Question regarding the Many-Worlds interpretation

[stevendaryl]

This is what we observe, but for the MWI to work a proof is required. Currently we do believe in decoherence to provide the proof that this is approximately true, i.e. that states like |U>*|d> are "dynamically suppressed".


Again this is what we observe, and for which a proof is required.

You're absolutely correct there. That (in my opinion) is a real problem with any no-collapse interpretation of quantum mechanics. Measurement has to be an irreversible process, and there is a question of how irreversible can arise from reversible dynamics. Of course, it's the same sort of problem with classical physics, but there people have the argument that fundamental physics is reversible, but that the initial conditions are such that one direction is much more probable than the other. I don't know how that argument would work in MWI.

The 1st step means that a preferred basis is singled out i.e. that off-diagonal terms are suppressed, the 2nd step means that the preferred basis (branching) is stable i.e. that off-diagonal terms stay suppressed.

My step 1 assumes that there is such a thing as a measurement device. By definition, a measuring device for a property such as spin must become correlated with the spin in a definite way. So you're certainly right that there is a gap in the argument, which is the proof that there are such things as measurement devices. That's a difficult problem, it seems to me, because it necessarily, as I said, involves irreversibility, which involves huge numbers of particles. But I don't see that that is particularly a problem for MWI. You have to have measurement devices to make a "collapse" interpretation work, as well.

But besides the fact that a sound proof for realistic systems seems to be out of reach, it is unclear whether Gleason's theorem shall tell us anything in the MWI context (I think this is what mfb wanted to stress). The theorem says that the only valid probability measure is the Born measure. The theorem (no theorem!) tells us why we should interpret a measure as a probability! The question is "probability for what?"
For the state being in a subspace? No, the state is still in a superposition
For observing "UU"? Why shall a prefactor of a specific subspace be a probability?

When you're talking measures on "possible worlds", you're really not talking about probability, in the strict sense, because probability is connected with the results of repeated measurements in a single "possible world". So it's not a probability, it's a measure on "possible worlds", where a possible world is given by what I was calling an "observation", which is an assignment of eigenvalues to a mutually commuting set of observables.

I know that many do not like why-questions in physics, but this why-question is key for the whole MWI debate!

There is one fact regarding the MWI which is really very disappointing: the whole story starts with a clear and minimalistic setup. But the ideas to prove (or to motivate) the Born rule have become awefully complicated over the last decades. That means that MWI misses the point!

To me, what motivates MWI is the fact that alternatives such as the collapse hypothesis propose the existence of an interaction (the collapse) which only affects macroscopic objects with persistent memories (like humans and devices) but not microscopic objects like electrons and atoms. That is very suspicious to me. Surely, the physics of macroscopic objects should follow from the physics of the microscopic objects that it's made out of?

So to me, intellectual coherence requires either that quantum mechanics (the smooth evolution of the wave function according to Schrodinger's equation) applies to all objects, no matter how small, or else there is some new type of interaction that should be observable in the small. There are "stochastic" interpretations of quantum mechanics that don't have a measurement-induced collapse, but instead particles are always randomly having their wave functions collapse. I don't very much like that, but I like it better than the usual "collapse" interpretation, which makes an unsatisfying distinction between macroscopic and microscopic objects.

I think of MWI as more of a research program than an interpretation--it's really seeing how far can we push a version of QM that does not have a "collapse". If you don't have collapse, then macroscopic superpositions are inevitable, and "Many Worlds" is just a way to picture macroscopic superpositions.

 

[stevendaryl]

I took the setup to be essentially that of a quantum system and a detector with a memory; in order to decide the contents of the memory, you have to do a measurement on the complete system.

If you have a detector with memory, you can let it run for, say, 100 measurements. Afterward, assuming the correctness of the detector and its memory, the combination of Detector + Electron will, I'm claiming, be in the state:

$\alpha (|UUUU...U\rangle \otimes |u\rangle) + \beta (|DDD...D\rangle \otimes |d\rangle)$

So, in a "collapse" interpretation, we can push the moment of collapse back to the time that a human being examines the content of the detector's memory, and he will find 100 "up" measurements with probability $|\alpha|^2$ and 100 "down" measurements with probability $|\beta|^2$. So there is no need to assume that the measuring device "collapsed" the wave function--you can put off the collapse till later.

But then, the same sort of putting off of collapse can happen with the experimenter. You can assume that the experimenter (+ detector + electron) is in a superposition of states until he reports his findings to his advisor. Then the advisor's observing his student's state causes the student's state to collapse. Or you can put off the moment of collapse further...

So if you stick with a "collapse" interpretation, then my claim is that there is no feasible experiment that can tell you when the collapse took place: at the detector, at the experimenter, at his advisor, etc. I consider MWI as a kind of limit in which you put off the moment of collapse indefinitely far into the future.

 

[S.Daedalus]

So if you stick with a "collapse" interpretation, then my claim is that there is no feasible experiment that can tell you when the collapse took place: at the detector, at the experimenter, at his advisor, etc.

