediately squared with property instantiations in branching worlds.

 

[kered rettop]

The MWI is very simple as far as its basic premises go: the wave function is real and contains all of reality, and the time evolution of the wave function is always unitary. Everything I have said is a simple mathematical consequence of those two basic premises. I understand that it's very counterintuitive and many people are skeptical that any such thing could possibly be true. I am one of those people. But being skeptical about whether it's true doesn't mean one can't describe what it says.

Surely MWI requires decoherence theory to complete it? In which case there needs to be a third premiss, namely that there is an environment with certain properties, such as 1) a large number of degrees of freedom, 2) a high degree of interactivity with the system, and 3) the ability to propagate (disseminate or "amplify") information about an outcome. In fact you recently mentioned a case where there is no environmental interaction, namely the isolated entangled qubits in a quantum computer. They are, erroneously in your view and also in mine, referred to as worlds by some authors. Whatever they may be, they are not worlds in the MWI sense.

Of course I am not suggesting that your skepticism should imply that you would question the fact that there is an environment!

 

[Morbert]

I don't see how we can do without it.

If I prepare the single particle state $|\uparrow\rangle + |\!\downarrow\rangle$ and perform the corresponding spin measurement, branching occurs. Have I measured spin up or spin down? On the one hand, we have to say "There's a world where I have measured spin up and a world where I have measured spin down. But looking at the needle of my apparatus I see it pointing upwards and conclude "I have measured spin up".

So either we have a contradiction or the "I"s in the previous two sentences don't refer to the same thing. The "I" in the second sentence is what I would call something like an "instance", "version", etc. of the generic "I" of the first sentence.

Vaidman's description is probably useful here. Re/ a measurement in a conventional Stern-Gerlach experiment, he says.

The MWI tells that in the future there will be “I” that see “up” and another “I” that see “down”. In the MWI I advocate, it is meaningless to ask which “I” shall “I”, making the experiment, be. There is nothing in the theory which connects “I” before the experiment to just one of the future “I”s

I.e. All instances of you after the experiment are distinct, but equally continuous with the instance of you before the experiment. An alternative approach is offered by Wilson. He accounts for scenarios like the above with diverging instances of you. I.e. even before measurement there were two instances of you. They are just qualitative duplicates. And after measurement, they diverge, each continuous with their own history. Ultimately there is no single account agreed upon by all Everettians.

 

[kered rettop]

Ultimately there is no single account agreed upon by all Everettians.

Is that fair on Everettians? You-counting would appear to be a matter of semantics. The two approaches are different and I liked your clear exposition, thank you. But the physics is the same whether you leave the wave function intact or chop it up (I hesitate to use the word decompose!) into two identical half-amplitude wave functions.

So, should you say "There's one you spread over two wave functions" , or "There are two yous, one in each wave function"? It depends on the context, there is no single correct way. They are not different accounts, though, that's for sure. I think.

 

[vanhees71]

1. None of my comments in this post should be taken as disagreement with you. Every time I examine what MWI says about the details, I get squirmy answers (in sources supporting MWI) to the obvious tough questions. So let's examine your 2. and 3. in a very specific MWI example.

I didn't take it as disagreement with my opinions. As I said, I don't understand, what the MWI solves wrt. the observable facts, which for me imply that there's "objective randomness" in Nature, i.e., that we cannot find any causes for the outcome of a measurement of an observable which was not determined by the state preparation before this measurement. For me, from a purely empirical point of view, it also doesn't help that MWI claims that the universe splits into branches, because this also doesn't explain in any way, why the outcome on a specific system was the one that is observed in "my branch".

---

We have a straight Type I PDC setup outputting a pair of entangled photons in the |HH> + |VV> Bell basis. The inputs are single photons oriented diagonal at 45 degrees (which could also be considered an equal superposition of |H> + |V>). Each entangled output pair is sent to linear polarization detector setups far distant from each other, and are measured at the same angle - but at an angle randomly selected mid-flight and outside the light cone of the photons at time of selection. Here are the questions I have:

The input photons are prepared in the pure state
$$\hat{\rho}_{12}=|\Psi \rangle \langle \Psi| \quad \text{with} \quad \frac{1}{\sqrt{2}} (|HH \rangle +|VV \rangle).$$
The single photons' state is then given by the so-called "reduced state", which is the partial trace over the other photon. You get
$$\hat{\rho}_1 = \hat{\rho}_2=\frac{1}{2} \hat{1}.$$
They are not in a pure state but in the maximally uncertain (maximum entropy) state, i.e., perfectly unpolarized photons.

i. The output pairs must not yet have a specific definite polarization, correct? Because we need them to match at whatever angle they are to be detected at, and that has not been selected yet. So they must still be in a superposition (due to their "preparation" as you call it).

Indeed they their polarization is maximally uncertain.

ii. The selected angle by some RNG is 120 degrees. Alice measures first (say), and gets result V. When exactly does that branching occur? We know in some other MWI branch the outcome was definitely H, right? The polarization detection setup itself consists of 3 components: the polarizing beam splitter (PBS) and the 2 avalanche detectors (one H, and one V). The branching occurs at one or more of these spots: a) the PBS; b) the V detector; and/or c) the H detector (which didn't fire in our branch). And in fact, the relative time of fire of the V and H detectors can be adjusted (by distance of placement after the PBS) so that they are clearly separated. Where/when does the branching occur? a)? Of course, this is a point at which the action is still reversible. b)? Of course, there has certainly been branching by this point in our particular branch, because we measured the V outcome. c)? The H detector did not fire in our branch, but we are certain it did in the other branch. But that outcome presumably came later in that branch, right?

You select to set both polarization filters to be oriented at an angle $\phi$ wrt. the direction you label with H. The states when measuring the linear polarization wrt. to that direction I label with $|\phi_{\parallel} \rangle$ and $|\phi_{\perp} \rangle$. In terms of the original basis it's
$$|\phi_{\parallel} \rangle=\cos \phi |H \rangle + \sin \phi |V \rangle, \quad |\phi_{\perp} \rangle=-\sin \phi |H \rangle + \cos \phi |V \rangle.$$
The possible outcomes are $\phi_{\parallel} \phi_{\parallel}$, $\phi_{\parallel} \phi_{\perp}$, $\phi_{\perp} \phi{\parallel}$, and $\phi_{\perp} \phi_{\perp}$. The probabilities are given by
$$\langle \phi_{\parallel} \phi_{\parallel}|\Psi \rangle=\frac{1}{\sqrt{2}} (\cos^2 \phi+\sin^2 \phi)=\frac{1}{\sqrt{2}} \Rightarrow P(\phi_{\parallel},\phi_{\parallel})=1/2,$$
$$\langle \phi_{\parallel} \phi_{\perp}|\Psi \rangle=\langle \phi_{\perp} \phi_{\parallel}|\Psi \rangle =\frac{1}{\sqrt{2}} (-\cos \phi \sin \phi + \cos \phi \sin \phi)=0 \Rightarrow P(\phi_{\parallel},\phi_{\perp})= P(\phi_{\perp},\phi_{\parallel})=0,$$
$$\langle \phi_{\perp} \phi_{\perp}|\Psi \rangle=\frac{1}{\sqrt{2}} (\sin^2 \phi + \cos^2 \phi)=\frac{1}{\sqrt{2}} \; \Rightarrow \; P(\phi_{\perp},\phi_{\perp})=\frac{1}{2},$$
i.e., you get with probability 1/2 either both photons being $\phi_{\parallel}$-polarized or both photons being $\phi_{\perp}$ polarized, i.e., you have 100% correlation between the outcome of measurements although the single photons' polarization states where maximally uncertain before the measurement.

