Will quantum computers ever be possible?

[colorSpace]

...Zombie arguement, well read Daniel Dennetts explanation of such complex "zombies", they would by definition BE conscious humans.
Consciousness is not some special thing(as I bet you know)

There is no working definition of consciousness which would include the subjective experience of seeing colors. Nothing is consciousness "by definition".

Consciously seeing colors, hearings sounds, etc, is indeed a special thing, that even Daniel Dennett knows nothing about.

Just as a side note, I'm not going to discuss this here.

 

[confusedashell]

Nah ofcourse we don't know all about consciousness, but do we really need to?
All we know is that it's ALL related to the brain and not some mystical dualistic immaterial soul

 

[vanesch]

So is this a joke, like this "philosophical stance", or supposed to mean that MWI gives you a way to disentangle the wavefunctions of multiple entangled photons?

The crux of the "local" explanation of EPR situations is that the correlation only happens upon the meeting of the protagonists, and not "when they did their measurement at spacelike intervals".

As both outcomes (at both sides) take place, there is no "spooky action at a distance". The observers simply get entangled with the received entangled particles (and doing so, "split" into different contributions, or different "observed measurements"). It is only when they MEET, that the correlations (which have been inherited through the original entangled pair of particles) show: that is to say, that the right "Alice measurement state" pairs up with the right "Bob measurement state", so that they both seem to observe correlations. But at that point, they are LOCAL to each other.

EDIT:

I've written this out at least 10 times on PF here, so I just picked out one random version of it. Here it is:
https://www.physicsforums.com/showpost.php?p=937905&postcount=10

 

[vanesch]

Well, look upon it this way. Your reaction is a bit like that of the Pythagoreans, when they discovered the irrational numbers. Imagine someone propose that space is described by a 3-dimensional REAL space, which maps upon a Euclidean space, instead of a 3-dimensional RATIONAL space.
Then this Occam argument you use would sound like:
"Do you realize how many unidentifiable points you've now added to space, just because of this silly property of diagonals of a square ?"

I want to add something to this. I wanted to edit this post already yesterday, but the server went down. I think that this "switch from rational to real numbers" has many properties which are similar to the switch from one universe to many in MWI, and illustrate my stance on it.

For the Pythagoreans, the "rational" numbers had some clear meaning, and the discovery of irrationality was shear horror. We are now used to the real number system (or at least we think so), but we seem to forget how horribly big it is! MOST real numbers cannot even be defined (written down). No measurement ever can result in a real number (it is always a rational number). As such there is no ounce of "evidence" of the existence of "points in space" which correspond to elements of R^3 which are not in Q^3. For practical things, at no point we need really "real numbers", and when we do numerical calculations, we always use rational numbers.

So why do we even consider these in physics ? If ever there is one or other form of discreteness of spacetime, then the real numbers are also physical nonsense. So the introduction of real numbers in the description of (Euclidean) space has the following properties:
- it blows up the "number of space points" incredibly
- it has no measurable basis, no observation has ever "confirmed" the existence of real number coordinates
- it might even be fundamentally wrong (if space turns out to be discretized)

Why consider such "nonsense" ? Shouldn't Occam's rasor do away very quickly with such horror ?

Well, when doing NEWTONIAN MECHANICS, we need real numbers. We need to postulate that space is Euclidean with real numbers, because otherwise the concept of derivative wouldn't make mathematical sense. It would be very difficult to formulate Newtonian mechanics if space was made up of Q^3, because limits wouldn't exist (and hence, derivatives wouldn't exist, and Newton's law F = m.a wouldn't be possible).

So the "natural way" of looking at space in Newtonian mechanics is to consider that space is a Euclidean space, isomorphic to R^3. Despite the huge amount of "useless" spacepoints. Despite the fact that it might be fundamentally wrong, and observationally impossible. The *theoretical* construction is simpler this way. So Occam works on the conceptual side, not on the "number of space points".

Well, I see MWI in the same way. It is, to me, the natural way to look upon quantum theory. Quantum theory postulates the superposition principle, well, we apply it to everything. Whether this is physically "true" or not. And this simplifies the conceptual side of quantum theory. No "spooky action at a distance", no "collapse upon observation", no "dichotomy between physical interaction and observation". Occam doesn't count the number of states, but the number of different concepts.

Is space "really" made out of R^3 points, or not ? I don't know. Could be, couldn't be.
Does the superposition principle apply to humans ? I don't know. Could be, couldn't be.

 

[colorSpace]

The crux of the "local" explanation of EPR situations is that the correlation only happens upon the meeting of the protagonists, and not "when they did their measurement at spacelike intervals".

As both outcomes (at both sides) take place, there is no "spooky action at a distance". The observers simply get entangled with the received entangled particles (and doing so, "split" into different contributions, or different "observed measurements"). It is only when they MEET, that the correlations (which have been inherited through the original entangled pair of particles) show: that is to say, that the right "Alice measurement state" pairs up with the right "Bob measurement state", so that they both seem to observe correlations. But at that point, they are LOCAL to each other.

EDIT:

I've written this out at least 10 times on PF here, so I just picked out one random version of it. Here it is:
https://www.physicsforums.com/showpost.php?p=937905&postcount=10

Thanks for the link.

Your explanation seems a bit different than the one discussed in the thread I mentioned. In a sense, it is more "solipsistic", since it "postpones" all collapses until a specific observer is confronted with any results. So I am not quite sure yet whether the argument using GHZ entanglement, will also apply to your version.

However, independently, this argument may now become even stronger due to additional requirements:

Postponing the second "collapse" turns it from a 'random' event into a very 'intelligent' event. The second collapse for each observer has "limited choices", it needs to collapse in a way consistent with the rules of entanglement. In your description, you wrote down a 'non-local' state description, but a local universe can't do that.

When Bob meets Alice, each of his worlds (or at least each in which he meets Alice) needs to have access to each of Alice's possible states, which have now developed into complex-ly different branches, and somehow any of Bob's worlds needs to be able to "pick" the corresponding one which matches his own measurement results. That is, it would seem to me, the second collapse now has to be a more Copenhagen-like collapse since it can't realize all possibilities anymore. Furthermore, the information to make this 'choice' needs to be available in a form that some physical process can make such a choice.

I don't yet see how it should be possible:
a) to make this information available in usable form, and
b) where should this physical process of making the correct choice happen? and
c) how should this choice then influence the collapse?

This is where I think the non-locality may now be hidden: In the lack of 'space' for making this choice. (Or in the need to use non-local state-descriptions all the same). The non-locality may now be in this monster-collapse that doesn't fit into physical space anymore.

[Edit added:] And, it seems to me, that now a possibly huge developed state at Alice's side needs to be collapsed either all at once, or in a impossible looking gradual process.

 

[colorSpace]

[Addition to last post.]

I think the GHZ entanglement with its triangular situation will also pose problems to your version. In the thread in which I discussed it, the problem became that copies of two systems needed to be matched up without information from the third location. In your version the problem is perhaps just postponed, such that this match becomes "real" and later on, when meeting with the third location's effects, it will turn out the the situation which has already become real is impossible, meaning something that has in a sense already happened then needs to be erased from history in hindsight, since it runs into a paradox.

