Many Worlds Interpretation and act of measuring

[julcab12]

..

That's exactly why it a useless criteria. What some accept as 'it is exactly' varies widely eg Penrose believes the math literally is what it is exactly. You probably don't. But in supporting your position you will find its philosophical discourse, and, as I have pointed out innumerable times, that discipline never reaches any conclusions accepted as 'true' like science does.

.

What about Penrose? Regardless of his belief. He made a very good argument and/or mathematical structure about a possibility of universe in a continuum using simple dynamics. Is it consistent? It depends on the criteria. In the context of QM's postulate its weak due to inconsistencies -- unless certain postulate is realized. In GR it is a natural solution. Multiplicity is also well handled in GR as a natural phenomenon.

Of course. Science never reaches any conclusion but we have temporal results, constants and constraints that is workable and consistent to a point. So we consider it as 'true' to the limit of our understanding/science. I think your referring to absolutes?

 

[bhobba]

..In the context of QM's postulate its weak due to inconsistencies -- unless certain postulate is realized. In GR it is a natural solution. Multiplicity is also well handled in GR as a natural phenomenon.

What QM postulate would that be?

Of course. Science never reaches any conclusion but we have temporal results, constants and constraints that is workable and consistent to a point. So we consider it as 'true' to the limit of our understanding/science. I think your referring to absolutes?

I am referring to exactly what I said. In science, at any point in time we have a generally accepted picture - it may be true or false - who knows what future research will bring. In philosophy we have all sorts of views and no generally accepted answer to the type of questions it asks. Indeed history shows philosophical views are generally way off the mark as far as future scientific progress is concerned eg Gauss vs Kant on non Euclidean geometry- Kant was wrong - Gauss correct.

Thanks
Bill

 

[kith]

Ok let's move the discussion (temporarily at least) away from the probabilities issues since it's so heavily loaded with philosophy and instead move over to the ontological issues of the factorization issue. Why isn't his sufficient enough to disuade you from thinking that MWI is a solid interpretation?

Non-rhetorical counter question: how exactly does the factorization problem trouble you?

 

[RUTA]

Why not accept that no one understands quantum physics and move on ? rather than create theories that don't make any sense... no math will solve this, each time someone tries to solve the problems of quantum physics more problems appear, srsly.. Quantum physics is beyond our logic..understanding classical physics is enough!

Most physicists are of that mindset, actually. "Shut up and calculate!" per Mermin. But, many of us in foundations of physics believe a deeper understanding of quantum physics will lead to new physics altogether.

 

[Quantumental]

Non-rhetorical counter question: how exactly does the factorization problem trouble you?

Well without a solution it diretly contradicts physical reality, so even if you had ignored the probability problem, you're still left with an incomplete hypothesis. You could obviously say that: "Let's just postulate the perference". And that'd be alright, just like Bohmians postulate a pilot wave or Copenhagenists postulate collapse. But for a theory that is supposed to be the underlying final answer to reality such postulates that fly in the face of what the initial hypothesis says? That's ugly in my opinion.

Let me ask the question back:why doesn't it trouble you?

 

[julcab12]

What QM postulate would that be?

As i told you earlier postulate in QM (1-6 incl abstract) are built upon a literal mathematical framework or to satisfy certain mathematical conditions because of probabilistic interpretation. In consequence, we assign operators and eigenstates to act as if it is real in a sense but in reality we don't know if it's the ONLY case. Anyways QM --normalization techniques is built upon that. The wavefunction boils into a sum of position "eigenstates" - simpler wavefunctions which correspond to the particle(s) having definite positions which is the more general rule, is that -- to get predictions for some observable property, you break the wavefunction into a sum of eigenstates or eigenfunctions for that particular observable property. BUT that is only on a mathematical basis. We assign worlds to each values as consequence of math. Same is true in GR's limit's assumption on flat Minkowski space.

I am referring to exactly what I said.

You have a general way of saying so. And i don't disagree. Truth/true to me is temporal and accountable to the limit of our scientific endeavor that doesn't include any unverified predictions -- multiverses and MWI's. However, i don't see them as without merit.

 

[RUTA]

The discussion so far has involved only the probabilistic nature of MW (of which I'm dubious at this point). What does MW have to say about quantum non-locality?

