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Old 19th July 2019, 06:10 AM   #1
Roboramma
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Many Worlds and probabilities

In this paper: https://arxiv.org/pdf/1405.7907.pdf Sean Carroll and Charles Sebens argue that the Born rule for deriving probabilities from the wavefunction can be derived from the Many Worlds Interpretation of Quantum Mechanics.

To quote the paper:
Quote:
A longstanding puzzle in the Many-Worlds or Everett approach to quantum mechanics (EQM) [2, 3] is the origin of the Born Rule: the probability of finding a post-measurement system in an eigenstate |ai of an observable A, given that the system is prepared in state |ψi, is given by |ha|ψi|2. Here we summarize and discuss the resolution of this problem that we
recently developed [1], in which the Born Rule is argued to be the uniquely rational way of dealing with the self-locating uncertainty that inevitably accompanies branching of the wave function. A similar approach has been advocated by Vaidman [4]; our formal manipulations
closely parallel those of Zurek
I'm having a hard time understanding the reasoning, and was wondering if it makes any sense to anyone else. I find myself stuck on what they call a naive view, that the probabilities that any individual observer should expect, if the many worlds interpretation were true, should be evenly distributed between the number of worlds.

Specifically, if I measure the spin of an electron, under many worlds what happens is that I become entangled with the electron. I am in a super-position of states where the electron is spin up and and I measure it up, and the electron is spin down and I measure it down. There are two "worlds", one in which the electron is up and the other in which it is down. Because of decoherence these worlds can no longer interact with each other.

So far so good. Given these two worlds, both of which happen, it's not the case that there was, say, a 50% chance that the electron would be up and 50% chance that it would be down. Instead there's 100% chance that it will be both. Rather there are two me's. Okay.

Now, the next step in the argument is that there's a moment after the measurement, after the worlds split, in which I don't know which world I'm in. I can now say, "well, I don't know which world I'm in, but I can assign some probability to which one", and that gives us the probabilities associated with QM.

Here's where I get to the issue. The "naive" view is that since there are two worlds, both of which occur, and I don't know which one I'm in, I should assign a 50/50 chance to each. But, we can prepare the electron in any state we like. I can prepare it in an initial state with a detector aligned at any angle I like relative to the detector I'm using to measure it's spin now. So the probability distribution can be anything I like from 0 to 1 of getting spin up or spin down. And yet, if the probability is 10% up and 90% down, there are still only two worlds, one associated with up and the other with down. Where do those probabilities come from under many worlds?

To quote the paper again:
Quote:
The main idea we use is that of self-locating uncertainty [14]: the condition of an observer who knows that the environment they experience occurs multiple times in the universe, but doesn’t know which example they are actually experiencing. We argue that such a predicament inevitably occurs in EQM, during the “post-measurement/pre-observation” period between when the wave function branches due to decoherence (measurement) and when the
observer registers the affect of the branching (observation). A naive analysis might indicate that, in such a situation, each branch should be given equal likelihood; here we demonstrate that a more careful treatment leads us inevitably to the Born Rule for probabilities.
Another quote making the same point:
Quote:
Naively, the combination of indifference over indistinguishable circumstances and selflocating uncertainty when wave functions branch is a disaster for EQM, rather than a way forward. Consider a case in which the amplitudes are unequal for two branches:

Edit by Roboramma: the forum didn't parse this equation correctly, so I've ommited it, please click the link to see, the point of interest is that there are probabilities of 1/3 and 2/3 to the separate outcomes(10)

The conditions of the two observers would seem to be indistinguishable from the inside; there is no way they can “feel” the influence of the amplitudes multiplying their branches of the wave function. Therefore, one might be tempted to conclude that Elga’s principle of indifference implies that probabilities in EQM should be calculated by branch-counting rather than by the Born Rule – every branch should be given equal weight, regardless of its amplitude. In this case, equation (10), that means assigning equal 50/50 probability to up and down even though the branch weights are unequal. This would be empirically disastrous, as real quantum measurements don’t work that way. We will now proceed to show why such reasoning is incorrect, and in fact a proper treatment of self-locating uncertainty leads directly to the empirically desirable conclusion. In Section 6 we generalize our result to cases
where there is both classical and quantum self-locating uncertainty, as in the cosmological multiverse.
So, how do they derive the Born Rule rather than giving each branch equal weight?