However I need to think about this further before describing it in detail.

 

[vanesch]

Your explanation seems a bit different than the one discussed in the thread I mentioned. In a sense, it is more "solipsistic", since it "postpones" all collapses until a specific observer is confronted with any results. So I am not quite sure yet whether the argument using GHZ entanglement, will also apply to your version.

The "collapse" in that link is not physical of course, but is from a single observer's viewpoint. It is what one would have called a collapse in a CI viewpoint. There are as many alternative "collapses" as there are observer versions, and I picked out one single observer "line" in that example. Sorry if that was confusing.

When Bob meets Alice, each of his worlds (or at least each in which he meets Alice) needs to have access to each of Alice's possible states, which have now developed into complex-ly different branches, and somehow any of Bob's worlds needs to be able to "pick" the corresponding one which matches his own measurement results. That is, it would seem to me, the second collapse now has to be a more Copenhagen-like collapse since it can't realize all possibilities anymore.

That is because the "second collapse" is nothing else but a correlation, where we have already a first "known" result (have picked out already a previous "bob" observer amongst the many).

Note also that the "collapse" for a certain "alice" state results in a different outcome for this Alice than the Alice that was in the "collapse" for a certain Bob state. This is because "collapse" is relative, and there's a collapse for each of the terms in fact, I just picked out a single example for bob and a single example for alice, to show how for THAT SPECIFIC ALICE things LOOK AS IF a collapse took place.

 

[vanesch]

[Addition to last post.]

I think the GHZ entanglement with its triangular situation will also pose problems to your version. In the thread in which I discussed it, the problem became that copies of two systems needed to be matched up without information from the third location. In your version the problem is perhaps just postponed, such that this match becomes "real" and later on, when meeting with the third location's effects, it will turn out the the situation which has already become real is impossible, meaning something that has in a sense already happened then needs to be erased from history in hindsight, since it runs into a paradox.

However I need to think about this further before describing it in detail.

I think the situation you describe cannot happen, because it would mean that there is a real macroscopic observation which is reversible (quantum-erased). Normally, something that is macroscopically observed is so much entangled with the environment that the decoherence of it is irreversible.

 

[colorSpace]

The "collapse" in that link is not physical of course, but is from a single observer's viewpoint. It is what one would have called a collapse in a CI viewpoint. There are as many alternative "collapses" as there are observer versions, and I picked out one single observer "line" in that example. Sorry if that was confusing.

Either it wasn't confusing, or it still is. :)
I think that's how I understood it.

That is because the "second collapse" is nothing else but a correlation, where we have already a first "known" result (have picked out already a previous "bob" observer amongst the many).

Note also that the "collapse" for a certain "alice" state results in a different outcome for this Alice than the Alice that was in the "collapse" for a certain Bob state. This is because "collapse" is relative, and there's a collapse for each of the terms in fact, I just picked out a single example for bob and a single example for alice, to show how for THAT SPECIFIC ALICE things LOOK AS IF a collapse took place.

Ok, "correlation" then. My point above, appears to apply all the same.

I have tried to explain it carefully, and I don't see how you addressed the question of how these states are going to be correlated. The question where all the information comes from, which will allow some process to match up exactly those states which are allowed by the entanglements rules. This appears to require either a non-local mechanism, such as hidden in non-local state descriptions, or a lot of information being passed along in the local states, which allows them to be matched up correctly when they meet, as I have explained above.

[Edit added:] It seems in your description, Bob already carries around with him a state description of Alice's superposition, and it's relation to his own, but in a local universe this wouldn't be "allowed" as a mechanism to explain the interaction.

 

[colorSpace]

I think the situation you describe cannot happen, because it would mean that there is a real macroscopic observation which is reversible (quantum-erased). Normally, something that is macroscopically observed is so much entangled with the environment that the decoherence of it is irreversible.

Of course it cannot happen. That's why I say it is not possible.

 

[vanesch]

[Edit added:] It seems in your description, Bob already carries around with him a state description of Alice's superposition, and it's relation to his own, but in a local universe this wouldn't be "allowed" as a mechanism to explain the interaction.

The way this is written in the Schroedinger picture looks a bit non-local indeed. Each "state" (sub-state in fact) carries with it the "phase information" of with which sub-states of other systems it is entangled, as well as the phase relation to its "cousin-substates".

If I write:
|u+> |v-> - |u-> |v+>,

then the "u+" state carries with it the fact that it is entangled with |v->, and also that it has a 180 degree phase shift wrt |u->. This is encoded in the wavefunction.

But the important point to note is that this information is never *changed* at a distance. So you can see it that "u+ and v-" share a kind of "phase tag" that they were in a product state, and that "u- and v+" share also another phase tag that they were in a product state, and that u+ and u- (and, through the sharing of the tags) also share a phase relationship that they have 180 degrees difference (and eventual amplitude differences). If ever v- evolves into something else, say, (|vx> + |vy>) then they inherit this "term tag" so that later on, in an interaction, when they interact with the u-system, they "remember" being in the same term (sharing the same term tag).

This is just a story that is implemented by the algebra of the terms in the wavefunction and the linearity of the interaction operators.

So, yes, if you want to look upon it this way, a specific substate "carries with it" all the "information" of product (term sharing) and phase relationship to its cousins, which is transmitted to its descendants. It's a peculiar way of doing algebra

But this can be worked out much better in the Heisenberg picture, there's a paper on that:
arxiv:quant-ph/0204024v2

 

[colorSpace]

The way this is written in the Schroedinger picture looks a bit non-local indeed. Each "state" (sub-state in fact) carries with it the "phase information" of with which sub-states of other systems it is entangled, as well as the phase relation to its "cousin-substates".

If I write:
|u+> |v-> - |u-> |v+>,

then the "u+" state carries with it the fact that it is entangled with |v->, and also that it has a 180 degree phase shift wrt |u->. This is encoded in the wavefunction.

But the important point to note is that this information is never *changed* at a distance. So you can see it that "u+ and v-" share a kind of "phase tag" that they were in a product state, and that "u- and v+" share also another phase tag that they were in a product state, and that u+ and u- (and, through the sharing of the tags) also share a phase relationship that they have 180 degrees difference (and eventual amplitude differences). If ever v- evolves into something else, say, (|vx> + |vy>) then they inherit this "term tag" so that later on, in an interaction, when they interact with the u-system, they "remember" being in the same term (sharing the same term tag).

This is just a story that is implemented by the algebra of the terms in the wavefunction and the linearity of the interaction operators.

So, yes, if you want to look upon it this way, a specific substate "carries with it" all the "information" of product (term sharing) and phase relationship to its cousins, which is transmitted to its descendants. It's a peculiar way of doing algebra

But this can be worked out much better in the Heisenberg picture, there's a paper on that:
arxiv:quant-ph/0204024v2

I did expect that the "algebra" you suggest (the "Heisenberg picture") would remove the non-local references (at least as one possibility). This would, so far, only mean that my argument above actually applies. You have only confirmed, so far, the problem I've outlined.

