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

B Many Worlds Interpretations and probabilities

  1. Mar 15, 2017 #1
    This probably has been asked before but I didn't find it. As I understand it with the Many Worlds Interpretation of quantum mechanics, a different "world" exists for each outcome. I have read about the an issue regarding probability outcomes within a world but cannot remember the answer. The issue was roughly that if there were ten outcomes numbered 1 - 10 and they followed a normal distribution for example (analogous to measured quantum positions), the MWI would suggest a "world" for each outcome. But how does it explain that we tend to find ourselves in the worlds in which the outcome had the higher probability (as opposed to all 10 worlds being equally likely)? I can see that an answer can be given that all worlds have equal probability but some outcomes have more worlds, but is that the answer?
     
  2. jcsd
  3. Mar 15, 2017 #2

    DaveC426913

    User Avatar
    Gold Member

    Name a circumstance where an outcome has a higher probability.

    A coin lands on its face? Sure, there are only a few worlds where the geometry of the toss results in it landing on its edge. There are many worlds where the geometry results in it landing on its face.
     
  4. Mar 15, 2017 #3
    I had mentioned that the example I had given was analogous to measuring quantum positions, because I had thought that that the probability of finding a particle in a position varied depending on the position, and that the Schrodinger Equation gave the probability distribution. I have checked and found the Schrodinger Equation is thought (by many) to be a probability distribution. http://www.physlink.com/education/askexperts/ae329.cfm states regarding the Schrodinger Equation: "The associated wavefunction gives the probability of finding the particle at a certain position."
     
  5. Mar 15, 2017 #4
    The contradiction between quantum state being reality and the definition of probability is the biggest turn off of many world interpretation for me too. :frown:
    I think that we can speculate that the answer lies in metaphysics. The universe with low quantum probability may simply cannot be considered real, that is if you think information is the basis of reality and consciousness. When amplitude exist in all possibility, the low amplitude possibilities would contribute no information from the perspective of the multiverse. Just like when you draw with a pencil on a paper, you can paint the whole canvas grey first then draw something in black, then the grey part would be ignored by the viewer.
     
  6. Mar 16, 2017 #5

    Demystifier

    User Avatar
    Science Advisor

    No. The origin of probability (Born rule) is one of the main problems of MWI that still does not have a satisfying solution. See e.g.
    https://arxiv.org/abs/0808.2415
     
  7. Mar 19, 2017 #6

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    MW is entirely deterministic - but the question is - what world will you experience. There is no way of telling - you must resort to the probability of what world would some observer experience if you randomly picked one. There is a discipline called decision theory to handle things like that. Low and behold, applying it to MW you get the Born rule. Its somewhat controversial and you can google the objections to it.

    I personally have a slightly different take. Due to the nature of the MW interpretation what world an observer experiences has this property called non-contextuality - its actually a theorem you can prove. It in an appendix of Wallace's book on the subject:
    https://www.amazon.com/Emergent-Multiverse-Quantum-according-Interpretation/dp/0198707541

    Now there is the theroem called Gleasons theroem that providing you have non-conntextuality Born's rule follows:
    https://en.wikipedia.org/wiki/Gleason's_theorem

    Thanks
    Bill
     
    Last edited by a moderator: May 8, 2017
  8. Mar 20, 2017 #7
    Would it be possible to take one of those, and explain in a bit more depth how it gets around the problem that I outlined please? It was not so much what probability is given to each world, but an explanation of why one version of the world would be more probable than another when there is one version of the person in each for example.
     
    Last edited by a moderator: May 8, 2017
  9. Mar 20, 2017 #8

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Ok let's assume all possibilities of an observation are equally likely. You have a state and an observation that lights up a red or green light depending on the output of the observation. You would think its 50/50. Lets assume it is. You then take one of those outcomes (the red one) and observe it to get two other outcomes and light up red or yellow. Again you would think its 50/50. Now lets form an observation as follows. If red you do the other observation and get red or yellow. They are all in boxes so you cant see their internals. This observation has three outputs red, green and yellow. So you would think its 1/3, 1/3, 1/3 - but its really 1/2, 1/4, 1/4. They are all legit observations but you get inconsistent answers

    Wallace's book examines this and other intuitive assumptions. They all fail. The only one that works, and there is a theroem that proves it, is the Born rule.

    Thanks
    Bill.
     
  10. Mar 20, 2017 #9
    Hi, I didn't see anything inconsistent there. You just did 2 observations of 2 phases. In neither phase were all three lights lighting of equal probability. In the first phase, the probability of yellow was 0 as only the red or green lit up, and they were both 50/50. In the second phase the probability of green was 0, as only the red or yellow lit up. So there was a 0.5 prob of a green light in the first phase in which case the experiment stops, and if it was red it went on to the second phase, and in that it was 0.5 for red, or 0.5 for yellow so 0.5 (1st phase) * 0.5 (2nd phase) for red, and 0.5 (1st phase) * 0.5 (2nd phase) for yellow. I wouldn't expect 1/3 for each because it wasn't one observation of one of three outcomes of equally likely possibility. So I am not sure how this helps. Why should MWI be thought of as analogous to different phases etc., rather than as one observation of the lights where all are possible?