iii. Here's the hard part: how does the branching from ii. above affect the photon Bob is getting ready to detect? That photon is far away. How does the branching action over by Alice affect Bob? Because we presumably determined Bob's photon was still in superposition as a result of i. above, right? Some of us here suspect that something "nonlocal" might be occurring. Even Vaidman seems to acknowledge something along this line. To quote, and note that there were no answers to any of my questions in his paper (and certainly no answers in his "next" section):

"But there are connections between different parts of the Universe, the wave function of the Universe is entangled. Entanglement is the essence of the nonlocality of the Universe. “Worlds” correspond to sets of well localized objects all over in space, so, in this sense, worlds are nonlocal entities. Quantum measurements performed on entangled particles lead to splitting of worlds with different local descriptions. Frequently such measurements lead to quantum paradoxes which will be discussed in the next section."

I'd say the branching occurs as soon as the outcome of the first measurement occuring. I.e., in your assumption when A's detector fixes the polarization state of her photon. Then, because of the preparation in the original entangled state, according to our above analysis, the other photon's polarization, i.e., what Bob will measure later, is also determined to be the same, because you have $\phi_{\parallel} \phi_{\parallel}$ or $\phi_{\perp} \phi_{\perp}$, and thus the split is in these two possible branches.

But in his parlance, whatever "nonlocal" occurs cannot quality as "action at a distance". I don't have a particular objection to this characterization, but I would not call it "spot on" either.

According to relativistic QFT there's no action at a distance. What's non-local is the correlation due to the preparation in the entangled state, i.e., a correlation between the outcomes of measurements at far distant polarization-measurement places, not the interaction between the measurement devices and the single photons. They are local at the place where the equipment is built up to measure the polarization.

The above analysis in fact is based on the assumption that A's measurement doesn't influence in any way B's photon, before B measures its polarization.

iv. And finally, this little gem of a question which is often overlooked with Type I PDC. We may say MWI is deterministic, but this leads to something of a paradox. Type I PDC consists of 2 thin orthogonal crystals placed face to face. One has an input of H and produces |VV>, while the other takes an input of V and produces output of |HH>. Neither of those are entangled outputs! So how does the entanglement occur? The answer is that the diagonal input to the pair of crystals takes an indistinguishable path, and the particular spot where down conversion occurs is indeterminate. So for the MWI explanation to make sense, we need to assert that NO branching occurs as the input photon splits into 2 entangled photons. What? So branching occurs everywhere else BUT the very spot where/when there's a choice of paths through the PDC setup. Huh?

As you say, the entanglement occurs, because you can't say whether you get $|VV \rangle$ or $HH \rangle$ when choosing precisely those photon pairs, where this "which-way information" is not known, i.e., that they come out precisely in the said state $\hat{\rho}_{12}$.

Concerning the PDC process you have of course a lot of splittings, according to all possible outcomes of sending a coherent laser-light state into the crystal. The two-photon down-conversion probabilities are usually in the order of magnitude of $10^{-6}$ only!

We must have the entangled pair exit in a superposition for the rest of the MWI magic to occur. And yet, we need there to be branching by the time Alice and Bob read and record their respective results. But aren't we capable of establishing a consistent rule as to when branching occurs that doesn't appear ad hoc? Because I say that according to the MWI concept of definite deterministic outcomes: the diagonal input photon split at either the H PDC crystal (in our branch) or the V PDC crystal (in the other branch, or vice versa) - and would NOT have led to an entangled state if either of those things occurred. They would instead exit as VV or HH, and there would not be perfect correlations when later measured at 120 degrees (as selected by the RNG).

But I thought according to MWI the splitting always occurs according to the possible outcomes of measurements given the state, i.e., the branchings can only be into 100% correlated $120_{\parallel} 120_{\parallel}$ or $120_{\perp} 120_{\perp}$ branches.

---

Making sense of this kind of setup causes me all kinds of confusion, and yet this is precisely the kind of experiment that a viable interpretation should explain today. I am *not* trying to support or reject MWI by any of my comments, I am just trying to understand the rules MWI plays by. Every interpretation seems to have some consistency issues at some level, and I believe MWI does too.

