Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

MWI, Alice, Bob and Alfred

  1. Mar 13, 2006 #1


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi Patrick. Btw, thanks for all your very interesting posts.

    That brings me to a question which maybe should be in a different thread (I started a new thread with that question a short while ago but it went unnoticed). Hopwfully it won't be too rude to post it here.

    Consider an EPR type of experiment between Bob and Alice, located 26 ly away (Bob is near Vega, say, with Alice here). What's the MWI view of this?

    Bob measures the spin of let's say one gazillion elctrons while Alice measures the spin of the corresponding one gazillon positrons. Bob memorizes the results (he is good!) and also writes them down, giving a copy to his friend Alfred who stays on Vega. He then travels to Earth to compare his results with Alice.Of course, they find perfect correlation between there results. I know that you prefer the view that it's only when Bob and Alice meet that there is a collapse (even if it's a subjective one) and that sounds good to me. But Bob could be in any of 2 to the one gazillion states corresponding the the possible measurements he may have made.

    My question is: what causes the (subjective) collapse to be the one that corresponds to the state where all his results correlate with Alice's? It seems to me that even though there is no actual collapse, the fact that the subjective collapse will be such that the results with Alice will correlate in agreement with the Copenhagen interpretation is amazing to me...I guess I am probably missing something which has to do with the subjective collapse and whether it just moves the mystery from one place to another or if it comes out in a more satisfying manner.

    Of course, there is still Alfred on Vega with the list of a gazillon results (or the superposition of Alfred with the 2^gazillon lists). I guess that nothing happens to Alfred (in terms of a collapse) when Alice and Bob compare reults (?). But when Bob travales back and meets with Alfred, is there another subjective collapse (this time of Fred??) which, again, happens to be such that his list agrees exactly with the list that Bob have??

    I hope this makes sense, as a question.

    Thanks for all your excellent posts, once more!

  2. jcsd
  3. Mar 14, 2006 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I took the liberty of moving your post to a new thread,...
  4. Mar 14, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes. In fact, there "is" a Bob in each of these states! But for a particular "Bob" experience to be in one of them, you have to apply the Born rule.

    The point is that there is not ONE Bob meeting with ONE Alice, there is a 2^gazillion Bob's meeting with 2^gazillion Alices, and for one Bob and one Alice experience to experience one of those possibilities, you have to use the Born rule.

    There's a problem in language here, because "Bob" means traditionally several things: Bob's "body", Bob's "mental state" and "a Bob experience", things which are intuitively so intimately entangled o:) that we have difficulties making the difference.

    Now, I won't type down a gazillion terms in this post, but let's do it with 2 particles. Bob and Alice exchange 2 particles (do two measurements). We will end up, after doing all the math, with:

    |Bob++> (a11 |Alice++> + a12 |alice+-> + a13 |alice-+> + a14|alice-->)
    + |Bob+-> (a21 |Alice++> + a22 |alice+-> + ...)
    + |Bob-->(... a44 |Alice-->)

    Bob's body state is in a superposition of 4 states: |Bob++>, |Bob+-> ...|Bob-->. If you are a "Bob experience", you will experience one of them, with probabilities given respectively by the norm of the respective vectors containing each of the 4 states, namely:
    to experience Bob++, you have a probability |a11|^2 + |a12|^2 +...|a14|^2 ;
    to experience Bob+-, you have a probability |a21|^2 + |a22|^2 + ...|a24|^2

    So, from Bob's POV, there are 4 "worlds" to choose from, and a random "Bob experience" will experience one of them, with Born rule probability.

    From Alice's point of view, we have to re-write the SAME wave function as:

    |Alice++> (a11 |Bob++> + a21 |Bob+-> + a31 |Bob-+> + a41|Bob-->)
    + |Alice+-> (a12 |Bob++> + a22 |Bob+-> + ...)
    + |Alice-->(... a44 |Bob-->)

    So, Alice's body is also in a superposition of 4 possible states, namely Alice++, Alice+-...
    As such, an "Alice experience" will randomly experience ONE of these states, with probabilities: p1 = |a11|^2 + |a21|^2 + |a31|^2 + |a41|^2 etc...

    So there are also 4 "Alice" worlds, but they are not the same than the 4 Bob worlds.

    Now, this is at first sight a bit strange, because you can say that there are 4 Bob states, and hence 4 Bob experiences, and to "be one of them", the probability should be 1/4. But (here I'm a heretic MWI-er ; most MWI-ers do indeed say that, and then run into troubles with the Born rule!) although this "equal probability rule" sounds intuitively attractive, it doesn't have to be the case. Consider the "norm" of the Bob vector a "cross section" to capture a "Bob experience" in a way.

    To be honest, it moves the mystery from one place to another - but it does - IMO - also come out slightly more satisfying. I will not hide that it is still very mysterious, but we're pushed into issues which are anyhow mysterious, and over which philosophers have been pondering for centuries: namely what is the relationship between subjective experience and physical reality. In a way, MWI tries to get the cleanest view on the "physics" part, but then has some troubles explaining subjective experience (but classical physics ALSO has problems there, although they are usually less well aknowledged because of the evident link between physical reality and subjective experience, it is easier to do away with it by a snearing comment like "that's stuff for philosophers, not for physicists".)
    The clean part of physics in MWI (the main reason why I like it) is that the physical picture is very clear: there is a physical state, and a physical state space (a point in a projective Hilbert space, or, if you like, a ray in Hilbert space), this corresponds, like in the old days, to something "physically out there" (as was the matter point in Newtonian physics, the EM field in classical EM, the spacetime manifold in GR...), and we have a clear (even deterministic) evolution equation, the Schroedinger equation, which describes the dynamics. No "undescribable" physics between measurements, no inconsistency (choice between incompatible Schroedinger evolution and collapse), no positivist denial of ontological existence apart from measurement... we're back to physics as we know it: a mathematical structure which is a model of reality, a dynamics etc...