    To put it clearer, if the scenario is analogous to having 3 boxes one with a red cube inside, another with a yellow cube inside, and another with a green cube inside, why is the probability of choosing a particular cube not 1 in 3, or, why is the scenario not analogous?
     
    Last edited: Mar 20, 2017
  11. Mar 20, 2017 #10

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    Its two connected observations forming a single one. QM makes no difference between observations that can be broken down into simpler ones. Its a theory about any observation.

    Lets go through it again.

    Imagine observations in a box with lights. If you have two lights a red and a green its 1/2, 1/2. Ok I make another box with 3 lights, green, yellow and red. Inside the box you have the red green device and it lights up the red light if whatever triggers that occurs. But instead of lighting the green light it activates the observation that lights yellow and green with 50/50. Now we have a box that does an observation with 3 outcomes red, yellow, green. According to the naive view if someone gave you the box and you didn't look inside you would say each would light with 1/3 probability. But it doesn't - it lights with 1/2, 1/4, 1/4. They are both valid observations - it makes no difference if they can be broken down into simpler ones - QM makes no such distinction. It leads to a contradiction.

    I cant explain it better than that so if you want to go further you will need someone else to help, or get Walllace's book, maybe the way he explains it will help you better.

    Thanks
    Bill
     
  12. Mar 20, 2017 #11
    Ok, so there weren't two observations, there was one observation of lights that didn't have the same probability of lighting up. Sure if you thought they all had the same probability then you would think that the probability would be 1/3 for each but it isn't, because they don't. But declaring that the probabilities aren't equal for each world doesn't seem to me to be an explanation. As I understand it we know from experimentation that the probabilities for the outcomes aren't equal, the issue is how is that explained from an MWI perspective (the problem being that it appears that they would be equal from an MWI perspective). To simply state that the probabilities aren't equal in the MWI perspective doesn't seem like an answer as to how the inequality is explained.

    So for example regarding my previous question: If the scenario is analogous to having 3 boxes one with a red cube inside, another with a yellow cube inside, and another with a green cube inside, why is the probability of choosing a particular cube not 1 in 3, or, why is the scenario not analogous?

    Do you understand why the three boxes analogy is not analogous to Wallace's conception of MWI? The box is supposed to be analogous to a world and the cube colour analogous to the outcome the world contains.
     
    Last edited: Mar 20, 2017
  13. Mar 20, 2017 #12

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    I didn't declare them not equal, I proved it led to a contradiction.

    If you can't see it :frown::frown::frown::frown::frown::frown::frown::frown::frown:.

    I can't explain it any better

    Because what the boxes contain is not determined by an observation, my lights example is.

    Thanks
    Bill
     
    Last edited: Mar 20, 2017
  14. Mar 20, 2017 #13
    There was no contradiction and the probabilities for each light weren't equal in what you wrote. Lights could easily be wired up to come on as you suggested, there was no contradiction. And wired up like that the probability for each light coming on is not the same. Perhaps you are suggesting the wiring itself is supposed to be analogous to something in the model. And are just pointing out, that so wired, there is no probability bias at any junction in the wiring. But in that case, you haven't mentioned what the wiring is supposed to be analogous to in the model. Did you think it would be analogous to something, such that it formed part of an explanation that I should have been able to follow? The reason I ask is that if not, you just end up with three lights that have different probabilities of coming on (there being nothing in Wallace's MWI model analogous to the wiring without any probability bias at each junction).
     
  15. Mar 20, 2017 #14

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    I proved there was a contradiction in the idea of equal probabilities - why you cant see it is beyond me. What wireing did I talk about? You are confusing yourself about something trivially simple.

    Someone else will need yo help you I can't.

    Thanks
    Bill
     
  16. Mar 20, 2017 #15
    Well it could perhaps help if you could answer the question I gave. As I mentioned the lights could easily be wired up like that, and in the circuit at each "decision point" there would be equal probability of each outcome. That is simple to understand. But are you suggesting that such wiring would be analogous to anything in the Wallace MWI model? That is a simple "yes" or "no" answer. If "yes" then could you mention what you think it is analogous to, if "no" then what part contains the equal probability (as that is in the wiring at the "decision points")? If you cannot understand what I am asking could you perhaps mention it?
     
    Last edited: Mar 20, 2017
  17. Mar 20, 2017 #16

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    I mentioned nothing about wiring.

    Look I have a box. You feed in something to be observed and you get some outputs. That's what happens in MW with the lights representing worlds.

    Now I have one box with two lights ie worlds. I feed something to be observed into it and because it has two outcomes according to your view each light will come on 50/50. But assuming that its easy to make a box, containing boxes with two outputs in such a way it has 3 outputs where two of the outputs are triggered by one of the outputs of the first two output box. You feed something into it and it gives 3 outputs, each output would according to you would be 1/3. However its not 1/3 - its 1/2. 1/4, 1/4. Ergo you idea of equal probabilities leads to a contradiction.

    Thanks
    Bill
     
  18. Mar 20, 2017 #17
    Ok, it seems as though you weren't following what I was stating, so I'll go through it again, following pretty much your description so there should be no misunderstanding.

