Can the Born Rule Be Derived Within the Everett Interpretation?

[straycat]

I think maybe Wallace, or somebody else (there is related work by Simon Saunders...) devoted some effort to ruling it out explicitly (I'll post it if I find a reference)... maybe just through establishing noncontextuality given certain assumptions.

I still don't think I completely understand the difficulty with "noncontextuality" ... I'll be rereading sec 4 of Patrick's paper tonight ...

David

 

[straycat]

I still don't think I completely understand the difficulty with "noncontextuality" ... I'll be rereading sec 4 of Patrick's paper tonight ...
David

OK, reading Patrick's paper: "It is a property of AQT that changing the resolution of a measurement can change the probabilities of the outcome of the crude measurement, which is not the case under SQT." Is it not? Consider the quantum zeno effect, according to which (for example) we can change the probability of decay of a particle by changing the time-resolution of our measurements of the particle's state.
http://en.wikipedia.org/wiki/Quantum_Zeno_effect .

Later: "in AQT ... the probability of measuring 10 for X depends on whether we have measured Y or not ..." This sounds to me reminiscent of the 2-slit experiment: the probability of detecting the electron at a certain spot on the detector depends on whether we have measured which slit was traversed by the electron.

So it seems to me that some of the "strange properties of AQT" are in fact not so dissimilar to standard, good ol' quantum weirdness. In which case they do not disqualify it, but perhaps *qualify* it as a possible candidate of a physical theory of the world! Does this make sense?

David

 

[vanesch]

Hello M. Barnum,

Welcome to PF !

Concerning the following:

Patrick's detailed exploration of an alternative probability rule (which happens to be a rule we devoted two sentences to on page 1180 of our paper, noting that it was contextual
but not obviously ruled out by Deutsch's other assumptions) is quite worthwhile, I think. I have only just read it, a couple of times through, but it looks basically right to me. FoP might be a good place for it. I think maybe Wallace, or somebody else (there is related work by Simon Saunders...) devoted some effort to ruling it out explicitly (I'll post it if I find a reference)... maybe just through establishing noncontextuality given certain assumptions. But any such effort is likely to be based on measurement neutrality or something similar.

As I said already elsewhere, I'm doing this "as an interested amateur", so it is pretty obvious that I don't know the entire litterature of the domain although I did my part of reading up. And it seemed to me too that the reasoning I put forward in the paper was - at least informally - already presented a few times, but I found it useful to explore it in detail and try to write it down as formally as possible, because I think that is has important implications. I should probably make this clearer in the introduction. The main implication is that we should look for the best EXTRA postulate to introduce. Maybe the text was seen too much as an attack on Deutsch, which it wasn't, but Deutsch' work seemed to present the most obvious "case study" to illustrate the point I tried to make.

I think all these people do important work, but it seems that they are overlooking a point, namely that they WILL need, anyhow, to introduce something extra. Now, it is not forbidden to introduce something extra of course, if that makes the scheme work. So instead of minimizing the "extra assumption", or even try to hide it, it should be made clear and explored. As such, we could concentrate on the essential part, namely the meaning of the extra postulate - after it has been shown that that postulate makes things come out "as if" Copenhagen QM were true. But of course, as an amateur, one feels a bit uneasy to draw such a conclusion about people working in the field!

cheers,
Patrick.

 

[RobinHanson]

World counts incoherent?

Hello all, I'd like to join your conversation, a few days late.

This is true, but in section 5.3, Greaves argues that egalitarianism (which is the APP, but phrased in terms of utilities instead of objective probabilities) is *incoherent*, whether or not you accept measurement neutrality, because in a real-world setting where branch-splitting happens through decoherence, there is no well-defined number of branches. ... Patrick van Esch's case. If his intent is to prove that the APP is a consistent theory that "could have been true" (not just in an idealized model of a measurement/branching, but in messy statistical mechanics), then he needs to address these arguments. ... The question is whether you can justify measurement neutrality (or some equivalent assumption like equivalence or branching indifference or whatever they were called); for example, by showing that alternatives are incoherent, or require a huge amount of arbitrary input, or correspond to rationality principles that aren't even workable in theory. Wallace has a lot of philosophical discussion in his papers about this; for example, see section 9 in http://users.ox.ac.uk/~mert0130/papers/decprob.pdf .

This seems to me to be the essential issue. Wallace and Greaves and many others seem to accept the claim that if there are naturally distinguishable branches/worlds in the Everett approach, then it is natural to assign probabilities proportional to world counts, producing a difficult conflict with the Born rule. They claim, however, that world counting is incoherent. Page 21 of Wallace's paper cited above gives the most elaboration I've seen defending this view.

I'd like to discuss this point further. But being new here I'm not sure - does convention dictate that I should start a new thread or continue in this thread? So while I await instruction on this point, I'll just make one point.