    The obvious difficulty is that we end up with macroscopic superpositions, and this seems to clash with everyday observation. The answer to this riddle is that everyday observation is something which has only a subjective existence, and here we enter the philosopher's domain (they tried to tell this already since 2000 years). There's nothing, I repeat, nothing, in the objective quantum description which is contradicted, if it weren't for our subjective experience of "only one state". So if we now state that this is a strict property of subjective experience, and not of "objective state of the world", then all one has to do is to POSTULATE a rule which links the "objective state of the world" with the "subjective experience". And one does that with the Born rule, namely that what is, by a certain subjective experience, really experienced, is probabilistically derived from the state of the world. This remains as mysterious as it was before, except that we now DO have a rule which explains correctly our empirical observations (which are nothing else but subjective experiences!). That's all we can do.

    Classical physics has exactly the same difficulty, up to one point. The rule in classical physics, that links subjective experience to the objective world, is this: "the subjective experience is given deterministically by the state of the world", while in MWI-QM, it is: "the subjective experience is given probabilistically by the state of the world, using the Born rule"
    In BOTH cases, there's no real explanation of what exactly IS a subjective experience. There's no reason why, when a certain nerve cell fires, you EXPERIENCE "blue". There's even no reason why you experience Pat's body, and not mine, for instance. Philosophers found out that point already since a long time. But, as in classical physics, the relationship is 1-1, one can afford not to talk about this "philosophers' stuff", and keep just to the physics (and intuitively say that the physical state of the universe is identified with subjective experience). In quantum theory, however, although you COULD happily continue to calculate and do physics with the wave function, at a certain point, you would LIKE to make a link to subjective empirical observation, and then you do enter this slippery philosopher's issue, because the rule is now not 1-1 anymore.

    So the main difference between the classical and the quantum link between subjective experience and physical state is that in classical physics, it is 1-1, while in quantum physics, it is not 1-1, and stochastical. However, the fundamental mystery of the link between both remains in both viewpoints ; only, in classical physics, one can "close one's eyes and think of England", while in quantum theory, one is forced to consider it.

    If there's also an Alfred in the game, which interacted with Bob, then Alfred will be in similar states than Bob:

    |Bob++>|Alfred++>(a11 |Alice++> + a12 |alice+-> + a13 |alice-+> + a14|alice-->)
    + |Bob+-> |Alfred+-> (a21 |Alice++> + a22 |alice+-> + ...)
    + |Bob-->|Alfred-->(... a44 |Alice-->)

    Note that there are no terms with, say, |Bob++>|Alfred-+>. This is due to the interaction between Bob and Alfred, when they exchanged the same measurement results.
    For instance, if Bob first did his measurement, and then told Alfred, we had, before Bob told him:

    |alfred0>(a |bob++> + b|bob+-> +...)

    and after telling him (this changed alfred's state):

    a |alfred++>|bob++> + b|alfred+->|bob+-> ...

    So this is the origin of the non-existence of a mixed term between bob and alfred.

    So the "bob" worlds are identical to the "alfred" worlds. For each possible "bob" experience, he'll find a corresponding "alfred" state.

    Now, let's assume that Bob travels (in the 4 different bob worlds) to earth to meet Alice. Let us assume that we follow the story from Bob's POV, and that, upon measurement, we are a Bob experience that goes with the Bob state |Bob+-> (upon the entanglement with the measurement apparatus, we have to pick a state).

    So we have (I put an asterix in our specific state we're in):

    |Bob++>|Alfred++>(a11 |Alice++> + a12 |alice+-> + a13 |alice-+> + a14|alice-->)
    + |Bob+-*> |Alfred+-> (a21 |Alice++> + a22 |alice+-> + ...)
    + |Bob-->|Alfred-->(... a44 |Alice-->)

    when Bob travels to Alice, and meets her, and learns about her results, we will have:

    + |alfred+-> (a21|bob*+-/++> |alice++/+-> + a22 |bob*+-/+->|alice+-/+-> + a23...)

    But we can't have that ! We cannot have the asterix on different bob states, we have to pick one according to the Born rule. Say it comes out to be |bob+-/++>, so we have now (marked with **):

    + |alfred+-> (a21|bob**+-/++> |alice++/+-> + a22 |bob+-/+->|alice+-/+-> + a23...)

    In this Bob's world, he remembers having measured +- himself, and met an Alice who measured ++ (and who knows now that he measured +-), and remembers an alfred who knew he had +-. If ever he goes back seeing alfred, he'll not be surprised that Alfred is still in the state |alfred+->.

    The overall chance for a Bob experience to subjectively experiencing this, is |a21|^2.
  5. Mar 14, 2006 #4
    Bravo. Excellent post.

    (As far as more philosophical, less pragmatic thinking is required in fundamental physics research, everybody should read http://www.nyas.org/publications/UpdateUnbound.asp?UpdateID=41 )

    As far as MWI, I think it should be mention that its main problem is its ridiculous proliferation of worlds. It's not many, it's crazy absurdly unbelievable many. That's the first reaction to MWI and also after understanding the merits of the MWI approach it remains the main objection in accepting it.

    And what about eigenbasis selection? The observer can decide/ define a lot to measure. How does MWI cope with that?
    Last edited: Mar 14, 2006
  6. Mar 14, 2006 #5


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    But that's already the case for microscopic quantum systems. Hilbert space is unbelievably huge ! (and given that every separable Hilbert space is isomorphic, this is just as acute an objection to a microscopic state space than to the bigger one). Also, note that the concept of "world" is sometimes misunderstood in MWI. There are no "objective worlds" (there's only one wavefunction). "Worlds" is a relative concept in relationship to an observer, corresponding to the different states of the body of the observer which are corresponding to distinguishable subjective experiences. So there are "worlds according to Bob" and "worlds according to Alice" and so on. One sometimes hears about "each time there's a quantum event on Andromeda, the worlds split", but that's a misunderstanding. The only things that make MY world (or BOB's world) split are interactions of my body with the environment which result in states which are sufficiently different that they correspond to different subjective experiences. This is a huge coarse graining! Hence the "set of my possible worlds" are eigenspaces which split up the Hilbert space of states, and which correspond to different subjective experiences of the observer of which we are talking (consider it the ultimate measurement operator: the different outcomes are different subjective experiences). There are many of them, but not *that* many.