 

[colorSpace]

[Continuation from the previous message.]

I just found that the linked PDF does mention the first problem I've described, and calls it the "problem of label proliferation". Apparently this problem hasn't been resolved yet:

On page 2:

The amount of information which even a simple electron carries with it regarding the other particles with which it has interacted is thus enormous. In Ref. 22 I termed this the problem of “label proliferation,” and suggested that the physical question of how all this information is stored might receive an answer in the framework of quantum field theory.

And the whole text ends in addressing this topic once more:

As for the label-proliferation problem, quantum field theory provides no explanation, beyond that provided by first-quantized theory, for the manner in which this information is recorded. The representation of the label information does seems more natural in quantum field theory than in point-particle quantum mechanics. In quantum mechanics, the operators pertaining to each particle acquire tensor-product factors acting in the state spaces of other particles with which the particle in question interacts. In quantum field theory, each operator acts in an infinite-dimensional space (see, e.g., Ref. 49 for an explicit representation) and changes the nature of its action in this space based on the nature of nearby operators. But, be it quantum-mechanical or quantum-field-theoretic, a single quantum operator is capable of carrying an unlimited amount of information regarding past interactions.

I haven't read the whole text yet (much of which is beyond my mathematical level), I just found these passages so far. Yet so far it seems that the problem is still understated. For example it seems to be explained as if this "enormous" information would apply only to the entangled particle and Alice' or Bob's state of mind. However, they need not meet in person, one could send the results in a plain email. Then it would follow that all this "unlimited amount of information regarding past interactions" would have to go through the fingers of the typist into the keyboard, and then over the internet.

In a local universe, it is no trivial problem to store, and transmit everywhere, an "unlimited amount of information".

Unless I'm missing something, this seems absurd. And this would even be just the problem of the information that needs to be available, in addition there needs to be an explanation of how this complex information is going to be evaluated in its mutated form such than when this email arrives, the correct "pairing-up" can happen. (I haven't yet read enough in this PDf to see whether that is mentioned except in a single sentence where it is called "pairing-up".)

And then there is still the triangular challenge I mentioned above (and in the other thread).

 

[colorSpace]

BTW, this is, I think, the text which I mentioned in a different thread that I had read earlier, linked from the old homepage of D.Deutsch, from 1999, and already mentions the "Heisenberg picture", but apparently less developed at that point in time.

http://xxx.lanl.gov/abs/quant-ph/9906007

 

[vanesch]

I haven't read the whole text yet (much of which is beyond my mathematical level), I just found these passages so far. Yet so far it seems that the problem is still understated. For example it seems to be explained as if this "enormous" information would apply only to the entangled particle and Alice' or Bob's state of mind. However, they need not meet in person, one could send the results in a plain email.

Well, the particles in the fingers typing, in the electrons and atoms of the silicon circuits, and of the EM fields used in the wireless transmission (as well as the air molecules etc...) all just entangle with them of course. I don't see why this would be a particular problem. In fact, about all material objects which have the experiments in their past lightcone will - unless one takes great care and pain to avoid this - end up entangled with the particles in the experiment: all the air molecules, the EM field (suppose that a red light flashes if it is "up" and a green if it is "down") etc... So about all subsystems that have an "interaction possibility" with the tested particle will end up "measuring" it and hence entangling with it. So I don't see why you make such a big deal about those fingers and that e-mail.

Then it would follow that all this "unlimited amount of information regarding past interactions" would have to go through the fingers of the typist into the keyboard, and then over the internet.

Yes, of course, but over the "quantum internet" of course ! The "internet" you think about, is just one classical state of the "quantum internet" which can have all thinkable states of the internet, and the different entanglement informations you talk about in the e-mail go with the quantum-email (think q-bits), of which a simple e-mail is just one state.

THIS picture is BTW why Deutsch claims quantum computers are so much more powerful. But MWI just *illustrates* it, it comes just from the *hugeness of hilbertspace*. It is this hugeness which you are discovering here, not "MWI craziness". MWI "craziness" just puts in light what is enclosed in strict quantum theory.

In a local universe, it is no trivial problem to store, and transmit everywhere, an "unlimited amount of information".

It's not unlimited, but it is very big. But you are thinking of a *classical* universe. A *quantum universe* is mindbogglingly bigger, but that's already the case from the start: the quantum states are a HILBERT SPACE spanned over the classical configuration space: with each POINT of classical configuration space corresponds a DIMENSION in Hilbert space. That's not MWI, that's quantum theory.

Unless I'm missing something, this seems absurd. And this would even be just the problem of the information that needs to be available, in addition there needs to be an explanation of how this complex information is going to be evaluated in its mutated form such than when this email arrives, the correct "pairing-up" can happen. (I haven't yet read enough in this PDf to see whether that is mentioned except in a single sentence where it is called "pairing-up".)

Well, that's just how the dynamics in hilbertspace occurs. You see, your surprise is a bit like that of the Pythagoreans again. Imagine they say: yes but that would mean that the position of a point particle is now given by 3 REAL numbers. Where does it store this infinite amount of information (3 real numbers contain indeed an infinite amount of information, as compared to the finite amount of information in 3 rational numbers) ? And on top of that, it even has to store its velocity, which is also 3 real numbers ?

So you see, one of the advantages of an MWI view is to ILLUSTRATE the mindbogglingly huge statespace of quantum theory.

And then there is still the triangular challenge I mentioned above (and in the other thread).

I thought we agreed that the problem you mentioned could not occur ?

 

[colorSpace]

Well, the particles in the fingers typing, in the electrons and atoms of the silicon circuits, and of the EM fields used in the wireless transmission (as well as the air molecules etc...) all just entangle with them of course. I don't see why this would be a particular problem. In fact, about all material objects which have the experiments in their past lightcone will - unless one takes great care and pain to avoid this - end up entangled with the particles in the experiment: all the air molecules, the EM field (suppose that a red light flashes if it is "up" and a green if it is "down") etc... So about all subsystems that have an "interaction possibility" with the tested particle will end up "measuring" it and hence entangling with it. So I don't see why you make such a big deal about those fingers and that e-mail.
Yes, of course, but over the "quantum internet" of course ! The "internet" you think about, is just one classical state of the "quantum internet" which can have all thinkable states of the internet, and the different entanglement informations you talk about in the e-mail go with the quantum-email (think q-bits), of which a simple e-mail is just one state.

THIS picture is BTW why Deutsch claims quantum computers are so much more powerful. But MWI just *illustrates* it, it comes just from the *hugeness of hilbertspace*. It is this hugeness which you are discovering here, not "MWI craziness". MWI "craziness" just puts in light what is enclosed in strict quantum theory.
It's not unlimited, but it is very big. But you are thinking of a *classical* universe. A *quantum universe* is mindbogglingly bigger, but that's already the case from the start: the quantum states are a HILBERT SPACE spanned over the classical configuration space: with each POINT of classical configuration space corresponds a DIMENSION in Hilbert space. That's not MWI, that's quantum theory.
Well, that's just how the dynamics in hilbertspace occurs. You see, your surprise is a bit like that of the Pythagoreans again. Imagine they say: yes but that would mean that the position of a point particle is now given by 3 REAL numbers. Where does it store this infinite amount of information (3 real numbers contain indeed an infinite amount of information, as compared to the finite amount of information in 3 rational numbers) ? And on top of that, it even has to store its velocity, which is also 3 real numbers ?

