Many Worlds Interpretation and act of measuring

[bhobba]

It is not simple at all

Since its logically equivalent to Kolmogorov's axioms I disagree. Its as simple or as hard as those axioms. This however has been discussed many times and going over it again won't resolve anything.

Thanks
Bill

 

[bhobba]

Sorry if I got the context wrong - but a mixed state after decoherence is a state of a subsystem. It is not a state of the world. The worlds are all in a superpositional state - the state of the global wave function of the universe.

Sure. But if that's its context then maybe it needs updating.

Thanks
Bill

 

[bhobba]

which universe lives the real 'me'? what If I've already died in another 13 universes and I keep changing every time of Universe and I'm immortal? so are you guys, let's pour a champagne

All of you are equally real, alive, dead or not even existing. It's part of its weirdness - a weirdness I personally eschew. I am with Murray Gell-Mann who concedes its valid - but exactly why bother - his Consistent Histories in a sense is Many Worlds without the Many Worlds. However its more subtle than that as chapter 3 of Wallaces book that I reviewed last night delevs into.

Thanks
Bill

 

[atyy]

But what about decoherence being only approximate? If recoherence and accordingly the merging of worlds is possible, the analogy between the two structures breaks down. They don't seem to address this but take the ever-splitting universe as given.

I think they take all experiments to always yield all outcomes, so somehow even Newtonian Mechanics or Bohmian Mechanics involve all outcomes always occurring. Then in the special case in which the probabilities are consistent with the Born rule, there is a description of the universe as deterministically evolving. I think the paper by Dawid and Thebault I linked to in #231 discusses the Greaves and Myrvold paper along these lines.

Here's part of the Greaves and Myrvold paper (p22) that I think indicates that they simply always assume a branching reality: "Suppose, now, that our agent, having read Borges' The Garden of Forking Paths," (Borges, 1941, 1962) thinks of an experiment as an event in which the world divides into branches, with each outcome occurring on some branch. On each of the branches is a copy of herself, along with copies of everyone else in the world, and each payoff is actually paid on those branches on which the an outcome associated with that payoff occurs. How much of the foregoing analysis would have to be revised? We claim: none of it. The Savage axioms are requirements on the preferences of a rational agent, whether the agent conceives of an experiment in the usual way, with only one outcome, or as a branching occurrence, with all of the payoffs actually paid on some branch or another."

 

[rootone]

I have to say that while I am reading this, it's difficult to comprehend the possiblity that I am also simultaneously dead or being in a state of having never existed.

 

[bhobba]

It seems to say that many objections against the MWI can be made against classical probability theory as well because the structure of a probability tree is very similar to that of a branching universe. stevendaryl has written a number of posts on this and I think there is some truth to it.

That's the trouble I have with this discussion about probability. I have Feller's famous text on it (Introduction To Probability Theory And Its Applications) and I will quote what he says which sums up my view exactly.

The first chapter goes into more detail but basically it is summed up from page 3 'We shall no more attempt to explain the true meaning of probability than the physicist explains the real meaning of mass and energy, or the geometer discusses the true nature of a point. Instead we shall prove theorems and show how they are applied'

The theorems are based on the primitive of event and the Kolmogerov axioms. When applying it, some, often unstated, further reasonableness assumptions are required. Its very common in applied math. Philosophy types like to latch onto that sort of thing ie applying the law of large numbers means you have to reasonably interpret the fact the convergence is almost surely. But as Feller also says, again from page 3, 'The philosophy of the foundations of probability must be divorced from mathematics and statistics exactly as the discussion of our intuitive space sense is now divorced from geometry'.

The definition of probability in the decision theory axioms are proven logically equivalent to the Kolmogorov axioms. That IMHO should be the end of it. Beyond that is philosophy and won't really get anywhere. I don't think its really part of math or physics.

Thanks
Bill

 

[bhobba]

Also another question: has the idea that the Born rule may be valid only in *some* worlds been discussed in the literature? I'm wondering if this is strictly incompatible with Gleason's theorem.

Interesting question. Gleason requires basis independence, that's the biggie anyway, the question then would be why it would not be true in some worlds. Cant see how that would be possible myself - but if others have any ideas I am all ears.

