Question regarding the Many-Worlds interpretation

[stevendaryl]

But the assumption that you will draw a red ball 9/10s of the time has a plausible grounding in the situation: if nothing interferes, it's what you should rationally expect.

I think the word "rationally" is ambiguous. There are two different types of reasoning that are both called "being rational", but they are very different: (1) mathematically precise, rigorous reasoning, and (2) reasoning based on experience. If you are talking about (1), then I don't think that it's justified, because there is no proof in either case. If you're talking about number (2), it seems to me that it's rationally justified just because that kind of reasoning has worked well in the past.

There is no similarly plausible grounding of the Born rule in the MWI. Knowledge of the MWI gives you no reason to expect Born probabilities. To use tom.stoer's metaphor, it just gives you numbers painted on the balls, but no reason to expect these to correspond to anything at all. That they give you probabilities of drawing the balls would ordinarily be taken as evidence for there to be something else at work, as the MWI alone simply fails to account for it.

Ultimately, I think it's a matter of postulating a connection between a fact about the current state and a fact about relative frequencies. It's as much of a postulate when we say:

"Since 9/10 of the balls are red, I assume that 9/10 of the time, I will draw a red ball." You can't justify your base assumptions, other than empirically.

 

[S.Daedalus]

Come on, you can't honestly be trying to tell me that in the scenario outlined by tom.stoer, you'd assign the same probabilities to both buckets?

 

[tom.stoer]

But the assumption that you will draw a red ball 9/10s of the time has a plausible grounding in the situation: if nothing interferes, it's what you should rationally expect (and since it's irrational to expect an unknown interference, it's what you should expect, period). You don't expect this draw for the negative reason of lack of a plausible alternative, but for the positive reason of it being the natural conclusion to draw, given your knowledge of the situation.

There is no similarly plausible grounding of the Born rule in the MWI. Knowledge of the MWI gives you no reason to expect Born probabilities. To use tom.stoer's metaphor, it just gives you numbers painted on the balls, but no reason to expect these to correspond to anything at all. That they give you probabilities of drawing the balls would ordinarily be taken as evidence for there to be something else at work, as the MWI alone simply fails to account for it.

You got it - 100%

stevendaryl, all what I want to indicate is that MWI as an interpretation is counter-intuitive in this sense and does not provide a natural explanation for probabilities; even a mathematical proof that exactly one unique probability measure is singled out does not explain why any probability at all shall arise.

The problem is that MWI tries to interpret the formalism in terms of branches, but that these branches do not provide a probability measure in a natural way; the probability measure enters the formalism w/o entertaining the ideas of MWI regarding branches. This is not inconsistent but very unsatisfying for an interpretation.

 

[stevendaryl]

You got it - 100%

stevendaryl, all what I want to indicate is that MWI as an interpretation is counter-intuitive in this sense and does not provide a natural explanation for probabilities; even a mathematical proof that exactly one unique probability measure is singled out does not explain why any probability at all shall arise.

The problem is that MWI tries to interpret the formalism in terms of branches, but that these branches do not provide a probability measure in a natural way; the probability measure enters the formalism w/o entertaining the ideas of MWI regarding branches. This is not inconsistent but very unsatisfying for an interpretation.

As I said in another post, the way I think of motivating MWI is to start with a "collapse" interpretation, and then gradually move the time of the collapse later and later. MWI is in some sense the limit as you push the time of the collapse off to infinity.

 

[stevendaryl]

Come on, you can't honestly be trying to tell me that in the scenario outlined by tom.stoer, you'd assign the same probabilities to both buckets?

I'm not saying that I don't share your (and Tom's) intuitions about this--I'm just skeptical about how meaningful our intuitions are in situations that are so far removed from the examples where we developed those intuitions.

 

[lukesfn]

Let's compare two experiments:

1)
A hat with 9 red and 1 green balls;
A (repeated) experiment where a single ball is drawn and placed back;
Result strings like s = "RRGRRRG...";
Statistical frequencies and calculated probabilities 0.9 and 0.1;

2)
A hat with 1 red and 1 green ball;
The red and the green balls have labels "0.9" and "0.1", respectively;
A (repeated) experiment ...
Result strings like s = "RRRGRRGRR...";
A witness confirming that NEVER a single ball is drawn but ALWAYS a PAIR like ["red with label 0.9" and "green with label 0.1"];
Statistical frequencies 0.9 and 0.1 extracted from the result strings;

My question is why the labels "0.9" and "0.1" do affect the statistical frequencies.

No matter how many times you rephrase your question, it is always perfectly clear to me, and answers always seem frustratingly like misdirection or riddles. However, I have a theory about the source of miss understanding.

If we alter your case 2, and instead say that 10 balls are drawn, always 9 red, and 1 green then the frequencies make sense right?

Of course, to get closer to MWI, it is only possible to observe 1 out come, so we could say there are 10 observers, 9 observing a red ball, 1 observing a green ball. But, the probabilities are still perfectly clear through branch counting.

However if we have 9 observers of the red ball, then there is nothing obvious that differentiates them. The are identical. We could label them to make the difference clear, but, what I think many prefer to do is not differentiate them, and intact, think of them as the same entity, but with a measure of existence, or an amplitude.

So instead of thinking of a 9 red balls, and 1 green ball, we some think of it as a red ball with a measure of existence of .9 and a green ball with a measure of existence of .1

To replicate QM fully, instead of 10 observers, obviously you would need a lot more, or perhaps infinite, however, where I would count infinite identical branches, others count 2 branches with amplitudes attached.

Does that make sense?

Edit:
Additionally, you could say that there is room for probability to emerge where there is ignorance about not only which branch you are in, ignorance but how many branches there are, or what a branch actually is.

 

[tom.stoer]

lukesfn, I am not sure whether I get your point.

When I started the thread the intenation was to learn how "branch counting" allows us to derive Born's rule. I had to learn that this is impossible, you can neither define nor count these branches unambiguously. So yes, you can define a probability measure, but no, it is not related to the branches.

All what I wanted to explain with case (2) is this problem. I never expected to rephrase (2) so that it perfectly fits to MWI, nor do I expect to repair MWI such that it fits to classical reasoning.

You are correct when saying "instead of thinking of a 9 red balls, and 1 green ball, we think of it as a red ball with a measure of existence of .9 and a green ball with a measure of existence of .1", but that is not an interpretation of the formalism, it's the formalism itself, a tautology. You do not get additional insight from this as long as you cannot explain what "existence" and "measure of existence" do mean. The problem is that w/o being able to identify branches you cannot even associate a "probability of existence" with it.

 

[S.Daedalus]

As I said in another post, the way I think of motivating MWI is to start with a "collapse" interpretation, and then gradually move the time of the collapse later and later. MWI is in some sense the limit as you push the time of the collapse off to infinity.

Even if you can do this, it doesn't entail you can get rid of the collapse.

I'm not saying that I don't share your (and Tom's) intuitions about this--I'm just skeptical about how meaningful our intuitions are in situations that are so far removed from the examples where we developed those intuitions.

But what interpretation is all about is to create a compelling narrative that accounts for our observations and the mathematical formalism build from them. Your argument would entail a sort of instrumentalist or operationalist stance: we can't picture the quantum world, so we shouldn't try to; so shut up and calculate. To me, while useful for calculations etc., this however falls far short from the goal of science. All other sciences get to develop narratives: archaeologists don't think of ancient cultures as being merely a theoretical device in order to account for pottery shard distributions, and paleontologists don't believe that dinosaurs are just a construct accounting for certain bone-shaped rocks; rather, they take these things (ancient cultures, dinosaurs) to be the very object of their study, investigated by means of the empirically accessible evidence. Assuming that something like this isn't possible for physics would seriously impoverish it, to me, reducing us physicists essentially to skilled operators of black boxes whose functioning we don't dare guess at.

I also have an issue with your use of the terms 'intuition' and 'rationality'. In general, rationality is not bound to either of your definitions above, but rather, is simply the process of using reason to arrive at a conclusion in line with all available knowledge; and this reason is typically not taken to be reducible to simple intuition. From the setup in tom.stoer's (1), it's reasonable to arrive at the probability assignments, using a principle of indifference justified by the symmetry of the situation. This can at least plausibly be arrived at from complete ignorance of similar situations, so I'd dispute it being simply due to intuition. But in the second setup, there's just no way from it to the postulated distribution; to say that it's nevertheless reasonable to assign these probabilities smells of vested interest to me.

No matter how many times you rephrase your question, it is always perfectly clear to me, and answers always seem frustratingly like misdirection or riddles. However, I have a theory about the source of miss understanding.

If we alter your case 2, and instead say that 10 balls are drawn, always 9 red, and 1 green then the frequencies make sense right?

The problem here is simply that you have used your knowledge of what the right probabilities are in order to construct this case. But this introduces a circularity. This is ex post facto reasoning: you modify the account of the MWI after knowing how things should shake out; but then, this means that the MWI account itself is unable to provide sufficient justification.

 

[lukesfn]

lukesfn, I am not sure whether I get your point.

When I started the thread the idea was to learn how "branch counting" allows us to derive Born' rule. I had to learn that this is impossible, you can neither define nor count these branches unambiguously. So yes, you can define a probability measure, but no, it is it related to the branches.
.

tom.stoer, I'm sure I am more ignorant then you, so I might be talking nonsense, however, I suspect that this is where you have gone wrong, and that it is actually possible to "count branches" and derive the Born rule if you define branches in an appropriate way, however, that way might give people enough of a headache that they prefer to just believe in a measure of existence, or just find it necessary to think about it further.

If somebody can point me back to the reason why branch counting must fail to derive the correct probabilities under any possible definition of branching, then I would like to see that, however, I suspect that it is under the condition of assumptions that some people would prefer to accept a measure of existence to avoid braking. Again I am very ignorant so fully accept I could be wrong.

From my very naive point of view, if saying there is 0.9 probability of a QM prediction, I can't see we couldn't define spitting such that 90% of identical worlds will go one way, while 10% will go the other. It seems straightforward to me to replace amplitudes or a measure of existence with a fraction of a continuous distribution of worlds. Unfortunately, I don't know near enough about QM to even guess where that kind of thinking could go wrong. I'd love somebody else to help me out here.

I do find the idea of a continuous distribution of worlds an easier concept to accept then a measure of existence though.

 

[lukesfn]

The problem here is simply that you have used your knowledge of what the right probabilities are in order to construct this case. But this introduces a circularity. This is ex post facto reasoning: you modify the account of the MWI after knowing how things should shake out; but then, this means that the MWI account itself is unable to provide sufficient justification.

I built the probabilities straight into the MWI account I gave.

My MWI account is 10 words, 9 with a red ball, 1 green.

It follows all things being even that the probability of being in word is the red ball is .9

Certain assumptions might be made, but there is no circular reasoning I can see.

I was told how things should shake out, and I made an account to explain why.

Like wise...

QM tells us how things should shake out, so why can't we also succeed in making an account to explain it? That is the point of this discussion right? It may not be the correct account, and QM may even be false its self, however, that is all beside the point. We have a formulation of QM, and we want to find a MWI formulation that is consistent with it. The probabilities don't need to just fall out of it, but they do need to be able to be added to it in a way that is logically consistent.

There is no requirement for there to me one unique correct MWI that the correct probabilities just fall out of. However, it is does seem important that MWI can be formulated to be consistent with the expected probabilities in a logically consistent manner.

Logically consistent to me does not mean that the world can be replace into 2 equal worlds with and the probability of each being something other then 50/50.

 

[stevendaryl]

Even if you can do this, it doesn't entail you can get rid of the collapse.

It seems to me that it does. If we can push it back indefinitely, then that means that perhaps no collapse has ever occurred. Yet. If that's the case, then it's hard for me to see that the meaningfulness of probabilities could depend on a collapse that happens 1000 years from now.

But what interpretation is all about is to create a compelling narrative that accounts for our observations and the mathematical formalism build from them.

I agree. I'm not an MWI advocate, but I have a hard time finding anything MORE compelling.

I also have an issue with your use of the terms 'intuition' and 'rationality'. In general, rationality is not bound to either of your definitions above, but rather, is simply the process of using reason to arrive at a conclusion in line with all available knowledge;

What does "in line with" mean? Logically implied by? Logically consistent with?

and this reason is typically not taken to be reducible to simple intuition. From the setup in tom.stoer's (1), it's reasonable to arrive at the probability assignments, using a principle of indifference justified by the symmetry of the situation.

I agree it's a natural assumption. But the problem with interpretations of quantum mechanics is that the collection of all natural assumptions seem to collectively be inconsistent.

 

[Jazzdude]

I agree. I'm not an MWI advocate, but I have a hard time finding anything MORE compelling.

You could try http://arxiv.org/abs/1205.0293. It's a realist alternative to MWI, but sufficiently different to not run into the same problems.

Cheers,

Jazz

 

[S.Daedalus]

I built the probabilities straight into the MWI account I gave.

My MWI account is 10 words, 9 with a red ball, 1 green.

It follows all things being even that the probability of being in word is the red ball is .9

Certain assumptions might be made, but there is no circular reasoning I can see.

I was told how things should shake out, and I made an account to explain why.

Yes, but the ideal way would be that the theory tells you how things should shake out, and then you go and check. The addition of sufficiently many worlds in order to make the probabilities come out right goes the other way around.

I also must confess to having troubles seeing how this 'measure of existence'-thing is supposed to be interpreted. Let's say we have two universes: one with a single history, and the other with that same history, just copied twice. What exactly would be the difference between these universes? I'm not sure that 'the universe contains two copies of the history' has any kind of content. Leibnitz introduced the idea of the identity of indiscernibles; according to this, one should identify the two copies of the history, and hence, the two universes.

It seems to me that it does. If we can push it back indefinitely, then that means that perhaps no collapse has ever occurred. Yet. If that's the case, then it's hard for me to see that the meaningfulness of probabilities could depend on a collapse that happens 1000 years from now.

Well, I have some sympathies with that line of thinking. I toyed around with the idea of a particular 'objective collapse' type of theory, in which we introduce a special particle, the collapson, which induces a collapse whenever it is encountered (in fact, Penrose's objective redution is such a theory, with the collapson being the graviton). Then, we take the number of collapsons smoothly to zero, which corresponds to the collapse happening 'at infinity'. If there's no phenomenological change, then the collapse shouldn't matter, and can be done away with, right?

Unfortunately, I don't think this trick will work, because you end up with different 'asymptotical' states: one that's a proper mixture (when you have a collapse at infinity), and one that's a superposition (when you remove the collapse entirely). So while in one case, you can again basically attach a probability distribution over histories with Gleason, you can't do so in the case without collapse entirely, because the world simply fails to have one particular history.

What does "in line with" mean? Logically implied by? Logically consistent with?

Ideally, the former, but you'd be right to point out that real-world reasoning practically never works that way. However, the latter is certainly not enough, since there are innumerable possibilities at all times consistent with what we know, and putting them on the same footing would introduce an epistemic anarchism making any sort of informed decision making (and with that, science) impossible.

I agree it's a natural assumption. But the problem with interpretations of quantum mechanics is that the collection of all natural assumptions seem to collectively be inconsistent.

That's not a reason to throw all of them out at once, however, but rather, to proceed as conservatively as possible, doing away with only what you are absolutely forced to renounce.

 

[lukesfn]

Yes, but the ideal way would be that the theory tells you how things should shake out, and then you go and check. The addition of sufficiently many worlds in order to make the probabilities come out right goes the other way around.

Would this be of any negative for MWI when compared to most other interpretations? I guess it depends on your point of view. Still, I do see the point that there are certain coincidences in physics that seem to hint at a deeper explanation and adding them in an ad hoc way seems deeply unsatisfying.

I also must confess to having troubles seeing how this 'measure of existence'-thing is supposed to be interpreted. Let's say we have two universes: one with a single history, and the other with that same history, just copied twice. What exactly would be the difference between these universes? I'm not sure that 'the universe contains two copies of the history' has any kind of content. Leibnitz introduced the idea of the identity of indiscernibles; according to this, one should identify the two copies of the history, and hence, the two universes.

Thanks for that little bit of info. I certainly have no problem imagining multiple identical copies of history myself, even if it all sounds a bit hard to believe.

 

[S.Daedalus]

Well, I have some sympathies with that line of thinking. I toyed around with the idea of a particular 'objective collapse' type of theory, in which we introduce a special particle, the collapson, which induces a collapse whenever it is encountered (in fact, Penrose's objective redution is such a theory, with the collapson being the graviton). Then, we take the number of collapsons smoothly to zero, which corresponds to the collapse happening 'at infinity'. If there's no phenomenological change, then the collapse shouldn't matter, and can be done away with, right?