So you see, one of the advantages of an MWI view is to ILLUSTRATE the mindbogglingly huge statespace of quantum theory.

It sounds like you are not distinguishing two very different things:

1. The state of superposition that the universe will be in from around the entangled particle. This is mind-boggling but "just" a huge state of superposition.

2. The "problem of label proliferation", which means that huge amounts of additional information about the past states needs to be carried along in addition to the superposition, in order to later-on enable the "pairing-up". As the text says, here "quantum field theory provides no explanation". If you think there is no "particular problem" here, then I submit you haven't recognized the problem yet.

I thought we agreed that the problem you mentioned could not occur ?

No, the situation cannot occur, and that is the problem. When an observer receives information from two of the measurements A and B at the midpoint AB, this will require pairing-up A states and B states, yet the possibilities of pairing-up depend on not-yet available information from C (the GHZ measurement angle at C, in the GHZ scenario). That means, or seems to, that some of the superpositions that develop at Ab will later-on become impossible. At least that is the challenge to be answered in this scenario.

 

[fermio]

quantum computers already do exist.

Here's a snippet from a news article about using quantum computers to factor numbers [emphasis added]:

"...One team is led by Andrew White at the University of Queensland in Brisbane, Australia, and the other by Chao-Yang Lu of the University of Science and Technology of China, in Hefei. Both groups have built rudimentary laser-based quantum computers that can implement Shor’s algorithm - a mathematical routine capable of defeating today’s most common encryption systems, such as RSA."

I think this optical quantum computer is exponentionly ineffiecent like all over quantum computers. I read PDF of this QC and nothing found about results and how good they are. And in contrast with all over computers unsuccess, I don't believe about good success of this quantum computers. I think all quantum computers are just probabilistic machines and all results showing this.

 

[colorSpace]

I think this optical quantum computer is exponentionly ineffiecent like all over quantum computers. I read PDF of this QC and nothing found about results and how good they are. And in contrast with all over computers unsuccess, I don't believe about good success of this quantum computers. I think all quantum computers are just probabilistic machines and all results showing this.

Recently, for example, an experimental quantum computer has successfully factorized the number 15. Increasing the bit-width, and thereby usefulness, is a matter of improving things that already work.

 

[fermio]

"Recently, for example, an experimental quantum computer has successfully factorized the number 15. Increasing the bit-width, and thereby usefulness, is a matter of improving things that already work."

I read that strenght of signal decreasing exponentionaly with number of qubits so it's means that quantum computer which factorized 15 was working like probabilistic computer I think and there is discusion do that computer is really quantum.

 

[f95toli]

"Recently, for example, an experimental quantum computer has successfully factorized the number 15. Increasing the bit-width, and thereby usefulness, is a matter of improving things that already work."

I read that strenght of signal decreasing exponentionaly with number of qubits so it's means that quantum computer which factorized 15 was working like probabilistic computer I think and there is discusion do that computer is really quantum.

No, there is no question quantum computer do work and 8 bit quantum computer have been demonstrated (as far as I remember the first factorization of 15 was done 7 years ago using NMR).
There is, however, some doubt whether or not the QC that was recently demonstrated by D-Wave (a Canadian company) is really "quantum". The reason is that they are using what is known as adiabatic quantum computing which is not "universal" since it only needs next-neightbor coupling. Unfortunately it is very difficult to tell whether or not it is really a true quantum computer or not(or merely "probabilistic"), spectroscopic methods do not work so the only way to do it is do demonstrate exponential speedup which they haven't done yet.

Maybe this is what you have been reading about?

 

[vanesch]

It sounds like you are not distinguishing two very different things:

1. The state of superposition that the universe will be in from around the entangled particle. This is mind-boggling but "just" a huge state of superposition.

2. The "problem of label proliferation", which means that huge amounts of additional information about the past states needs to be carried along in addition to the superposition, in order to later-on enable the "pairing-up". As the text says, here "quantum field theory provides no explanation". If you think there is no "particular problem" here, then I submit you haven't recognized the problem yet.

That is because your 1. and 2. are exactly the same thing !

The "labels" we are talking about here, is the "term number" in the superposition!

Look at this:
imagine a universe with 3 particles in it. In "quantum speak", we take it that the first two particles are entangled, and the 3rd one is in a product state:

(|u1>|v1> + |u2>|v2>) |w0>

In "label talk", we have "two labels" here: one for the first term, and one for the second:

u1 gets "label A" together with v1.
u2 gets "label B" together with v2.

w0 doesn't have a label yet (in a product state).

Now, whatever will evolve out of the term |u1>|v1> will carry label A with it. Same for |u2>|v2> (label B).

Imagine now that the third particle interacts with, say, the first one:

w0 will now entangle with the u-states:

|u1>|v1>|w1> + |u2>|v2>|w2>

w now "inherits" the labels from u, that is to say, w1 inherits label A, and w2 inherits label B (from u1 resp. u2). In algebra, we simply had that |u1>|w0> evolved into |u1>|w1> and that |u2>|w0> evolved into |u2>|w2>, but because we're trying not to talk about wavefunctions, we have to do the algebra with "labels".
Label A means: gets into the first term, and label B means: gets into the second term.

Ok. Now let us consider a more complicated system:
|keyboardAlice0>|brainAlice0>|computerAlice0> (|u+>|v+> - |u->|v->) |thunderbird_bob0>|brainbob0>

There are two terms here, given by the entanglement of u and v, so we have two labels: A and B.
u+ and v+ have label A, u- and v- have label B.

Suppose that Alice does a measurement on u, but under a different angle. We have:
|u+> = x |uu+> + y |uu->
|u-> = -y |uu+> + x |uu-> with x and y the cos and sin of the angle of alice's analyser.

We rewrite this, using labels:
|keyboardAlice0>|brainAlice0>|computerAlice0> ((x |uu+A> + y |uu-A>)|v+A> - (-y |uu+B> + x |uu-B> )|v-B>) |thunderbird_bob0>|brainbob0>

Now, Alice's brain interacts with the measurement device (which interacts with the uu+ and uu- states). However, because this interaction is again a "product state which entangles", we need to introduce new labels (because there are new terms in the wavefunction): C,D,E and F:

|keyboardAlice0>|computerAlice0> ((x |uu+AC>|brainalice+AC> + y |uu-AD>|brainalice-AD>)|v+A> - (-y |uu+BE>|brainalice+BE> + x |uu-BF>|brainalice-BF> )|v-B>) |thunderbird_bob0>|brainbob0>

Note that there is some double usage (C and D include "A" and E and F include "B"). We could do better if we wanted but it doesn't matter.

The brain of alice states inherit now the labels A,B,...F. Note that this is of not much meaning in the wavefunction, as we know of course in which terms they are. But if you do not want to write an algebraic wavefunction, then you can write the "term number" with these labels. AC is the first term, AD is the second one, BE is the third one and BF is the fourth one.

