Many Worlds Interpretations and probabilities

[name123]

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?

 

[DaveC426913]

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.

 

[name123]

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.

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."

 

[Xu Shuang]

The contradiction between quantum state being reality and the definition of probability is the biggest turn off of many world interpretation for me too.
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.

 

[Demystifier]

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?

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

 

[bhobba]

I have read about the an issue regarding probability outcomes within a world but cannot remember the answer.

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/dp/0198707541/?tag=pfamazon01-20

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

 

[name123]

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/dp/0198707541/?tag=pfamazon01-20

Now there is the theroem callled Gleasons theroem that providing you have non-conntextuality Borns rule folllows:
https://en.wikipedia.org/wiki/Gleason's_theorem

Thanks
Bill

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.

 

[bhobba]

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. Let's 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 let's form an observation as follows. If red you do the other observation and get red or yellow. They are all in boxes so you can't 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.

 

[name123]

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. Let's 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 let's form an observation as follows. If red you do the other observation and get red or yellow. They are all in boxes so you can't 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.

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?

 

[bhobba]

You just did 2 observations of 2 phases.

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 can't 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

 

[name123]

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 can't 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

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.

 

[bhobba]

But declaring that the probabilities aren't equal for each world doesn't seem to me to be an explanation

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

If you can't see it .

I can't explain it any better

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.

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

Thanks
Bill

 

[name123]

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

If you can see it .

II cat explain it any better

Thanks
Bill

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).

 

[bhobba]

There was no contradiction and the probabilities for each light weren't equal in what you wrote.

I proved there was a contradiction in the idea of equal probabilities - why you can't 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

 

[name123]

I proved there was a contradiction in the idea of equal probabilities - why you can't see it is beyond me.

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

Thanks
Bill

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?

 

[bhobba]

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,

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

 

[name123]

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

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?

 

[DaveC426913]

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.)

 

[name123]

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.)

As I wrote in the original post:

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?

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.

 

[bhobba]

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).

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 what's 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

 

[name123]

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 what's 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

I do not know what you mean by "under your idea". I am not supposing with either example you gave that each output of the 3-output box you gave would have a probability of 1/3. They wouldn't in either example you gave, that is obvious. Nor do I think MWI would have a problem in explaining the results either. To make it clear there is no problem with your "in the box" examples. With the splitter there is one event where there is one world A in which the output went one way in the first splitter and the light went on or whatever, and another world B in which it went the other way to another splitter. Then in world B there is other splitter event where it split one way or another. So 2 events (one at each splitter). You could, with the MWI do a tree diagram, and would have no problem in explaining the different probabilities. So just to be clear, as far as I know no one is suggesting that any MWI has a problem matching the probability outcome in the type of examples you gave, and as far as I know no one would be expecting the outputs of the 3-output box to be 1/3 in those situations.

The issue that I was bringing up is with a single event which has numerous outcomes which have different probabilities. This is a key point you seem not to have got. Your explanation is done by adding extra events, and I have repeatedly asked you whether those extra events are supposed to be analogous to anything in the MWI hypothesis. https://www.physicsforums.com/threa...ations-and-probabilities.907796/#post-5721393 . Each time though, you ignore the question and don't give a yes or no answer. So let me give you a made up example of a response: You could answer that "yes" those extra events do have an analogy in the theory, the theory posits that there are some hidden events which we don't observe, and each leads to a tree diagram type split of the worlds and that is how the theory explains the different probabilities of the outcomes in an event which could have been thought of as a single event. But if you aren't claiming that those extra events are analogous to anything in the MW interpretation that you are trying to explain, then you cannot use them as part of an explanation, because they aren't analogous to anything within the theory (and if that was the case, try explaining without adding extra events).

 

[bhobba]

The issue that I was bringing up is with a single event which has numerous outcomes which have different probabilities

There is no such thing as a 'multiple' event observation like you are thinking of in QM.

That is the key point you are missing.

The box I describe with 3 outputs is a single event described by one observable in QM, even though inside the box is two things going on. This is one of the key ideas about QM.