 

[atyy]

That's exactly the issue I have. Decision Theory is a well developed area of math used in a number of mathematical areas such as Actuarial Science. It has a number of key theorems from its axioms - one being that its notion of probability, which I gave previously, is equivalent to the Kolmogorov axioms. That being the case its a perfectly valid basis as an interpretation of probability in QM, just like Bayesian or frequentest, or even just using the Kolmogorov axioms themselves.

This philosophy stuff leaves me cold because no agreement is ever reached. Previous things like Kant's idea that Euclidean geometry was a-priori true proved a crock - in fact it was clear, logical, mathematical reasoning that proved it so - not philosophical mumbo jumbo.

Thanks
Bill

But why can decision theory be applied in the first place? Decision theory requires uncertainty, but it is unclear why there is any uncertainty here. To justify it, there are two approaches, but as these two papers discuss, neither is uncontroversial.
Wallace, http://arxiv.org/abs/0712.0149 (section 4.5)
Greaves, http://users.ox.ac.uk/~mert2255/papers/pitei.pdf (section 3.1)

Also, the derivation assumes decoherence in order to get apparent collapse, which requires the application of the Born rule before any decision has been taken.
Zurek, http://arxiv.org/abs/quant-ph/0405161 (long comment on Deutsch/Wallace on p27)
Dawid and Thiebault, http://philsci-archive.pitt.edu/9542/1/Decoherence_Archive.pdf

 

[kith]

Well without a solution it diretly contradicts physical reality, so even if you had ignored the probability problem, you're still left with an incomplete hypothesis. You could obviously say that: "Let's just postulate the perference".

Why do we need a preference? Why is the arbitrariness of the factorization a problem?

Let me ask the question back:why doesn't it trouble you?

Since I haven't understood what exactly bothers you, I can't answer yet.

 

[bhobba]

As i told you earlier postulate in QM (1-6 incl abstract) are built upon a literal mathematical framework or to satisfy certain mathematical conditions because of probabilistic interpretation. In consequence, we assign operators and eigenstates to act as if it is real in a sense but in reality we don't know if it's the ONLY case.

I quite likely have missed something - but I can't find the axiom you are talking about. Can you tell it to me again?

My axioms are along the lines of the following - see post 137:
https://www.physicsforums.com/threads/the-born-rule-in-many-worlds.763139/page-7

That's the most elegant I know of. My preferred ones are the following though:
http://arxiv.org/pdf/quant-ph/0101012.pdf

It shows QM is basically the simplest generalised probability model that allows continuous transformations between pure states.

Thanks
Bill

 

[Quantumental]

Why do we need a preference? Why is the arbitrariness of the factorization a problem?

It's the equivalent of pointing in a direction in space and saying "this is fundamentally left" Nothing in reality works like this, yet MWI forces us to assume that on a fundamental leevel, it *does* work like that

 

[kith]

The discussion so far has involved only the probabilistic nature of MW (of which I'm dubious at this point). What does MW have to say about quantum non-locality?

I feel like I can't comment on this properly because I haven't seen a model of nonlocal decoherence yet. /edit: I'd really like to see this, so if someone can point me to a paper please do so.

 

[Ilja]

Ok, but, what's the best interpretation of MWI? I know there are many..could you explain to me ?

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

 

[kith]

It's the equivalent of pointing in a direction in space and saying "this is fundamentally left" Nothing in reality works like this, yet MWI forces us to assume that on a fundamental leevel, it *does* work like that

You still don't say why you think a preferred factorization has to be assumed or what it is. What corresponds to "fundamentally left" and why can't it be "arbitrary left"?

 

[bhobba]

But why can decision theory be applied in the first place? Decision theory requires uncertainty, but it is unclear why there is any uncertainty here.

Decision theory doesn't require uncertainty - it accommodates it - but doesn't require it. Its because we do not know what world we are in all you can do is give a probability.

Also, the derivation assumes decoherence in order to get apparent collapse, which requires the application of the Born rule before any decision has been taken.

Now you have hit on a genuine issue requiring care. The Born rule is required for decoherence. Wallace doesn't show the required care assuming the existence of observations in deriving the Born rule. The way it may be done is using the strategy of Consistent Histories and deriving the generalised Born rule using the history concept which is independent of the concept of observation - but I haven't actually seen that.