Now, let's say that Bob does his measurement (along the original z axis). we now have:

|keyboardAlice0>|computerAlice0> ((x |uu+AC>|brainalice+AC> + y |uu-AD>|brainalice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE> + x |uu-BF>|brainalice-BF> )|v-B>|brainbob-B>) |thunderbird_bob0>

At this moment, bob's brain inherits also the two labels A and B, from the v-states. Note that algebraically, A and B simply mean: first term and second term (from Bob's PoV).

Right, now Alice is going to send an email to bob with her results. First her keyboard gets hits from her fingers:

|computerAlice0> ((x |uu+AC>|brainalice+AC>|keyboardAlice+AC> + y |uu-AD>|brainalice-AD>|keyboardAlice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE>|keyboardAlice+BE> + x |uu-BF>|brainalice-BF> |keyboardAlice-BF>)|v-B>|brainbob-B>) |thunderbird_bob0>

It gets its label of course from Alice's brain state.

Same for the computer:
((x |uu+AC>|brainalice+AC>|keyboardAlice+AC>|computerAlice+AC> + y |uu-AD>|brainalice-AD>|keyboardAlice-AD>|computerAlice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE>|keyboardAlice+BE>|computerAlice+BE> + x |uu-BF>|brainalice-BF> |keyboardAlice-BF>|computerAlice-BF>)|v-B>|brainbob-B>) |thunderbird_bob0>

After sending the e-mail to Bob's email client (thunderbird), this e-mail agent gets also his label from this:
((x |uu+AC>|brainalice+AC>|keyboardAlice+AC>|computerAlice+AC>|thunderbird_bob+AC> + y |uu-AD>|brainalice-AD>|keyboardAlice-AD>|computerAlice-AD>|thunderbird_bob-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE>|keyboardAlice+BE>|computerAlice+BE>|thunderbird_bob+BE> + x |uu-BF>|brainalice-BF> |keyboardAlice-BF>|computerAlice-BF>|thunderbird_bob-BF>)|v-B>|brainbob-B>) Again, I want to stress that the labels do nothing else but to number the terms in the wavefunction! If you have the labels, you can reconstruct the wavefunction, and if you have the wavefunction, you can find the labels.

Right, now comes the crux: bob's going to read his e-mail:x |uu+AC>|brainalice+AC>|keyboardAlice+AC>|computerAlice+AC>|thunderbird_bob+AC> |v+AC>|brainbob++AC>
+ y |uu-AD>|brainalice-AD>|keyboardAlice-AD>|computerAlice-AD>|thunderbird_bob-AD> |v+AD>|brainbob+-AD> + y |uu+BE>|brainalice+BE>|keyboardAlice+BE>|computerAlice+BE>|thunderbird_bob+BE> |v-BE>|brainbob-+BE> - x |uu-BF>|brainalice-BF> |keyboardAlice-BF>|computerAlice-BF>|thunderbird_bob-BF>|v-BF>|brainbob--BF>Though the interaction with his e-mail, bob's brain interacts with the result of Alice, and learns about it (second sign + or - on the ket). It also inherits the labels.

We see that Bob has now 4 brainstates (++,+-,-+ and --) which correspond to 4 terms in the wavefunction, and to 4 labels (AC, AD, BE and BF) which have labelled these 4 terms.

So we see that the "labels" do nothing else but indicate the terms in the wavefunction. So it is EXACTLY the information of the superposition which is locked in these labels. We re-discover again the superposition principle, and the size of hilbertspace...EDIT: I will add something. In "bob's lifepath" he will first "split" over labels A and B (two "worlds") and later on, when he learns things from Alice, split again (in AC, AD, BE or BF).
So the "label proliferation" is nothing else but the consistent history of a particular Bob state in MWI. The number of labels corresponds to the number of histories. And these are nothing else but the different decohered terms in the "wavefunction of the universe".

So you can say that the "information to be carried by a state" is "the world in which it was, with its history". "know your world", as they say...

No, the situation cannot occur, and that is the problem. When an observer receives information from two of the measurements A and B at the midpoint AB, this will require pairing-up A states and B states, yet the possibilities of pairing-up depend on not-yet available information from C (the GHZ measurement angle at C, in the GHZ scenario). That means, or seems to, that some of the superpositions that develop at Ab will later-on become impossible. At least that is the challenge to be answered in this scenario.

I don't understand this. Could you work out the wavefunction symbolically (as I did with Alice and Bob) ?

 

[colorSpace]

That is because your 1. and 2. are exactly the same thing !

The "labels" we are talking about here, is the "term number" in the superposition!

Look at this:
imagine a universe with 3 particles in it. In "quantum speak", we take it that the first two particles are entangled, and the 3rd one is in a product state:

[snip... quote shortened here.]

So the "label proliferation" is nothing else but the consistent history of a particular Bob state in MWI. The number of labels corresponds to the number of histories. And these are nothing else but the different decohered terms in the "wavefunction of the universe".

So you can say that the "information to be carried by a state" is "the world in which it was, with its history". "know your world", as they say...

What you are not distinguishing is information in your mathematical description of the physical state, and the information that needs to be present in the physical state itself, in order to allow some physical process to "pair-up" the correct states when they meet. Your response doesn't even mention this problem.

Or are you perhaps hoping to confuse me with mathematics?

I don't understand this. Could you work out the wavefunction symbolically (as I did with Alice and Bob) ?

Have you read the descriptions in the thread I referred to? Could you ask more specifically? Is your request to "work out the wavefunctions" rhetoric, or haven't you noticed that I am not doing that kind of thing?

 

[vanesch]

What you are not distinguishing is information in your mathematical description of the physical state, and the information that needs to be present in the physical state itself, in order to allow some physical process to "pair-up" the correct states when they meet. Your response doesn't even mention this problem.

I fail to see what's the difference between:
1) "the information in the mathematical description of the physical state"
2) "the information present in the "physical state itself"

To me, the mathematical description IS the physical state (*)! If not, can you give me your definition of what is a physical state ?

(*) or better: the mathematical description is a faithful representation of the physical state. That is: is mathematically equivalent to.

 

[colorSpace]

I fail to see what's the difference between:
1) "the information in the mathematical description of the physical state"
2) "the information present in the "physical state itself"

To me, the mathematical description IS the physical state (*)! If not, can you give me your definition of what is a physical state ?

(*) or better: the mathematical description is a faithful representation of the physical state. That is: is mathematically equivalent to.

Well, unless I missed something, you understood "labels" as something that is added to the mathematical notation. You wrote:

I want to stress that the labels do nothing else but to number the terms in the wavefunction!

and

So we see that the "labels" do nothing else but indicate the terms in the wavefunction.

How would a notational difference be reflected in the physical state?
There are often, if not always, different notational possibilities to describe the same physical state. Of course. Why do I have to explain this, is it so difficult to anticipate this response, even if it were a misunderstanding of what you meant?