QM is a theory about observations. An observation is the following - you send something to be observed into some apparatus that observes it. And you get something out. Whats going on inside the apparatus that observes it is irrelevant - its described by a single observable. Ok let's consider the right left photon set up. Call one side it comes out 1 the other 2. A photon goes in and you get 1 or 2 flash on a readout. Under the equal probability idea its 50/50. That is an example of 'a single event which has numerous outcomes'. Assume it is 50/50. Your whole issue is why are there different probabilities. Its a standard method of proving something to show otherwise leads to a contradiction. That is what I am doing.

Now we have two prisms with the right output going to another prism so you have 3 possibilities on a digital readout 1, 2,3. This is a single observational apparatus. QM does not worry what's going on inside - it could consist of a billion sub events or one or in this case two (it is actually billions because what's going on inside the prism is very complicated but that is by the by) - it matters not. QM describes it in exactly the same way. The observational apparatus is a black box - how it goes about its job of observing QM is silent on - it's irrelevant to QM. Now we apply the idea its equal probabilities but we find it isn't. Contradiction. I have proved, by the method of contradiction, a standard method of logic, the idea the outputs are always of equal probability is wrong - its contradictory. You must get cases where the probabilities are different.

I repeat the key point you are missing - what goes on inside the observing apparatus is irrelevant to QM - its a black box.

The fact the 1, 2, 3 occurs in different worlds is irrelevant - the same argument would apply to any interpretation of QM.

If you don't get it now I give up - someone else has to explain it.

Thanks
Bill

 

[name123]

There is no such thing as a 'multiple' event observation like you are thinking of in QM.

That is the key point you are missing.

The box I describe with 3 outputs is a single event described by one observable in QM, even though inside the box is two things going on. This is one of the key ideas about QM.

QM is a theory about observations. An observation is the following - you send something to be observed into some apparatus that observes it. And you get something out. Whats going on inside the apparatus that observes it is irrelevant - its described by a single observable. Ok let's consider the right left photon set up. Call one side it comes out 1 the other 2. A photon goes in and you get 1 or 2 flash on a readout. Under the equal probability idea its 50/50. That is an example of 'a single event which has numerous outcomes'. Assume it is 50/50. Your whole issue is why are there different probabilities. Its a standard method of proving something to show otherwise leads to a contradiction. That is what I am doing.

Now we have two prisms with the right output going to another prism so you have 3 possibilities on a digital readout 1, 2,3. This is a single observational apparatus. QM does not worry what's going on inside - it could consist of a billion sub events or one or in this case two (it is actually billions because what's going on inside the prism is very complicated but that is by the by) - it matters not. QM describes it in exactly the same way. The observational apparatus is a black box - how it goes about its job of observing QM is silent on - it's irrelevant to QM. Now we apply the idea its equal probabilities but we find it isn't. Contradiction. I have proved, by the method of contradiction, a standard method of logic, the idea the outputs are always of equal probability is wrong - its contradictory. You must get cases where the probabilities are different.

I repeat the key point you are missing - what goes on inside the observing apparatus is irrelevant to QM - its a black box.

If don't get it now I give up - someone else has to explain it.

Thanks
Bill

For standard QM for a single event there is nothing going on inside. It is a single event with a probability distribution. The result is random. With MWIs there is no randomness, the results are determined. And the issue is how they explain us observing probability distributions.

In your examples, there are different events going on inside. If there was a black box with multiple splitters inside, then (as I understand it) that would be significant to the expectations in any QM theory. There is not (as I understand it) any QM theory which would consider that to be insignificant.

I can understand your black box idea was:

1) supposed to be analogous to a single QM event
and
2) explain different probabilities for different outcomes

But

You are trying to explain how a model can explain the different probabilities and you do so by giving an analogy in which there are hidden events. The problem is that you aren't claiming that the model has anything analogous to the hidden events that you use to get the result in your analogy. If your model doesn't include anything analogous to hidden events, then show how it gets the result using an analogy that doesn't have them either (otherwise it isn't analogous to your model). Can you do it with an analogy that doesn't use hidden events?

I accept that you have shown how a model that had something analogous to hidden events could get the result.