I'm sad to say that part is unclear to me.

Here's a little diagram that seems to sum up the argument:


Quote:
Figure 1: A schematic representation of the setup behind our derivation of the Born Rule. The states |Ψ1i and |Ψ2i are on the left and right, respectively. Factors denote the observer, the spin, the coin, and the rest of the environment. Thin diagonal lines connecting the spin and coin represent entanglement within different branches of the wave function. The horizontal/vertical boxes made from dotted/dashed lines show two different ways of carving out the “Observer+System” subsystem from the “Environment.” The ESP implies that the probability of the system being in a particular state is independent of the state of the environment. Applying that rule to both the spin and coin systems implies the Born Rule as the uniquely rational way of assigning credences
Attached Images
File Type: jpg figure1.jpg (27.5 KB, 9 views)
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Old 19th July 2019, 06:28 AM   #2
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For those who are interested and might find it clarifying, here is a lecture with Sean Carroll, one of the authors of that paper, in which he goes through the logic in the paper:

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I AGREE


You might like to skip to around the 43 minute mark where he starts discussing this issue. I'm actually watching it again now, though I had watched it around 6 months ago and failed to completely follow.

I'd try to explain that logic, but the point of this thread is that I'm not really following it very well. Hoping someone here follows it better than I do and can help to clarify. Thanks.
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Old 19th July 2019, 06:42 AM   #3
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The paper has been around for a while, but he has only recently got it published in a peer reviewed journal.

I tried to follow the logic too but failed.
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Old 19th July 2019, 06:47 AM   #4
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I am extremely skeptical of the many world interpretation.
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Old 19th July 2019, 07:04 AM   #5
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I would like someone to explain to me what we can gain from using a many-world interpretation over more classical views.
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Old 19th July 2019, 08:11 AM   #6
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Originally Posted by The Great Zaganza View Post
I would like someone to explain to me what we can gain from using a many-world interpretation over more classical views.
The choice is not between MWI and classical views, rather between MWI and other interpretations of QM.

I gather that the advantage of MWI is simplicity.
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Old 19th July 2019, 08:16 AM   #7
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Originally Posted by Roboramma View Post
Here's where I get to the issue. The "naive" view is that since there are two worlds, both of which occur, and I don't know which one I'm in, I should assign a 50/50 chance to each. But, we can prepare the electron in any state we like. I can prepare it in an initial state with a detector aligned at any angle I like relative to the detector I'm using to measure it's spin now. So the probability distribution can be anything I like from 0 to 1 of getting spin up or spin down. And yet, if the probability is 10% up and 90% down, there are still only two worlds, one associated with up and the other with down. Where do those probabilities come from under many worlds?
What I have gathered so far is that the "naive" assumption is that there is a well defined number of branches.
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Old 19th July 2019, 08:25 AM   #8
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My initial understanding was something like this (and this is a dumbed down version), that say I prepare the measurement so that there will be a 10% chance it is "up" and 90% chance that it is down, I make the measurement but I am yet to observe it.

In that time I have branched not once, but an indefinite number of times and in 10% of those branches I will observe "up" and in 90% of those branches I will observe "down". I can now apply the principle of indifference and get the right answer.

I don't know if I am on the right track or not.
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Old 20th July 2019, 04:59 AM   #9
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Originally Posted by Robin View Post
My initial understanding was something like this (and this is a dumbed down version), that say I prepare the measurement so that there will be a 10% chance it is "up" and 90% chance that it is down, I make the measurement but I am yet to observe it.

In that time I have branched not once, but an indefinite number of times and in 10% of those branches I will observe "up" and in 90% of those branches I will observe "down". I can now apply the principle of indifference and get the right answer.

I don't know if I am on the right track or not.
I finished watching the lecture that I linked upthread, and I found it a little more clear than the paper (the audience are philosophers). So, it's not that there are more branches, but I think the idea is that it's as though there were more branches, because some branches are weighted differently than others.

Why?

I'm not clear.

Here's how much of the argument I can follow: When looking at probabilities in general we usually apply the principle of indifference. In this context that would mean treating each branch of the wavefunction as equally probable. He says that while this principle functions well in general, it actually follows from a deeper principle, and that principle is the one we should apply in assigning probabilities.

That principle is what he calls ESP: the Epistemic Separability Principle. This states that "When a system decomposes into "identical subsystems" plus an "environment" the credence you assign to being in any particular subsystem should depend on what is happening elsewhere in the universe."

He next says that ESP is the hidden assumption that leads to the principle of indifference classically. But when you apply ESP to Many Worlds, you don't get the principle of indifference. So you shouldn't treat each branch equally.

Why?

That's the step that seems like magic to me. Basically he derives a 50/50 probability for a simple situation where the probability should be 50/50 by treating the differences in the external environment as not impacting on the probability (ESP). But then when the amplitudes are different, we can't treat different branches the same because something other than the external environment (the amplitudes) is different.

So how do we compare them? He says that we need to decompose the states of the branches into equal length components. This leads to "branches with root2 larger amplitudes correspond to twice as many equal length components, and therefore twice the probability."

I don't see any explanation of why "length" has suddenly been treated as equivalent to probability here.

(this last bit is at approximately the 1hour:02minutes mark in the video linked upthread if you are interested)
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Old 20th July 2019, 05:00 AM   #10
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Originally Posted by 3point14 View Post
I am extremely skeptical of the many world interpretation.
Any reason why?
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Old 20th July 2019, 05:16 AM   #11
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Originally Posted by Roboramma View Post
Any reason why?

Because the maths is just a model, not the real thing. I think it's far more likely that the many worlds theory is an artifact of an imperfect model than that there are an infinite number of me knocking around in different dimensions all over the place.

Similar to how you can model gyroscopes to produce thrust.

Some of the physicist I have spoken to about this find it extremely difficult to separate the maths from the reality and believe that the maths is the reality.
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Old 20th July 2019, 05:52 AM   #12
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I recently read Brian Greene’s “The Hidden Reality” in which he discusses nine different “multiverse” ideas, including the many-worlds idea.
He mentions that there’s no real evidence for any of these notions, they all exist essentially as mathematical constructs.

I remember, years ago, reading what I believe is the first science-fiction story on this particular notion, Larry Niven’s “All The Myriad Ways”
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Old 20th July 2019, 06:27 AM   #13
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The evidence that a theory holds in places where we can't look is that it holds in all of the places that we can look. Quantum Mechanics has been tested in extreme detail in many ways. Every time it's turned out that it holds. The confirmation of the Higgs Boson is just the most recent. Prior to 2012 the Higgs was as much just an element of the model as are multiverse ideas, yet when we were able to test it, it turned out that the Higgs really does exist.

A similar thing could be said about gravitational waves. Just a few years ago you could have said of gravitational waves "the maths is just a model, not the real thing", or "there’s no real evidence for any of these notions, they all exist essentially as mathematical constructs.", and yet when we were able to experimentally test them, it turned out that they were there.

And by the way Einstein thought that we would never be able to experimentally confirm the existence of gravitational waves.

The ways in which we can test a theory should increase our confidence in all of it's implications.
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Old 20th July 2019, 06:48 AM   #14
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Originally Posted by Roboramma View Post
The evidence that a theory holds in places where we can't look is that it holds in all of the places that we can look. Quantum Mechanics has been tested in extreme detail in many ways. Every time it's turned out that it holds. The confirmation of the Higgs Boson is just the most recent. Prior to 2012 the Higgs was as much just an element of the model as are multiverse ideas, yet when we were able to test it, it turned out that the Higgs really does exist.

A similar thing could be said about gravitational waves. Just a few years ago you could have said of gravitational waves "the maths is just a model, not the real thing", or "there’s no real evidence for any of these notions, they all exist essentially as mathematical constructs.", and yet when we were able to experimentally test them, it turned out that they were there.

And by the way Einstein thought that we would never be able to experimentally confirm the existence of gravitational waves.

The ways in which we can test a theory should increase our confidence in all of it's implications.


Given that the model that claims the existence of many worlds is self evidently incomplete (Quantum physics doesn't reconcile with general relativity as I understand it. (Please correct me if I'm wrong)) I believe it's far more likely that it's the evidently broken model that is producing odd artifacts than there are many of me in different realities.

The universe doesn't actually do maths.
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Old 20th July 2019, 07:00 AM   #15
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Originally Posted by 3point14 View Post
Given that the model that claims the existence of many worlds is self evidently incomplete (Quantum physics doesn't reconcile with general relativity as I understand it. (Please correct me if I'm wrong)) I believe it's far more likely that it's the evidently broken model that is producing odd artifacts than there are many of me in different realities.
Would you have said the same about the existence of the Higgs prior to 2012?

If not, is it just the fact that you find many world contrary to your intuitions that makes you accept one prediction of the model and not another, or is there something else?
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Old 20th July 2019, 07:12 AM   #16
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Originally Posted by Roboramma View Post
Would you have said the same about the existence of the Higgs prior to 2012?
I don't know. But this is a poor parallel. You're evidencing something that was then later found. Hindsight is 20/20. You can't say "We found this unlikely/unexpected thing, therefore all unlikely/unexpected things exist"



Quote:
If not, is it just the fact that you find many world contrary to your intuitions that makes you accept one prediction of the model and not another, or is there something else?

It's a broken model. When the results of a broken model seem ridiculous,, I think they can be discarded. Nobody's trying to build a gyro powered space ship. As and when a grand unified theory predicts many worlds then I'd change my view.

None of it's important anyway. It doesn't impact on my life. I'm not a physicist.

I just find it a particular feature of some physicists that they are unable to acknowledge that what they model with numbers isn't actually the real world and that their model is broken.
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Old 20th July 2019, 07:25 AM   #17
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Originally Posted by 3point14 View Post
I don't know. But this is a poor parallel. You're evidencing something that was then later found. Hindsight is 20/20. You can't say "We found this unlikely/unexpected thing, therefore all unlikely/unexpected things exist"
The point is that it wasn't unlikely or unexpected. It was a prediction of the model. Most physicists thought it would be found and weren't surprised when it was. What would have been surprising is if it hadn't been found. I'm arguing that many worlds falls into a similar (not identical*) category of things implied by the theory.

Sure, it's true that QM might imply some things that turn out not to be correct. As you say that theory isn't complete. Similarly Newtonian physics implied some things that turned out not to be correct. But we aren't in a position to guess which things, any more than people in the 1800s were likely to guess where Newtonian physics would break down. For any particular thing implied by QM, it's very likely to be true, and I base that on the success of all of the predictions that we have been able to test so far.

I don't trust your (or anyone's) ability to guess at which of the implications of the theory will turn out to be wrong, guided only by your intuition. When it comes to QM our intuitions really aren't a good guide.

* I actually think there's some non-trivial chance that many worlds will turn out not to work. This thread is about a problem with the Many Worlds interpretation (specifically, it seems not to lead to the correct probabilities), and an attempt to fix that problem, but so far I haven't been able to understand very well whether or not that attempt succeeds.
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Old 20th July 2019, 08:16 AM   #18
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Originally Posted by Roboramma View Post
The point is that it wasn't unlikely or unexpected. It was a prediction of the model. Most physicists thought it would be found and weren't surprised when it was. What would have been surprising is if it hadn't been found. I'm arguing that many worlds falls into a similar (not identical*) category of things implied by the theory.

Sure, it's true that QM might imply some things that turn out not to be correct. As you say that theory isn't complete. Similarly Newtonian physics implied some things that turned out not to be correct. But we aren't in a position to guess which things, any more than people in the 1800s were likely to guess where Newtonian physics would break down. For any particular thing implied by QM, it's very likely to be true, and I base that on the success of all of the predictions that we have been able to test so far.

I don't trust your (or anyone's) ability to guess at which of the implications of the theory will turn out to be wrong, guided only by your intuition. When it comes to QM our intuitions really aren't a good guide.
Fair point.

I don't trust the results of broken models when the only evidence for that result comes from the broken model.

I realise I speak from a position of ignorance but in this instance I really don't have anything on the line. I also get annoyed with physicist who present their interpretation of their model as reality.
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Old 20th July 2019, 08:38 AM   #19
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Originally Posted by 3point14 View Post
Fair point.