I think, all that can be observed are what's really measured, and the outcome is random, i.e., there's no cause for a specific outcome. What "additional explanation" MWI gives, to solve this quibble of the measurement problem, i.e., to find a cause for the specific outcome, I never understood since in which branch of the world my equipment will be and determining to what I as the experimenter read off as a measurement result is simply random with probabilities given by Born's rule.

 

[Morbert]

Is that fair on Everettians? You-counting would appear to be a matter of semantics. The two approaches are different and I liked your clear exposition, thank you. But the physics is the same whether you leave the wave function intact or chop it up (I hesitate to use the word decompose!) into two identical half-amplitude wave functions.

So, should you say "There's one you spread over two wave functions" , or "There are two yous, one in each wave function"? It depends on the context, there is no single correct way. They are not different accounts, though, that's for sure. I think.

The use of "I" and "you" either way is fine so long as everyone is on the same page. The differing accounts I was referring to was deeper though, pointing to ontological differences. E.g. Carroll and Sebens present a "global branching" account, where a measurement causes everywhere to branch instantly. Vaidman and Wallace present a local account where distant systems do not immediately branch. Wilson presents an account where numerically identical, overlapping branches are replaced with qualitatively duplicate, locally diverging histories. When you move into Everettian field theory it gets even hairier with $\rho$-realism and spacetime-state realism. etc etc. All of these have different metaphysical commitments, with their own strengths and weaknesses.

 

[kered rettop]

The use of "I" and "you" either way is fine so long as everyone is on the same page. The differing accounts I was referring to was deeper though, pointing to ontological differences. E.g. Carroll and Sebens present a "global branching" account, where a measurement causes everywhere to branch instantly. Vaidman and Wallace present a local account where distant systems do not immediately branch. Wilson presents an account where numerically identical, overlapping branches are replaced with qualitatively duplicate, locally diverging histories. When you move into Everettian field theory it gets even hairier with $\rho$-realism and spacetime-state realism. etc etc. All of these have different metaphysical commitments, with their own strengths and weaknesses.

Great. Thanks. For what it's worth I think that "global branching vs local" can also be settled by being careful with what you mean. (I am moderately familiar with both ideas and know some of the reasoning behind them, though I'd have to grovel to Google to check whether it's what your authors mean.) The instantaneous branching presumably reflects the way the global wave function branches; the local branching presumably reflects the expansion of the region which has actually interacted with the system in decoherence and where information about the interaction has reached. Totally different things, therefore no confusion - as long as you make sure you don't use the same word. No idea what people mean when they talk about different kinds of realism. K.I.S.S. is what I say!

 

[PeroK]

Read the Vaidman 2014 paper also. Although I disagree strongly with his final conclusion(s)*, he covers the pros and cons better than anything I've seen anywhere else. It's 25 pages, and 175 references!

*"The theory of Universal wave function is deterministic, local, free of paradoxes, and fully consistent with
our experience."

That it is fully consistent with our experience is stretching a point, IMO. Or, to turn it round, our experience is hardly consistent with MWI!

 

[PeterDonis]

You adopted a specific convention re/pronouns, not insisted upon by the interpretation

I don't know what you mean. You have to take into account what I said about pronouns in order to talk consistently about the MWI. You cannot use pronouns the way we do in ordinary language; if you do, you will be saying wrong things about the MWI.

They are pointing out that the lab experience of performing measurement and observing a unique outcome is not immediately squared with property instantiations in branching worlds.

And that means they do not think the MWI is correct. Which is fine in itself--but it does not mean they can misstate what the MWI says. The MWI says what it says, and requires pronouns to be interpreted in the way I described. You can't say, "Well, I think the MWI is wrong so I'm going to describe it in a way that misstates what it says."

 

[PeterDonis]

Surely MWI requires decoherence theory to complete it?

In the modern view, yes, decoherence is required for branching to occur in the MWI.

In which case there needs to be a third premiss, namely that there is an environment with certain properties, such as 1) a large number of degrees of freedom

A large number of untrackable degrees of freedom, yes.