 

[bhobba]

For standard QM for a single event there is nothing going on inside. It is a single event.

There is nothing going on inside an observational apppartus? That makes no sense.

Can you do it with an analogy that doesn't use hidden events?

No. All observational apparatus have tons of 'hidden' events. The prism example I gave for explanation purposes considered a single event is in fact billions of events.

Its obvious you don't like my explanation.

OK - here is the full math:
https://arxiv.org/abs/quant-ph/9906015

As I said at the start its controvesial and you can do a serach on the objections.

I don't do it that way - I do it by non-contextuality and Gleason:
http://www.kiko.fysik.su.se/en/thesis/helena-master.pdf

There is, as I said, a theorem in MW, the non-contextuality theorem, that says it must be non-contextual hence Gleason applies.

Thanks
Bill

 

[name123]

There is nothing going on inside an observational apppartus? That makes no sense.

The wave collapse is a single event. And I have assumed in MWI the splitting into multiple worlds is a single event.

Its obvious you don't like my explanation.

It isn't about liking or disliking, I just didn't understand your explanation. You used hidden events to explain the different probabilities but gave no explanation of what you were claiming they were analogous to in the model. So while I can see how it could be an explanation for a model which involved something analogous hidden events, I didn't understand how it was an explanation for models that didn't have anything analogous to them.

OK - here is the full math:
https://arxiv.org/abs/quant-ph/9906015

I wasn't quite sure what all the symbols meant, but on https://en.wikipedia.org/wiki/Many-worlds_interpretation I read the following:
---
A decision-theoretic derivation of the Born rule from Everettarian assumptions, was produced by David Deutsch (1999)[33]and refined by Wallace (2002–2009)[34][35][36][37] and Saunders (2004).[38][39] Deutsch's derivation is a two-stage proof: first he shows that the number of orthonormal Everett-worlds after a branching is proportional to the conventional probability density. Then he uses game theory to show that these are all equally likely to be observed. The last step in particular has been criticised for circularity.[40][41] Some other reviews have been positive, although the status of these arguments remains highly controversial; some theoretical physicists have taken them as supporting the case for parallel universes.[42] In the New Scientist article, reviewing their presentation at a September 2007 conference,[43][44] Andy Albrecht, a physicist at the University of California at Davis, is quoted as saying "This work will go down as one of the most important developments in the history of science."[42]
---

Which made it sound as though he might have used a type of "all worlds have equal probability but some outcomes have more worlds" idea that I mentioned in the original post. Though in https://plato.stanford.edu/entries/qm-manyworlds/#4.3 it stated:
---
Thus, if all the worlds in which a particular experiment took place have equal measures of existence, then the probability of a particular outcome is simply proportional to the number of worlds with this outcome. The measures of existence of worlds are, in general, not equal, but the experimenters in all the worlds can perform additional specially tailored auxiliary measurements of some variables such that all the new worlds will have equal measures of existence. The experimenters should be completely indifferent to the results of these auxiliary measurements: their only purpose is to split the worlds into “equal-weight” worlds.
---

Which made it sound as though the theory had the concept of a "measure of existence" which seemed to be linked to the idea of the splitting that could be done in order to create a number of equally probable worlds (worlds with equal "measure of existence"). Seemingly implying that there was a theoretical basis for the "measure of existence" and that the number of worlds that would exist with equal "measure of existence" could be derived and wasn't just an ad hoc choice. Was that in line with your understanding?

I don't do it that way - I do it by non-contextuality and Gleason:
http://www.kiko.fysik.su.se/en/thesis/helena-master.pdf

There is, as I said, a theorem in MW, the non-contextuality theorem, that says it must be non-contextual hence Gleason applies.

In layman's terms how is Gleason's idea different to Deutsch's?

 

[Blue Scallop]

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

They worry a lot about deriving Born Rule in MWI. But how is Born Rule derived in the Orthodox Copenhagen and why is it not a problem?

 

[Demystifier]

But how is Born Rule derived in the Orthodox Copenhagen and why is it not a problem?