I don't trust the results of broken models when the only evidence for that result comes from the broken model.
Here's my view: When Copernicus modeled the solar system, that was just a mathematical model, but it turns out that, at least with respect to the rather non-intuitive result that the earth was moving, it accurately reflected reality.

When Einstein discovered special relativity much of the mathematics had already been worked out (there's a reason it's call the Lorentz transformation), but it took Einstein to take the leap to really see that space and time were not absolute, and made incredible progress by treating that as real.

He did something similar when he treated the apparent particle-like behavior of light as an indication that light really does come in quanta, and not just a trick of the math, despite how odd that is given that we knew by then that light is an electromagnetic wave. QM was born from treating math as real.

You might say, again hindsight is 20/20 and I'm just choosing the hits here. But I don't think I am. Are there some good examples of us taking the implications of our theories too seriously? Perhaps the false prediction of a planet within the orbit of Mercury? Maybe Lord Kelvin's estimation of the age of the earth? Those are the best that I can come up with. But when you have a theory that's very well tested I really think that for any specific question the assumption should be that it will give the correct results for that question too, even if we we can't directly test that question right now, and even if we might guess that there will be some small fraction of questions about which it will be wrong.

Quote:
I realise I speak from a position of ignorance but in this instance I really don't have anything on the line. I also get annoyed with physicist who present their interpretation of their model as reality.
I'm not suggesting that any theory is right about everything, only that the probability that any particular implication of the theory will turn out to be correct is high.
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Old 20th July 2019, 08:46 AM   #20
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Thought I should add a simple point:
Originally Posted by 3point14 View Post
I don't trust the results of broken models when the only evidence for that result comes from the broken model.
Do you disbelieve in the existence of gravitons, which are implied by a "broken model" and the evidence of which is only the success of that "broken model"?
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Old 20th July 2019, 08:53 AM   #21
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Originally Posted by Roboramma View Post
Here's my view: When Copernicus modeled the solar system, that was just a mathematical model, but it turns out that, at least with respect to the rather non-intuitive result that the earth was moving, it accurately reflected reality

When Einstein discovered special relativity much of the mathematics had already been worked out (there's a reason it's call the Lorentz transformation), but it took Einstein to take the leap to really see that space and time were not absolute, and made incredible progress by treating that as real.

He did something similar when he treated the apparent particle-like behavior of light as an indication that light really does come in quanta, and not just a trick of the math, despite how odd that is given that we knew by then that light is an electromagnetic wave. QM was born from treating math as real.

Okay, I see your point.

Copernicus' theory was later confirmed by, well, just looking, once we had telescopes powerful enough.

Einstein's theories are, at least in part, verified by putting a clock on earth and a clock in space ship moving at x and later comparing them.

The behaviour of light as both a wave and a particle can be demonstrated by a practical, double slit experiment.

What experiment that doesn't invoke the quantum theory from which it derives can demonstrate many worlds theory?


Quote:
You might say, again hindsight is 20/20 and I'm just choosing the hits here. But I don't think I am. Are there some good examples of us taking the implications of our theories too seriously? Perhaps the false prediction of a planet within the orbit of Mercury? Maybe Lord Kelvin's estimation of the age of the earth?
I must admit that in my first response to you I was intending to list some. Or at least find one. The existence of Aether was all I could come up with. I honestly couldn't think of/find anything with anything approaching the mathematical backing of MWT.



Quote:
Those are the best that I can come up with. But when you have a theory that's very well tested I really think that for any specific question the assumption should be that it will give the correct results for that question too, even if we we can't directly test that question right now, and even if we might guess that there will be some small fraction of questions about which it will be wrong.
I have to return to the fact that the model is broken. Not unproven, but demonstrably not able to completely model that which it intends to.


Quote:
I'm not suggesting that any theory is right about everything, only that the probability that any particular implication of the theory will turn out to be correct is high.

Accepted. And again, I realise I, in fact, lack the education to make grand pronouncements as I have here with any confidence. It can be educational though.
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Old 20th July 2019, 11:45 PM   #22
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Thanks for the discussion, 3point14, it was interesting. A bit of a digression from the topic of the thread, and I think we both expressed our views, so I think we should probably leave it there, but I enjoyed it.
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Old 21st July 2019, 01:07 AM   #23
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Originally Posted by Roboramma View Post
So how do we compare them? He says that we need to decompose the states of the branches into equal length components. This leads to "branches with root2 larger amplitudes correspond to twice as many equal length components, and therefore twice the probability."

I don't see any explanation of why "length" has suddenly been treated as equivalent to probability here.

(this last bit is at approximately the 1hour:02minutes mark in the video linked upthread if you are interested)
I will watch the video and see if I can make sense of that.
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Old 21st July 2019, 04:55 AM   #24
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Wrong thread
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Old 22nd July 2019, 02:46 AM   #25
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Originally Posted by Robin View Post
Wrong thread
That seems so ironic given the topic of this thread!
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Old 22nd July 2019, 04:02 AM   #26
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Originally Posted by Roboramma View Post
Thanks for the discussion, 3point14, it was interesting. A bit of a digression from the topic of the thread, and I think we both expressed our views, so I think we should probably leave it there, but I enjoyed it.
Oh, your knowledge is far greater than mine. One of us learnt something. My thanks.
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Old 23rd July 2019, 04:34 AM   #27
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Originally Posted by Roboramma View Post
In this paper: https://arxiv.org/pdf/1405.7907.pdf Sean Carroll and Charles Sebens argue that the Born rule for deriving probabilities from the wavefunction can be derived from the Many Worlds Interpretation of Quantum Mechanics.

{...}

So, how do they derive the Born Rule rather than giving each branch equal weight?

I'm sad to say that part is unclear to me.
Equation 14 in the paper is the crux of it. It's the assumption that the probabilities are invariant under a unitary transformation of the environment, which then after some more reasoning and arithmetic gets you the Born rule. Are you specifically looking to understand this particular argument or just any way to get the Born rule in the MWI? Because if the latter, you might want to look at the decision theory based argument (referenced in the introduction of the paper) which, at least, I personally find a lot more intuitive to grasp.
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Old 23rd July 2019, 06:50 AM   #28
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Originally Posted by caveman1917 View Post
Equation 14 in the paper is the crux of it. It's the assumption that the probabilities are invariant under a unitary transformation of the environment, which then after some more reasoning and arithmetic gets you the Born rule. Are you specifically looking to understand this particular argument or just any way to get the Born rule in the MWI? Because if the latter, you might want to look at the decision theory based argument (referenced in the introduction of the paper) which, at least, I personally find a lot more intuitive to grasp.
The former will do, but yeah, I am more interested in the latter. Thanks for the suggestion. I'd heard of the decision theory based argument but haven't actually looked into it in any detail. I'll try to find some time to do so.
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Old 25th July 2019, 09:35 PM   #29
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Another problem I have is I don't know the exact claim of MWI

As an analogy, say I have a program to simulate the toss of a coin. I have one button "Toss" that when pressed the program randomly selects heads or tails. The second button "Show" shows the face selected.

I have set up the program to be slightly unfair and give heads 60% of the time and tails 40% of the time.

John (knowing the above) has clicked "Toss" and not yet clicked "Show". If P(H) and P(T) respectively represent his credence that a head or a tail has been chosen then P(H)=0.6 and P(T)=0.4.

If I tell him that the process that chose the head or the tail also forked the program into two streams, of which he is only seeing one, then this does not change those figures, but it may be that sometimes the two copies of the program have chosen the same face.

However, if I tell him that the process that chose the head or the tail forked the program into two streams in such a way that if one stream has heads then the other has tails, and if one stream has tails then the other must have heads, then he will be left scratching his head.

We appear to have entered some kind of feedback loop on probabilities. This is also analogous to what I don't understand about the situation with measuring spin in MWI. In what sense were there different probabilities if both eventuate?

On the other hand, if I reveal that there were always 5 programs running and 3 were set to select Heads when the button was clicked and the rest were set to select Tails, and he doesn't know which one he is looking at, then we are back to P(H)=0.6 and P(T)=0.4.

I had initially supposed that this last scenario was the closest to what Carroll and Sebens are suggesting (only with more 'worlds').
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Old 26th July 2019, 12:42 AM   #30
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Originally Posted by Robin View Post
Another problem I have is I don't know the exact claim of MWI

As an analogy, say I have a program to simulate the toss of a coin. I have one button "Toss" that when pressed the program randomly selects heads or tails. The second button "Show" shows the face selected.

I have set up the program to be slightly unfair and give heads 60% of the time and tails 40% of the time.

John (knowing the above) has clicked "Toss" and not yet clicked "Show". If P(H) and P(T) respectively represent his credence that a head or a tail has been chosen then P(H)=0.6 and P(T)=0.4.

If I tell him that the process that chose the head or the tail also forked the program into two streams, of which he is only seeing one, then this does not change those figures, but it may be that sometimes the two copies of the program have chosen the same face.

However, if I tell him that the process that chose the head or the tail forked the program into two streams in such a way that if one stream has heads then the other has tails, and if one stream has tails then the other must have heads, then he will be left scratching his head.

We appear to have entered some kind of feedback loop on probabilities. This is also analogous to what I don't understand about the situation with measuring spin in MWI. In what sense were there different probabilities if both eventuate?

On the other hand, if I reveal that there were always 5 programs running and 3 were set to select Heads when the button was clicked and the rest were set to select Tails, and he doesn't know which one he is looking at, then we are back to P(H)=0.6 and P(T)=0.4.

I had initially supposed that this last scenario was the closest to what Carroll and Sebens are suggesting (only with more 'worlds').
The number of branches isn't well-defined, your example of "5 programs of which 3 select Heads" doesn't work for that reason. What is well-defined, though, is equivalence classes of branches (fe the class of branches that result in Heads). The probabilities of these classes isn't derived from counting branches as you can't count branches.
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Old 26th July 2019, 05:23 AM   #31
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It doesn't need to be 3 and 5. I could spin up any number. Let's say I have an anemometer on my roof connected to my computer and I spin up programs at a rate proportional to the force of the wind, but still in the same proportions. John's calculations would be the same.
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Old 26th July 2019, 05:43 AM   #32
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Originally Posted by Robin View Post
It doesn't need to be 3 and 5. I could spin up any number. Let's say I have an anemometer on my roof connected to my computer and I spin up programs at a rate proportional to the force of the wind, but still in the same proportions. John's calculations would be the same.
You're missing the point, the number of branches in the MWI isn't well-defined, your comparison to a number of programs fails because of this. This, ie counting the number of branches (programs), isn't the basis for the probabilities being derived. The question "How many branches are there for this event?" does not have a well-defined answer. John's calculations requires him to know the number of programs being spun up, this does not translate to the MWI. Try reading the decision theory based argument, it's - at least in my opinion - a lot more intuitive to understand than Carroll's argument.
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Old 26th July 2019, 06:02 AM   #33
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Originally Posted by caveman1917 View Post
You're missing the point, the number of branches in the MWI isn't well-defined, your comparison to a number of programs fails because of this. This, ie counting the number of branches (programs), isn't the basis for the probabilities being derived. The question "How many branches are there for this event?" does not have a well-defined answer. John's calculations requires him to know the number of programs being spun up, this does not translate to the MWI. Try reading the decision theory based argument, it's - at least in my opinion - a lot more intuitive to understand than Carroll's argument.
In my second example there is no branch counting, John doesn't know how many programs there are and doesn't need to know
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Old 26th July 2019, 06:42 AM   #34
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I must admit that much of this goes over my head. The reason why I like MWI happens to be based on an explanation by Sean Carroll, that I have read in a book and once in a blog post. He wrote that MWI does not actually mean that the many worlds exist, but that there are possibilities for all of these worlds. When we make a measurement, we find out which of the possibilities actually exists.

The paper and the posts in this thread seem to contradict that explanation, so I am somewhat puzzled. Has Carroll changed his mind? Did I misunderstand his explanation?
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Old 26th July 2019, 07:21 AM   #35
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Originally Posted by steenkh View Post
I must admit that much of this goes over my head. The reason why I like MWI happens to be based on an explanation by Sean Carroll, that I have read in a book and once in a blog post. He wrote that MWI does not actually mean that the many worlds exist, but that there are possibilities for all of these worlds. When we make a measurement, we find out which of the possibilities actually exists.