    Well, the eigenbasis is the (degenerate) set of eigenvectors which span the above-mentioned eigenspaces of body states corresponding to different subjective experiences. Note that many different microscopic bodystates correspond to identical subjective experiences, so they belong to the same "world".
    Consider hence the "worlds" as the eigenspaces of a particular (hermitean) measurement operator on my bodystate, with each different outcome corresponding to a different subjective experience. THIS is the basis in which my "measurements" are performed ; they seem to correspond roughly to classical states of the world around me, and they also correspond to the stable terms in decoherence theory.
    When I do a specific measurement on a quantum system, I arrange the measurement apparatus in such a way that what will correspond to different mental states of my body (the eigenspaces I mentioned before) will correspond to different "pointer states" (macroscopically and classically different states) of the measurement apparatus, and hence will determine the eigenspaces of the measurement operator corresponding to the apparatus.

    As such, the "slicing up" of the Hilbert space in "different worlds according to my view" is nothing else but the slicing up into eigenspaces according to the one and only "measurement" I'm constantly making, and which is given by how my body states map onto mental states which are experienced differently, subjectively. What we call "classical worlds" are nothing else but what corresponds to these eigenspaces of my body, and through its interactions with the environment, what corresponds to states of the environement that correspond to these bodystates.

    It is a property of what constitutes "subjective experiences" that determines what we call "classical worlds".
    Last edited: Mar 14, 2006
  7. Mar 14, 2006 #6


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    A good read, that article. Must be a smart guy, that Lee Smolin :approve: o:) :redface:

    One point, maybe. It might be very clear, sorry if what I write is redundant, but the "abundance of worlds" in the Landscape is a totally different issue than it is in MWI. The Landscape is a (huge) set of possible *theories*, while in MWI, we're supposing to know the theory (a quantum theory with a known hilbert space and dynamics on it) and we're talking about its dynamical aspect only.
  8. Mar 14, 2006 #7


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Thank you Patrick for your detailed reply.. I appreciate the effort and the time!!

    there is a lot of stuff to discuss but let me first focus on one specific (probably dumb) question.

    That is all fine...

    Ok. A good point to make.

    All this makes perfect sense. But here is where I get confused. I am sure that it's a dumb question but hey, I am beyond worrying about looking dumb:wink:

    The example I had in mind was one in which the electron/positron pair (say) were in a singlet spin state. Therefore, if Alice finds herself in the (++) world, Bob must be in the (--) world. And so on. There should be no overlap between Bob(--) and Alice (--) or Bob(+-) and Alice (--) and so on. I am wondering how this would be accounted for in the MWI.
    I mean, at the instant Bob is taking is measurements, it seems that all the worls should be possible (+-), (--) etc. But when he meets Alice, something else happens. It seems to me (but again, I am surely missing something) that there are two steps (I don't dare use "collapses"!)...one is that for some reason, only the worlds |Bob(--) Alice(++)>, |Bob(+-)Alice(-+)>, |Bob(++) Alice (--)> and |Bob(-+)Alice(+-)> "survive". And *then*, one of these world is picked up as an experience of Bob and Alice.

    In other word, my question is about entanglement. At what point does this entanglement occurs. Are Bob and Alice entangled when they are making their measurements (so that we could only talk about a |Bob(++) Alice(--)> + b |Bob(+-) Alice(-+)> .....) ? If that's the case then it is going back to a nonlocal type of effect which I thought was not required in MWI.

    On the other hand, if the entanglement occurs when Bob and Alice meet ("interact"), this seems to me to require an extra "thing" in th etheory, beyond the "collapse" to the exprience of one world. For some reason, the collapses to the experience of Bob's world and Alice's world are entangled!

    Thanks for the post again. And the point about Alfred was interesting. There is more to say but I will keep it at that single question for now.


  9. Mar 14, 2006 #8


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No problem. I was considering the general case, where the orientations of Alice's and Bob's analysers had arbitrary angles. The geometry of the setup (the angle between the polarizers) determines the values of the coefficients a11, a12 ... but I was too lazy to work it out.
    In the case of parallel polarizers, so that they are strictly correlated, this will simply result in all non-diagonal elements in the a_ij matrix to be 0. This will be given by the initial correlation of the (|+>|-> - |->|+>) pair, which will induce, through the measurement interaction, only states of the kind |Bob++>|Alice--> and so on.

    No, because the different factors within a term are linked (through the original product |+>|-> in the singlet state, for instance ; it is the absense of a |+>|+> state in the singlet state which is responsible for this correlation), and a Bob state can only meet an Alice state in his own term.

    No, again, in this case, the link is established because you stay within one term. So a term |alice->|bob-> was never present from the beginning.
    Again, even though a Bob state may get spatially far away from an Alice state, it stays "linked" with it through the wavefunction, because it remains linked to the Alice in HIS term. This is not "action at a distance" but rather "bookkeeping of terms in the wavefunction".

    The entanglement came from the original entanglement of the singlet state, and the "keeping within the same term". Again, there's no action at a distance required, but only a "remembering which term we were in".
  10. Mar 14, 2006 #9


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Ah, of course (slapping myself for such a dumb question :yuck:).

    Ok, I see. So that leaves the "collapse" to the experience of one world...

    Ok. That brings me to my next question but this is more philosophical and therefore more vague. I see that this approach is nice because there is no no need for a collapse of a wavefunction at a distance and all that stuff.

    But it is still very strange to have to consider that somehow, the experiences of Alice and Bob collapse together... This is as mysterious as the collapse in the Copenhagen interpretation. I mean, when does this occur and how does this occur is very strange. Bob and Alice meet...For some reason, their experiences collapse together in the same world. When? How? Does this happen when Bob starts reading his results to Alice?? When her brain becomes conscious of his results? If Bob reads his results before meeting her, why would his experience collapse to one world only when he meets her?

    He reads her his result...when does his experience collapses to one world? When he reads his results (can't be, since this would have occured when he took the measurements and we are back to nonlocality)? When she hears his results? (but then, he collapses just when she collapses, which is nonlocal).

    My head is spinning...