2) a high degree of interactivity with the system

Not necessarily "high", just enough for entanglement to spread. Most of the interactivity could be within the environment itself; only a few degrees of freedom in the environment would need to interact with the system and the measuring apparatus.

and 3) the ability to propagate (disseminate or "amplify") information about an outcome.

This "information about an outcome" is not retrievable, so it is not where the person doing the experiment, for example, would read off the result. They would do that from the trackable degrees of freedom of the measuring apparatus.

The environment does of course "store information" about the outcome because that information gets spread through entanglement among the degrees of freedom in the environment. But the environment doesn't need any extra "ability" to do this; it's already there as soon as 1) and 2) above are satisfied.

you recently mentioned a case where there is no environmental interaction, namely the isolated entangled qubits in a quantum computer. They are, erroneously in your view and also in mine, referred to as worlds by some authors. Whatever they may be, they are not worlds in the MWI sense.

Yes, agreed. I believe I said that I do not think authors who talk this way are correct. (If I didn't in this thread, I have in other threads on this topic. )

 

[PeterDonis]

there is no single account agreed upon by all Everettians.

Yes. I believe I have commented before on this as well. That's why, when I describe the MWI, I focus on the basic premises that all accounts do share: that the wave function is real and contains all of reality, and that the dynamics is always unitary. I try to limit my discussion to what can be deduced just from those premises.

 

[PeterDonis]

The instantaneous branching presumably reflects the way the global wave function branches; the local branching presumably reflects the expansion of the region which has actually interacted with the system in decoherence and where information about the interaction has reached.

That's how I understand the two descriptions as well.

One of the references in another thread on "Is the MWI local" had what it claimed to be a completely local description, but this interpretation involved having each qubit carry with it a potentially unbounded amount of information about all of its past interactions (this information would play the same role as the global wave function in the "instantaneous branching" interpretation).

 

[Morbert]

For what it's worth I think that "global branching vs local" can also be settled by being careful with what you mean. (I am moderately familiar with both ideas and know some of the reasoning behind them, though I'd have to grovel to Google to check whether it's what your authors mean.) The instantaneous branching presumably reflects the way the global wave function branches; the local branching presumably reflects the expansion of the region which has actually interacted with the system in decoherence and where information about the interaction has reached. Totally different things, therefore no confusion - as long as you make sure you don't use the same word. No idea what people mean when they talk about different kinds of realism. K.I.S.S. is what I say!

Vaidman describes his stance re/ Sebens and Carroll here

Contrary to our analysis, Sebens and Carroll work under the assumption that “branching happens throughout the wavefunction whenever it happens anywhere". [...] Consequently, “observers here on Earth could be (and almost surely are) branching all the time, without noticing it, due to quantum evolution of systems in the Andromeda Galaxy." [...] Sebens and Carroll concede that this global branching picture is psychologically unintuitive (p11). But it also goes against the spirit of the many worlds interpretation, which involves removing as much nonlocality as possible. Thus, after removing the nonlocality of collapse, they reinsert a different kind of nonlocality.

Vaidman hopes to find a separable description of the wavefunction, but accepts that it doesn't exist at the moment. He accepts this kind of nonlocality. But he sees the Sebens and Carroll account as elevating nonseparability to a stronger nonlocality, where doing something here instantly affects something there. I don't see how this disagreement can be attributed to a confusion due to imprecise use of words.

 

[kered rettop]

That's how I understand the two descriptions as well.

One of the references in another thread on "Is the MWI local" had what it claimed to be a completely local description, but this interpretation involved having each qubit carry with it a potentially unbounded amount of information about all of its past interactions (this information would play the same role as the global wave function in the "instantaneous branching" interpretation).

We seem to be agreeing to an unnerving degree today, Peter. I think I'd better quit while I'm winning,

 

[kered rettop]

A large number of untrackable degrees of freedom...

Fair enough. I was not trying to define the third postulate precisely, only to point out there has to be one. Happy to leave the details to people who are capable.