So on my side, I fail to see how this information (apparently only a notational difference) is going to help Bob's brain (BTW, is this "Many Minds" or "Many Worlds" ?) to pair up the correct states.

When the measurement angles are aligned, for electron spins, the possibilities are only +- and -+, so how does Bob know, long after the fact, that his "+" has to be paired up with the states that have evolved out of Alice's "-", since the "-" might not be present in that state anymore. When Bob receives the email, which is in a superposition of two states, how will Bob's "+" state (where the "+" might not exist anymore either) know that it needs to be paired up with the email state corresponding originally to Alice's "-"?

 

[colorSpace]

[Continuation of my the previous message]

To make it even more obvious: Before Alice sends an email, the whole experimental set-up may have been destroyed on both sides, only the results written down, on both sides, on a piece of paper. Since all information needs to be local, no non-local state description may be used. Bob may have moved away, only Bob's successor who doesn't know anything else than the paper remaining. How do the paper and the email know which of their states correspond to each other? How do they know the email isn't from a different experiment 10 years ago? If everything has to be in local states?

 

[colorSpace]

[This message doesn't replace the two previous one's, it is in addition to them.]

Now, let's say that Bob does his measurement (along the original z axis). we now have:

|keyboardAlice0>|computerAlice0> ((x |uu+AC>|brainalice+AC> + y |uu-AD>|brainalice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE> + x |uu-BF>|brainalice-BF> )|v-B>|brainbob-B>) |thunderbird_bob0>

At this moment, bob's brain inherits also the two labels A and B, from the v-states. Note that algebraically, A and B simply mean: first term and second term (from Bob's PoV).

Right, now Alice is going to send an email to bob with her results. First her keyboard gets hits from her fingers:

[This message doesn't replace the two previous one's, it is in addition to them.]

Your state description of "Bob's brain" already includes states from Alice, even before she sends the email. But as far as Bob is concerned, Alice might not even have performed the experiment, or with different measurement angles, or she might have gone to sleep and be dreaming, and/or sold her computer, or who knows what.

Therefore it is a non-local state description, and your use of non-local state descriptions may be part of the reason why you don't see the problem yet. You look only at these state descriptions, but they are non-local, and therefore they don't show the problem.

 

[vanesch]

[This message doesn't replace the two previous one's, it is in addition to them.]



[This message doesn't replace the two previous one's, it is in addition to them.]

Your state description of "Bob's brain" already includes states from Alice, even before she sends the email. But as far as Bob is concerned, Alice might not even have performed the experiment, or with different measurement angles, or she might have gone to sleep and be dreaming, and/or sold her computer, or who knows what.

Therefore it is a non-local state description, and your use of non-local state descriptions may be part of the reason why you don't see the problem yet. You look only at these state descriptions, but they are non-local, and therefore they don't show the problem.

No, look carefully to the state you quoted:

|keyboardAlice0>|computerAlice0> ((x |uu+AC>|brainalice+AC> + y |uu-AD>|brainalice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE> + x |uu-BF>|brainalice-BF> )|v-B>|brainbob-B>) |thunderbird_bob0>


At this point, bob's brain is in 2 different states:

brainbob+A and brainbob-B.

It got the labels A and B from the particle v, which was transmitted by local interactions (v was the particle Bob did a measurement on). As such, it doesn't "include states from alice".

Alice's states are
brainalice+AC
brainalice-AD
brainalice+BE
brainalice-BF

The label A and B, she got from the particle u, and the labels C,D E and F she also got from the particle u, after it got written in another basis (angle of her analyser).

So alice's states get their labels ALSO from purely local interactions at Alice's place.

As I said before, the labels are unnecessary when writing down the wavefunction, because they simply "indicate the algebraic tree structure" of it. But the labels can be useful if you write things just as lists. Mind you, next to the labels, you need then also to keep track of the complex amplitudes.

So we can redo the story but this time without wavefunction.

There are two entangled particles u and v:

we have:
u+A and u-B for u
and
v+A and v-B for v

and with labels A and B goes a phase factor +1 and -1 respectively.

All the other states of systems in our thing are in a product state wrt this, so we don't write them down yet.

Next, Alice does her measurement along an axis on u.

This means that she measures on all the states of u, in the new basis.

So u+A is to be written:
|u+A> = x |uu+A> + y |uu-A>

and Alice's brain is going to entangle with it, so we have to write two new labels:
u+A> = x |uu+AC> + y |uu-AD>

where label C carries "amplitude x" and D amplitude "y".

and we have now:

brainalice+ AC
brainalice- AD

when alice interacted with u+ (that's locally, at her place)

but she also interacts with u-B:
u-B> = -y |uu+B> + x |uu-B>

and again we'll need two new labels because there's going to be an entanglement:
u-B> = -y |uu+BE> + x |uu-BF>

these labels E and F carry amplitudes -y and +x

and alice interacts with it
brainalice+ BE
brainalice- BF

Note that alice's states only inherited labels by local interactions! It came from the u-particle. She doesn't know what bob is going to do here.

On Bob's side, bob received a particle v which was in two states:

v+A and v-B

upon measuring along the z-axis, bob's brain entangled with them:

bobbrain+A
bobbrain-B

He doesn't know at all what alice did. He got his labels only locally.

Alice does now what she wants, like sending an e-mail (after having interacted with her fingers, keyboard, air, ocean, moon, the sun, Jupiter, ... who all get sooner or later entangled with her, directly or indirectly, through successive local interactions and will inherit the labels AC, AD, BE and BF).

So at a certain moment, we have:
half-of-the-universeAlice AC, containing the information that alice had a +
half-of-the-universeAlice AD, containing the informaton that alice had a -
half-of-the-universeAlice BE, containing the information that alice had a +
half-of-the-universeAlice BF, containing the information that alice had a -

We can tell the same story of Bob: he will interact with his environment, with the dinosaurs who still live on his planet, which will interact with the air, the water, etc.. on his remote planet, Bob will maybe die, do whatever, so 10 years later, we also have:

half-of-the-universeBob A containing the information that bob had +
half-of-the-universeBob B containing the information that bob had -

In the common part of these "half-of-the-universeAlice" and "half-of-the-universeBob", say, on a planet midway between both, there will have been an interaction with the AC part and with the A part, which will be recognized being the same label A.

So in the AC part in this common part, the information will be available that alice had + and bob had - ; in the AD part, it will be that alice had - and bob had +, in the BE part it will be that alice had + and bob had - and in the BF part, it will be that alice had - and bob had -.

"information available" will simply say, there has been a chain of local interactions through which it is *in principle* possible to find out. But that can be of course in an "obvious" way, such as an e-mail, or an old book in which, Alice wrote her result 100 years ago, or in an undisentangible configuration of air molecules or something. If Alice and bob did record their measurements in a readable way, say a book and a hard disk, then Joe, which will be in 4 different "universes" 100 year later, will be in 4 different states:
joeAC with a bookAC and a disk AC
joeAD with a bookAD and a disk AD
joeBE with a book BE and a disk BE
joeBF with a bookBF and a diskBF

On it, he will find the necessary information (book for alice's result and disk for bob's result).

