In what sense does MWI fail to predict the Born Rule?

[Mentz114]

[..]
For the purpose of honesty let me just say my preferred interpretation of QM is "I'm really confused and the more I learn about QM the less I understand", that is the "I wish I could shut up and calculate" interpretation.

I want to thank you for your work in explaining the Wallace opus to those of us who don't have the inclination/time/ability required to read it. Your efforts have not been a waste of time.

A good antidote to your confusion (and mine) is A.Neumaiers Coherent foundations article
which has a prospectus for the thermal interpretation which promises

The measurement problem turns from a philosophical riddle into a scientific problem in the domain of quantum statistical mechanics, namely how the quantum dynamics correlates macroscopic readings from an instrument with properties of the state of a measured microscopic system.

This puts the current difficulties into perspective.

I've downloaded the first Allahverdyan et al. paper (147 pages !) and I'll drool over it for while before atempting to read it.

 

[DarMM]

Summing up, in case my previous posts are confusing (and because summaries stick better in one's head I find), Wallace's argument has four classes of contentions:

1. It assumes one can obtain a stable robust quasi-classical branching structure without using the usual trace based derivations of decoherence. This is acknowledged by Wallace, but he sketches reasons why he thinks this can be done. In my opinion, this flat out needs to be shown by a research program, not assumed as justified by handwaving arguments.
   Wallace's argument in places assumes an idealised branching structure, not an approximate one. Since it is likely the above research program, even if successful, will only have the Macrostates as approximate structures, the proof will need to be modified to reflect this.
2. Some of the preference order axioms assume that the unique way of being rational is similar to one held by somebody who believes in one world. Of these I think the objections to "Branching indifference" are the most valid. This is currently undergoing discussion in the literature, but I do agree with the main point that it is odd that a superposition of identical rewards must always be held as being as valuable as simply evolving into one world with that reward.
3. Contradictions arising from axiom U6, erasure. This seems overly powerful, non-physical and in direct contradiction to the irreversibility assumed by the other axioms in places.
4. Even if we can avoid 1,2,3 all we have shown is that using the Born Weights to make decisions is rational. How does this connect to actually seeing Born frequencies in experimental results? This is the topic of a forthcoming paper by Mandolesi, so I will leave it.

Make of these objections what you will. For me it is really 1. and 3. that prevent me from viewing this as a derivation of the Born weights.

 

[Derek P]

Summing up, in case my previous posts are confusing
[...]
Make of these objections what you will. For me it is really 1. and 3. that prevent me from viewing this as a derivation of the Born weights.

Thanks for all of that. I put my hand up to being one of @Mentz114's "those of us who don't have the inclination/time/ability required to read it". All three in my case, at least until adequately motivated to spend a year focussed on it . Which on current showing appears to be vanishingly unlikely. Or, as I am learning to say, "On the assumption that I am a rational agent, my optimisal strategy for maximising my chosen reward, that of understanding quantum mechanics better, is to act as if there is not a snowflake in hell's chance of getting anything from Wallace".

But I have a problem with 4.

1. Wallace's proof presumably (purports to) eliminate personal preferences from the argument, so that using the Born Weights is optimal whether you just want to get to work on time or have a penchant for quantum suicide.
2. So let's say it optimises your reward if you act as if there were a 50/50 chance of Schroedinger's cat being alive or dead.
3. You appear to be saying that this does not imply 50% frequency.
4. It seems to me that it does.
5. Because of 1, the decision to act as if the frequency were 50% must include cases where the reward is to estimate the frequencies correctly.
6. So the optimised stategy for estimating the frequencies correctly is to use the Born Weights.
7. If the Born Weights are well-defined and the frequencies are well-defined then there is only one correct estimate.
8. Therefore using the Born Weights for estimating the frequencies does, in fact, yield the correct value.

I've probably missed what you're saying or perhaps my argument is invalid. But if it seems valid to you we had better tell Mandolesi that he can stop what he's doing and ... ...

 

[Derek P]

I'm not at all suggesting a principled reason for choosing one coarse-graining over another. But I was postulating a very specific coarse-graining, which is that the coarse-grained state determines, for every volume of space down to some minimal volume, the particle content, total energy, total momentum, average electric field, average magnetic field, etc. I'm assuming that a single coarse-grained state would not be compatible with a cat being both alive and dead. As far as what's going on in Alice's mind, I don't actually know about that. That could require very fine-grained information, or maybe not.