Thanks
Bill

 

[atyy]

As I have said, that's a problem with probabilistic laws in general. If it happened to be the case that you flipped a coin 10,000 times and get heads-up each time, you would probably decide it was not a fair coin. But it could have just been a fluke. Maybe if you flipped it 100,000 times, you would get 50/50.

If you're so unlucky as to get a very "atypical" result, then you're going to make mistaken conclusions about probabilities. In MWI, there will definitely be worlds like that, where all the results (so far) are atypical. I think you're right, that such people would not develop the same laws of physics.

I think the argument is that there is no sense of "typical" or "atypical", so the situation differs from ordinary probability. In the basic form of MWI, there is just branching and the quantum amplitude attached to each branch - there is no sense in which a branch is typical or atypical, since there is no probability yet. In the Deutsch-Wallace form of MWI, there is probability, but it is unclear whether the decision theoretic probability of an observer within one branch has anything to say about the probability of his branch being typical, which I think is related to kith's point about whether the Deutsch-Wallace MWI is consistent with our ordinary practice of science.

Greaves and Myrvold propose an answer, but it seems that we have to assume that even if quantum mechanics were false, that the universe is branching.

 

[atyy]

Every interpretation of MWI is the best - in some world. SCNR.

All Bohmian interpretations are alike, but each Everettian interpretation is flawed in its own way.

http://en.wikipedia.org/wiki/Anna_Karenina_principle

 

[Rajkovic]

All of you are equally real, alive, dead or not even existing. It's part of its weirdness - a weirdness I personally eschew. I am with Murray Gell-Mann who concedes its valid - but exactly why bother - his Consistent Histories in a sense is Many Worlds without the Many Worlds. However its more subtle than that as chapter 3 of Wallaces book that I reviewed last night delevs into.

Thanks
Bill

Okay, but who is controlling me in other universes, if I'm here?
btw, in this "theory", If I die here in our Universe, I'm dead correct? Or I will be transferred to another "I" and I'm immortal?

 

[EmilyCA]

Hi - I'm the author of the paper http://arxiv.org/abs/1504.01063 which was being discussed earlier in this thread. I guess the discussion has moved on a little, but I'm particularly interested in the discussion you're having now about classical vs many worlds probability.

The main point I tried to make in that paper is simply that if you believe all possible results of a measurement always occur, then you learn nothing new about the world when you observe a measurement result. Therefore in such a world no amount of measurement data could possibly serve to confirm any scientific theory, including quantum mechanics; so the Everett approach is self-undermining because it tells us we shouldn't even believe that quantum mechanics is correct.

I agree that the status of probability is problematic even in non-branching theories - as someone said a few pages back, `if you are unlucky enough to get a run of 20 (or 20,000) heads in a row while tossing coins, then you will come to a false conclusion about whether you have a fair coin.' Nonetheless in a probabilistic setting it is still possible to claim that probabilities, whatever they are, are somehow responsible for the unique sequence of outcomes that we have seen, and therefore we can reasonably expect that we are learning something about probabilistic laws from observing measurement results (while accepting that we might be making mistakes if we have been unlucky). In the Everett approach it is never reasonable to expect this, because there is no unique sequence of outcomes from which we could learn something.

The Deutsch-Wallace account of `probability' does nothing to change this fact - it shows us that there might still be something that looks like probability in the many worlds context, but fails to show that this something would be connected to truth or typicality in the right sort of way for us to actually learn about the world from it.

 

[bhobba]

Hi - I'm the author of the paper http://arxiv.org/abs/1504.01063 which was being discussed earlier in this thread.

Thanks for chiming in - much appreciated.

I guess the discussion has moved on a little, but I'm particularly interested in the discussion you're having now about classical vs many worlds probability.

Again great to hear.

The main point I tried to make in that paper is simply that if you believe all possible results of a measurement always occur, then you learn nothing new about the world when you observe a measurement result. Therefore in such a world no amount of measurement data could possibly serve to confirm any scientific theory, including quantum mechanics; so the Everett approach is self-undermining because it tells us we shouldn't even believe that quantum mechanics is correct.

A problem I had when reading the paper is my background is applied math and it was using arguments that I simply couldn't follow. I have to say I can't really follow the above either. I have Wallace's book on MW and it was expressed in my kind of language - theorems, proofs etc etc. My take on MW is, while all outcomes do occur at once, they are in separate worlds. Because of that, when you say you learn nothing new about the world I am scratching my head - obviously you do learn about the world you inhabit which seems the key thing. That others learn different things about their world doesn't worry me because they are in a different world.

I agree that the status of probability is problematic even in non-branching theories

I think in math and physics the philosophical issues with probability, is as per the post I did from Feller's well known text: 'The philosophy of the foundations of probability must be divorced from mathematics and statistics exactly as the discussion of our intuitive space sense is now divorced from geometry'.

To my way of thinking there are a number of theorems in Wallaces text that show the decision theoretic approach he uses is equivalent to Bayesian probability, which is itself equivalent to the Kolmogorov axioms. I can't really see what more is required.

Thanks
Bill

 

[bhobba]

Okay, but who is controlling me in other universes, if I'm here?

Why you believe anyone is controlling anyone in any world has me beat.

Thanks
Bill

 

[stevendaryl]

I think the argument is that there is no sense of "typical" or "atypical", so the situation differs from ordinary probability.

There is a sense of "typical", which is the worlds where relative frequencies work out to be roughly the same as the Born probabilities. I think what you mean is that there isn't an independent, non-circular notion of "rarity" such that you could prove that the atypical worlds are rare enough to be ignored. I don't know how devastating that is. For us to be able to do physics based on QM, it seems that we need to assume that our world is typical (in the sense that frequencies = Born probabilities). I don't see why it's relevant to my use of physics to know that there are worlds with atypical frequencies.

The way it seems to me is something like this:

Suppose we have a set \mathcal{H} of possible histories of the universe. We think of one of these as "our" history, but we don't know which one is ours (although we know the initial events in it). A priori, we don't have any way to talk about some histories being more likely than others. So can we do any kind of probabilistic reasoning, to make predictions about our future.

No, we can't in a rigorous sense, because any prediction we might make could be falsified in some possible history. But what we can do is this: There is a subset \mathcal{H}_{nice} of histories that are "nice" in the sense of having consistent relative frequencies (that is, the relative frequencies approach a limit as the number of trials goes to infinity). If we assume that our history is one of the nice ones, then we can do probabilistic reasoning. Of course, if we're not in one of the nice ones, then our probabilistic reasoning will eventually fail, but we might as well be optimists about it.

In the basic form of MWI, there is just branching and the quantum amplitude attached to each branch - there is no sense in which a branch is typical or atypical, since there is no probability yet. In the Deutsch-Wallace form of MWI, there is probability, but it is unclear whether the decision theoretic probability of an observer within one branch has anything to say about the probability of his branch being typical, which I think is related to kith's point about whether the Deutsch-Wallace MWI is consistent with our ordinary practice of science.

To me, this situation is much like ordinary probability. Suppose that we have a universe that, for simplicity, is completely deterministic except for one tiny bit of nondeterminism: There is a truly random coin. When you flip this coin, it either ends up "heads" or it ends up "tails". As far as anyone knows, there is nothing in the laws of physics that allows you to figure out whether a particular flip will end up "heads" or "tails". So it seems like we have a nondeterministic universe, to which probability is applicable.

Now, unknown to us mere mortals, what's going on is this: Every time we flip a coin, the universe splits into two copies, and one copy gets "tails" and the other gets "heads". So the dynamics of the "multiverse" is deterministic, even though the dynamics of the individual universes seems nondeterministic. Now what you could do is to give a "counting" measure for the number of the worlds, and say that if half the worlds get "heads" and half the worlds get "tails", then that means it's a 50/50 probability. If at every coin flip, the universe instead splits into THREE copies, two of which give "heads" and the other gives "tails", then we would be justified by the counting measure to assign probabilities 66/33. But here's the point: If I only live in one world, then how could it possibly make any difference to me whether the splits produce two worlds, or three worlds, or 1000 worlds? How are MY relative frequencies affected by the presence or absence of other worlds?

I say they're not. I can reason by symmetry that the coin flip has a 50/50 chance, and use that as my basis for probabilistic predictions. Of course, I might be unlucky enough to be in a world where the reasoning by symmetry gives the wrong answer, but until I have evidence that I'm in one of the bad worlds, I might as well assume that I'm in a good one.

 

[stevendaryl]

Hi, Emily! I'm so glad that you could join us in the discussion.

The main point I tried to make in that paper is simply that if you believe all possible results of a measurement always occur, then you learn nothing new about the world when you observe a measurement result. Therefore in such a world no amount of measurement data could possibly serve to confirm any scientific theory, including quantum mechanics; so the Everett approach is self-undermining because it tells us we shouldn't even believe that quantum mechanics is correct.

But I really don't see how the situation is much different classically. Suppose we live in a Newtonian universe that is infinite in all directions, and further, we assume that there are infinitely many planets with intelligent life. The only nondeterminism in this world is due to microscopic details of initial conditions. Furthermore, let's assume some kind of "completeness" in the universe. That is, let's assume that for absolutely any finite collection of particles, and for any point in the phase space of that collection, there are worlds whose initial conditions are arbitrarily close to that point in phase space.

On the one hand, for people living on a single world, such as ours, I don't see how the existence of infinitely many other worlds should affect OUR ability to do probabilistic reasoning. We should be able to reason the probability of 100,000 heads in a row is negligible, or that entropy for macroscopic objects will never reverse. But there will be some worlds somewhere for which that reasoning will prove wrong.

In such a Newtonian world, we're in the same boat as you claim MWI is. Nothing we observe can tell us anything about the universe, because we knew ahead of time that there was some planet in the universe where that outcome would happen. But once again, why should the existence of other inhabitable planets have any relevance to our use of probability on our planet?

 

[RUTA]

Hi, Emily! I'm so glad that you could join us in the discussion.
But I really don't see how the situation is much different classically. Suppose we live in a Newtonian universe that is infinite in all directions, and further, we assume that there are infinitely many planets with intelligent life. The only nondeterminism in this world is due to microscopic details of initial conditions. Furthermore, let's assume some kind of "completeness" in the universe. That is, let's assume that for absolutely any finite collection of particles, and for any point in the phase space of that collection, there are worlds whose initial conditions are arbitrarily close to that point in phase space.

On the one hand, for people living on a single world, such as ours, I don't see how the existence of infinitely many other worlds should affect OUR ability to do probabilistic reasoning. We should be able to reason the probability of 100,000 heads in a row is negligible, or that entropy for macroscopic objects will never reverse. But there will be some worlds somewhere for which that reasoning will prove wrong.

In such a Newtonian world, we're in the same boat as you claim MWI is. Nothing we observe can tell us anything about the universe, because we knew ahead of time that there was some planet in the universe where that outcome would happen. But once again, why should the existence of other inhabitable planets have any relevance to our use of probability on our planet?

Again, we don't have to assume that all possible combinations are realized. We can rather assume that every planet will measure the correct distribution. There's no reason the probability can't be instantiated in that manner. But, in MWI, the assumption is otherwise by design. That's one difference.

 

[EmilyCA]

My take on MW is, while all outcomes do occur at once, they are in separate worlds. Because of that, when you say you learn nothing new about the world I am scratching my head - obviously you do learn about the world you inhabit which seems the key thing. That others learn different things about their world doesn't worry me because they are in a different world.

I think the problem here is some ambiguity about the word `world.' It's a bit of a misnomer to refer to the separate MWI branches as `worlds', because they all exist in one and the same world, i.e. (presumably) the world governed by standard quantum mechanics. When you learn a measurement result, you learn which branch you are in, but that is not a new fact about the world, since you already knew there would be a conscious observer in every branch. You don't, for instance, learn that some measurement outcomes are more likely than others in the real world, because you know that all measurement outcomes occur in the real world. So the measurement result doesn't give you any new information which could serve either to confirm or falsify any scientific theory.

Hi, Emily! I'm so glad that you could join us in the discussion.
But I really don't see how the situation is much different classically. Suppose we live in a Newtonian universe that is infinite in all directions, and further, we assume that there are infinitely many planets with intelligent life. The only nondeterminism in this world is due to microscopic details of initial conditions. Furthermore, let's assume some kind of "completeness" in the universe. That is, let's assume that for absolutely any finite collection of particles, and for any point in the phase space of that collection, there are worlds whose initial conditions are arbitrarily close to that point in phase space.
...
In such a Newtonian world, we're in the same boat as you claim MWI is. Nothing we observe can tell us anything about the universe, because we knew ahead of time that there was some planet in the universe where that outcome would happen. But once again, why should the existence of other inhabitable planets have any relevance to our use of probability on our planet?

I think the difference here is that in the Newtonian world, there is a fact of the matter all along about which set of intelligent observers we actually are (because the thoughts that we are having are located at one point in spacetime rather than another), and so when we observe an outcome we do learn something about the world - we learn which outcome occurs for the particular observers that we happen to be. Thus we can treat ourselves as a random sample from the full set of observers, which makes it reasonable to expect that the measurement outcomes we have seen are mainly high-probability ones. Whereas in the MWI world the observers in different branches are distinguished only by the different outcomes they experience, so there is not a fact of the matter all along about which of the subsequent MWI bservers we happen to be, which means there is no fact to learn when we make an observation.

 

[stevendaryl]

Again, we don't have to assume that all possible combinations are realized. We can rather assume that every planet will measure the correct distribution.

The "correct distribution" INCLUDES a nonzero probability of weird initial conditions. If something has a nonzero probability, and you repeat the experiment infinitely often, then it will almost certainly happen (unless there is some unknown conservation law that prohibits it).

For example, the odds are 1 in 2^{10^6} that flipping a coin one million times will end up "heads" each time. If you assume that relative frequencies are always equal to theoretical probabilities, then that implies that it will happen roughly once in every 2^{10^6} worlds. To assume that it never happens, on any world, is to contradict your assumption that relative frequencies approach the theoretical probability.

 

[Rajkovic]

Why you believe anyone is controlling anyone in any world has me beat.

Thanks
Bill

not controlling, I mean, who is "me" in another universe, I mean, this is confusing.. my brain hurts

 

[bhobba]

You don't, for instance, learn that some measurement outcomes are more likely than others in the real world, because you know that all measurement outcomes occur in the real world. So the measurement result doesn't give you any new information which could serve either to confirm or falsify any scientific theory.

But surely that's just semantics. Call the universal wave-function the multi-verse and each split a sub-world. The probabilities arise simply because the theory is deterministic, but since you don't know which world you will experience all you can give is a likelihood hence the use of decision theory to decide that likelihood.

I like the way Murray Gell-Mann describes it with reference to the Consistent Histories interpretation, and even Wallace uses some of its concepts. In that interpretation its a stochastic theory about histories. In MW its a stochastic theory about the worlds you will experience.

Thanks
Bill

 

[bhobba]

not controlling, I mean, who is "me" in another universe, I mean, this is confusing.. my brain hurts

In that case don't worry about it. Chose another of the myriad of interpretations available.

Thanks
Bill

 

[stevendaryl]

I think the difference here is that in the Newtonian world, there is a fact of the matter all along about which set of intelligent observers we actually are (because the thoughts that we are having are located at one point in spacetime rather than another),

I don't view that as a fundamental difference, it's just a difference of point of view. Instead of MWI, one could do consistent histories. So there is a multiverse of possible consistent histories of the universe, and one of those possible histories is ours. We just don't know which. To me, that's exactly analogous to the case with infinitely many Newtonian worlds where one is ours, but we don't know which.

In a mathematical sense, I feel consistent histories is equivalent to MWI, it's just different ways of talking about the same thing.

But I think it actually might be wrong to think that "we" are located in one world, in the Newtonian case. What makes me me is materialistic particulars: I have particular height, weight and chemical composition. My atoms are in such and such a configuration. In my immediate surroundings, there are atoms of particular types in particular configurations. In the infinite Newtonian universe that I described, everything that makes me me is likely repeated infinitely often throughout the universe. (Of course, the precise details won't repeat exactly, but I don't think that the precise details are relevant for the personal sense of who I am---if you slightly adjusted the positions or momenta of some of my atoms, I wouldn't even notice) Whether I consider all such instances "me" or not is just labeling, it seems to me.

and so when we observe an outcome we do learn something about the world - we learn which outcome occurs for the particular observers that we happen to be.

Hmm. I really don't see how things are any different in MWI. I flip a coin (or perform a spin measurement). Afterwards, I get some result. That result is part of what makes me me. Out of all possible worlds, I consider one of them "my world", and I learn that the coin is heads-up in my world. I don't see how that's different from the Newtonian case.

Thus we can treat ourselves as a random sample from the full set of observers, which makes it reasonable to expect that the measurement outcomes we have seen are mainly high-probability ones. Whereas in the MWI world the observers in different branches are distinguished only by the different outcomes they experience,

Once again, I think that's a labeling issue. Given the complete branching history of MWI, we can think of one of the paths--choices of which branch to take--as the history of a world. We can think of one of those histories as OUR history, we just don't know which. A measurement gives us more information about which one is ours. I just don't see the big difference between MWI and the Newtonian case.

 

[stevendaryl]

I like the way Murray Gell-Mann describes it with reference to the Consistent Histories interpretation, and even Wallace uses some of its concepts. In that interpretation its a stochastic theory about histories. In MW its a stochastic theory about the worlds you will experience.

That's a question that I've had ever since reading about consistent histories. My first impression was that it is just a different way of looking at MWI, and in some sense, they are equivalent.

 

[bhobba]

That's a question that I've had ever since reading about consistent histories. My first impression was that it is just a different way of looking at MWI, and in some sense, they are equivalent.

You're not the only one - Murray basically describes it as MW without the MW. So do I for that matter.

Thanks
Bill

 

[atyy]

That's a question that I've had ever since reading about consistent histories. My first impression was that it is just a different way of looking at MWI, and in some sense, they are equivalent.

You're not the only one - Murray basically describes it as MW without the MW. So do I for that matter.

It depends on whose version you use. The Griffiths version is not like MWI, but the Gell-Mann and Hartle version is.

 

[atyy]

There is a sense of "typical", which is the worlds where relative frequencies work out to be roughly the same as the Born probabilities. I think what you mean is that there isn't an independent, non-circular notion of "rarity" such that you could prove that the atypical worlds are rare enough to be ignored. I don't know how devastating that is. For us to be able to do physics based on QM, it seems that we need to assume that our world is typical (in the sense that frequencies = Born probabilities). I don't see why it's relevant to my use of physics to know that there are worlds with atypical frequencies.

The way it seems to me is something like this:

Suppose we have a set \mathcal{H} of possible histories of the universe. We think of one of these as "our" history, but we don't know which one is ours (although we know the initial events in it). A priori, we don't have any way to talk about some histories being more likely than others. So can we do any kind of probabilistic reasoning, to make predictions about our future.

No, we can't in a rigorous sense, because any prediction we might make could be falsified in some possible history. But what we can do is this: There is a subset \mathcal{H}_{nice} of histories that are "nice" in the sense of having consistent relative frequencies (that is, the relative frequencies approach a limit as the number of trials goes to infinity). If we assume that our history is one of the nice ones, then we can do probabilistic reasoning. Of course, if we're not in one of the nice ones, then our probabilistic reasoning will eventually fail, but we might as well be optimists about it.

In contrast, with ordinary probability, we don't have to be optimists about it, we can quantify it using probability, eg. using a Frequentist p value or a Bayesian posterior. This is why we say things like the Bell tests are inconsistent with local realism, when actually any finite number of experiments allows local realism - we just mean the p value is getting smaller and smaller.

To me, this situation is much like ordinary probability. Suppose that we have a universe that, for simplicity, is completely deterministic except for one tiny bit of nondeterminism: There is a truly random coin. When you flip this coin, it either ends up "heads" or it ends up "tails". As far as anyone knows, there is nothing in the laws of physics that allows you to figure out whether a particular flip will end up "heads" or "tails". So it seems like we have a nondeterministic universe, to which probability is applicable.

Now, unknown to us mere mortals, what's going on is this: Every time we flip a coin, the universe splits into two copies, and one copy gets "tails" and the other gets "heads". So the dynamics of the "multiverse" is deterministic, even though the dynamics of the individual universes seems nondeterministic. Now what you could do is to give a "counting" measure for the number of the worlds, and say that if half the worlds get "heads" and half the worlds get "tails", then that means it's a 50/50 probability. If at every coin flip, the universe instead splits into THREE copies, two of which give "heads" and the other gives "tails", then we would be justified by the counting measure to assign probabilities 66/33. But here's the point: If I only live in one world, then how could it possibly make any difference to me whether the splits produce two worlds, or three worlds, or 1000 worlds? How are MY relative frequencies affected by the presence or absence of other worlds?

I say they're not. I can reason by symmetry that the coin flip has a 50/50 chance, and use that as my basis for probabilistic predictions. Of course, I might be unlucky enough to be in a world where the reasoning by symmetry gives the wrong answer, but until I have evidence that I'm in one of the bad worlds, I might as well assume that I'm in a good one.

I think a major question is whether such optimism is rational. In Deutsch-Wallace MWI, the unique rational assignment of weights is according to the Born rule of the true amplitudes.

If a counting assignment of weights is rational, then it would seem that the Deutsch-Wallace assignment is not unique, contrary to their claim. Wallace discusses this explicitly in http://arxiv.org/abs/0906.2718 (p28) and identifies it as being ruled out by his axioms of branching indifference and diachronic consistency. I think his axioms are reasonable.

But that doesn't address how we could come to know the weights in the first place - how we could come to their definition of a rational behaviour? How could you know whether you are in a good world or bad world, in at least a probabilistic sense? I think it is argued that the Deustch-Wallace argument doesn't address this at all, and so Greaves and Myrvold http://philsci-archive.pitt.edu/4222/ try to fix this.

 

[EmilyCA]

But surely that's just semantics. Call the universal wave-function the multi-verse and each split a sub-world. The probabilities arise simply because the theory is deterministic, but since you don't know which world you will experience all you can give is a likelihood hence the use of decision theory to decide that likelihood.

I like the way Murray Gell-Mann describes it with reference to the Consistent Histories interpretation, and even Wallace uses some of its concepts. In that interpretation its a stochastic theory about histories. In MW its a stochastic theory about the worlds you will experience.

The problem with this view, I think, is that in order for it to be a stochastic theory about which world you will experience, there needs to be a fact of the matter about which worlds you will experience, and the MWI doesn't have enough structure to allow for this - it is certain that you will experience all the worlds, and so there is nothing that you don't know to which you could apply decision theory.

But I think it actually might be wrong to think that "we" are located in one world, in the Newtonian case. What makes me me is materialistic particulars: I have particular height, weight and chemical composition. My atoms are in such and such a configuration. In my immediate surroundings, there are atoms of particular types in particular configurations. In the infinite Newtonian universe that I described, everything that makes me me is likely repeated infinitely often throughout the universe. (Of course, the precise details won't repeat exactly, but I don't think that the precise details are relevant for the personal sense of who I am---if you slightly adjusted the positions or momenta of some of my atoms, I wouldn't even notice) Whether I consider all such instances "me" or not is just labeling, it seems to me.

I think the difference here is that we can give a non-indexical account in terms of the physical locations of thought-events: when I have the thought 'I wonder which outcome I am going to see?' there is a fact about where in spacetime that thought-event occurs, and so there is a unique answer to this question, since there is a unique outcome that is going to occur in the vicinity of the thought. In the Everettian case this isn't possible: if prior to the measurement we wonder which outcome we're going to see, there is no unique answer since there is only one thought-event but many different outcomes that are going to be seen.

 

[bhobba]

it is certain that you will experience all the worlds, and so there is nothing that you don't know to which you could apply decision theory.

You won't experience all worlds. 'You' are not the multiple copies that appear in many worlds. You are one copy experiencing one world.

I know its a weird interpretation and because of that leaves open all sorts of semantic difficulties. That's one reason I don't ascribe to it. But like all interpretations there are pro's and con's. MW's pro is you simply have this evolving state.

Thanks
Bill

 

[EmilyCA]

You won't experience all worlds. 'You' are not the multiple copies that appear in many worlds. You are one copy experiencing one world.

What, precisely, do you mean by `you'? If `you' are merely a person-at-a-time rather than a continuant over time, then there is no fact of the matter about which outcome `you' will see when you perform the measurement. Whereas if `you' are an entity that persists over time, then it seems that `you' will indeed experience all the worlds, since the observers who see the different outcomes are not distinct before the time of the measurement.

Either way, it seems that there is nothing here which can play the necessary stochastic role.

 

[bhobba]

What, precisely, do you mean by `you'? If `you' are merely a person-at-a-time rather than a continuant over time, then there is no fact of the matter about which outcome `you' will see when you perform the measurement. Whereas if `you' are an entity that persists over time, then it seems that `you' will indeed experience all the worlds, since the observers who see the different outcomes are not distinct before the time of the measurement.

'You' means what you experience as a sequence of worlds. You never experience more than one world at a time.

Thanks
Bill