 

[colorSpace]

No, look carefully to the state you quoted:

|keyboardAlice0>|computerAlice0> ((x |uu+AC>|brainalice+AC> + y |uu-AD>|brainalice-AD>)|v+A>|brainbob+A> - (-y |uu+BE>|brainalice+BE> + x |uu-BF>|brainalice-BF> )|v-B>|brainbob-B>) |thunderbird_bob0>At this point, bob's brain is in 2 different states:

brainbob+A and brainbob-B.

It got the labels A and B from the particle v, which was transmitted by local interactions (v was the particle Bob did a measurement on). As such, it doesn't "include states from alice".

Alice's states are
brainalice+AC
brainalice-AD
brainalice+BE
brainalice-BF

The label A and B, she got from the particle u, and the labels C,D E and F she also got from the particle u, after it got written in another basis (angle of her analyser).

So alice's states get their labels ALSO from purely local interactions at Alice's place.

As I said before, the labels are unnecessary when writing down the wavefunction, because they simply "indicate the algebraic tree structure" of it. But the labels can be useful if you write things just as lists. Mind you, next to the labels, you need then also to keep track of the complex amplitudes.

The complex amplitudes? I guess I forgot about those. Never heard about them!

On looking carefully once more, I only find confirmed what I said: You have associated each of Bob's states with two of Alice's state, and they even already share the same labels, A and B.

How is that not non-local?

So it appears that in the "back of your mind", so to speak, you are performing a non-local split of states right in the beginning. The "pairing-up" is there right in the beginning, non-locally.

So we can redo the story but this time without wavefunction.

We can redo the story as often as you want. I don't see you getting even one inch closer to answering my points.

There are two entangled particles u and v:

we have:
u+A and u-B for u
and
v+A and v-B for v

and with labels A and B goes a phase factor +1 and -1 respectively.

All the other states of systems in our thing are in a product state wrt this, so we don't write them down yet.

Next, Alice does her measurement along an axis on u.

This means that she measures on all the states of u, in the new basis.

So u+A is to be written:
|u+A> = x |uu+A> + y |uu-A>

and Alice's brain is going to entangle with it, so we have to write two new labels:
u+A> = x |uu+AC> + y |uu-AD>

where label C carries "amplitude x" and D amplitude "y".

and we have now:

brainalice+ AC
brainalice- AD

when alice interacted with u+ (that's locally, at her place)

but she also interacts with u-B:
u-B> = -y |uu+B> + x |uu-B>

and again we'll need two new labels because there's going to be an entanglement:
u-B> = -y |uu+BE> + x |uu-BF>

these labels E and F carry amplitudes -y and +x

and alice interacts with it
brainalice+ BE
brainalice- BF

Note that alice's states only inherited labels by local interactions! It came from the u-particle. She doesn't know what bob is going to do here.

On Bob's side, bob received a particle v which was in two states:

v+A and v-B

upon measuring along the z-axis, bob's brain entangled with them:

bobbrain+A
bobbrain-B

He doesn't know at all what alice did. He got his labels only locally.

Alice does now what she wants, like sending an e-mail (after having interacted with her fingers, keyboard, air, ocean, moon, the sun, Jupiter, ... who all get sooner or later entangled with her, directly or indirectly, through successive local interactions and will inherit the labels AC, AD, BE and BF).

So at a certain moment, we have:
half-of-the-universeAlice AC, containing the information that alice had a +
half-of-the-universeAlice AD, containing the informaton that alice had a -
half-of-the-universeAlice BE, containing the information that alice had a +
half-of-the-universeAlice BF, containing the information that alice had a -

Maybe Bob got his labels locally, but Alice already got Bob's labels inherited (A and B).

Again, how is that not non-local?

Bob's result should depend on his measurement angles which he chooses after Alice has received her particle already, and Alice's states should be free of any reference to Bob's.

According to what I can tell, you haven't understood my objections at all.

We can tell the same story of Bob: he will interact with his environment, with the dinosaurs who still live on his planet, which will interact with the air, the water, etc.. on his remote planet, Bob will maybe die, do whatever, so 10 years later, we also have:

half-of-the-universeBob A containing the information that bob had +
half-of-the-universeBob B containing the information that bob had -

In the common part of these "half-of-the-universeAlice" and "half-of-the-universeBob", say, on a planet midway between both, there will have been an interaction with the AC part and with the A part, which will be recognized being the same label A.

That's trivial since you shared the label A already at the beginning of your story.

So in the AC part in this common part, the information will be available that alice had + and bob had - ; in the AD part, it will be that alice had - and bob had +, in the BE part it will be that alice had + and bob had - and in the BF part, it will be that alice had - and bob had -.

"information available" will simply say, there has been a chain of local interactions through which it is *in principle* possible to find out. But that can be of course in an "obvious" way, such as an e-mail, or an old book in which, Alice wrote her result 100 years ago, or in an undisentangible configuration of air molecules or something. If Alice and bob did record their measurements in a readable way, say a book and a hard disk, then Joe, which will be in 4 different "universes" 100 year later, will be in 4 different states:
joeAC with a bookAC and a disk AC
joeAD with a bookAD and a disk AD
joeBE with a book BE and a disk BE
joeBF with a bookBF and a diskBF

On it, he will find the necessary information (book for alice's result and disk for bob's result).

I didn't get the slightest clue where or how this information is supposed to be available. It all appears to depend on the initial pairing-up of states and labels, which you preform at the beginning when everything is supposed to be spacelike separated.

In my book, your story is a non-local story.

 

[colorSpace]

[Continued from the previous message]

Are you perhaps assuming hidden variables?

If so, it would appear that your theory is quite different than the one in the link, and the one I discussed before.

In that case, I would assume that arguments related to local-hidden-variable theories will apply here as well.

[Again, continued from the previous message]

 

[colorSpace]

Actually, it looks almost like in your scenario, the splitting happens before the entangled particles separate...

 

[colorSpace]

Yes, Vanesh, it was difficult for me to tell, since you seemed to describe everything 'subjectively' from Bob's point of view, which would make the situation naturally asymmetrical.

However, what you have done appears to be, more or less, that you made the first universe-split before the particles separate, and then in each universe you develop a local-hidden-variable based situation. Except that you complicate it with an additional split only on Alice's side regarding some "amplitudes" that I haven't heard of, neither when talking about polarized photons, nor when talking about electron spins, which are the common examples for entanglement. The second split appears somewhat bogus, in one of your earlier messages you even use the description "to show how for THAT SPECIFIC ALICE things LOOK AS IF a collapse took place".

So if one removes this complication on Alice's side, what's left is two universes with a local-hidden-variable situation in each, and the same arguments that apply to disproving a local-hidden-variable theory in a single universe, also apply here to each of the two universes, since the split happens before the particles are separated, and becomes irrelevant to the application of Bell's theorem.

 

[vanesch]

The complex amplitudes? I guess I forgot about those. Never heard about them!

On looking carefully once more, I only find confirmed what I said: You have associated each of Bob's states with two of Alice's state, and they even already share the same labels, A and B.

OF COURSE, but these labels do not come from "bob" or from "alice" but from the SOURCE OF THE ENTANGLED PARTICLES.

The source of the entangled particles (which is a *local* happening, right ?) makes two particles, u and v, in an entangled state:
|u+>|v+> - |u->|v->

It is *this entangled state* (the fact that there are two terms here) that makes up for the labels A and B. They are "produced" locally in the source of the entangled particles. You could even look at it this way. Imagine, in the source, that we have two particles "sitting there and waiting to be entangled": u and v.

They are as of yet "independent systems": u is in the state u0 and v is in the state v0.
As long as this remains so, we can treat u in its hilbertspace Hu and v in its hilbertspace Hv.
But now, inside the source, an interaction is provoked between the u-system and the v-system. Well, the superposition principle requires us now to use the tensor product state space Hu x Hv. What does this mean ? It means that different states from u can "couple" with different states from v. It is when this happens, that we have to introduce labels, if we want to keep track of which state of u goes with which state of v.

But, and this is the core of the locality in quantum theory: this coupling can only occur for states which share the same spacetime points. This is a property of the locality of the interactions. It didn't need to be, but that's the way it turns out to be. It is a property of the interaction hamiltonian.

Well, a state of particle u that "is in the neighbourhood of point P" can interact with a state of particle v that is "in the neighbourhood of point P", that is, they can change into an eventual superposition of states of u and v, all in the neighbourhood of point P.

Before the interaction, they were "independent", after the interaction, if there are multiple terms, they are "entangled".

We take it that our states u0 and v0 respectively are "in the neighbourhood of the source". So they can now interact, and form an entangled state:

a|u1>|v1> + b|u2>|v2> + c|u3> |v3>

where, remember, u1,u2, u3 and v1, v2, v3 are also states "in the neighbourhood of the source".

It is when THIS happens, that we can introduce LABELS (which do nothing else but codify for the algebraic expression above):

state "u0" "v0" evolved into a SUPERPOSITION OF:

state u1 with v1 with amplitude a, which we give LABEL A
state u2 with v2 with amplitude b, which we give LABEL B
state u3 with v3 with amplitude c, which we give LABEL C

the labels are nothing else but a way to say that it was state u1 that got with state v1, and not with state v2, that it was state u3 that got with state v3, and not v1.

When you write out the wavefunction algebraically, this is evident of course, but if you want to keep track "per system" of what happens, then you need the labels.

Remember that these labels come from two things:
1) the superposition principle applied to the union of two systems, which requires the existence of entangled states
2) the fact that a LOCAL interaction (at the source in this case) can make a product state (independent states for the two subsystems) evolve into such an entangled state (superposition of product states).

How is that not non-local?

Because it came forth of a past local interaction.

In our example, we used 3 terms in the entangled state (with labels A, B and C), but usually when using the spin states of photons or electrons, we only have two states available for each, so we only have two terms, and need two labels, A and B:

|u+A>|v+A> - |u-B>|v-B>

Remember that this entangled system is LOCALLY produced in the source.

Next, u will evolve (in both its states + and -) towards Alice, and v will evolve towards Bob, but they ALREADY HAVE THEIR LABELS.

Note that this is interesting: it is not possible to "entangle at a distance". If u was independently at Alice, and v at Bob, it would not have been possible to create an entangled state. It is in the source, locally, that the states of u and v got entangled.

So it appears that in the "back of your mind", so to speak, you are performing a non-local split of states right in the beginning. The "pairing-up" is there right in the beginning, non-locally.

Nope, locally, in the source. But I'm sorry not having mentioned that, I thought that that was obvious.

Maybe Bob got his labels locally, but Alice already got Bob's labels inherited (A and B).

Again, how is that not non-local?

I hope that this is cleared up now. A and B come from the source of entangled particles.

Bob's result should depend on his measurement angles which he chooses after Alice has received her particle already, and Alice's states should be free of any reference to Bob's.

Consider that bob did his measurement first then. Given that they are at spacelike intervals, you can choose which one is "first" :-) You can always write the entangled state "in the basis of one of the measurers". True, you can work it out in more generality, it is just more typing, it comes down all the same.

I didn't get the slightest clue where or how this information is supposed to be available. It all appears to depend on the initial pairing-up of states and labels, which you preform at the beginning when everything is supposed to be spacelike separated.

Indeed, it all depends on the initial pairing up... which happened in the source of the particles. Sorry for not having made that clear.

Indeed, if you think that "particles just become entangled at a distance" then you are right that this would be a non-local phenomenon.

 

[colorSpace]

Nope, locally, in the source. But I'm sorry not having mentioned that, I thought that that was obvious.

Meanwhile I did figure this out, in my last two messages, where I wrote that you are splitting the universe before the particles are separated. Thank you for the confirmation.

After writing my last message, I also looked again more closely at the thread of your previous discussion with 'nrqed', and especially this quote (of you) was clarifying:

If you are now going to consider the case of A PARTICULAR BOB, then the rule is, that the corresponding state you have to pick out for THAT Bob is given by the Born rule. In this case, it is 50-50: so *a particular bob* will experience, with 50% chance, the first category of "bob states", and with 50% chance, the second category of "bob states".
And if he waits until "Alice" comes along, he will meet with the particular Alice that was in his branch of course.

(The thread is at https://www.physicsforums.com/showthread.php?t=114207 )

So you are keeping the corresponding "particular Bob" and "particular Alice" in the same branch from the beginning. Of course this doesn't make it difficult for them to find each other again. Actually, that is now trivial.

This is indeed a new situation for me, and I saw that it also took 'nrqed' quite a while to figure it out.

However before we go into the details, allow me to ask you whether you are familiar with the way in which local-hidden-variable theories have been disproved, and how you would (very shortly) describe this in your language. I am asking this question because of what I have written in my previous message.

 

[vanesch]

However before we go into the details, allow me to ask you whether you are familiar with the way in which local-hidden-variable theories have been disproved, and how you would (very shortly) describe this in your language.

Yes, I think I know Bell's theorem quite well.

I am asking this question because of what I have written in my previous message.

We are NOT in a local hidden variable theory here, simply because there has not been a deterministic outcome at the two measurements: the two possible outcomes exist.

I am btw not keeping a particular bob and a particular alice in the same branch. Bob "doesn't know" with which alice he's going to "pair up".

 

[colorSpace]

We are NOT in a local hidden variable theory here, simply because there has not been a deterministic outcome at the two measurements: the two possible outcomes exist.

The two possible outcomes appear to be distinguished (and labelled) at the beginning. From then on, each of the two branches behaves like a local-hidden-variable scenario, since all further outcomes are defined by the initial pairing-up.

I am btw not keeping a particular bob and a particular alice in the same branch. Bob "doesn't know" with which alice he's going to "pair up".

According to everything I can tell, Bob doesn't know it, but each particular Bob is in a branch with the corresponding particular Alice. You just wrote yourself that the pairing-up happens at the source: "Indeed, it all depends on the initial pairing up... which happened in the source of the particles. Sorry for not having made that clear."

This is what I finally figured out from our discussion, and saw confirmed in your discussion from which I quoted in my last message.