Thanks
Bill

 

[kith]

The Born rule is required for decoherence.

I have read this a number of times but I can't reconcile it with my understanding. Decoherence in the subsystem corresponds to maximal entanglement in the full system. So if my initial conditions and dynamics are such that I have a long period of nearly maximal entanglement, I have approximate decoherence in the subsystem. I don't see where the Born rule enters if we look at things from this angle.

 

[atyy]

I have read this a number of times but I can't reconcile it with my understanding. Decoherence in the subsystem corresponds to maximal entanglement in the full system. So if my initial conditions and dynamics are such that I have a long period of nearly maximal entanglement, I have approximate decoherence in the subsystem. I don't see where the Born rule enters if we look at things from this angle.

The partial trace assumes the Born rule.

 

[kith]

The partial trace assumes the Born rule.

But do we need the partial trace? All statements about the subsystem can be translated to statements about the full system.

 

[atyy]

But do we need the partial trace? All statements about the subsystem can be translated to the full system.

But the full system is just a unitarily evolving wave function. To get rational observers making measurement choices, it seems we need decoherence.

 

[bhobba]

I have read this a number of times but I can't reconcile it with my understanding.

It comes from formally justifying the use of a partial trace:
http://physics.stackexchange.com/qu...ake-the-partial-trace-to-describe-a-subsystem

I don't think its an issue that can't be resolved with care - as I said previously.

Thanks
Bill

 

[kith]

But the full system is just a unitarily evolving wave function. To get rational observers making measurement choices, it seems we need decoherence.

Do Deutsch/Wallace really try to derive the existence of observers or do they only talk about how a given observer acts? If the latter, is the objection which people have against their argument that they should derive the existence of observers?

 

[atyy]

Do Deutsch/Wallace really try to derive the existence of observers or do they only talk about how a given observer acts? If the latter, is this exactly the objection people have against their argument?

I think the concern is that they assume observers who know that MWI is true. If the observer uses decision theory to derive probability and MWI, he gets the Born rule. However, since the observer knows that MWI is true, he must have presumbly derived the wave function of his subsystem using decoherence, and hence assumed via the partial trace the Born rule. So the question is why probability makes sense in the initial use (before the application of decision theory) of the Born rule to get the partial trace.

What is interesting of course is that this could be seen as huge support for Deutsch-Wallace - it is internally consistent - but the whole argument is so tricky, I am not sure.

 

[bhobba]

Do Deutsch/Wallace really try to derive the existence of observers or do they only talk about how a given observer acts? If the latter, is this exactly the objection people have against their argument?

Wallace assumes the existence of observations, measurements etc without being exactly clear about what they are. This is a weakness in his approach as far as the assumption that MW is simply the working out of a universal wavefunction and that's it. I think it can be overcome using the concept of history - but haven't seen that approach.

Thanks
Bill

 

[bhobba]

I think the concern is that they assume observers who know that MWI is true.

He uses the concept of rational agent - not observer. Such is necessary due to the decision theory definition of probability used. It doesn't mean the rational agent is in the world observing it or anything like that - its simply means given that information what would a rational agent conclude.

Thanks
Bill

 

[RUTA]

I think the concern is that they assume observers who know that MWI is true. If the observer uses decision theory to derive probability and MWI, he gets the Born rule. However, since the observer knows that MWI is true, he must have presumbly derived the wave function of his subsystem using decoherence, and hence assumed via the partial trace the Born rule. So the question is why probability makes sense in the initial use (before the application of decision theory) of the Born rule to get the partial trace.

I think this is Dawid and Thebault's complaint. Since their paper was published I assume the complaint was properly vetted (almost certainly by a supporter of MWI). Of course, the paper was received Aug 14 and only appeared in Jan 15, so maybe the MWI crowd is yet preparing a response.

 

[bhobba]

I am just reviewing Wallace.

I may have been a bit hasty here. Looking again at Chapter 3 he may in fact have done what I suggested with the Branching Decoherence Theorem on page 93. He states the Born rule on page 94 in terms of histories. He examines and uses aspects of Consistent Histories throughout that chapter.

Tricky.