This I agree with totally. (And such 'Wigner's friend'-type tales are the reason I consider all collapse theories to be unworkable.)

 

[tom.stoer]

To me, what motivates MWI is the fact that alternatives such as the collapse hypothesis propose the existence of an interaction (the collapse) which only affects macroscopic objects with persistent memories (like humans and devices) but not microscopic objects like electrons and atoms. That is very suspicious to me. Surely, the physics of macroscopic objects should follow from the physics of the microscopic objects that it's made out of?

So to me, intellectual coherence requires either that quantum mechanics (the smooth evolution of the wave function according to Schrodinger's equation) applies to all objects, no matter how small, or else there is some new type of interaction that should be observable in the small. There are "stochastic" interpretations of quantum mechanics that don't have a measurement-induced collapse, but instead particles are always randomly having their wave functions collapse. I don't very much like that, but I like it better than the usual "collapse" interpretation, which makes an unsatisfying distinction between macroscopic and microscopic objects.

I think of MWI as more of a research program than an interpretation--it's really seeing how far can we push a version of QM that does not have a "collapse". If you don't have collapse, then macroscopic superpositions are inevitable, and "Many Worlds" is just a way to picture macroscopic superpositions.

Excellent, I fully agree, especially to your last remark regarding whether MWI is an interpretation or a research program. It seems that what has been an interpretation was - at least partially - turned into a research program: "emergence of dynamically isolated and stable branches due to decoherence", "derivation of Born's rule", ... So there is less room for interpretations and more need for theorems. In addition there are means to motivate statements or even derive them based on the formalism, which is not possible in collapse interpretations. So MWI is really a long and stony path for the brave ...

And it seems that we agree on the key issues, namely how time-asymmetry observed "within a branch" does emerge from a time-symmetric formalism, and how observed statistical frequencies can be explained via a probability (or a measure or whatever) to emerge from a fully causal and deterministic formalism.

 

[stevendaryl]

I have a probability distribution over marbles in a hat as follows: P(Green)=0.5, P(Blue)=0.3, P(Red)=0.2. I draw a marble from a nearby urn. What's the probability that it's green?

I don't know, and I don't see the relevance. What I'm saying is that the wavefunction is used to calculate a measure on "possible worlds", where a possible world is (in my "many-observers" interpretation) a possible result of a measurement--an assignment of eigenvalues to a collection of mutually commuting Hermitian operators. You seem to be saying that I can't use the wave function to compute a measure unless I collapse the wave function afterward. That doesn't make a bit of sense.

 

[stevendaryl]

Excellent, I fully agree, especially to your last remark regarding whether MWI is an interpretation or a research program. It seems that what has been an interpretation was - at least partially - turned into a research program: "emergence of dynamically isolated and stable branches due to decoherence", "derivation of Born's rule", ... So there is less room for interpretations and more need for theorems.

I think if you look at Everett's original paper, his actual contribution was showing that the use of mixed states can arise naturally, without assuming "collapse", if you take into account the entanglement between one system and a second system that "measures" the first. So you don't actually need collapse in order to understand how mixed states can arise in quantum mechanics, and you don't need collapse in order to understand why, after a measurement of an electron's spin direction, you no longer see any interference between alternatives. Both are effects of entanglement.

Historically, it was Dewitt who tried to elevate Everett's work to a new interpretation of quantum mechanics. I don't actually think it's a new interpretation, I think it's a research program.

And it seems that we agree on the key issues, namely how time-asymmetry observed "within a branch" does emerge from a time-symmetric formalism, and how observed statistical frequencies can be explained via a probability (or a measure or whatever) to emerge from a fully causal and deterministic formalism.

Yes. Some of it, I fear, might be just too hard to actually solve. Once macroscopic objects are involved, you no longer have two and three particle wave functions (which are difficult enough), but wave functions involving $10^{23}$ particles. We can't hope to solve equations for such a system. Hopefully, there are ways to get insights about such a system that doesn't require solving it.

 

[S.Daedalus]

I don't know, and I don't see the relevance. What I'm saying is that the wavefunction is used to calculate a measure on "possible worlds", where a possible world is (in my "many-observers" interpretation) a possible result of a measurement--an assignment of eigenvalues to a collection of mutually commuting Hermitian operators. You seem to be saying that I can't use the wave function to compute a measure unless I collapse the wave function afterward. That doesn't make a bit of sense.

The relevance is simply that you have a probability distribution over the eigenspaces (thx Gleason) of some observable you are measuring, and a state not in any of those eigenspaces---just as you have a probability distribution over marbles in a hat, and a marble not from that hat.

Your 'many observers' theory presumes a working measurement framework, in order to leave you with an assignment of eigenvalues to a collection of observables, because typically, the state won't be an eigenstate of your observables.

 

[stevendaryl]

This I agree with totally. (And such 'Wigner's friend'-type tales are the reason I consider all collapse theories to be unworkable.)

Well, it seems to me that you have the horns of a dilemma, then. Either there is no collapse, which to me means MWI or some variant, or there is some kind of new physics (maybe stochastic collapse at the microscopic level, or maybe some kind of nonlocal interaction as in the Bohm theory).