    So you have a box which takes 1 input and has 2 outputs, each output lights up a light which is analogous to a world. An input triggers one of the outputs and each output has equal probability to it. That seems simple enough.

    Then there is a box (I'll refer to it as the MainBox) with 1 input and 3 outputs (a red, yellow or green light, presumably representing three worlds). Inside that box are two more boxes, which I'll refer to as Box1 and Box2. Each of which is a box which takes 1 input and has 2 outputs (which I'll refer to as Out1 and Out2). The input from MainBox becomes the input to Box1 which triggers an output of either Box1.Out1 or Box1.Out2, both having equal probability. If the output is Box1.Out1 that feeds to the MainBox green light (which lights up). If the output is Box1.Out2 then that becomes the input to Box2 which triggers either Box2.Out1 or Box2.Out2. Both outputs have equal probability. If Box2.Out1 then that feeds to the MainBox yellow light, and if Box2.Out2 then that feeds to the MainBox red light.

    That seems simple enough and if you think I have misunderstood up to this point please let me know.

    If you feel that I have so far been able to follow it, then to help you understand my earlier posts, I had referred to the internal workings of MainBox as the "wiring" and a box within it as a "junction" or "decision point". That is just a labelling issue though, and while I have mentioned it to help you if you look back, I will use the terms MainBox, MainBox internals, Box1, Box2 etc.

    So the Box1 outputs have the same probability and the Box2 outputs have the same probability. I had understood this before as illustrated when I wrote there "is no probability bias at any junction in the wiring" and when I wrote 'at each "decision point" there would be equal probability of each outcome'.

    The outputs of MainBox do not have the same probability (if they did the probability would be 1/3 for each). Which is what I meant when I wrote things like "the probabilities for each light weren't equal."

    There seems to me to be no contradiction in the outputs of Box1 and Box2 having equal probability but not the outputs of MainBox (the inequality of the probability of the outputs of the MainBox can be explained in terms its internal connections).

    So to try to translate my earlier question to you: Are the internals of MainBox supposed to be analogous to anything in the Wallace MWI model? If "yes" then could you mention what you think it is analogous to, if "no" then what part (in the Wallace MWI Model) contains the equal probability (as in the analogy the equal probability was contained in Box1 and Box2 which were part of the internals of MainBox)?

    If you still cannot understand what I am asking could you please mention it?
     
    Last edited: Mar 20, 2017
  19. Mar 20, 2017 #18

    DaveC426913

    User Avatar
    Gold Member

    Why don't we go with the simpler example of a coin toss?

    For simplicity, imagine a universe where coin tosses are quantized; say there are only 360 initial configurations of the coin when it is tossed.

    Each possible initial configuration leads to a new world.
    In 178 of them, the coin has landed face up (because there are that many initial configs of coin/hand/toss/bounce that will result in a coin landing face up).
    In 178 of them, the coin has landed tails up (because there are that many initial configs of coin/hand/toss/bounce that will result in a coin landing tails up).

    But there are 4 initial configs of coin/hand/toss/bounce that will result in the coin landing on its edge.

    So, of 360 worlds created, 4 of them have the coin landing on its edge.


    (178 and 4 are arbitrary numbers, but not unreasonable. A coin is very unlikely to land on its edge.)
     
    Last edited: Mar 20, 2017
  20. Mar 20, 2017 #19
    As I wrote in the original post:

    You seem to be going for that option. Apart from the accusation that it is an ad hoc suggestion to get around the implied probability not matching the experimental probability issue, I'm not sure of the problem with it, which is why I was wondering if it was the answer MWI believers went with.
     
  21. Mar 20, 2017 #20

    bhobba

    User Avatar
    Science Advisor
    Gold Member

    If I handed you a box with three lights representing three worlds your idea of equal probability would be whatever observation is going on inside the box would give 1/3, 1/3, 1/3. That is you exact question - why are they not equal. Your hypothesis is they are equal. Now I have described a situation, based on your idea of them being equal, which they must be in the case of two outputs under your idea, where it is not equal. That by definition is a contradiction.

    Lets get more concrete. Imagine a beam splitter - a photon goes in and either come out on side of the other. This is an observation. Under your idea it must be 50/50. Ok we set up a different observation - and again it is one observation - the photon that comes out the right side goes into another beam splitter - again its 50/50 under your idea. We put them in a box with 3 outputs depending on which side it came out of the splitters. This again is an observation but this time with 3 outputs. Under your idea it would be 1/3, 1/3,1/3. But you find its 1/2, 1/4, 1/4. Contradiction - so this idea of equal probabilities can't be right. We have an observation under one view that is 1/3, 1/3, 1/3 but is really 1/2, 1/4, 1/4. By the definition of contradiction the hypothesis of equal probabilities for each world after an observation is wrong. The key thing that makes it wrong is in either case in QM its described by one observation - we have one observable - it makes no difference whats going on inside the box, the hypothesis of QM is the outputs of an observation is described by a single observable. That's the fallacy of the equal probability argument.

    Thanks
    Bill
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted