Many Worlds Interpretation and act of measuring

[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

 

[RUTA]

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.

I should've said every planet will discover the correct probability, not distribution. Of course in establishing the correct probability, everyone will see the correct distribution. Again, you're just making an assumption otherwise. There's no logical reason that has to be the case. Given your assumption for the way the probability of classical physics is instantiated in reality, then I agree, MWI is no worse off.

 

[stevendaryl]

e

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.

I disagree. For probability theory to be HELPFUL, in the sense of providing useful tips on how to bet on future occurrences (I'm using "bet" in a loose sense here--if I take a plane, I'm betting my life that it won't crash), the future relative frequencies should be roughly what is predicted by my probability theory. If that isn't the case, then I've wasted my time computing probabilities. But whether the future turns out the way probabilities predict is luck. They may not.

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.

I'm only claiming that a counting assignment of weights is AN approach to dealing with nondeterminism. If all you have to go on is a set of possibilities, and you have no basis for distinguishing the different possibilities, then a counting weight is as good as anything. It's sort of a "minimalist" assumption.

The case of quantum mechanics is a little more complicated, because we do have other information that simply the number of possible outcomes. We have the amplitudes, as well. Various people have argued that if we assume that a weight is derivable from amplitudes, then something like the Born rule is the only possibility consistent with certain other criteria for reasonableness.

Basically, we decide that a particular way of assigning weights is best because the other alternatives have unmotivated, ad-hoc elements that we find objectionable. There's the same sort of thing going on in statistical mechanics. We compute such things as entropy by making the assumption (or maybe definition) that for a thermally isolated system in equilibrium, all states with the same energy are equally likely. We don't really know that that's the case, but we have no basis for assuming anything different.

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?

I don't think that that's mysterious, at all. We perform the same experiment a bunch of times, and compute relative frequencies. Then we assume that they reflect some kind of probability, and we develop a theory to allow us to calculate it. If the relative frequencies hadn't turned out that way, we would have discarded the theory.

How could you know whether you are in a good world or bad world, in at least a probabilistic sense?

I think it's just an assumption. If we don't assume that future relative frequencies can be calculated, then we can't make predictions about the future. We can't do science. We can't do technology. We can't do medicine. So we assume that we live in a nice, predictable world, because we have no other way to reason about it. If our assumption is wrong, then we're screwed. But as I said, we might as well be optimists about it.

 

[EmilyCA]

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

Thanks
Bill

In that case, it is true as a matter of definition that `you' see whatever outcome it is that you see. Therefore there is nothing to be learned in a measurement: you are defined as the agent who sees outcome A, so the measurement yields only the tautology, `The agent who sees outcome A sees outcome A.' This sort of fact cannot possibly confirm or falsify a scientific theory.

 

[bhobba]

In that case, it is true as a matter of definition that `you' see whatever outcome it is that you see. Therefore there is nothing to be learned in a measurement: you are defined as the agent who sees outcome A, so the measurement yields only the tautology, `The agent who sees outcome A sees outcome A.' This sort of fact cannot possibly confirm or falsify a scientific theory.

That I agree with. Its more or less tautological in the interpretation that you will experience one world because that's what human beings do. If that's a problem I don't really see it.

Thanks
Bill

 

[stevendaryl]

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.

I wouldn't say that we KNOW that there is a fact of the matter about such questions. We don't. As far as I can see, it's just an attitude toward the theory, it's not inherent in the theory.

Take my Newtonian universe, with infinitely many worlds that fill up all of phase space. The question is: What is "Daryl" or "Emily"? We can take an indexical approach, where we say that Daryl is defined by the person at an unobservable location in spacetime. Or we can take a subjective approach, where "Daryl" is defined by a coarse-grained equivalence class of all systems in the universe with subjectively equivalent situations. From the latter point of view, I don't have a unique location in the universe, and the future for me is nondeterministic. Mathematically, the two ways of viewing things are equivalent. Given the first, we can get to the second by taking equivalence classes, and given the second, we can get to the first by introducing a "hidden variable" that determines my first experiences (this hidden variable is equivalent to knowing my "true" location in the universe).

 

[stevendaryl]

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.

If the future is not determined, then it seems that, by definition, there is no "fact of the matter" about future events. They become facts when they happen, and get entered into our memories. So the only facts are facts about the past (and possibly facts that hold in all possible futures). I don't see that branching or stochastic events makes any difference. In both cases, the past is definite, and the future is indefinite.

 

[Quantumental]

If the future is not determined, then it seems that, by definition, there is no "fact of the matter" about future events. They become facts when they happen, and get entered into our memories. So the only facts are facts about the past (and possibly facts that hold in all possible futures). I don't see that branching or stochastic events makes any difference. In both cases, the past is definite, and the future is indefinite.

In MWI the future is definite. You know that pre-branching that you will see all outcomes post-branching.

 

[bhobba]

In MWI the future is definite

Yes - but what you experience isn't.

Thanks
Bill

 

[stevendaryl]

In MWI the future is definite. You know that pre-branching that you will see all outcomes post-branching.

It depends on what you mean. The future of the universe as a whole is definite. But if you think of your personal history as a path through the branches, then your history up to one point in time doesn't determine your future history.

 

[atyy]

I disagree. For probability theory to be HELPFUL, in the sense of providing useful tips on how to bet on future occurrences (I'm using "bet" in a loose sense here--if I take a plane, I'm betting my life that it won't crash), the future relative frequencies should be roughly what is predicted by my probability theory. If that isn't the case, then I've wasted my time computing probabilities. But whether the future turns out the way probabilities predict is luck. They may not.

All observations are consistent with complete randomness and no laws of physics. But why do we act as if Copenhagen quantum mechanics or equilibrium statistical mechanics are better theories than complete randomness? The reason is that we are typical in Copenhagen and equilibrium statistical mechanics, but we are not typical in complete randomness. So MWI has to find some way of arguing that the results we see are "typical" in some sense, otherwise we could not choose between MWI and complete randomness.

One way to argue that we are "typical" in MWI in some sense is to assign a weight, such as the branch counting measure you mention. But there are potential problems with this.

(1) It is unclear whether we are typical given a branch counting measure, and some argue that we are not typical given such a measure.

(2) It seems to conflict with the Deutsch-Wallace argument. At the very least, it would seem that MWI does not make sense unless additional structure is introduced, such as the branch-counting measure. Maybe this would be ok, if we start with the branch counting measure as a guess, and then are able to update it as one gets more data. I think this is what Greaves and Myrvold try to do.