Incidentally, a somewhat similar way of thinking that I'm not quite as convinced doesn't work comes from taking advantage of the asymptotically de Sitter nature of the universe: while decoherence alone can't ensure the emergence of a proper mixture, maybe as soon as the entangled parts of the wave function recede from each other at faster than light speed, you could sort of argue that now, it's not even possible in principle to tell the difference between proper and improper mixture, and consider the decoherence to be final, as any recoherence is now impossible.

But it seems somewhat strange to me that the interpretation of quantum mechanics should depend on the large-scale structure of the universe (and I'm not sure the argument goes through at all, as I don't know the properties of the cosmological horizon in dS space well enough; if it's like a black hole or Rindler horizon, one might have to expect that the information 'leaks out' again)...

Thanks for that little bit of info. I certainly have no problem imagining multiple identical copies of history myself, even if it all sounds a bit hard to believe.

Well, it's just like having three identical red balls; what makes it such that there are three? How do you count them? There's no way, with them being identical, to point to one and call it 'number 1' or even just 'that one there', as all properties are shared between the balls. So how could one conceivably arrive at the number three? (One must resist the temptation of imagining the balls as being somewhere in space, because then, their spatiotemporal characteristics serve to distinguish them.)

 

[lukesfn]

Well, it's just like having three identical red balls; what makes it such that there are three? How do you count them? There's no way, with them being identical, to point to one and call it 'number 1' or even just 'that one there', as all properties are shared between the balls. So how could one conceivably arrive at the number three? (One must resist the temptation of imagining the balls as being somewhere in space, because then, their spatiotemporal characteristics serve to distinguish them.)

But what if I define the weight of a ball, and I show you a number of indistinguishable balls sitting on a set of scales. Could you not work out the count, even though you can not distinguish in any way, including position is space?

I don't see why something must be distinguishably countable to have a number. If it is there, it is there, directly distinguishable or not. I can't see an issue with that personally, but I guess this is one reason why some people prefer to think of a measure of existence, rather then numerous identical histories.

However, given certain assumptions, a count of identical histories could be inferred through the probabilities. (Ignoring dealing properly with infinities here)

In practice, because the can't be directly observed, non identical histories can't be counted either and only inferred given certain assumptions. Therefore, identical or different doesn't cause much confusion in my mind.

If I want to imagine identical histories, or identical balls as distinguishable, I don't see why I can't imagine them positioned uniquely along an invisible dimension. In fact this interpretation might fit quite well in MWI, where each branch is replaced by a slice of Multiple World space.

 

[S.Daedalus]

But what if I define the weight of a ball, and I show you a number of indistinguishable balls sitting on a set of scales. Could you not work out the count, even though you can not distinguish in any way, including position is space?

What if the guy in the shop scammed you, and gave you three 50g-balls instead of five 30g-ones? How do you find out? If you suspect the fraud, how would you convince a judge?

 

[lukesfn]

What if the guy in the shop scammed you, and gave you three 50g-balls instead of five 30g-ones? How do you find out? If you suspect the fraud, how would you convince a judge?

Isn't this getting a bit too far into pure philosophy?

How can you prove anything? How do you know that everything you have taught wasn't a lie? How do you know any of your perceptions of reality work correctly? How do you know that your brain functions correctly and your ability to reason isn't fundamentally impaired? That line of reasoning always leads to the only think to you can be sure of "I think there for I am", and I am not even sure of that.

However, life becomes simpler if we make some working assumptions.

We are talking about interpretations here. It is not what is knowable that is so important, rather that things are logically consistent.

I made some assumptions in my argument. I defined the weight of the balls, I assume the scales work accurately.

I see how you could try to philosophically claim that there is really one 900g ball, not nine 10g balls, however, that is just an interpretation, and I guess that is why some people like to think in a 'measure of existence'

However I my self am perfectly comfortable with the concept of 9 balls. It would be very simple to write a computer simulation with indistinguishable objects occupying the same space, where the count has an effect on the physics, and the running computer program could be considered as objective reality. In fact, I've had this happen by ancient before, fortunately I didn't have to question the the concept of a number of indiscernible objects, instead, I was instead able to discern the.objects by looking at the code.