    And when he is talking to her, he can remember the results he had got when he had taken the measurements, 30 years earlier near Vega. So his brain collapses in a state in which he has those specific memories...

    This is all very strange :-), as strange as the Copenhagen interpretation. Th eproblem is moved to this "experience collapse" and the questions are as difficult as for the Copenhagen interpretation.

    Any comment/opinion?

  11. Mar 15, 2006 #10


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It's the main reason why I like it: the physical picture is clearer that way (I agree that the mental picture is now taking all the burden!).

    I don't see what you mean by "collapse together". You seem to think that there's ONE Alice and ONE Bob, while I think that the right viewpoint is that one should say: let's look on it from AN Alice POV (and that we don't start counting how many there are, and what they all do and so on), or A Bob POV.

    Again, there is no concept of a "world" independent of the related observer's experience. "Worlds" are just the possible alternatives of subjective experiences from an observer's POV. So one cannot say that Bob and Alice are "in the same world". You can only say that in a particular BOB's world, there is an Alice state, with which he did interact, and you can say that in a particular Alice world, there is a certain Bob state with which she did interact, and of which there are now remnants in the relevant bodystate and hence the experience that goes with it.

    Again, there's a difference between Bob's brain (which will be in different states, and correspond to different potential conscious experiences), and then ONE particular conscious Bob experience which will be "linked" to one of these brain states in a probabilistic way. There's no reason why *a particular* Bob experience should be in the same branch as *a particular* Alice experience, but *a particular* Bob experience will be in a branch with a certain Alice BODY state compatible with the memories of the body state of Bob.

    I know that it is conceptually difficult at first to make the difference between the different body states and subjective experiences because we're so used to have them in a 1-1 relationship.

    So let's take it again, in a simple case, from the start. Let's imagine, at a certain point, that Bob's body is in 2 states, and Alice's body is in 3 states, and these are "independent" initially:

    |psi0> = (|bob1> + |bob2>) (|alice1> + |alice2> + |alice3>)

    In this case, if bob interacts (in his two worlds) with alice, and they exchange results (the exchange of results is an interaction which will modify (through unitary evolution) the state of bob and alice), we will obtain:

    |psi1> = |bob1_1>|alice1_1> + |bob1_2>|alice2_1> + |bob1_3>|alice3_1> + |bob2_1> |alice1_2> + ...

    Now, let's look upon this from Bob's POV. In |psi0>, bob's body occurs in 2 bodystates, this means, that there are 2 Bob-worlds. A bob experience will hence be attached to one of these, with probability given by the Born rule. So *if you are a bob experience*, you will have a certain chance to experience the bodystate of bob1 and a certain chance to experience the bodystate of bob2. Let's say, for the sake of argument, that the bob experience we're talking about is in the |bob1> state. In |psi1>, there are 6 Bob-worlds, of which 3 evolved out of the |bob1> state. You can have 2 viewpoints here: or you consider a continuity of the previous bob experience, or we start all over. In the continuity case, we say that the previous bob experience, which experienced "bob1", will now have to choose between "bob1_1", "bob1_2" and "bob1_3" (because these are the states that evolved out of bob1). In the other case, we forget about this previous "bob experience" and we start all over, and a "bob experience" is instantaneous and ephemere. I usually take the first (continuous) viewpoint. So our bob experience was first experiencing |bob1> and is, after the evolution and entanglement of |bob1> into 3 mentally distinguishable states |bob1-1>, |bob1-2> and |bob1-3> forced to jump into one of these, randomly, according to the Born rule. Let's say it jumps into the |bob1-3> state. This means that he has an experience which corresponds to a MEMORY STATE of bob1, and a MEMORY state of having seen and talked to an Alice3 state.

    We can talk about a similar case for Alice. In |psi0>, an Alice experience will have the choice between 3 states, |alice1>, |alice2> and |alice3>. Say that it picks |alice2>. So the particular Alice experience we're dealing with is "living" an |alice2> experience. Next (in the continuity approach), this alice2 state will interact with Bob's body, and there are now 6 Alice worlds, of which there are 2 issued from the |alice2> state, namely |alice2_1> and |alice2_2>. Our Alice experience will now jump into one of these two states, say, |alice2_2>. So it will have an experience corresponding to a memory state of alice in the alice2 state, and alice having met a Bob in the |bob2> state.

    Now of course, in the above scheme, because of the initial product state of the alice and bob states, there are no correlations between alice and bob.

    Let's go to a more sophisticated case, where there is an EPR kind of experiment. If we start out with an entangled 2-particle state and 2 remote, ignorant observers, we have:

    |bob0*>|alice0>(|+>|-> - |->|+>)

    There's only one bob state, namely bob0, so a Bob experience will experience bob0 with certainty. Idem for Alice.

    Bob does his measurement in his corner (and absorps his particle):
    this is a unitary evolution into:

    |alice0> (|bob+>|-> - |bob->|+>)

    This means, now, that a bob experience has to choose between bob+ and bob-. Say that it chooses bob+, we're going to follow that one with an *.
    |alice0> (|bob+*>|-> - |bob->|+>)


    Alice does the same on her side, but under a certain angle (a and b are the cos and sin of the angle):

    (|bob+*>(a|alice-> + b|alice+>) - |bob->(-b|alice-> + a |alice+>)

    Nothing happened to bob*, which is still living his bob+ experience.

    Now, bob travels to alice (or vice versa), and meets her and talks about her results. This talking is an interaction which changes the body state of bob (he now learns about her results) as well as the body state of alice:

    a|bob+/-*>|alice-/+> + b|bob+/+*>|alice+/+> + b|bob-/->|alice-/-> - a |bob-/+>|alice+/->

    This can't be: our experience cannot be in two different states, so our * will have to choose between |bob+/-> and |bob+/+> with a probability given by a^2 and b^2. Say our particular bob experience picks bob+/+:

    a|bob+/->|alice-/+> + b|bob+/+*>|alice+/+> + b|bob-/->|alice-/-> - a |bob-/+>|alice+/->


    So our bob experience is now experiencing a body state which remembers having measured +, and remembers having met an alice in the alice+ state.