Even if world counts are incoherent, I don't see that the Everett approach gives us the freedom to just pick some other probabilities according to convenient axioms. An objective collapse approach might give one freedom to postulate the collapse probabilities, but in the Everett approach pretty much everything is specified: the only places remaining for uncertainty are regarding particle properties, initial/boundary conditions, indexical uncertainty (i.e., where in this universe are we), and the mapping between our observations and elements of the theory (i.e., what in this universe are we). We might have some freedom to choose out utilities (what we care about) but such freedom doesn't extend to probabilities.

 

[vanesch]

Hello M. Hanson,

Welcome to PF ! Hope you'll enjoy this forum!

This seems to me to be the essential issue. Wallace and Greaves and many others seem to accept the claim that if there are naturally distinguishable branches/worlds in the Everett approach, then it is natural to assign probabilities proportional to world counts, producing a difficult conflict with the Born rule. They claim, however, that world counting is incoherent. Page 21 of Wallace's paper cited above gives the most elaboration I've seen defending this view.

I'd like to discuss this point further. But being new here I'm not sure - does convention dictate that I should start a new thread or continue in this thread? So while I await instruction on this point, I'll just make one point.

I think you can do here what you think is best. Feel free to start a new thread if you think it is a subject on its own (which it probably is).

 

[Tez]

[snip]---but if one accepts a subjective, decision-theoretic view
of probabilities (which I have no problem with, in this context), [snip]

And in which context do you have a problem with it Howard? (...we are watching you... )

 

[vanesch]

Even if world counts are incoherent, I don't see that the Everett approach gives us the freedom to just pick some other probabilities according to convenient axioms.

Well, the problem that I see is that in the Everett approach, there are NO probabilities at all. If we follow it strictly and we assume conscious awareness of our entire brain state, we should experience the entire state, and not just "one world". If they hit our toes with a hammer in one term, that should hurt us in any case :-)

Now, as people here know, I'm rather a proponent of Everett (as long as no naturally physical mechanism for a collapse is found), but I think that nevertheless *a* postulate about how we go from this quantum state to a perceived state, should be made. If we're going to perceive only ONE term of our brain state, I think that should be explicitly said and I find it a priori not evident why all states should get "equal probability" for me to perceive them. Of course, I understand that it is tempting, natural, etc... to do so, but not strictly necessary ; and in any case the rule should be postulated.

 

[straycat]

Well, the problem that I see is that in the Everett approach, there are NO probabilities at all. If we follow it strictly and we assume conscious awareness of our entire brain state, we should experience the entire state, and not just "one world".

When you say "entire brain state," I assume you mean (for example) the superposition of <Bob sees up> and <Bob sees down>. So your question is: why do you not "experience" up and down at the same time? Well, how do you know that you don't? In fact, the MWI predicts iiuc that you do experience both worlds, but actually "you" can be divided into two distinct halves, one of which experiences one world, the other of which experiences the other, and -- importantly -- the two distinct halves *cannot communicate with one another*. Therefore -- as Everett explains rather succinctly in a footnote in his original paper -- his formulation makes predictions that are entirely consistent with observation, and so my inability to experience multiple worlds at the same time cannot be used as an argument against the MWI, strict interpretation or otherwise.

Have you ever read about the "disconnection syndrome" in patients whose left and right hemispheres are not connected in the normal way via the corpus callosum? It is possible to demonstrate that the right half of the brain does not know what the left half knows, and vice versa. I think that this situation is analogous to the situation of Bob-sees-up and Bob-sees-down: if we imagine that Alice's corpus callosum has been cut, and the left half of her brain sees the number 1 while the right half sees the number 2, and we consider that the two halves cannot communicate to one another, then it seems apparent to me that there is no "unified Alice state" that "experiences" both brain inputs. And the key is that the two brain halves do not communicate. Likewise, Bob's two superpositional states do not communicate; that's why he does not "experience" both inputs at the same time.

David

 

[straycat]

APP follows from definition of probability?

If we're going to perceive only ONE term of our brain state, I think that should be explicitly said and I find it a priori not evident why all states should get "equal probability" for me to perceive them. Of course, I understand that it is tempting, natural, etc... to do so, but not strictly necessary ; and in any case the rule should be postulated.

I'm sort of on the fence regarding whether the APP requires a separate postulate. Certainly, if you are going to assume the Born rule, then that requires a separate postulate, as you (Patrick) argue in your paper. Therefore, it would stand to reason that if we assume something *other* than the Born rule, ie the APP, then that likewise requires a separate postulate.

However, there is a different part of me that thinks that probability could in fact be DEFINED in such a manner that the APP necessarily follows from the definition, and in fact rules out the Born rule (or any other non-APP contenders), so that a separate postulate is not necessary. The basic argument is spelled out in Graham's 1970-something paper, and recapitulated in the latest draft of my paper, and is also touched upon in Robin's powerpoint presentation of his work ( http://hanson.gmu.edu/mangledworlds.html ). The short version goes like this: define a predicted "probability measure" m_n, where m_n is specified by some rule eg the Born rule: m_n = |a|^2, or the APP: m_n = 1/N. Now define the observed frequency p_n, which is the frequency of observing outcome n -- say, spin "up," after doing M identical spin measurements. We could DEFINE probability as p_n, and then require (establish a "criterion") that in "most" worlds, the observed frequency p_n equals the predicted measure m_n. It turns out, I think, that the APP is the only "rule" that is consistent with this criterion.

Like I said, I'm sort of on the fence regarding whether the APP requires a separate postulate or can be derived from, say, the definition of "probability." But I'm not sure it matters to me which one it is. If the APP requires a separate postulate, then I think the APP could very well be given the status of a symmetry principle and postulated in the same sense that the "principle of relativity" is one of the postulates of GR, with justification nothing more nor less than an argument from symmetry.

Hmmm. Does the principle of relativity require its own separate postulate? I suppose it does. So I suppose that the APP, likewise, also requires its own separate postulate.

David

 

[vanesch]

In fact, the MWI predicts iiuc that you do experience both worlds, but actually "you" can be divided into two distinct halves, one of which experiences one world, the other of which experiences the other, and -- importantly -- the two distinct halves *cannot communicate with one another*.

I do realize that, I think it is one of the most important contributions of decoherence theory. But what does this have to do with probability ? As I argued in the other thread, why should there be an "equal probability" of "and you happen to be this and that" ?

Therefore -- as Everett explains rather succinctly in a footnote in his original paper -- his formulation makes predictions that are entirely consistent with observation, and so my inability to experience multiple worlds at the same time cannot be used as an argument against the MWI, strict interpretation or otherwise.

I think one should then make clear exactly what it means "to experience". It seems that in the concept, a classical view is already sneaked in. What we ultimately want to explain is how it comes that we experience consciously a brainstate that corresponds to one of those states in a high hilbert norm world.

Have you ever read about the "disconnection syndrome" in patients whose left and right hemispheres are not connected in the normal way via the corpus callosum? It is possible to demonstrate that the right half of the brain does not know what the left half knows, and vice versa. I think that this situation is analogous to the situation of Bob-sees-up and Bob-sees-down: if we imagine that Alice's corpus callosum has been cut, and the left half of her brain sees the number 1 while the right half sees the number 2, and we consider that the two halves cannot communicate to one another, then it seems apparent to me that there is no "unified Alice state" that "experiences" both brain inputs. And the key is that the two brain halves do not communicate. Likewise, Bob's two superpositional states do not communicate; that's why he does not "experience" both inputs at the same time.

What I do understand from Everett is that on an objective level - as a purely materialist interpretation - each brain state will act as if it were alone in its branch. So from a "god's viewpoint" there is no surprise that each individual state acts the way it does. From a "god's viewpoint", it is also clear that in the branches with the highest hilbert norms, brain states will have noticed the Born rule and have written books about it. Also from a god's viewpoint, in branches with very low hilbert norms, brain states will not have found the Born rule. They may even have found totally different laws of physics, given the weird events that they've been witnessing. But why should each of these worlds be given "equal a priori probability for me to be in" ? As I said, tongue in cheek: following the same reasoning: if there are 10^10 conscious ants, and 5 humans, then I should be, by an overwhelming probability, an ant, no ?
I have nothing against it, but I don't think it *follows* logically from anything. I think one STILL has to *postulate* that. Comparing to the second law of thermodynamics is, in my opinion, not exactly the same for the following reason: we assign equal probabilities there to "chunks of phase space" because these chunks evolve in one another, and come close to each other thanks to ergodicity. However, as you point out correctly, the brain states do not evolve into one another, they are separated for good. So there is no "ergodicity" that will make a "time average = ensemble average" when I'm hopping over all my possible brain states, giving me the impression that I have to deal with some probabilistic phenomenon when I only look at coarse-grained quantities. I "just happen to be" one of those brain states. How do you get a *probability* for that ?

 

[vanesch]

The short version goes like this: define a predicted "probability measure" m_n, where m_n is specified by some rule eg the Born rule: m_n = |a|^2, or the APP: m_n = 1/N. Now define the observed frequency p_n, which is the frequency of observing outcome n -- say, spin "up," after doing M identical spin measurements. We could DEFINE probability as p_n, and then require (establish a "criterion") that in "most" worlds, the observed frequency p_n equals the predicted measure m_n. It turns out, I think, that the APP is the only "rule" that is consistent with this criterion.

That is begging the question ! The fact that your CRITERION uses "most worlds" each with equal weight in the cost function IS ALREADY the APP.

Apply the same reasoning, but this time, you require as a cost function that in the worlds WEIGHTED WITH THEIR HILBERT NORM the observed frequency equals the predicted measure, and you will find the Born rule !

 

[straycat]

That is begging the question ! The fact that your CRITERION uses "most worlds" each with equal weight in the cost function IS ALREADY the APP.

Apply the same reasoning, but this time, you require as a cost function that in the worlds WEIGHTED WITH THEIR HILBERT NORM the observed frequency equals the predicted measure, and you will find the Born rule !

Yes, you are correct -- my "probability criterion" effectively assumes the APP, just as Deutsch's "measurement neutrality" assumes (or at least opens the door for the assumption of) the Born rule.

I'm not sure that it would be possible, though, to use my probability criterion to give rise to the Born rule. Sure, I could use cost functions, weightings, etc. But the basic idea is that I don't know how to interpret a "cost function," so I'd rather not even entertain the notion.

Here's one way to interpret a "cost function." I could postulate the existence of a Soul, and say that the Soul follows different trajectories with probability proportional to their "cost function." But such metaphyasical assumptions are precisely what I want to avoid. I'd rather just enumerate the different branches that exist, and leave it at that.

Let me digress once again to the notion of limits. Consider, for example, in differential geometry, the notion of the distance between two points, or the area of a region, in a curved spacetime. To define these terms, we need first to define the metric. To define the metric, we need a map from flat spacetime (the tangent space) to our curved spacetime. And in the tangent space, the notion of distance is a "natural" one, not too many conceptual steps away from counting discrete points. The point I am trying to make is that, whenever we use the concept of measure, we are ALWAYS relying, ultimately, on the notion of "counting discrete things."

So if we were hypothetically to associate a "cost function" or a "weighting" to different branches, then I would want to say this is analogous to the area of a region in curved spacetime in the preceeding paragraph. That is, I want to be able to go through the steps in the above paragraph, ie to work backwards until I reach a "natural" method of counting worlds. Somewhere in this process, I need to define a "tangent space" of worlds which is flat, ie in which I can easily and naturally calculate the number (or at least the density) of worlds within a given region. If this cannot be done, then the only way to interpret this cost function is metaphysically. And if it CAN be done, then you see that we have effectively explained the "cost function" in terms of world-counting!

Note that in my discussion of the probability criterion, the frequency p_n has a well-defined meaning -- it is the observed frequency that the n-th outcome was observed. The predicted quantity m_n is also well-defined: it is simply a calculated quantity, calculated by humans, and may or may not even be correct!

David

 

[straycat]

As I said, tongue in cheek: following the same reasoning: if there are 10^10 conscious ants, and 5 humans, then I should be, by an overwhelming probability, an ant, no ?

I worry that you are getting sucked into a tautological trap, like contemplating the sound of one hand clapping. You need to escape!

Patrick: Probabilistically, I should be an ant, right?
David: Who should be an ant?
Patrick: me.
David: Define "me."
Patrick: "me" = Patrick.
Well there you go, you have answered the question tautologically, ie by definition.

Try riddling this. Have you ever wondered why the year is 2005 and not, say, 1975, or 1224, or 3001? Or have you ever wondered why am I here, and not there? iow: why is spacetime point a located at spacetime point a, and not somewhere/sometime else? Well, the answer is that you have DEFINED a to be right there.

How do you get a *probability* for that ?

Forget probability: just define p_n and m_n as I do using my "probability criterion" discussion. That's all there is.

David

 

[straycat]

Just so everyone knows ... Robin started a thread "Are World Counts Incoherent?" which was moved to the philosophy section of PF, or you can link to it here:

https://www.physicsforums.com/showthread.php?t=101339

David

 

[Sherlock]

I do realize that, I think it is one of the most important contributions of decoherence theory. But what does this have to do with probability ? As I argued in the other thread, why should there be an "equal probability" of "and you happen to be this and that" ?
I think one should then make clear exactly what it means "to experience". It seems that in the concept, a classical view is already sneaked in. What we ultimately want to explain is how it comes that we experience consciously a brainstate that corresponds to one of those states in a high hilbert norm world.
What I do understand from Everett is that on an objective level - as a purely materialist interpretation - each brain state will act as if it were alone in its branch. So from a "god's viewpoint" there is no surprise that each individual state acts the way it does. From a "god's viewpoint", it is also clear that in the branches with the highest hilbert norms, brain states will have noticed the Born rule and have written books about it. Also from a god's viewpoint, in branches with very low hilbert norms, brain states will not have found the Born rule. They may even have found totally different laws of physics, given the weird events that they've been witnessing. But why should each of these worlds be given "equal a priori probability for me to be in" ? As I said, tongue in cheek: following the same reasoning: if there are 10^10 conscious ants, and 5 humans, then I should be, by an overwhelming probability, an ant, no ?
I have nothing against it, but I don't think it *follows* logically from anything. I think one STILL has to *postulate* that. Comparing to the second law of thermodynamics is, in my opinion, not exactly the same for the following reason: we assign equal probabilities there to "chunks of phase space" because these chunks evolve in one another, and come close to each other thanks to ergodicity. However, as you point out correctly, the brain states do not evolve into one another, they are separated for good. So there is no "ergodicity" that will make a "time average = ensemble average" when I'm hopping over all my possible brain states, giving me the impression that I have to deal with some probabilistic phenomenon when I only look at coarse-grained quantities. I "just happen to be" one of those brain states. How do you get a *probability* for that ?

I'm trying to understand what you guys are talking about.
Is there a real physical problem (that is so perplexing as to lead you to ponder the various probabilities of the existence of other worlds, whatever that might mean)? If so, then would it be possible, for the benefit of us interested laymen, to sort of delineate it clearly?

I mean, I understand that there is a problem with talking about quantum measurement processes --- eg., the 'projection postulate' isn't derivable. But the leap to other worlds seems unfounded.

You're not an ant, because, by definition, you're a human. We don't, by definition, experience, wrt probabilities attached prior to our experience, alternative realities. Reality is what it is, by definition. There's zero probability attached to possible outcomes which, prior to measurement, were alternatives to observed outcomes, because the probability attached to observed outcomes is 1. Once a detector registers a detection at a time, t, then there's no chance whatsoever that it didn't register a detection at a time, t.

You have happened to be in a particular brain state during any particular interval. The probability of any of those brain states happening is 1, because they happened. The probability that they didn't happen is 0, because they happened.

But, one might say, the unitary evolution of quantum processes, which exists and continues independent of measurement, indicates that all of the possible outcomes contained in the qm description have happened (albeit in some alternative reality). But, we don't live in, and quantum theory isn't being applied to a reality that is independent of measurement. Reality, as far as physics is concerned, is the set of all objective measurements. By definition, there is no alternative reality.

While you might be having some semantic fun, I don't understand how you're going to solve the physical problem of quantum measurement processes, or understand why the Born rule works or it's justification in the theory, by taking the approach that measurements which, by definition, have definite outcomes don't have definite outcomes.

As usual, I'm probably missing some important part of what it is that's being considered. Anyway, any clarification you can offer will be appreciated -- and if you don't have time, then I understand.

 

[RobinHanson]

What I do understand from Everett is that on an objective level - as a purely materialist interpretation - each brain state will act as if it were alone in its branch. So from a "god's viewpoint" there is no surprise that each individual state acts the way it does. From a "god's viewpoint", it is also clear that in the branches with the highest hilbert norms, brain states will have noticed the Born rule and have written books about it. Also from a god's viewpoint, in branches with very low hilbert norms, brain states will not have found the Born rule. They may even have found totally different laws of physics, given the weird events that they've been witnessing. But why should each of these worlds be given "equal a priori probability for me to be in" ? As I said, tongue in cheek: following the same reasoning: if there are 10^10 conscious ants, and 5 humans, then I should be, by an overwhelming probability, an ant, no ?

If all you know is that you are conscious, then yes you should be surprised to be one of the few conscious beings who are human. It would be surprising enough that you should look for an explanation, such as that you've been making a wrong assumption about something. In fact however, you also know the crucial fact that you are able to reason about the fact that you are conscious, and about what that might imply. Since ants can't do that, you should be much less surprised that you are asking the question.

Similarly, if all you know is that you have found yourself in a Born rule world, I think you should be very surprised.

 

[RobinHanson]

Try riddling this. Have you ever wondered why the year is 2005 and not, say, 1975, or 1224, or 3001? Or have you ever wondered why am I here, and not there? iow: why is spacetime point a located at spacetime point a, and not somewhere/sometime else? Well, the answer is that you have DEFINED a to be right there.

I think you are being a bit flippant. There are real and deep questions to consider here. It is indeed possible to be surprised to find oneself at a particular time or place - one can't simply exclude this by making definitions.

 

[straycat]

There are real and deep questions to consider here. It is indeed possible to be surprised to find oneself at a particular time or place - one can't simply exclude this by making definitions.

Yes, but the point I am trying to make is that we have to pay close attention to the question being asked before we decide to be surprised at the answer, because it may be that we are contemplating the WRONG question. Is it possible to be surprised to find oneself at a particular time or place? Of course it is. Example: given everything that I know about the world as it is today, I would be surprised to find myself in, say, Costa Rica tomorrow. (Pleasantly, perhaps ... ). This, I think, is a well-posed question. But should I be surprised that I am not an ant? Given (only) that I am "a living entity" in a room full of lots of ants and one human, then yes, it IS surprising that I am human, and not an ant. Or I could ask this: given (only) that I am a 70 kg lump of matter, is it surprising that I just so happen to be living, breathing, sitting in front of a computer, in the year 2005, on the earth? Yes! what were the odds of THAT? So here's the issue: why would I ever contemplate questions that were set up like these last two? I mean, I can contemplate them -- but do they have any physical significance?

David

 

[Sherlock]

What's wrong with modelling the universe as a sequence of unique configurations. Then you don't have the problem of world counts. Each universal configuration has one and only one descendent.
It seems to me that this would be a more physical way of approaching things.
Yesterday's probability that I would be writing this today doesn't matter as I write this. Probabilities regarding future events are just formalized guesses based on incomplete knowledge of reality. Probabilities regarding past events are meaningless.
We aren't, in fact, surprised by where we find ourselves at any particular moment (provided that we are operating with normal and sober, human biological functions) because we can and do, in fact, experience the uniqueness (and therefore, in a limited sense, track the temporal flow) of the instantaneous configurations encompassing our sensory range.

 

[Ontoplankton]

I agree that, in a sense, you can be surprised that you are you and not someone else.

For example, if one theory predicts that there exist 99 left-handed people and 1 right-handed person, and another theory predicts that there exist 1 left-handed person and 99 right-handed people (all isolated from each other) then if you find that you are left-handed, this confirms the first theory. If you believed the second theory was true, your left-handedness should surprise you. Or at least, it's not obvious that it shouldn't.

By the way, I second Robin Hanson's recommendation (in the other thread) of Nick Bostrom's book at anthropic-principle.com. It's a very confusing subject, I think.

 

[Sherlock]

Is it possible to be surprised to find oneself at a particular time or place? Of course it is.
Example: given everything that I know about the world as it is today, I would be surprised to find myself in, say, Costa Rica tomorrow. (Pleasantly, perhaps ... ).

If you do wind up in Costa Rica tomorrow, then I predict that you will not be surprised by it ... unless you black out a lot (does that count?).
If you suddenly find yourself in Costa Rica, then it would be a surprising realization. (Or if you've been right-handed your whole life and suddenly find yourself doing everything left-handed, or if your hair spontaneously turns green ... that would probably be surprising.)

But it isn't surprising that there is a quantum theory or that it employs something called the Born rule.

 

[straycat]

If you do wind up in Costa Rica tomorrow, then I predict that you will not be surprised by it ... unless you black out a lot (does that count?).
If you suddenly find yourself in Costa Rica, then it would be a surprising realization.

I'm just trying to imagine what sequence of events could possibly result in placing me in Costa Rica tomorrow. You know, the stuff novels are made of, like the CIA suddenly needs my unique blend of intelligence and good looks to solve the greatest threat known to mankind , which happens to be in Costa Rica, and all by Sunday ... Any scenario I come up with is, well, surprising -- of course, it is surprising, given the state of the world right now , from which we can calculate that the probability of the above sequence of events is about 0.01%, but with a bunch more "0"'s.

 

[Sherlock]

I'm just trying to imagine what sequence of events could possibly result in placing me in Costa Rica tomorrow. You know, the stuff novels are made of, like the CIA suddenly needs my unique blend of intelligence and good looks to solve the greatest threat known to mankind , which happens to be in Costa Rica, and all by Sunday ... Any scenario I come up with is, well, surprising -- of course, it is surprising, given the state of the world right now , from which we can calculate that the probability of the above sequence of events is about 0.01%, but with a bunch more "0"'s.

Just go with the flow, I say ... and good luck in making it to Costa Rica. It can be a fun place, and your dollars will buy more there than here, but I wouldn't want to live there.

Since my earlier posts I've read up on Everett's relative-state formulation. I'd classify the approach as interesting, but misguided ... and unfinished. Some of the resolutions to it are pretty wild. Definitely not good physics though. (as if I would know )

Anyway, wave function collapse and action-at-a-distance are pseudo-problems in my estimation.

 

[DrChinese]

Now, as people here know, I'm rather a proponent of Everett (as long as no naturally physical mechanism for a collapse is found)...

After following this thread a bit, I am beginning to understand better the attraction of the MWI. Reading Robin's "Mangled Worlds" page helped a lot too.

So here is my question: we have 2 entangled photons and perform a measurement on one at T=1 and a measurement on the other at T=2, let's assume they are more or less in the same location when the measurement is performed (perhaps we use coiled fiber optics on one so that the second measurement is delayed). These 2 particles were in a superposition. Can the measurement at T=1 be considered more fundamental in some respect than the one at T=2? I.e. did one "cause" the wave collapse while the other didn't?

In other words: does the branching (world counting) happen at T=1 and THEN at T=2? Or does half the time it is T=1, then T=2 and the other half of the time it is calculated as T=2, then T=1?

Also: is there any difference in how the MWer sees this as opposed to the orthodox QM view?

 

[vanesch]

Try riddling this. Have you ever wondered why the year is 2005 and not, say, 1975, or 1224, or 3001? Or have you ever wondered why am I here, and not there? iow: why is spacetime point a located at spacetime point a, and not somewhere/sometime else?

This was exactly the point I discussed in the epistemology forum (consciousness as an active ...) ! Indeed, given the "ontology" of the 4-d manifold in GR, one could then say that a brain is a 4-d structure (static and timeless) and your subjective world only "experiences" one timeslice of it.

 

[vanesch]

In fact however, you also know the crucial fact that you are able to reason about the fact that you are conscious, and about what that might imply. Since ants can't do that, you should be much less surprised that you are asking the question.

That only changes my argument in "I should experience the subjective world of an ant and not be surprised of my situation" . It doesn't explain that "I am experiencing a human subjective experience and am wondering why". It only explains that "those who are wondering why, must be humans"... and maybe we're underestimating the conscious abilities of ants

What I wanted to point out is that in assigning probabilities of our subjective experiences to different worlds, there is no a priori necessity to have them being given by a uniform distribution. I agree that it would be a "natural" thing to do, but if that gives problems with what is observed, I don't see what is so impossible to postulate anything different.

We are talking about assigning "your subjective experiences" to different aspects of the ontological physical reality. Nobody says that certain worlds, in this assignment, cannot have bigger weight than others. For instance, you could even postulate that worlds with high hilbert norm are "several times identically experienced". Why not ?

As I said in the beginning of this discussion, if "conscious experience" were to be strictly connected to a physical object such as a brain, we should experience a kind of "god's viewpoint" and have all these states in parallel.

The argument straycat used, with the two brain halves not communicating, can even be illuminating here:

Let us assume that it is possible to put a switch on the link between the two brain halves. Now suppose that YOU still have the switch closed, and you have a "normal" subjective experience of your body. Now, at a certain point, one flips the switch, and your two brain halves are separated. What do you think will be your subjective experience ? Left, right, or both ?

From the exterior, no difference can be made of course, and it will appear that the two brain halves have independent subjective experiences, and hard to say which one was "the original". But YOU will know. You will only experience one of both. Imagine to what you will feel when the switch is flipped... clearly you will NOT experience a god's eye view of BOTH halves, you will experience ONE of both and this will be the left one or the right one.

After closing the switch again, no difference can be made, because both brain halves will have recorded different souvenirs, and you will probably re-experience what you had before, with a joint memory of both halves without distinction ; so afterwards you will not KNOW which half YOU were.

But during the split, of course you will only experience ONE of both. Now, it could be that this is systematically, say, the right halve. But there is no way to convince the external world, because the other half will act in exactly the same way. But *you* know that you "went into the right halve". If this is systematical, then the probability is not 50 - 50, but 0 - 100.

 

[vanesch]

In other words: does the branching (world counting) happen at T=1 and THEN at T=2? Or does half the time it is T=1, then T=2 and the other half of the time it is calculated as T=2, then T=1?

"branching" in any MWI approach corresponds to the observer getting (FAPP) irreversibly entangled with environment, and this happens at an incredulous rate, independent of any actual "measurement" in the lab, which is just one little branching in this enormous amount of branching induced by the environment. But this "little branching" will have its results recorded in all its "descendants". So the measurement at T=1 will be one of these branchings, and have a lot of descendants with the result "up" in part of the arborescence, and the result "down" in the other part of the arborescence. Much later, at T = 2, all these descendents will again record the result "up" (together with the recorded result of T=1) or "down" and bifurcate further in an incredible frenzy of splitting, as imposed by interactions with the environment.

Now, the idea of many MWI proponents (but not me :-) is that all these branches are "equivalent" and you happen to experience only subjective ONE of them, "randomly picked out", while they give equal probabilities to each of these branches "for you to be in". And then, rats, you do not find Born rule probabilities for events, but rather the APP.

Now, the hope of many people is that if somehow you can introduce a CUTOFF based upon the Hilbert norm, that if you only count worlds ABOVE this cutoff, and let not count those underneath, and if the branching follows a certain pattern, that then in those worlds that are permitted to play, that you DO restore the Born rule. That's not really surprising, because worlds with a higher norm will have more descendants above the cutoff than smaller worlds, so when counting them, you kind of measure the original hilbert norm of the world at the moment of obtaining the measurement result. That is what Robin Hanson tries to do where the cutoff comes naturally from the remnant correlations in decoherence, which continuously mix (mangle) worlds of small hilbert norm. I find this an interesting proposition, btw, but he still needs a lot of as of yet unproven conjectures to get everything up and running (but I agree that it looks promising). One of the postulates that have to be added - I think - is that you cannot experience the "mangled" worlds. Ok, these are funny worlds which change constantly, but we STILL need to know why I'm not allowed to experience totally weird worlds. Hanson does give good arguments of why it would be natural to do so, but I still make a difference between what is "natural" and what is "postulated".

Nevertheless, my (lazy) point of view is that this is maybe not necessary, because the concept "the probability for you to experience a world" does not need to be uniform (that's what I'm trying to argue here). If you simply say that it is proportional to the Hilbert norm, then you get out (of course) the Born rule without any difficulty, and I fail to see why people go through a lot of trouble for not having to postulate that...

 

[Careful]

Read your paper : you might want to send it to Journal of Physics A.

 

[RobinHanson]

What I wanted to point out is that in assigning probabilities of our subjective experiences to different worlds, there is no a priori necessity to have them being given by a uniform distribution. I agree that it would be a "natural" thing to do, but if that gives problems with what is observed, I don't see what is so impossible to postulate anything different.

I'll continue to argue that if the physics is clear, there must be a right answer to the question of how to assign probabilities to branches. We might have trouble figuring out what that right answer is, but we can't just make convenient postulates. This problem is related to a more general problem that has received more attention, that of priors over indexical uncertainty. See Bostrom's book http://www.anthropic-principle.com/book/" . Uniform priors over possible discrete alternatives seems so far to be the best general approach.

 

[DrChinese]

So the measurement at T=1 will be one of these branchings, and have a lot of descendants with the result "up" in part of the arborescence, and the result "down" in the other part of the arborescence. Much later, at T = 2, all these descendents will again record the result "up" (together with the recorded result of T=1) or "down" and bifurcate further in an incredible frenzy of splitting, as imposed by interactions with the environment.
...

Thanks, Patrick. That exactly answers my question. A couple of other minor items - my apologies if these are a bit off-track:

1. Is there ever any interaction between worlds? Something to the effect of "interference" between them? Or, is there any mechanism to the effect that: equivalent worlds consolidate later (so there aren't quite as many branches) ? Seems like it would be nice to tidy things up later if that were possible.

2. In my question about T=1 and T=2: the branching as you describe makes sense to me. Would oQM have the Born rule applying in the same manner? I.e. the collapse at T=1 should occur objectively BEFORE the event at T=2? (Again, the events happen serially at the same place so there is no consideration required for different reference frames.) Or is this something that is generally not considered/discussed in examples of application of the Born rule because there is no apparent difference in the outcome?

In other words, it seems to me that the branching is something of a fundamental element of MWI: it would be "physical" even if not observable (because we only inhabit one branch at a time). Whereas in oQM the point at which the Born rule is applied affects our knowledge... but is somehow "less physical" than in MWI since nothing physical is actually postulated to occur at this point (even though the measurement has formal significance).

Thanks for any light you can shed on this.

 

[selfAdjoint]

In addition (or restatement?) of what Dr. Chinese asked, I would like to ask whether the relative Born probabilities might be determined sub specie aeternitatae by the total number of descendent branches (assuming no interaction or pruning).

 

[vanesch]

I'll continue to argue that if the physics is clear, there must be a right answer to the question of how to assign probabilities to branches. We might have trouble figuring out what that right answer is, but we can't just make convenient postulates.

I think that in any case, SOME postulate is necessary to link the quantum state to a perceived state if we are to accept strict unitarity. I think on the other hand that there are different esthetical criteria that one can use in order to judge, between observationally equivalent sets of postulates, which are more satisfactory than others. And, as I said, the uniform probabilities sound indeed rather "natural" ; but if that gives problems, I don't mind taking up eventually "less natural" postulates that lead to observed experience.

In the mean time I've been thinking, apart from the PP and the APP, about yet another "assignment" of probabilities of observation that not seem to contradict the postulates of unitary QM. I should check it, but I think that the "maximum length" world is ALSO compatible with unitary QM:

Take a finite number of "worlds" or outcomes or whatever, well, you will experience the one with the highest Hilbert norm with certainty. Let's call it the MPP (Maximum Projection Postulate). With the MPP, the resulting quantum theory is in fact deterministic: an observer will ALWAYS observe the outcome with maximum hilbert norm. This will of course also not lead to the Born rule, but I think it is just as well a logically consistent quantum theory.

 

[vanesch]

In addition (or restatement?) of what Dr. Chinese asked, I would like to ask whether the relative Born probabilities might be determined sub specie aeternitatae by the total number of descendent branches (assuming no interaction or pruning).

That is the holy grail of MWI proponents, but if NO pruning or cutoff is introduced, everything seems to point out that the number of decendents is independent of the hilbert norm and as such, the APP will result (which is kind of logical, if you apply the APP on the "lowest level" then it will "propagate upward"). If you apply the "born rule" to the "worlds", then you will get the "Born rule" also for the outcomes upward.


However, what people noticed is that if you apply the "APP" to an arborescence with a cutoff on the hilbert norm, that the NUMBER of descendents is (under appropriate conditions) then more or less proportional to the hilbert norm of the "parent" branch.
This is what Hanson (present here) tries to establish with his mangled worlds proposition, which introduces a kind of natural cutoff.

There are other propositions of different kinds, but as far as I understand, one always something extra to "prune" the APP in order to get out something that looks like the Born rule.

 

[vanesch]

1. Is there ever any interaction between worlds?

Normally not, because the different observers are entangled with a very complex environmental state:

|meseecatalive> |stuff1> + |meseecatdead>|stuff2>

here represented by stuff1 and stuff2. The idea is that stuff1 and stuff2 contain so many different degrees of freedom, and are (slightly) different, that they are orthogonal and will remain so for ever, under almost any thinkable unitary evolution. So all "interference" between both will have a factor (stuff1|stuff2) = 0 with it and hence be inobservable...

The only exception being if there is some "tagging" in the different worlds ; that's exactly what happens in EPR kinds of experiments ! Then the interference happens when the two "environments" finally communicate (through light or timelike channels), which will give us finally the "interference pattern" of the EPR correlations.

 

[mbweissman]

locality in branching

So here is my question: we have 2 entangled photons and perform a measurement on one at T=1 and a measurement on the other at T=2, let's assume they are more or less in the same location when the measurement is performed (perhaps we use coiled fiber optics on one so that the second measurement is delayed). These 2 particles were in a superposition. Can the measurement at T=1 be considered more fundamental in some respect than the one at T=2? I.e. did one "cause" the wave collapse while the other didn't?
In other words: does the branching (world counting) happen at T=1 and THEN at T=2? Or does half the time it is T=1, then T=2 and the other half of the time it is calculated as T=2, then T=1?
Also: is there any difference in how the MWer sees this as opposed to the orthodox QM view?

The branching order in MW is not important, fortunately, since the order of the events is generally not a Lorentz invariant. This issue is much less problematic for MWI than for collapse pictures. No choices are made in MWI, unlike collapse, so no superluminal communication is needed to keep spacelike separated choices coordinated in Bell-type experiments.