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B How do you understand MWI?

  1. Mar 23, 2017 #1
    It seems many people even experts don't understand the basic of MWI. In the double slit.. what is wrong with the statement that "that observer will "split" as well--one version of him for each way the double slit experiment came out.". Peterdonis wrote it. And I included it in a thread as reference. But Nugatory stated whether it is based on a solid premise. And I'm getting confused. The environment doesn't split, only the system, yes? So the observer should "split". No? Other synonyms for "split"?

    How do you use more accurate phrases to describe what happen to the observers in the double slit in MWI?
     
  2. jcsd
  3. Mar 23, 2017 #2

    bhobba

    Staff: Mentor

  4. Mar 23, 2017 #3
    In Q8 in your article. It's written:

    "The cat splits when the device is triggered, irreversibly. The
    investigator splits when they open the box. The alive cat has no idea
    that investigator has split, any more than it is aware that there is a
    dead cat in the neighbouring split-off world. The investigator can
    deduce, after the event, by examining the cyanide mechanism, or the
    cat's memory, that the cat split prior to opening the box."

    Why is this not a red herring and why is the double slit a red herring?
     
  5. Mar 23, 2017 #4

    PeterDonis

    Staff: Mentor

    The problem with the thread that got closed wasn't your statement (referring to mine) about "splitting". It was your statement that "MWI assumes the brain is classical". It doesn't.

    Nor is it really correct to view the different "worlds" that get split off in the MWI as classical. The MWI is an interpretation of quantum mechanics, not classical mechanics. It assumes that everything is quantum, including you and me.

    No. See below.

    You don't. You use math.

    The double slit is a bad example to use because there are not two distinct "results" of the experiment when it is run the same way multiple times. To change the result you have to change the experimental setup (close one of the slits, put measuring devices at the slits, etc.). That's not what the MWI is talking about.

    A better example is a measurement of the spin of a spin-1/2 particle about a fixed axis. Such a measurement, when run the same way multiple times, will yield one of two results each time, which we can call "up" and "down" and denote by the symbols ##+## and ##-##. For each run, the measuring device starts out in a state we can call "ready" and denote by the symbol ##R##, and ends up in either the "measured spin up" state or the "measured spin down" state, which we can denote by the symbols ##U## and ##D##. Mathematically, we write this evolution of states during the measurement as follows:

    $$
    \vert \Psi \rangle \vert R \rangle = \left( a \vert + \rangle + b \vert - \rangle \right) \vert R \rangle \rightarrow \vert \Psi' \rangle = a \vert + \rangle \vert U \rangle + b \vert - \rangle \vert D \rangle
    $$

    Here ##a## and ##b## are complex numbers that satisfy ##\vert a \vert^2 + \vert b \vert^2 = 1##.

    The best ordinary language term to describe the above evolution is not "splitting" but "entanglement": the state of the measuring device gets entangled with the state of the measured system. The term "splitting" comes from focusing on the fact that the measuring device starts out in the state ##R##, but ends up in a superposition of states (more precisely, as factors in two terms of a superposition: the measuring device in the entangled state after the measurement does not have a state that is separable from the state of the measured system). But that is focusing on just a piece of the wave function instead of the whole wave function. And notice that the other piece, the state of the measured system, does not change at all; there are ##+## and ##-## terms in ##\Psi## and there are ##+## and ##-## terms in ##\Psi'##, with the same coefficients.

    Also, the above evolution applies just as well if the "measuring device" is an observer like you or me: it just says that our state becomes entangled with the state of the measured system, so the states ##U## and ##D## are something like "I observed the spin to be up" and "I observed the spin to be down". So we ourselves, if we take the QM math at face value, end up in states that are not separable from the states of the things we observe.

    The two main types of QM interpretations are identical up to this point; where they differ is in what happens next. In no collapse interpretations like the MWI, nothing happens next; the wave function ##\Psi'## just keeps on undergoing unitary evolution, just as the process that goes from ##\Psi## to ##\Psi'## is unitary evolution. In collapse interpretations like Copenhagen, the state "collapses" from ##\Psi'## to one of the two terms in it; the probability of collapsing to each term is given by the squared modulus of its coefficient (##a## or ##b##).
     
  6. Mar 24, 2017 #5

    bhobba

    Staff: Mentor

    That's exactly what I meant - in discussing MW it's not a good example.

    Thanks
    Bill
     
  7. Mar 24, 2017 #6
    I mentioned the brain was classical because I thought each world of MWI was collapsed. When you see airplanes and roads.. they definitely looked collapsed. But in Everett times. there was not any concept of Decoherence. So did Everett think each world/branch of MWI is collapsed or not? Even now. Decoherence concept says each world of MWI forms because of decoherence. But within a world/branch.. it's also sustained by internal decoherence (our automobile is not in two places at once because the environment measures each atoms of the automobile putting it in classical state) and so each world/branch is not really collapsed? Did Everett think of this originally? Or did he think automobile are collapsed because each world/branch is collapsed? But in Everett times, where concept of decoherence didn't exist. How could he think of world as not collapsed and how was it sustained (if not by decoherence processes inside each world/branch)?