    We can do the story from the Alice side:

    |bob0>|alice0$>(|+>|-> - |->|+>)

    A particular Alice experience has no choice: it will experience alice0.

    Bob does his measurement, but this doesn't change anything for our alice experience:

    |alice0$> (|bob+>|-> - |bob->|+>)

    Alice does her measurement:

    (|bob+>(a|alice-> + b|alice+>) - |bob->(-b|alice-> + a |alice+>)
    = |alice-> (a|bob+> + b|bob->) + |alice+> (b|bob+> - a |bob->)

    Alice's experience now has to choose: |alice+> or |alice->. Say it picks |alice->

    |alice-$> (a|bob+> + b|bob->) + |alice+> (b|bob+> - a |bob->)


    next, alice and bob meet, and exchange results. During this interaction, as before, alice and bob's states change, because they learn about the other's result:

    a |alice-/+$>|bob+/-> + b |alice-/-$>|bob-/-> + b |alice+/+>|bob+/+> - a |alice+/->|bob-/+>

    Again, this cannot be, and our alice experience $ will have to choose between |alice-/+> and |alice-/-> with respective probabilities |a|^2 and |b|^2 ; let's say it picks |alice-/->:

    a |alice-/+>|bob+/-> + b |alice-/-$>|bob-/-> + b |alice+/+>|bob+/+> - a |alice+/->|bob-/+>


    Each time that his "current state" evolves in an entangled state of the body with different mental experiences. This, of course, happens only locally to the body of the observer.

    The "world collapse" (which is the choice of a state by a conscious experience) happens, whenever the body state with which the experience was associated, entangles in such a way that it now appears in 2 or more mentally distinguishable bodystates.

    For sure it is strange! However, I wanted to point out that this "strangeness" was already with us since ages, but could be "factored out" as a purely philosophical problem before, and is now at the heart of physics. Shifts from purely philosophical issues into the realm of science have happened before ! (the heavenly motions, life, illness, ...)

    However, the physics became cleaner. We can now take that the mathematical objects we use ARE corresponding to an ontological description of the world (which is forbidden in Copenhagen, and which I find totally irresponsable. How can you take seriously a theory which claims NOT to describe what it is, eh,... describing ?). I find the latter condition of utmost essence in doing physics, namely that we take it that the theory SAYS something about what is nature.
    We are even back to a really traditional scheme: a state space, and a deterministic dynamics on it. No inconsistency between two competing and incompatible state evolutions: "interaction/Schroedinger" versus "measurement/projection". EVERYTHING follows the same dynamics, namely Schroedinger unitary evolution.
    We now shift the mystery of "quantum collapse" to the already mysterious relationship between the physical world and subjective experience. It doesn't "solve" the issue, but - as this relationship was already a profound mystery - it doesn't add much strangeness. The only point now, is that the mystery of the link between subjective experience and physical reality, which was a separate "philosophers' problem", shifted now to the heart of physics. I do not consider that, as such, a bad thing. It makes you think about the relevance of the concept of subjective experience in the view on empirical observation.

    It makes for great science-fiction too :cool:

    EDIT: with this last comment, I mean, one could do (in principle) gedanken experiments in the OPPOSITE direction, namely when different bodystates merge again. Quantum erasure on the scale of the human body, say, in which observers and their environment perfectly *forget* things. Of course this is hopeless in practice.
    As the unitary dynamics is time-reversible, this is possible in principle- and it distinguishes from a Copenhagen view, where such a thing is strictly not possible (as the other states with which to merge are definitively projected out).
    Last edited: Mar 15, 2006
  12. Mar 27, 2006 #11


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi Patrick...

    I haven't had time to fully digest all your (very) interesting posts in this thread (am busy with teaching and moving).
    Just a quick note for now....

    I guess this is one point that I am struggling with...the difference between subjective experiences and body states.

    What I meant by "collapsing together" is that it seemed to me that Bob and Alice must have subjective experiences which agree with each other. If I am Bob and I am conscious of one sets of results ...and I talk to Alice and ask her to describe her measurements, to tell me her results, etc....I am interacting with an Alice which is having some subjective experience, it would seem to me. But this is not the way you describe it. This almost sounds like solipsism (I think that's the correct expresssion).


  13. Mar 27, 2006 #12
    Just a point....the subjective/objective experience thing is certainly an interesting subject, and works alongside the mind/body problem...there's a great article on wikipedia. For all you philosophers, anyways.

  14. Mar 28, 2006 #13


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    WARNING: the following post has highly philosophical content in its first part. This is because of the artificial separation of different matters into "physics" and "philosophy" ; while this is of course an interdisciplinary issue.

    The reference to http://en.wikipedia.org/wiki/Philosophy_of_mind is indeed a very good introduction to the issue and shows that the mind-brain problem is in fact independent of the physical theory that is supposed to rule the world: it stands as well in a classical environment as in a quantum / MWI environment. THIS is the important point to note, because the issue is often raised that MWI needs some weird "consciousness" babble, while the issue is clear in classical physics. Not so: the issue is relevant no matter what physical theory we are addressing. Once one recognizes that the issue exists ALSO in classical physics, it becomes easier to understand the MWI viewpoint. Not that MWI is going to SOLVE the mind-brain problem ; only, that the issue doesn't become much more involved in the MWI setting than it is in the classical setting, once one has understood what's the problem on the classical side. This - I hope - can take away the reluctance to consider the MWI viewpoint. After all, the ONLY objection to the MWI viewpoint - but a strong one, that is - is the "naah, too crazy" reaction, because it seems that the MWI viewpoint needs "crazy considerations concerning the relationship between mind and brain" while this issue is "clear as water in a classical setting". The issue is NOT clear as water in the classical setting. Once one realizes this, one can recognize that the MWI viewpoint is not any MORE crazy than the classical viewpoint - the only difference being that, in a classical setting, this issue is usually of no incidence to the physics involved, while in an MWI setting, it becomes an essential part of it.

    In order to understand MWI, one needs to adopt a certain form of dualism (for instance, Epiphenomenalism: http://en.wikipedia.org/wiki/Epiphenomenalism) because it is necessary to separate the notion of "body" and of "subjective experience", without necessarily having to be quite specific about the exact relationship.