In orthodox Copenhagen interpretation the Born rule is postulated as a fundamental law, so there is no need for derivation. In MWI it cannot be postulated as a fundamental law because it would contradict other fundamental postulates of MWI. In MWI it must be emergent (not fundamental), and therefore it must be derived (not postulated).

 

[Blue Scallop]

In orthodox Copenhagen interpretation the Born rule is postulated as a fundamental law, so there is no need for derivation. In MWI it cannot be postulated as a fundamental law because it would contradict other fundamental postulates of MWI. In MWI it must be emergent (not fundamental), and therefore it must be derived (not postulated).

What are the fundamental postulates of MWI that can't naturally derive the Born Rule?
Can't we derive the Born Rule in MWI by stating that in regions where there are more probabilities of occurrences, there are more probabilities of worlds occurring.

 

[Demystifier]

What are the fundamental postulates of MWI that can't naturally derive the Born Rule?

https://www.physicsforums.com/threads/why-mwi-cannot-explain-the-born-rule.364063/

 

[Demystifier]

Can't we derive the Born Rule in MWI by stating that in regions where there are more probabilities of occurrences, there are more probabilities of worlds occurring.

No, because we don't know which regions have "more probabilities of occurrences". Unless we assume the Born rule from the beginning, but then it's circular.

 

[bhobba]

In layman's terms how is Gleason's idea different to Deutsch's?

Probability theory is based on the Kolmogerov axioms. Decision theory is the mathematical study of optimal strategies that makes use of probability theory as part of its tools.

Gleason simply uses probability theory. You can actually prove for dimensions greater than 2 there is only one way of defining probability on a Hilbert space - the Born Rule, but a careful study of the proof shows an assumption - the probability does not depend on the basis - this is called non contextuality. There are others as well such as all superposition's at least in principle are possible, but non-contextuality is the main one. It turns out you can actually prove in MW that its non-contextual - the proof is in the appendix of Walllce's book. It too may be contentious like the decision theory approach, but I think it's fine and haven't seen anyone criticize it.

Thanks
Bill

 

[name123]

Probability theory is based on the Kolmogerov axioms. Decision theory is the mathematical study of optimal strategies that makes use of probability theory as part of its tools.

Gleason simply uses probability theory. You can actually prove for dimensions greater than 2 there is only one way of defining probability on a Hilbert space - the Born Rule, but a careful study of the proof shows an assumption - the probability does not depend on the basis - this is called non contextuality. There are others as well such as all superposition's at least in principle are possible, but non-contextuality is the main one. It turns out you can actually prove in MW that its non-contextual - the proof is in the appendix of Walllce's book. It too may be contentious like the decision theory approach, but I think it's fine and haven't seen anyone criticize it.

Thanks
Bill

Thanks but how does the probability link to the worlds? Are there more worlds for more probable outcomes?

 

[bhobba]

Thanks but how does the probability link to the worlds? Are there more worlds for more probable outcomes?

No.

It's the probability of if you picked a random person from a world what world would they be experiencing.

Thanks
Bill

 

[name123]

No.

It's the probability of if you picked a random person from a world what world would they be experiencing.

Thanks
Bill

So imagine there are n worlds, and you picked a person at random, why would it be more probable that you picked them from one world than another, why wouldn't it be 1/n for each world?

 

[Nugatory]

So imagine there are n worlds, and you picked a person at random, why would it be more probable that you picked them from one world than another, why wouldn't it be 1/n for each world?

And there's the problem...
Consider performing a measurement on a system in the state $|\Psi\rangle=\frac{\sqrt{3}}{2}|\psi_0\rangle+\frac{1}{2}|\psi_1\rangle$. There are two possible outcomes so MWI interprets this as splitting into two worlds and by the 1/n line of thinking we end up with a 50% chance of each - but according to the Born rule and experiment the actual odds are 75/25. If MWI predicted that we got three worlds in which $\psi_0$ was realized and one in which $\psi_1$ was realized (or 300,000 and 100,000, or ...) we'd be OK, but so far no one has been able to show that that behavior does emerge. Instead we have to put the Born rule in by hand, basically asserting that some of the worlds are more probable than others - and your original question back in #1 seems to show a justifiable dissatisfaction with that approach.