Thanks
Bill

 

[atyy]

I think this is Dawid and Thebault's complaint. Since their paper was published I assume the complaint was properly vetted (almost certainly by a supporter of MWI). Of course, the paper was received Aug 14 and only appeared in Jan 15, so maybe the MWI crowd is yet preparing a response.

They note that Zurek makes a similar criticism in http://arxiv.org/abs/quant-ph/0405161 (p27).

 

[Ilja]

Probabilities in MW is simple - they define it as per decision theory which is a variant of Bayesen probability.

It is not simple at all. Of course, nobobdy forbids to use common sense. And Bayesian probability is nothing but common sense for situations of uncertainty, everything can be derived from the basic idea of logical consistency to plausible reasoning.

But the wave function is nothing but a strange complex function on the space of all imaginable states of the world. And, according to MW, they all exist somehow. This is certainly not common sense. How can one apply the rules of plausible reasoning in a situation where the aim of plausible reasoning, of reasoning at all, to find out what happens, is questioned, because it is assumed that everything happens?

MW is conceptually simple. After decoherence you have a mixed state ∑ pi |bi><bi| and each |bi><bi| is interpreted as a separate world. Nothing hard about it.

A sufficiently hard question is along which line one subdivided. The decoherence presupposes a subdivision into systems.

In real experimental situations this is not problematic at all - all the classical things, starting with the Earth as a planet, allow to subdivide our world in sufficiently stable different parts. But MW cannot presuppose this. It needs an additional fundamental structure. Nobody defines it - thus, it is simply incomplete. And the main promise - not to use additional structures - cannot be realized.

 

[kith]

What is interesting of course is that this could be seen as huge support for Deutsch-Wallace - it is internally consistent - but the whole argument is so tricky, I am not sure.

Yes, I am really not sure what to think of this.

I think the concern is that they assume observers who know that MWI is true. If the observer uses decision theory to derive probability and MWI, he gets the Born rule.

What does assuming "MW is true" mean here? If in a world where I measure spins all my life and I never get the spin-down outcome for a |up>+|down> state, what do I have to assume in addition to the states and observables postulates to conclude that the Born rule is valid given my contradictory experimental results?

 

[Ilja]

Wikipedia is usually reliable - but on that its wrong. The worlds are NOT in superposition. That's exactly what a mixed state after decoherence isn't.

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

 

[atyy]

What does assuming "MW is true" mean here? If in a world where I measure spins all my life and I never get the spin-down outcome for a |up>+|down> state, what do I have to assume in addition to the states and observables postulates to conclude that the Born rule is valid given my contradictory experimental results?

I meant in Deutsch-Wallace, and am just reporting that if you make their assumptions, it does seem that the Born rule can be derived. I think that alone is a huge achievement. What is less clear is whether that fits in with MWI and decoherence, and the usual practice of science.

The issue is addressed by Greaves and Myrvold, Everett and evidence, http://philsci-archive.pitt.edu/4222/, and discussed by Dawid and Thebault, Against the Empirical Viability of the Deutsch Wallace Approach to Quantum Mechanics http://philsci-archive.pitt.edu/10703/.

 

[Rajkovic]

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

 

[TrickyDicky]

In order to get to some specific problem at the root of QM it's probably much more useful to concentrate on what unifies all interpretations, than on their differences, that are what bhobba refers to as philosophical gobbly gook, mumbo-jumbo, etc... And the issue that all interpretations confront(MW included, in the various ways that have been discussed here:probability issues, factorization, decoherence and Born rule, decision theory and assuming MW is true... ) is the preferred-basis problem even if it may go by a different name in different interpretations. It is not a philosophical but a deep mathematical inconsistency, not so much for QM as a way of solving physical problems which it does in a great way, but for QM as a formal theory. It is ok to be satisfied with QM just as a prescription to solve many physical problems, but it shouldn't be strange that there are also people in a physics forum preoccupied with the formal aspect as it bears also on the possibility of progress of the theory.
It is a purely mathematical fact that an empirical theory (including quantum observables, their measurement and preparation) that doesn't allow an abstract formulation in terms of linear operators that is explicitly basis-independent cannot be said to correspond to something living in a Hilbert space.

 

[kith]

The issue is addressed by Greaves and Myrvold, Everett and evidence

I've just finished skimming this paper. It is really well-written and contains some nice arguments but it also immediately raised a question for me.