    Let us dig a bit deeper in this, and let us assume for the moment an entirely classical world. Let us suppose that you are "Pat", and as such, you have (of course) a certain subjective mental experience, and a body. Now, let us suppose that I make an exact replica of your body, and paint a blue cross on that new body's left hand, and call it the Pat2 body. If - as we assume - the body "is responsible" for subjective experience, we can assume that the Pat2 body is "lived" by a subjective mental experience which is rather identical to your (Pat) mental experience - but it IS NOT -your- experience. When I show a blue light to the eyes of the Pat body, and a red light to the eyes of the Pat2 body, it is clear that you, Pat, will experience seeing a blue light, and that the red light in the eyes of Pat2 is NOT experienced by you. You will not somehow experience BOTH the red light and the blue light. So it is not because there are "nearly identical bodies" that they correspond to the SAME mental experience. But all this seems so trivial as to be not worth mentioning: after all, Pat2 is ANOTHER MATERIAL BODY, right ? So with it goes another subjective mental experience, right ? But it is not the one you, the Pat from the start, is living subjectively.
    Ok, so are it then the specific atoms in the Pat2 body that generate the Pat2 subjective mental experience ? Let's dig deeper here. Let us now suppose (possible in a classical context) that we replace, one by one, each atom in Pat's body. In fact, this already happens in real life: the atoms of your body you die with are not those you were born with. Does this changing of the atoms in Pat's body change Pat's mental subjective experience ? Is, after the change, Pat's mental experience now associated with the bag of waste that I put outside and which contains its original atoms ? Of course not. Your mental subjective experience is still living the "renewed" Pat body.
    Now, let's go further: let us assume that the atoms I collect from Pat's body, one by one (because they are replaced by others) are not put in a waste bag, but are used to construct the Pat2 body. And let's redo the blue light/red light test. What will you, Pat, experience ? I'd assume you'd still say: still the blue light !
    But now, look at what happened: the original atoms of the Pat body now make up the Pat2 body, while the Pat body is made up of entirely new atoms. Nevertheless, you are still living "the Pat body experience". Indeed, it won't make any difference to you if I put your old atoms in the dustbin, or I construct a new Pat2 body with them: you have been living the Pat body experience all the way.
    So there is a non-trivial association between a physical body, made up of atoms, and the subjective experience you're living. It is even not open to external investigation: from the OUTSIDE, where I only have access to the behavioural aspects of the bodies of Pat and Pat2, I cannot say which one is the "original" one, and which one is a "new copy". Both will have identical souvenirs (encoded in the physical structure of their identical brains), react in the same way to stimuli (= behavioural aspects) etc... But from the subjective inside, which only you, Pat, are living, there's a clear distinction between "your body" and "the copy of your body" or "the wastebag containing your old atoms" - you only being aware of "your body", and what happened to your old atoms doesn't affect this. So there is, as I said, a non-trivial association between your subjective experience "Pat", and the physical world: it is not associated with a particular set of atoms (you are experiencing a body made up of renewed atoms), and it is not associated with a specific organisation of matter independent of its history - you are not aware of your copy's experiences, even though its material structure is very similar. So there is some form of dualism: a non-trivial association between a material structure on one hand, and a subjective experience on the other hand.

    This is the part of dualism required to understand MWI, because the situation is not very different. In our classical example, we had two materially different bodies, in identical physical states, and you, Pat, as a subjective experience, experienced ONE of them. Why exactly you experienced THIS body, and not THAT body, is a difficult question to answer - it is in fact the entire issue ! We saw that the naive answer, because it is *materially different*, is not so obvious, because this experience does not necessarily stay attached to a certain, fixed set of atoms.
    We see that to certain material constructions, called bodies, are associated subjective experiences, and it is the physical state of those material constructions which are responsible for what subjective experience is experienced. So we can say that a subjective experience goes (emerges) from certain MATTER STATES, and not from a fixed set of atoms - but that it is not because there are similar matter states, that this corresponds to one and the same subjective experience. So identical matter states can give rise to INDEPENDENT (though similar) subjective experiences. In no case, you are experiencing the TWO Pat and Pat2 bodies simultaneously.
    The situation in MWI takes this one step further. To the SAME material body, there are now associated DIFFERENT STATES IN SUPERPOSITION. Saying this already implies the choice of a basis, and that's the entire point: we can take it that a subjective experience emerges from certain basis states. There is a basis, of which certain elements give rise to a subjective experience. Now, if two such states are in superposition, then there emerge two subjective experiences from them, which are independent, in the same way as the subjective experience of the Pat body was independent (although almost identical) to the subjective experience of the Pat2 body. And you, Pat, experience ONE of them. Which one ? That's to be specified by a specific rule. In the classical example, there was not a probability 50-50 for you, Pat, to experience the body of Pat, or the body of Pat2, when we were exchanging atoms one by one. You KEPT the experience to Pat's body, even though in the end, the Pat2 body contained all of your original atoms. There was a continuity of subjective experience going from one Pat body state to the next. In MWI, as there is usually ONE subjective-experience-emerging state evolving in a superposition of MANY, there has to be made a choice which one will carry "the original" experience. Well, take it to be the Born rule that does this. Why ? Nobody knows.
    What happens to the other states ? Well, you can postulate that they experience things as Pat2's body experiences things, but this has nothing to do with what YOU experience.

    So the major difference between our classical gedanken experiment, and the MWI situation, is that, in the classical case, a certain state of matter, corresponding to a body, can have ONE subjective experience emerge, while in the MWI situation, a certain state of matter can be in a superposition of which several terms can have a subjective experience emerge. In the classical case, one can take another material system, with an almost identical state, and have it emerge another, independent, but very similar, subjective experience, and in the MWI case, with the quantum state giving rise to one subjective experience can give rise, after evolution into a superposition, to the emergence of another subjective experience, which is independent, but very similar. But in both cases, the original subjective experience is not aware of this new, quasi identical subjective experience because it is ANOTHER one. There is another difference between the classical and the quantum case. In the classical case, INTERACTION between the "original" and the "copy" is possible: the original body can go and see its copy, say hello, and interact with it. In the quantum case, because of decoherence, there is no interaction possible between the "original" state and its "copy" (with which it is in superposition), and as such, you cannot meet your copy and say hello. As such, you've never met it, and you're inclined to think that it doesn't exist. This is the origin of the "naah, too crazy" rebuttal.
  15. Mar 28, 2006 #14


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hi Patrick (I sometimes feel that I am talking to myself:rofl: )

    Thanks for the amazing posts. I deeply appreciate the time you spend writing those clear and thoughtful posts. I am slowly absorbing everything you are writing (between classes and marking lab reports:yuck: ) and will get back to the more philosophical post (very interesting!).