    Thanks for all below. I understood what you meant how spin was better example of two distinct results than double slit. 5 stars.
     
    Last edited: Mar 24, 2017
  8. Mar 24, 2017 #7
    Once the particle gets detected at position x_i on the screen (I'm keeping it discrete for convenience and because ultimately the screen is made of atoms anyway), there is some kind of signal that is the detected by the observer. Result: you get states of the form |particle detected at x_i>|observer saw light coming from position x_i>, so MWI does assert that the worlds do split, once for each detection event. So I don't think this example is misleading, or a "bad question", or anything like that.
     
  9. Mar 24, 2017 #8

    PeterDonis

    Staff: Mentor

    There is no collapse in the MWI. So evidently you were thinking of the MWI wrong.

    They look the way they look, according to the MWI, because your state is entangled with their states. No collapse required.

    No. Decoherence explains why each "world" (branch of the wave function) remains self-consistent. It is not needed to explain how each branch forms: that's just simple unitary evolution.

    This is ok except for the last part: "putting in classical state". You should banish the word "classical" and anything connected with it from your thinking if you are trying to use the MWI. You should also banish the word "collapse", and banish the idea that decoherence has anything to do with collapse. It doesn't.
     
  10. Mar 24, 2017 #9
    In your spin example. You mean even if we don't observe it (and entangling with it) or there is no measuring device.. the spin up and spin down still form a branch?

    Does the Universal Wave Function has information on everything in the universe like the Higgs vacuum expectation values and all constant of nature? Or is the Universal Wave function just ignorant of them and separate from these information?

     
  11. Mar 24, 2017 #10

    PeterDonis

    Staff: Mentor

    No.

    The Higgs VEV is a property of quantum field interactions, so the wave function would include information about it. A constant like the fine structure constant--the coupling constant for electromagnetic interactions--isn't really a property of the wave function, it's a property of the Lagrangian.
     
  12. Mar 24, 2017 #11
    But you just mentioned that "No. Decoherence explains why each "world" (branch of the wave function) remains self-consistent. It is not needed to explain how each branch forms: that's just simple unitary evolution."

    You said decoherence not needed to explain how each branch forms. So I thought the branch already there even without decoherence. So you are saying that indeed decoherence is really needed to explain how each branch forms? What you mean "self-consistent". Please clarify your statements. Thank you.

     
  13. Mar 24, 2017 #12

    Nugatory

    User Avatar

    Staff: Mentor

    Not at all.... There is no collapse in MWI, and that is its biggest selling point.
     
  14. Mar 24, 2017 #13

    PeterDonis

    Staff: Mentor

    Yes, but that just means branches form some other way. That other way is by entanglement via interactions and unitary evolution. When you have two subsystems that interact, unitary evolution entangles them. I showed how in post #4.
     
  15. Mar 24, 2017 #14
    Above you emphasized that even without measuring device or observer that entangled with the measured system, there is still + and - or spin up and spin down in the superposition, why can't these spin up or spin down be called world/branches?

     
  16. Mar 25, 2017 #15

    PeterDonis

    Staff: Mentor

    It's only a superposition because of the basis we picked. But without an actual measurement in that basis--i.e., without an interaction that entangles the system's state with that of a measuring device--there is no physical reason to choose that basis over any other. That basis is only picked out because of the measurement that gets made. So without a measurement being made, we can't say whether the state is a superposition or not.

    Because in the absence of a measurement, there is no entanglement of the system's state with the state of a measuring device. It's the entanglement that creates "branching", to the extent that term is applicable at all. See my post #4.
     
  17. Mar 25, 2017 #16
    There is no word "basis" in your post #4. How do you use the example of spin + and - in this superposition and basis connection? Or how do you insert this basis business in your post#4? You are incredible helpful, thanks a lot!

     
  18. Mar 25, 2017 #17

    PeterDonis

    Staff: Mentor

    A basis is any set of mutually orthogonal vectors that span the space of all possible states of the system. In the case of spin for a spin-1/2 particle, the "up" and "down" states for any axis form a basis. So the states I called ##+## and ##-## in post #4 are a basis. But the only thing that picks out that particular basis is our choice of a particular axis about which to measure the spin; and that only has physical meaning if we actually make the measurement.
     
  19. Mar 25, 2017 #18
    Oh, going back to your "It's only a superposition because of the basis we picked". Can you give an example of basis we picked that won't make it a superposition?
     
  20. Mar 25, 2017 #19

    PeterDonis

    Staff: Mentor

    Sure, just pick the basis in which the state ##a \vert + \rangle + b \vert - \rangle##, which is the state that the system starts out in in post #4, is one of the basis states. The other basis state will then be ##b \vert + \rangle - a \vert - \rangle##. It's easy to show that these two states are orthogonal, just as the ##+## and ##-## states are orthogonal.
     
  21. Mar 25, 2017 #20
    I wrote earlier: "You said decoherence not needed to explain how each branch forms. So I thought the branch already there even without decoherence."

    So Decoherence is not in Unitary Evolution and not having "entanglement via interactions"? Because you said branches could form some other way. But Decoherence is entanglement of environment and subsystem so why can't it is referred as "entanglement via interactions"? And Decoherence is entanglement of environment and subsystem which is not dissimilar to two subsystems so like you mentioned above.. "unitary evolution entangles" them. So decoherence also obeys unitary evolution and it is intanglement via interactions. Yet you seemed to state Decoherence is neither of the two. Please clarify your statements. I greatly appreciated all the amount of help.
     
  22. Mar 25, 2017 #21

    PeterDonis

    Staff: Mentor

    No.

    No.

    This issue is really not a "B" level issue. You really need to spend some time working through a recent QM textbook. But even in this thread, in my post #4, which I have now referred to repeatedly, I explained how unitary evolution + entangement via interactions forms branches. There is no decoherence anywhere in that post. So decoherence is not required to form branches.

    Heuristically, decoherence comes in when we ask what happens next to the state we ended up with in post #4. For example, what prevents us from simply applying the reverse interaction to the one I described in post #4? Unitary evolution is always reversible, so such an interaction must exist. And that interaction would "undo" the entanglement that formed due to measurement (just reverse the arrow I gave in post #4).

    If we are dealing only with microscopic quantum systems and devices, like electrons and photons and beam splitters and so forth, we can actually do this in some cases. But in most real cases, we can't. Why not? Because the state we ended up with in post #4 interacts with the environment, which contains huge numbers of degrees of freedom that we can't keep individual track of. And because we can't keep individual track of all the environment degrees of freedom, we can't reverse the interaction any more, because it would not just be a matter of reversing the microscopic interaction I described in post #4, but of reversing all of the huge numbers of interactions (and entanglements) that take place between the system and the measuring device and the environment. And that process--the process of interactions becoming effectively irreversible due to interactions and entangments with a huge number of degrees of freedom in the environment--is decoherence.

    Note, btw, that the "environment" here can actually be part of what, in ordinary language, we would consider to be the measuring device. For example, in many photon experiments we use a device called a photomultiplier to detect photons at the end of an experiment. From the standpoint of post #4 and the above, the photomultiplier is an "environment": by the time you observe an output from the photomultiplier, the photon that was detected has already interacted with and been entangled with a huge number of degrees of freedom, i.e., with an "environment" in the sense I was using the term above. The "environment" in this case is all of the atoms inside the photomultiplier, the electrons inside the circuit that amplifies the photon detection, etc. The "measuring device" in the sense of post #4, the thing whose state goes from ##R## to ##U## or ##D##, is more like the first atom inside the photomultiplier that interacts with the photon, and whose state gets entangled with it. But it is only a very small fraction of a second before that atom's interaction with the photon has cascaded into a huge number of interactions inside the photomultiplier, so that the overall interaction is irreversible and decoherence has occurred.
     
  23. Mar 25, 2017 #22
    Decoherence is necessary, together with locality, for solving the basis selection problem, which is crucial to "branching".
     
  24. Mar 25, 2017 #23
    I asked "Can you give an example of basis we picked that won't make it a superposition?
    You answered:

    Can you give an example of basis we picked that WILL make it a superposition? This is just to make your statements complete and make sure I understood it right. Thanks.

    And oh, how come a measuring device can't entangled with both spin up and spin down at same time? so if the states
    ##U## = "I observed the spin to be up"
    ##D## = "I observed the spin to be down".

    why is "I observed the spin to be up and down" forbidden?
     
  25. Mar 25, 2017 #24

    PeterDonis

    Staff: Mentor

    The basis I originally wrote the state down in, where ##+## and ##-## are the basis states.

    Because of the physical nature of the device. More precisely, the name "spin measuring device" is a label we put on a device whose physical nature we have determined, by experiments, to be such that it always gives "up" or "down" as a result, never both. We have not found any physical device that gives a result "both up and down". And our current understanding of QM says that no such device should be possible.

    Mathematically, the operation of a measuring device is modeled as a Hermitian operator that describes the device. Applying that operator to the initial state, before the measurement, is how you mathematically compute the state after the measurement; that's how you would derive the time evolution I gave in post #4. There is no Hermitian operator that gives a time evolution where "I observed the spin to be both up and down" is a possible result.
     
  26. Mar 25, 2017 #25
    Thanks for the clarifications. Let's say the spin up and down is exposed to the environmental heat bath (or decoherence) so a photon is entangled to spin up, another photon is entangled to spin down.. and another one to spin up and down and so on. If we view the system, would we see spin up or spin down?
     
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