The paper and the posts in this thread seem to contradict that explanation, so I am somewhat puzzled. Has Carroll changed his mind? Did I misunderstand his explanation?
That's not my understanding of the explanation or MWI. I struggle to get my head around it though and it seems unfeasible to my layman's mind.
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Old 26th July 2019, 07:28 AM   #36
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Originally Posted by Robin View Post
In my second example there is no branch counting, John doesn't know how many programs there are and doesn't need to know
You're still implicitly counting branches by your statement that you're spinning up programs in "the same proportions" - the notion of "proportion" still implicitly relies on branch counting.
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Old 26th July 2019, 07:29 AM   #37
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Originally Posted by steenkh View Post
I must admit that much of this goes over my head. The reason why I like MWI happens to be based on an explanation by Sean Carroll, that I have read in a book and once in a blog post. He wrote that MWI does not actually mean that the many worlds exist, but that there are possibilities for all of these worlds. When we make a measurement, we find out which of the possibilities actually exists.

The paper and the posts in this thread seem to contradict that explanation, so I am somewhat puzzled. Has Carroll changed his mind? Did I misunderstand his explanation?
You must have misunderstood something there, that (your first paragraph) is not the MWI.
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Old 26th July 2019, 08:59 AM   #38
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Here is Sean Carroll describing the paper under discussion and the talking about the case of branches with unequal amplitudes (my bolding):
Originally Posted by Sean Carroll
What if the amplitudes for the two branches are not equal? Here we can borrow some math from Zurek. (Indeed, our argument can be thought of as a love child of Vaidman and Zurek, with Elga as midwife.) In his envariance paper, Zurek shows how to start with a case of unequal amplitudes and reduce it to the case of many more branches with equal amplitudes. The number of these pseudo-branches you need is proportional to — wait for it — the square of the amplitude. Thus, you get out the full Born Rule, simply by demanding that we assign credences in situations of self-locating uncertainty in a way that is consistent with ESP.

http://www.preposterousuniverse.com/...omment-page-2/
In my example about the program I was trying to create an analogy of the part I bolded, as I understood it.
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Old 26th July 2019, 09:18 AM   #39
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Originally Posted by Robin View Post
Here is Sean Carroll describing the paper under discussion and the talking about the case of branches with unequal amplitudes (my bolding):

In my example about the program I was trying to create an analogy of the part I bolded, as I understood it.
This particular point seems to be made in Zurek's paper then, have you read it? I haven't read it (yet) but I'm strongly suspecting we're not talking about actual branches here but a mathematical "trick" to reduce the problem as if there are a bunch of branches with equal probability with such required proportions. ETA: and irrational amplitudes can not be reduced to integer proportions so whatever it is that Zurek is doing it's going to involve some sort of limit rather than just a simple finite number of pseudo-branches.
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Old 26th July 2019, 12:46 PM   #40
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The only problem I have with the many worlds model is that it doesn't really seem to add anything new to just doing the probabilities anyway.

I mean, let's say I do something macroscopic like roll a pair of standard six-sided dice. I rolled two sixes, which has a probability of 1 in 36. I can even roll the dice a few million times and confirm that, yep, it's 1 in 36, the dice aren't loaded.

Now I could imagine there are many worlds, and every time I roll the dice, the world splits into 11 different worlds, corresponding to the totals between 2 and 12, each with their own probability. Like it's 6 times less probable I'm in this world where I rolled a 12, than in the world where I rolled a 7.

But that doesn't really add anything to just accepting that random stuff happens in just one world. Whether it's just one world where I rolled a 12, or many worlds and I'm in the one where a 12 has been rolled, nothing really differs. Or rather, nothing testable. Thus the other 10 worlds are just unneeded extra entities, so that fails Occam's razor.


And it seems to me like the same applies to QM.

Instead of rolling dice, I could, for example, send a pair of entangled photons down a fiber optic. Which is actually what quantum cryptography does at the moment. And I'll generate them via some nuclear decay or such, so it's truly random. And I can do it some 30 times, to get a decent encryption key that nobody else can possibly eavesdrop on. That's about a billion possibilities.

Now, whatever key I've got, I could pretend that now there are a billion universes and I'm in the one where I got exactly this key. Or I could accept that there is just one and that's what the random numbers produced.

Is there anything actually testable to show that the other billion or so worlds actually were produced by my generating a key?
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