Well your ∏ operator seemed to extract exactly one bit of information from a ket, namely whether Alice thinks "dead ket" or "alive ket". Her mind as such doesn't come into it. She could be an electron whose spin preparation is determined by the state of the detector. One qubit in, one classical bit out! I'll talk with you about coarse-graining soon.

 

[DarMM]

But I have a problem with 4

I get what you're saying. To some people it's because there isn't a clear mechanism given for the rationality as discussed in Wallace's paper. I think Wallace can't give a clear mechanism because it depends on exactly how the non-trace based derivation of decoherence will actually work when it is brought to fruition.

Mandolesi for example has another paper where he sketches a research program for deriving decoherence via causal stability. In it macrostates with large amplitudes are more resilient to interference and hence have more microstates "implementing" them where interference isn't so strong as to prevent the existence of rational agents (which require stable memory, an arrow of time, etc). That is they have a higher microworld count where they can give rise to beings like us. Hence you'd take the Born weight into account when assessing a macroworld, because there will more microworlds refining it with a you in them. I'm still digesting that paper, so I might be slightly off in that summary. I'll return with a correction if I'm significantly wrong. Though note the many-minds nature of the explanation.

So even accepting Wallace's proof, we don't know "why" the Born weights are the rational weights, just that they are. I think I'll await Mandolesi's third paper before commenting on this more, because he might have explicit examples where the Born weights are rational to use, but don't manifest in a world's experimental history.

 

[akvadrako]

I'm just asking why the more-or-less obvious approach is said to fail as well as all others.

There are quite a few approaches and even if you discover one is technically sound, you haven't dealt with the main issue of why they are all said to fail. Your focus on macro-states and course-graining is an attempt to do basically the same thing as Gleason's theorem, which says roughly if there is a probabilistic interpretation of WMI, it must be the Born rule. So it's not that there are viable alternatives to the Born rule, but you have to accept the premise.

That is why all the other approaches exist; an attempt to demonstrate this premise. Given a deterministic system where almost everything happens, how can we interpret it probabilistically from the perspective of something inside the system?

 

[DarMM]

I'm currently reading Zurek's papers and follow up articles concerning his envariance proof of the Born rule. This is the second method to derive the Born rule in Many-Worlds and does not use decision theory as Wallace does. I will again provide a summary here, so that we have both of the major derivations of the Born rule covered.

I will say already it is much clearer than the decision theory derivations, as Zurek gives an explicit physical meaning to everything he says.

 

[A. Neumaier]

I'm not at all suggesting a principled reason for choosing one coarse-graining over another. But I was postulating a very specific coarse-graining, which is that the coarse-grained state determines, for every volume of space down to some minimal volume, the particle content, total energy, total momentum, average electric field, average magnetic field, etc.

This will give you precisely the hydromechanic field variables. There is a very principled way of doing this, described in the book on nonequilibrium quantum field theory by Calzetta and Hu, resulting (after some approximation) in classical hydromechanic equtions. Or, for the nonrelativistic case, see the statistical physics book by Linda Reichel, who starts from N-particle quantum mechanics.

The coarse-graned observables are precisely the expectation values of associated quantum fields. Thus with your vision you come very close to my thermal interpretation.

 

[Derek P]

I get what you're saying. To some people it's because there isn't a clear mechanism given for the rationality as discussed in Wallace's paper.

That's the sort of statement that has me baffled. I really can't attach any meaning to "mechanism for rationality". I'm guessing it means something like a physical model for a rational decision. Which is a very specific philosophical stance, essentially that "we of the xyz school do not accept that logic can be decoupled from human thinking, and therefore logical propositions are experimental hypotheses subject to Popperian falsification and empirical verification." I may be overstating it a little. But maybe you're talking about something completely different.

So even accepting Wallace's proof, we don't know "why" the Born weights are the rational weights, just that they are. I think I'll await Mandolesi's third paper before commenting on this more, because he might have explicit examples where the Born weights are rational to use, but don't manifest in a world's experimental history.

Well I bet he can't except in the trivial sense of inherently one-off events, if there are such things. We shall see, And I'll let someone else digest the proffered argument for me!

 

[stevendaryl]

I guess I've made this point before, so it's a little redundant, but it's a little ridiculous to me to ask about what's a rational agent's motivation for accepting the Born rule. I don't think there is any more to it than the fact that his experience of previous experiments show relative frequencies in agreement with the Born rule. That seems necessary and sufficient for the rational agent to accept the rule.

The problem with Many Worlds is that there are possible worlds where the Born rule gives the wrong relative frequencies. Well, in those worlds, people just aren't going to accept the Born rule. They are not going to be persuaded by a decision-theoretic argument, no matter how mathematically sound.

 

[DarMM]

That's the sort of statement that has me baffled. I really can't attach any meaning to "mechanism for rationality".

I think it just means "why is it the rational way to act?"

Is it because for worlds with high Born weight there are more copies of that world, or worlds with that outcome are more stable, or worlds with that outcome have more subworlds with rational agents, etc?

 

[DarMM]

I guess I've made this point before, so it's a little redundant, but it's a little ridiculous to me to ask about what's a rational agent's motivation for accepting the Born rule. I don't think there is any more to it than the fact that his experience of previous experiments show relative frequencies in agreement with the Born rule. That seems necessary and sufficient for the rational agent to accept the rule.

The problem with Many Worlds is that there are possible worlds where the Born rule gives the wrong relative frequencies. Well, in those worlds, people just aren't going to accept the Born rule. They are not going to be persuaded by a decision-theoretic argument, no matter how mathematically sound.

That's fine, but it really implies the coefficients have no real intrinsic meaning physically. There are just some worlds where the ratios between outcomes randomly happen to align with them, but such worlds aren't "common" in any sense, worlds with uniform ratios are just as common. Nor should you expect the Born rule to continue to work, as your history has just randomly happened to align with it thus far, but since they don't really mean anything why would you expect this to continue.

I think to trust the Born rule regarding the future, you have to have some reason why an agent would use or trust them.

 

[stevendaryl]

I guess I've made this point before, so it's a little redundant, but it's a little ridiculous to me to ask about what's a rational agent's motivation for accepting the Born rule. I don't think there is any more to it than the fact that his experience of previous experiments show relative frequencies in agreement with the Born rule. That seems necessary and sufficient for the rational agent to accept the rule.

I guess the issue is whether the rational agent would continue to believe the Born rule after you've explain "Many Worlds" to him.

 

[Derek P]

I guess the issue is whether the rational agent would continue to believe the Born rule after you've explain "Many Worlds" to him.

I wonder how Wallace deals with that.

 

[Derek P]

That's fine, but it really implies the coefficients have no real intrinsic meaning physically. There are just some worlds where the ratios between outcomes randomly happen to align with them, but such worlds aren't "common" in any sense, worlds with uniform ratios are just as common. Nor should you expect the Born rule to continue to work, as your history has just randomly happened to align with it thus far, but since they don't really mean anything why would you expect this to continue.

I think to trust the Born rule regarding the future, you have to have some reason why an agent would use or trust them.

It's called the Principle of Induction. It's a principle that has always worked in the past so it's bound to work in the future

 

[DarMM]

It's called the Principle of Induction. It's a principle that has always worked in the past so it's bound to work in the future

The point would be without some physical account of the Born weightings and given the truth of Many Worlds, the principle of induction would be invalid to apply to the Born rule. You would know that worlds where it continues to hold, even given it has held, are in an almost vanishing minority.

 

[Derek P]

I think it just means "why is it the rational way to act?"

Is it because for worlds with high Born weight there are more copies of that world, or worlds with that outcome are more stable, or worlds with that outcome have more subworlds with rational agents, etc?

Well obviously it's no use asking me what Wallace thinks, if that's still the context. I cannot imagine how he escapes using a statistical argument to define an expectation value. But if, as this would imply, his method freely uses the idea of probability when applied to propositions - the chances of P being true - then you don't need any tarradiddle about rational agents... But what would I know?