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.

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

 

[kith]

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.

 

[stevendaryl]

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

It's not the Born rule is only valid in some worlds, it's that relative frequencies are only equal to the theoretical probability in some worlds. But that's just a "small numbers" effect; if you perform an experiment only a finite number of times, then there is a chance that the relative frequencies could be different from the probability. But in MWI, it's more than just chance: it definitely happens, in some branch.

There was a strange mathematical argument that I read long ago that claimed to prove that there are literally no worlds in which the relative frequency differs from the predictions of the Born rule for an actually infinite sequence. The argument showed that the amplitude goes to zero, and you don't need the Born rule to say that you can ignore amplitude-zero possibilities.

What's weird about the mathematical argument is that you need to assume a state space with a literally infinite memory, and there is no such state space in a separable Hilbert space.

 

[kith]

It's not the Born rule is only valid in some worlds, it's that relative frequencies are only equal to the theoretical probability in some worlds. But that's just a "small numbers" effect; if you perform an experiment only a finite number of times, then there is a chance that the relative frequencies could be different from the probability. But in MWI, it's more than just chance: it definitely happens, in some branch.

Yes and I'm wondering how people in such a world would talk about physics. We think the Born rule is correct because of experimental evidence. But as you say, there are worlds where the observed frequencies are very different from the probabilities of the Born rule. So people in these worlds wouldn't deduce the Born rule as a fundamental law from their measurements but a different law (and given Gleason's theorem, they wouldn't even arrive at something similar to QM because their law would be incompatible with the Hilbert space structure).

For them, our observed frequencies would look like an unlikely statistical deviation from their law. Is there a way to decide who has the correct law?

 

[carllooper]

We can question the concept of the observer (or an observation) being associated with only a single outcome (or single world) as in when one says "in one world I get this result - in another world I get that result".

For observations can be defined in terms of ensemble ones as well: be it in terms of the large number of brain cells that we (or a machine) possesses, or the large number of silver halide particles detecting photons in a photograph, etc. Such observations are themselves irreduceable to (or can't be characterised by) any single observation in such. For example, a visible interference pattern, produced in a photograph, is not characterised by what is visible at any single point in the photograph. The visibility of the interference pattern literally vanishes. A statistical ensemble approach (or some equivalent alternative along MWI lines) is required for characterising these sorts of observations, as much as any "reality" behind such observations.

In other words, when speaking of observers we should allow aggregate entities as well. And indeed we should question the legitimacy of always assuming otherwise. By way of an analogy, a single cell organism (in an ocean of such organisms) might indeed always get heads in a long chain of coin flips (or we can find one that does, given a large enough population), but without such a cell connecting with all the other organisms in the ocean, it is unable to fathom the peculiarity of it's specific observation, and is unable to generalise such (incorrectly or otherwise). For it is incapable of thinking. But in a multi-cellular organism, not only are ensemble observations enabled, but the statistics of what such an ensemble might conclude (such as their laws of physics) become far less troublesome.

The concept of the observer (the "I") as being some single point in a system can be understood as far too peculiar.

C

 

[stevendaryl]

Yes and I'm wondering how people in such a world would talk about physics. We think the Born rule is correct because of experimental evidence. But as you say, there are worlds where the observed frequencies are very different from the probabilities of the Born rule. So people in these worlds wouldn't deduce the Born rule as a fundamental law from their measurements but a different law (and given Gleason's theorem, they wouldn't even arrive at something similar to QM because their law would be incompatible with the Hilbert space structure).

For them, our observed frequencies would look like an unlikely statistical deviation from their law. Is there a way to decide who has the correct law?

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.

 

[atyy]

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

Maybe there are no (rational) observers when recoherence occurs.

 

[bhobba]

It is not simple at all

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

Thanks
Bill

 

[bhobba]

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

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

Thanks
Bill

 

[bhobba]

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

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

Thanks
Bill

 

[atyy]

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

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

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

 

[rootone]

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

 

[bhobba]

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

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

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

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

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

Thanks
Bill

 

[bhobba]

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

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

Thanks
Bill

 

[atyy]

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

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

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

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

 

[atyy]

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

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

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

 

[Rajkovic]

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

Thanks
Bill

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