It's possible that new physics will solve the conundrum, but if it's necessary, that's kind of weird, it seems to me. We don't actually have any experimental evidence that quantum mechanics is ever wrong. It seems weird that we have to go beyond quantum mechanics in order to understand quantum mechanics.

 

[S.Daedalus]

Well, it seems to me that you have the horns of a dilemma, then.

Certainly. My stance regarding interpretation is roughly the same as my stance regarding political parties: I'm not really close to any, but differently far away from each. I do hope that some variant of 'unitary quantum mechanics only' can be made to work, as from a purely aesthetical point of view, they're the most appealing to me (which is why I am particularly critical regarding their problems). I don't think I like the MWI much, because the talk of worlds just seems like a kind of classical papering-over a fundamentally quantum reality (and there's the Albert/Barrett problem on what it takes to be a world that makes me think that the notion of 'worlds' is simply not a well defined one); I'm more partial towards things like the 'relative facts' proposal of Saunders, as I generally think that the quantum formalism is best interpreted in terms of correlations, rather than the actual values of observations. I was partial to modal proposals for a while, along the Dieks/Kochen/Healey line; but I'm no longer certain these things can be made to work in a really appealing way.

So I guess the bottom line for me is, it's difficult!

 

[tom.stoer]

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.

 

[stevendaryl]

Let's compare two experiments:

1)
A hat with 9 red and 1 green balls;
An (repeated) experiment where a single ball is drawn and placed back;
Result string 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 ball have labels "0.9" and "0.1";
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.

I think that the distinction is not as big as you think. How does the fact that there are 9 red balls and only 1 green ball imply that 9 out of 10 draws will result in a red ball? It doesn't, actually. It's a plausible assumption, but it doesn't logically follow without additional assumptions about how the drawing process works.

If the red balls are all truly indistinguishable, then there is really no difference between there being 9 red balls and there being a "red-ball-counter" that has value 9. It's like the transition from many-particle quantum mechanics to quantum field theory, where instead of asking which state each particle is in, you ask what the occupany number of each state is. They are equivalent.

 

[tom.stoer]

I think that the distinction is not as big as you think. How does the fact that there are 9 red balls and only 1 green ball imply that 9 out of 10 draws will result in a red ball? It doesn't, actually. It's a plausible assumption, but it doesn't logically follow without additional assumptions about how the drawing process works.

If the red balls are all truly indistinguishable, then there is really no difference between there being 9 red balls and there being a "red-ball-counter" that has value 9. It's like the transition from many-particle quantum mechanics to quantum field theory, where instead of asking which state each particle is in, you ask what the occupany number of each state is. They are equivalent.

The basic difference is that in case (1) there is a plausability assumption we are used to in numerous contexts, whereas in case (2) there is none - not even in the MWI context - not in the sense most people will understand "plausible".

All what I am reading about "reasonable agents" etc. is horrible complicated and by no means "plausible".

 

[S.Daedalus]

I think that the distinction is not as big as you think. How does the fact that there are 9 red balls and only 1 green ball imply that 9 out of 10 draws will result in a red ball? It doesn't, actually. It's a plausible assumption, but it doesn't logically follow without additional assumptions about how the drawing process works.

Nevertheless, you wouldn't accept an even-odds bet on drawing the green ball, I presume. And presented with the results of the experiment, you'd point to the distribution of balls as an explanation for the observed relative frequencies. There's a natural hypothesis to be formulated in this setup, and one you will find confirmed. Nothing of that sort presents itself regarding probabilities in the MWI.

It's true that one must always be mindful of Humean skepticism: no amount of evidence will logically entail that the sun rises tomorrow. But that doesn't mean that all hypotheses are equal; that the sun rises deserves a far higher credibility than that it explodes, is actually the egg of a giant world-carrying turtle, or that we are living in a simulation and the cleaning lady's just about to pull the plug to get power for her vacuum cleaner. In this sense, probability in collapse interpretation simply has a far better standing than in the MWI.

 

[stevendaryl]

Nevertheless, you wouldn't accept an even-odds bet on drawing the green ball, I presume. And presented with the results of the experiment, you'd point to the distribution of balls as an explanation for the observed relative frequencies. There's a natural hypothesis to be formulated in this setup, and one you will find confirmed. Nothing of that sort presents itself regarding probabilities in the MWI.

Assuming that 9/10 balls are red implies that 9/10 of the time, you will draw a red ball is only natural because (1) there is no other plausible alternative, and (2) in our experience, that seems to be born out. I think that the same two apply in MWI. There is no plausible alternative to the Born rule, and besides, it is born out by experience.

 

[S.Daedalus]

Assuming that 9/10 balls are red implies that 9/10 of the time, you will draw a red ball is only natural because (1) there is no other plausible alternative, and (2) in our experience, that seems to be born out. I think that the same two apply in MWI. There is no plausible alternative to the Born rule, and besides, it is born out by experience.

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.

 

[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.