 

[DarMM]

But if, as this would imply, his method freely uses the idea of probability when applied to propositions - the chances of P being true

It doesn't. More clearly what he does is show that assuming a branching structure can be derived without use of tracing (something that has yet to be even half-rigorously shown), a certain level of control over the environment and assuming a certain form to rational reasoning (that is a definition of rationality in an Everettian world), then the Born weights can be shown to be involved in any rational decision.

This doesn't, as such, show they have anything to do with probabilities. It just shows that any rational decision (where "rational" is defined by his axioms) will involve them.

 

[Derek P]

The point would be without some physical account of the Born weightings and given the truth of Many Worlds, the principle of induction would be invalid to apply to the Born rule. You would know that worlds where it continues to hold, even given it has held, are in an almost vanishing minority.

The Principle of Induction does not depend on the physical account. That's kind of the point of it.

 

[DarMM]

The Principle of Induction does not depend on the physical account. That's kind of the point of it.

I think something is confused here.

Many Worlds, without some physical meaning behind the Born weights, would predict that they shouldn't continue to hold as ratios of experiments with almost certain probability.

Consider General Relativity and a being who has only experienced Newtonian gravitational wells. If you place him near a Neutron Star, by the principle of induction he would say Newtonian gravity should continue to hold, but General Relativity will say this is going to be wrong and it is in fact wrong.

Many-Worlds without a physical meaning for the Born Weights, which I'll just call Raw Many Worlds, would predict they will fail to hold as ratios of outcomes. You can use the principle of induction if you want, but Raw Many Worlds will say you will be wrong.

Hence the issue here is a prediction of Raw Many Worlds, I don't think the principle of induction matters to that.

 

[DarMM]

The Principle of Induction does not depend on the physical account. That's kind of the point of it.

Another way of coming at this, of course one can use the Principle of Induction, but why is that relevant when the theory is predicting that Born ratios are going to fail to hold.

 

[Derek P]

And another way of coming to it is to notice the smily!

 

[Derek P]

I think something is confused here.

Many Worlds, without some physical meaning behind the Born weights, would predict that they shouldn't continue to hold as ratios of experiments with almost certain probability.

Consider General Relativity and a being who has only experienced Newtonian gravitational wells. If you place him near a Neutron Star, by the principle of induction he would say Newtonian gravity should continue to hold, but General Relativity will say this is going to be wrong and it is in fact wrong.

Many-Worlds without a physical meaning for the Born Weights, which I'll just call Raw Many Worlds, would predict they will fail to hold as ratios of outcomes. You can use the principle of induction if you want, but Raw Many Worlds will say you will be wrong.

Hence the issue here is a prediction of Raw Many Worlds, I don't think the principle of induction matters to that.

You've lost me. There's always a physical meaning to the Born Weights. The principle of induction doesn't depend on it though and yes it will mislead you on occasion. I don't know what you're getting at at all.

 

[Derek P]

There are quite a few approaches and even if you discover one is technically sound, you haven't dealt with the main issue of why they are all said to fail. Your focus on macro-states and course-graining is an attempt to do basically the same thing as Gleason's theorem, which says roughly if there is a probabilistic interpretation of WMI, it must be the Born rule. So it's not that there are viable alternatives to the Born rule, but you have to accept the premise.

That is why all the other approaches exist; an attempt to demonstrate this premise. Given a deterministic system where almost everything happens, how can we interpret it probabilistically from the perspective of something inside the system?

There is no difficulty at all in having probabilities in a deterministic theory. (I have a horrible feeling I may have said the opposite at some point, but if so I was wrong.) Probabilities arise through someone inside the system not knowing which "part" they are in. That would not help if there was only one observer or observer-state. But if each "part" has its own version, the observer can say "the probabilty of my being in such-and-such a subset of all the states is ..."

 

[DarMM]

There's always a physical meaning to the Born Weights

I was talking about Wallace's proof where this physical meaning is not obvious or stated. Or Many-Worlds prior to the Born Rule where it is absent.

What is the physical meaning in the version of Many Worlds you are considering?

 

[DarMM]

You've lost me. There's always a physical meaning to the Born Weights. The principle of induction doesn't depend on it though and yes it will mislead you on occasion. I don't know what you're getting at at all.

I will explain this in more detail.

There have been two points here:

1. The point that Wallace leaves you with no idea as to why using the Born weights is more rational, just that in his version of Many-Worlds it is. However he does not provide a structure to the branching multiverse that explains their use. There a several possible handwaving models you could conceive of that would explain their use, but they are all quite different and don't have rigorous mathematical baking as of 2018.
2. The idea that Many-Worlds, ignoring any proofs of the Born rule, like Wallace's and Zurek's will always have some worlds where the Born weights are the ratios of experimental observations. The problem here is that without some proof connecting the weights to physical observations, these worlds are simply (vanishingly rare) flukes, not in any sense common. There will also be worlds where the ratios are $f(\alpha_k)$ rather than $\alpha_k$ and these worlds are no more or less common.
   Hence the Born rule fails to be predictive, regardless of the induction principle.

 

[DarMM]

Well Zurek's proof is very simple.

The idea is take a Schmidt state:

$$\psi = \Sigma_{i} \alpha_{i} |\sigma_{i}\rangle |\eta_{i}\rangle \tag 1$$

with $|\sigma_{i}\rangle$ being states of the microscopic system and $|\eta_{i}\rangle$ being environment states.

The state is said to be envariant under a transformation, $U_{s}$, of the microscopic system, if it can be undone by a transformation, $U_{\eta}$, of the environment .

Lemma 1: For states with $|\alpha_i| = |\alpha_k|$ for some $i,k$, then swapping $|\sigma_{i}\rangle$ and $|\sigma_{k}\rangle$ is an envariant transformation.
That is, for Schmidt states, swaps of microsystem states with equal magnitude coefficients can be undone by the environment.

Next Zurek has four axioms, with a theorem that can be proved from the first three.

A1. To represent an alteration of a system $S$, a unitary transformation must act on its Hilbert Space $\mathcal{H}_{S}$
A2. All information on observables, their values and their probabilities for a system $S$ is fully captured by the state of $S$. This state might be mixed or pure.
A3. The state of a subsystem is fully specified by the state of the total system.

From these three axioms you can conclude:
Theorem 1: Phases do not affect probabilities, i.e. probabilities depend only on $|\alpha_{i}|$.

The final axiom comes in three versions, anyone of them may be added to the list as the final axiom.

B1. If swapping two orthogonal states leaves the state of the system $S$ unchanged, the probabilities of the outcomes associated with those states are the same.
B2. If all unitary transformations within a subsystem $\bar{S}$ of $S$ leave $S$ unchanged, then the probabilities of any state in an orthonormal basis of $\mathcal{H}_{\bar{S}}$ are equal.
B3. The probabilistic meaning of a Schmidt state is that the environment and the state are perfectly correlated, i.e. observing $|\sigma_{i}\rangle$ means $|\eta_{i}\rangle$ will be observed with probability 1.

Any one of these axioms allows him to prove the following:
Theorem 2: Terms with equal amplitudes in Schmidt states like $(1)$ have equal probabilities.
Corollary: In a Schmidt state with all $N$ coefficients equal, all outcomes are equally likely, i.e. $1/N$.

Looking ahead I will say that using B2 permits you to prove this without using A2.

From there he uses the fact that the environment can always be enlarged by adding an extra system to reduce the unequal amplitude case to the equal amplitude case. As an example say we have:

$$\psi = \sqrt{\frac{1}{3}}|\sigma_1\rangle|\eta_1\rangle + \sqrt{\frac{2}{3}}|\sigma_2\rangle|\eta_1\rangle \tag 2$$

We can introduce another system, $\beta$, essentially enlarge the environment so that this becomes:

$$\psi = \sqrt{\frac{1}{3}}|\sigma_1\rangle|\eta_1\rangle|\beta_1\rangle + \sqrt{\frac{2}{3}}|\sigma_2\rangle|\eta_2\rangle|\beta_2\rangle \tag 3$$

Then provided the new environment $\beta$ is large enough so that most of its eigenstates (the states that couple to the microscopic system) are degenerate, we can expand them enough to counterweight the unequal amplitudes:

$$\beta_1 = \gamma_1 \tag 4$$

$$\beta_2 = \sqrt{\frac{1}{2}}\gamma_{2,1} + \sqrt{\frac{1}{2}}\gamma_{2,2} \tag 5$$

and so, substituting $(4),(5)$ into $(3)$:

$$\psi = \sqrt{\frac{1}{3}}|\sigma_1\rangle|\eta_1\rangle|\gamma_1\rangle + \sqrt{\frac{1}{3}}|\sigma_2\rangle|\eta_2\rangle|\gamma_{2,1}\rangle + \sqrt{\frac{1}{3}}|\sigma_2\rangle|\eta_2\rangle|\gamma_{2,2}\rangle$$

Hence this is now an equal amplitude case, and by Theorem 2 all have equal probability $1/3$. Since $\sigma_2$ appears twice, we can say it has $2/3$ chance of being seen.

And so Zurek obtains the Born rule for amplitudes that are roots of rationals.

To obtain it for all reals, he uses the fact that $\mathbb{Q}$ is dense in $\mathbb{R}$ and that an "arbitrarily" fine grained* larger environment can be found.

Thus we have the Born rule. Issues to follow.

*In the sense of having as large as necessary expansion in the form of $(5)$

 

[Derek P]

I will explain this in more detail.

There have been two points here:

1. The point that Wallace leaves you with no idea as to why using the Born weights is more rational, just that in his version of Many-Worlds it is. However he does not provide a structure to the branching multiverse that explains their use. There a several possible handwaving models you could conceive of that would explain their use, but they are all quite different and don't have rigorous mathematical baking as of 2018.
2. The idea that Many-Worlds, ignoring any proofs of the Born rule, like Wallace's and Zurek's will always have some worlds where the Born weights are the ratios of experimental observations. The problem here is that without some proof connecting the weights to physical observations, these worlds are simply (vanishingly rare) flukes, not in any sense common. There will also be worlds where the ratios are $f(\alpha_k)$ rather than $\alpha_k$ and these worlds are no more or less common.
   Hence the Born rule fails to be predictive, regardless of the induction principle.

Obviously we need a "proof connecting the weights to physical observations"! If Wallace fails to provide it, why are we even discussing his work?

 

[DarMM]

Obviously we need a "proof connecting the weights to physical observations"! If Wallace fails to provide it, why are we even discussing his work?

First of all, because it is one of the two major purported proofs of the Born rule in Many Worlds. The thread is about "in what sense does MWI fail to predict the Born rule", answering that requires addressing the failures of the major approaches.

Also he does provide one, but it requires features (e.g. branching structure without using the normal decoherence formalism, powerful erasure operations) that have not been themselves proven to be valid. Hence in a Wallacean Multiverse, provided it can actually be shown to arise from pure unitary QM with no assumptions, does have physically relevant Born weights.

 

[Derek P]

Well Zurek's proof is very simple.

The idea is take a Schmidt state:
[...]
Thus we have the Born rule. Issues to follow.

Excellent. Thanks. I eagerly await the "issues" because, from where you say "From there ...", it looks remarkably like what I have been calling "state counting" and which Price's proof (which was immediately pooh-poohed) uses and which @stevendaryl seems to be heading towards and which I had, until this thread, assumed was the only one anyone would ever consider to be mainstream. I guess I was misled by the obvious fact that orthogonal vectors add by Pythagoras but their probability measures add linearly - ergo Born.

I think the fact that Zurek uses a Schmidt decomposition needs an axiom or three - certainly his use of it would explain why at some point he says MWI requires a postulate that systems exist. With such an axiom you can create the necessary composite system out of subsystems. Otherwise I suppose you would have to prove that a sufficiently large system's state space can be factorized in a way recognisable as subsystem state spaces. Or something like that, no doubt expressed more elegantly. As a non-mathematician I imagine it would be another can of worms.

Anyway, the thing that strikes me immediately is that axioms B mention probability without saying what it means. I don't think Zurek would be silly enough to introduce a Deus ex Machina. But before quantifying it as amplitude squared, B needs to be related to some definition of probability. Otherwise we are back to "If there is zippettybopp and the following axioms which quantify zippettybopp apply, then zippettybopp follows the XYZ Rule". Not much use in a model of the real world if nobody knows what zippettybopp means. And I'm not going to tell you.

 

[bhobba]

The point that Wallace leaves you with no idea as to why using the Born weights is more rational, just that in his version of Many-Worlds it is.

That is the big problem with Wallace - it took me about 6 months to fully study it. It is very mathematical and I could not break any of it's theorem's - but its just that - very mathematical. In fact it helped me understand decoherent histories a lot better. I have said its mathematically very beautiful - but math is not physics. The big issue is can the assumptions it makes ie can you use decision theory to deduce the Born Rule. If you accept yes its fine - if not its challengeable. But if you have a deterministic theory that does not give the version of you that is in a particular world then what can you do? If you reject it then the whole thing goes down the gurgler in the sense in MW all you have is a wave-function and that's it.

Personally even without the non-contextuality proof I don't think contextuality makes much sense in MW so you have Born via Gleason. But like all interpretations I guess it's a matter of personal taste. I think MW is just too silly to believe - that's not scientific - just my gut feeling. I remember a long discussion with a philosopher who thought I could not think like that - I must have a rational reason. In the end all I could say is this is science - not philosophy. There are certain indefensible beliefs such I think most scientists think we are slowly getting closer and closer to some objective truth - I certainly do. I can't prove it, but I believe it very strongly. Guess that's the difference between science and philosophy.

Thanks
Bill

 

[AlexCaledin]

I think MW is just too silly to believe - that's not scientific - just my gut feeling.

I think MW is just requiring to take it easy! If a theorist says there are "really" many worlds - and many "real" variants of me - then, the important thing is to remember that that "realness" (and anyone's "belief" in it) is theoretical. My actual business, anyway, is to see that, in the world I am observing, I be not too bad - so, to calculate what I need, I have to add the wavefunction collapse to that theory and "return to Copenhagen" - with better understanding as to whence that collapse comes (namely, from the rules of the actual business of life).

 

[Stephen Tashi]

I guess the issue is whether the rational agent would continue to believe the Born rule after you've explain "Many Worlds" to him.

Is the rational agent supposed to know the Born weights? For example, if he is an agent in a "maverick" world, do we assume he knows the correct values of the Born weights? - or would he believe some erroneous (from a global viewpoint) values for them?

 

[Derek P]

I think MW is just requiring to take it easy! If a theorist says there are "really" many worlds - and many "real" variants of me - then, the important thing is to remember that that "realness" (and anyone's "belief" in it) is theoretical. My actual business, anyway, is to see that, in the world I am observing, I be not too bad - so, to calculate what I need, I have to add the wavefunction collapse to that theory and "return to Copenhagen" - with better understanding as to whence that collapse comes (namely, from the rules of the actual business of life).

Judging from the discussion of Wallace here, it may very well be that, to make any decisions at all in life, the best strategy is always to act "as if" Born probabilities apply to the outcome of events - i.e. we have the appearence of Copenhagen collapse even if that is a bit of a legal fiction. The trouble is, deciding what is best may depend on whether you think MWI is true. So if you think you live in an MWI-universe and you think that quantum immortality/suicide makes sense, you will arrange for a spectacular but painless death confident that you will survive and be feted as The Man Who Cheated Death. You are still using Born, it's just that the cost in worlds where you die is rated at precisely zero. Under Copenhagen, you cannot argue this way. unless you have a reckless disregard for death. That may sound like a good reason for believing the CI :)

 

[Stephen Tashi]

I think MW is just too silly to believe - that's not scientific - just my gut feeling.

Without digressing into metaphysics, we can look at the assumptions made about the sensation of self - namely that we think of ourselves (at time t) as being a unique physical phenomena. So, assuming our sensation of self is implemented by physical phenomena, we assume that we are not being implemented by two distinct phenomena. For example, if somehow an exact duplicate of our bodies was created we would assume that we would remain ourself. The duplicate would think it was us, but, from our point of view, be mistaken. It seems to me that in mathematical discussions about a rational agent "the agent" (at time t) denotes a unique physical phenomena and the agent makes decisions thinking of itself as a unique physical phenomena. Is that correct? Or do the technicalities of macroscopic vs microscopic phenomena undermine the uniqueness of an agent as a unique physical phenomena?