    For now, let me get back to something in a previous post:

    Everything was quite clear to me until the last equation above, when Bob talsk with Alice. I am not sure what "|bob+/->" means, for example.

    Also, but that will probably be clear once I know the answer to the first question, but I don't quite understand why there is |bob+/-*>|alice-/+> and|bob+/+*>|alice+/+> but no |bob+/+>|alice-/->, say.

    I will be able to formulate better questions once I understand this.

    Thanks again!!!

  16. Mar 29, 2006 #15


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    I have that feeling all the time. And then the men in white coats give me some pills to swallow, and I feel better :rofl:

    Sorry, I should have stated that explicitly: the |bob+/-> state is:
    bob's body is in a brain state where he remembers HIS OWN measurement result being "+" and remembers Alice telling him her result was "-". It is the interaction with Alice (her telling him, and him remembering the talk) which altered the state from |bob+> into |bob+/->.

    I guess that's clear now: |bob+/+> |alice-/-> cannot exist because bob cannot have interacted with |alice-> and remember |alice+> (unless he's somehow suffering from Alzheimer, which wasn't taken into account in the picture...)

    Last edited: Mar 29, 2006
  17. Apr 7, 2006 #16


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I think that this is the part that confuses me a bit. Let's say that they both use th esame axis (both measurments are along z, let's say). Then a =1 and b =0 if Bob has measured +. And vice versa if Bob has measured -. But this assignment of probabibilities to Alice's experiences depends on Bob's measurement, which seems to put back in the "spooky action at a distance". So I am clearly missing something. Maybe you are saying that the probabibilities a and b are assigned when Alice and Bob meet?

    Sorry if I am being slow, I really want to understand this.

  18. Apr 8, 2006 #17


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No, not at all. a and b do not depend on the outcomes! If they both measure along the same axis, then a = 1 and b = 0, period.

    The a and b come about because of the way the original "Alice" particle was written. It was written in the z-basis (for instance). But if Alice measures along a u-axis, then we first have to write this |z-> state in the eigenbasis of her measurement, so |z-> = a |u-> + b |u+>. This, because Alice's measurement device will correlate her state with the outcome of |u-> or |u+>, not of |z->. So we simply had to rewrite the |z-> as a function of the |u-> and |u+> states. We are always free to rewrite a state as a combination of other states, this doesn't change anything to the actual state, right ?
    And note that this only happened because we started out with the original state written in components in the z-direction ; if we would have written them in the u direction, things for Alice would have been more straightforward (but then we would have had to change the basis for Bob of course).
    And, of course, this a and b have *nothing to do* with whatever 'outcome' bob might have observed. They are just the re-decomposition of the states in the local basis of the measurement device (the thing that will entangle the observer's state with the microstate).
  19. Apr 9, 2006 #18


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Of course. I do understand that.
    But to make my point more clear, let`s stick with both of them working along the z axis. Here is the source of my confusion.
    Bob could have experienced either + or -. But if he does experience +, then Alice *must* experience -, right?
    Why? where does it come out in the MWI?

    I am *guessing* that you will reply ''well, the singlet state is proportional to (+-) - (-+)'' (sorry, I can't figure out how to get out of the darn French keyboard setting and I can't write kets!).
    And then you will say ''so if Bob experiences +, this leaves the state - for Alice to experience.

    But now, switching to Alice`s point fo view, she could in principle experience either + or - when she makes her measurement. That should not depend on what Bob experiences!

    I guess you will say that you must either stick to seeing things from the point of view of Bob *or* from the pov of Alice and not switch. But then, let's say you are Bob. Do you mean that that it is an irrelevant question to ask what Alice has experienced before Bob talks to her? Not only a question that he does not know the answer to, but a question which is meaningless?

    I am probably not making much sense because I am quite confused, in which case I apologize. I guess that my point is that I am taking the approach that it is sensible to talk about what Bob experiences *and* what Alice experiences at the same time. That if I am there when they meet and ask them what they are experiencing, that it is a sensible question and their experiences are ''real'' as much as my own experience. I also take the point of view that when they tell me what they experience and that they *remember* having experienced this the day before when they did their experiement, that this is also ''real''. That they ''collapsed'' to an experience when they did the measurements, not only when they met to talk about it. But maybe this is not your point of view at all, so before pushing the discussion, I would love to hear your point of view about these issues.
    Last edited: Apr 9, 2006
  20. Apr 10, 2006 #19


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You're hitting the "difficult to accept" part of MWI of course.
    Let's consider the case where the two polarization directions are parallel, which means that after Bob and Alice did their measurements (but didn't talk to eachother yet, and are still at spacelike separated events).
    The state is then:
    |bob+>|alice-> - |bob->|alice+>

    What does this mean ? What has Bob seen, and what has Alice seen ?
    The answer, according to MWI, is the following:
    there are now TWO types of "Bob" experience: one in which there is *A* Bob having seen "+" and one in which *A* Bob has seen "-" ; and there are now also TWO types of "Alice" experience, one in which there is AN Alice which has seen "-" and one in which there is AN Alice which has seen "+".

    So you cannot ask WHAT Bob has seen, because then I ask you: WHICH Bob ? I even hesitate to say that there are TWO Bobs, because that depends on how "finegrained" we're going to look, and there might be a multitude of "very similar" Bobs in each state, and this could even result in a continuum of slightly different bobs for each term ; this depends upon exactly how Bob has decohered with his local environment and so on. What one can say is that there are essentially two distinguishable KINDS of Bob states, one kind in which all the Bobs have seen "+", and another kind in which all the Bobs have seen "-".
    And for Alice, we can do the same. So there is a class of states which is characterized by Bobs who saw "+", which is in a product with a class of states with Alices who saw "-", and there is another class of states which is characterized by Bobs who saw "-" which are in a product state with Alices who saw "+".

    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.
    And from Alice's PoV, exactly the same: for A PARTICULAR ALICE, the rule is similar: the corresponding state will be "drawn" by the Born rule, and with 50% chance, she'll be in the category of Alices that saw "-" and with 50% chance, she'll be in the category of Alices that saw "+".

    Now, of course, if you draw *a particular alice* of the multitude of Alices that's around, and *a particular bob* of the multitude of bobs that are around, chances are few that they will meet !

    Now, in the case of strict alignment with the z-axis for both, the story is not very interesting. The reason is that Alice and Bob, each by doing their measurement, already appear in one or the other branch, and that nothing special happens when they meet ; because the "split according to Alice" is the same as the "split according to Bob".

    It's more interesting when the angle is 45 degrees.
    In that case, the state is (screw normalization :-):

    |bob+> (|alice-> + |alice+>) + |bob-> (|alice-> + |alice+> )

    after each of them have done their measurements, but are still at spacelike separated intervals.

    The same explanation as before holds, but now, of course, even if you pick "a particular bob" and he happens (according to the Born rule) to be, say, bob+, he will not be able to say what his corresponding Alice will have seen, because "his corresponding alice" is, according to him, in a superposition of alice+ and alice-.
    And from Alice's PoV, we can re-write the terms with Alice factored out, and then each alice will have "her corresponding bob" in a superposition of bob+ and bob-. But there's no problem here: bob is at a spacelike interval.

    Now, WHEN they do meet, this is "as if Bob measured Alice's state" and vice versa. This means again, that bob's states will now split, and alices states will now split, and we'll end up with FOUR cases:
    |bob+1>|alice-> + |bob+2>|alice+> + |bob-3>|alice-> + |bob+4>|alice+>
    THIS now means, that *for a particular bob* he can be in a state that is a bob+ state or a bob- state, and so does *a particular alice*.
    With a particular bob goes a corresponding alice.
    So if our particular bob was of the kind of "bob+2", then he'll be with an alice of style alice+. Etc...
    And the probability, for a particular bob, to be in one of the classes "bob+1", or "bob+2" ... is simply given by the Born rule. And idem for "a particular Alice".

  21. Apr 12, 2006 #20


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    It is, but my main difficulty is already there with the two setups in the same orientation! Since you don't see anything interesting in that case, I guess that I haven't made my concerns clear enough :shy:

    You say that they already appear in the same branch. Ok. But when did this happen?Does it happen only when they meet? Or when they do their measurements (which would not make much sense since different observers will agree about the time and even the order in which they made their measurements).

    Let's say that the experience of Bob "collapses" to the observation of a spin up. So we get |Bob +>|->

    On the other side of the galaxy, alice makes a measurement. I am assuming (which may be the flaw in my reasoning) that when she makes her measurement, her experiences collapses to either observing + or -. She makes a measurement and has 50% of experiencing observing one or the other, right? Or wrong? Let's say she observes + also. But then, when she meets Bob, she will always meets a Bob that has experienced +!! And never the other case!!

    I am completely baffled by this. I can only think of 3 solutions. Maybe I am missing completely a fourth solution....


    a) When the experiences of Bob collapses to observing a spin up, it automatically implies that Alice may only observe a spin down. But that is back to standard spooky action at a distance, except that now it is applied to experiences instead of the usual observations in the Copenhagen interpretation.

    Maybe that's what MWI says and that's it. The nonlocality is still there, except that it is applied to experiences instead of observations.
    That would be fine. It is just that I was in the impression that you did not have that type of nonlocality in MWI.
    It's possible that I am confusing apples and oranges here. That your view of MWI eliminate for the collapse of wavefunction "a la Copenhagen" but it still has the spooky action at a distance feature, except that it is now applied to experiences. This is still weird (and it one level of weirdness higher than the basic MWI idea of "collapsing into an experience" because of the spacelike correlation between *experiences*. This sounds even more strange than the usual Copenhagen style EPR correlation! At this point I am just about ready for the white guys to come get me and join you in yoru nice padded room!:tongue2: )

    b) Or, as long as Bob and Alice are not exchanging informations, they still are in both a superposition of experiences of + and -. And only when they meet do there experiences "collapses" in a correlated way. That would take care of nonlocality completely! but it opens up other weird aspects...how do experiences may collapse like this upon being in "contact"...That is one degree of weirdness lower than the previous situation (at least they are spacelike separated), however.

    Here is another way of saying all this.
    Bob makes his measurement, we get
    |Bob+>|-> + |Bob->|+>

    But he may only experience one state so maybe his experiences collapses to observing a spin up.

    Now forget about Bob . Alice makes her measurement:

    |+>|Alice-> + |->|Alice+>

    But she may only experience one possibility, so her experience collapses to....To what? Well, does it depend on what Bob experienced? It should not. But then what prevents her of getting + also?

    c) I guess one might say : the rightway to look at it is to say they both make a measurement and we get

    |Bob+>|Alice-> + |Bob-> |Alice+>

    Fine...but they must experience one result so their experiences collapse...But why do they have to collapse in the same term?!?!?!?!
    Using a * to denote what each experienced, why can't we have:

    |*Bob+>|Alice-> + |Bob-> |*Alice+>

    Maybe you will say "no problem..that may happen... So then I guess we have to talk about things from either Bob's pov or Alice's pov??
    Maybe it's a bit like relativity...one cannot take about "absolute time" so here we can't talk about "absolute experience"??
    That might be...but would be very strange because Bob talks to a Alice who tells him what she did in her lab and so on...she is clearly sentient and everything, but she is not experiencing this meeting at all!

    I am not saying this is impossible, but it would certainly send us in a different discussion!


    Cheers.... I hope the guys in white blouses are giving you nice colored pills these days!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook