What Is an Element of Reality?

[DrChinese]

Ah we're home
You think of "collapse of the wavefunction". Well, let me tell you something: EVERYBODY AGREES that collapse of the wavefunction in this way would be bluntly non-local. So I fully agree with you that such a thing is just as ugly non-local as Bohm !

cheers,
Patrick.

Well said! (And the same "non-local" collapse happens in single particle experiments too, not just in EPR setups. In EPR setups, we see it more clearly.)

 

[vanesch]

"Let us summarize once again the logic that leads to the impasse. The EPRB correlations are such that the result of the experiment on one side immediately foretells that on the other, whenever the analyzers happen to be parallel. If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of QM. So we *cannot* dismiss intervention on one side as a causal influence on the other." (pg 149-50 of Speakable...)

Well, again, we've switched vocabulary, but Bell is wrong on this issue. "causal influence" in my book, corresponds to information transfer. It is because he cannot get rid of the old paradigm of deterministic theories in which of course ALL correlations between A and B are related to 1) direct causal influence or 2) indirect "common cause" causal influence.

The reason for this, in a deterministic paradigm, is that we only know of one mechanism to have randomness, namely the lack of information we have of internal degrees of freedom. And then it is clear that upon the observation of correlations between the observed randomness of A and B, you have somehow to "transport these internal degrees of freedom", or, directly from A to B (1), or you had to transport them from a common origin C to A and to B (2). And Bell cannot get out of that view. (1) is non-local, and (2) is Bell Locality. He cannot conceive the possibility that these correlations "just are", and are not related to a lack of knowledge. After all, it has been the paradigm that has been with us for all of classical physics. Einstein was apparently a bit smarter: he believed in this paradigm too, but understood that it could be different (but he didn't want to accept it "God doesn't play dice").

But if you now switch to another paradigm, which is the one of fundamentally stochastic theories, "god does play dice" and the fundamental quantity this time is the probability distribution (the n-point correlation function ; usually in our examples 2-point correlations are sufficient) then you do not need to assume that all randomness is related to lack of knowledge of internal degrees of freedom. And thus you do not need anymore to conclude that correlations can only come about through 1) or through 2). It is by forcing such a fundamentally stochastic theory in the deterministic paradigm that you end up drawing conclusions about locality or about the age of your mother in law.

The deterministic paradigm (randomness only comes about by incomplete knowledge of internal degrees of freedom) comes under many terms:
"complete state" (the internal degrees of freedom), "realism", Bell Locality, ...

cheers,
Patrick.

 

[Cat]

That is a logical flaw. You want it both ways. You refuse to accept it as conclusive evidence when folks stop looking; and you see it as supporting your position when they are looking!

Of course it's not "conclusive evidence" if they stop looking! It just means that they've given up the search for common-sensical explanations for the time being.

From your logic, it makes no sense to repeat an experiment, either! (Presumably that would mean that the experimented does not accept the initial results.) There are a lot of reasons to do experiments, even ones in which the essential results are not in question.

You're right in a way, in that I'm so convinced the world is both real and local that I'll eat my hat if Grangier's team's experiment manages to infringe the CHSH test!

The proposal in question is:

R. García-Patrón Sánchez, J. Fiurácek , N. J. Cerf , J. Wenger , R. Tualle-Brouri , and Ph. Grangier, “Proposal for a Loophole-Free Bell Test Using Homodyne Detection”, Phys. Rev. Lett. 93, 130409 (2004)
http://arxiv.org/abs/quant-ph/0403191

Though the result as it stands is a forgone conclusion, the experiment could, I think, be modified so as to settle the matter of how the detection loophole works once and for all. As it stands, they propose to treat as the + results all voltage differences greater than zero, and - all negative ones. Since there will always (except on a set of measure zero) be some voltage difference they will have no non-detections. [Even if I've misinterpreted their intentions slightly here, they've got the "event-ready" detectors to ensure that they define their sample before analysing the results, so it will be, by definition, "fair".]

But they could instead look at the raw voltages and digitise these, using (as in Aspect's experiments) some minimum threshold voltage to decide what to count. They could then explore what happens as the threshold is altered. When it is zero, we have effectively "perfect" detectors; when very high we have very low efficiency ones and lots of non-detections. What then happens to the CHSH test statistic? Under local realism, this is predicted to increase and eventually infringe the inequality, as per Pearle's 1970 argument.

Cat

 

[ttn]

I am quoting him (EPR): "...[...]"

As I noted here earlier, Einstein did not write the EPR paper. Podolsky did. And Einstein was rather disappointed with how the paper turned out. This is a well-documented historical fact. So you can't quote the EPR paper and assert that this is revealing the views of Einstein. I quoted a passage that was actually written by Einstein in which he states with complete clarity that he thought the point of EPR -- the point that was unfortunately "smothered" in Podolsky's text -- is that there is a *dilemma* between locality and completeness. Both cannot be true for QM. This is hardly an "out of context comment made later." This was rather Einstein's attempt to set the historical record straight given that the author had, in Einstein's own written opinion, flubbed the argument in the EPR paper.

Re: Bell, I suppose we will have to agree to disagree. I simply don't understand how you can claim that what he proved has nothing to do with (i.e., is not openly premised on) locality. The whole point of the theorem is that a theory in which the outcomes of measurements are pre-determined by some kind of "instruction set" in the particles -- AND THAT RESPECTS THE BELL LOCALITY CONDITION -- cannot agree with experiment. i.e., local hidden variable theories are ruled out.

BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

That means to me that there are NO hidden variables ANYWHERE.

Bell was for about 20 years pretty much the only living human being who actively pursued, lectured on, wrote about, and studied Bohmian mechanics. To claim that he believed he had proved that hidden variables theories as such are impossible, is thus rather odd.

I agree with your deduction [reference 1 above] that an observation on one side is causally connected to the results on the other. And the reason I believe that has nothing to do with whether QM is local or non-local!

Then you must be confused about what Bell proved. Bell's theorem shows that, if you try to "complete" QM by adding local hidden variables, the theory you get cannot both respect the Bell Locality condition and agree with experiment. So, as lots of people say, if you want a local theory, you'd better stick with QM and its completeness doctrine, and not go down the hidden variables road. But that strategy obviously presupposes that QM itself is local -- otherwise, saying "you should stick with QM and not pursue hidden variable theories, on pain of nonlocality" just makes no sense.

And the final piece: Bell states openly that, he thinks, nonlocality is a fact, period -- that it's *not* something which merely afflicts hv theories. As he says, you *cannot* dismiss the operations on one side as causal influences on the other. How can he believe this? What else would he need to have to believe to make this claim given the above paragraph? Obviously he would have to think that orthodox QM was *also* nonlocal. IF it wasn't, there'd be no grounds for claiming that all possible alternatives -- i.e., nature -- were nonlocal.

I believe that because I believe in the QM formalism and that is what it says is the most complete specification of the system possible.

Perhaps you could explain why you believe the completeness doctrine. Bell's theorem is no argument in its favor, since QM itself is just as nonlocal as the hidden variable theories you'd want to dismiss on Bellian grounds. And if anything has come out very clearly in this thread, it's that Bohmian mechanics (a real honest to god hidden variable theory that reproduces all the predictions of QM) and regular QM are exactly parallel when it comes to their various senses of locality and nonlocality. So how could there possibly be a conclusive argument in favor of the completeness doctrine? I have never heard one, but I would certainly like to if it exists.

 

[vanesch]

BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

It is indeed trivial to associate to every stochastic theory a deterministic nonlocal hidden variable theory, which gives you exactly the same outcome.
A stochastic theory is fully determined when the n-point correlation functions are given as a function of all the parameters of free choice that are given to the user(s), such as the choice of the polarizer, activating or not a laser etc...
It is of course possible to set up a hidden variable theory with as random variable an n-tuple of numbers which has the same n-point correlation function as a function of the parameters, call these random variables "hidden variables" which determine the outcomes in a strict 1-1 way and I'm done.

So there's no point in saying that such a theory is possible. It is always possible.

What is more interesting is to do what Bell did: to prove that a certain stochastic theory (in casu QM) predicts probabilities that cannot be generated by deterministic local hidden variable theories, where local means local in the internal information sense, which, together with the deterministic part, leads to the Bell locality condition ; which leads to the Bell inequalities.

So the choice is between respect of the internal information locality or determinism.

Given the fact that a theory like QM is on the outside information-local, I prefer to sacrifice determinism, because I would consider sacrificing internal information-locality as a kind of conspiracy (why does the internal machinery not respect it, but does the outside user not notice it ?).

cheers,
Patrick.

EDIT: just to repeat: what I mean by "information-local" is that the probability distribution of all quantities pertaining to something local at A cannot depend on all FREE CHOICE parameters which are fixed elsewhere at B. If it were, I have an information channel that allows me, by doing experiments at A, to know what was the message, sent by B (by making use of his free choice of parameters).
What I mean by "external information-local" is what I said above, with real, executable measurements. What I mean by "internal information-local" applies moreover to a super-creature that has access to all local hidden variables at A even if some strange principle forbids me to turn them into real experiments.
But the free choice of settings at B remains fundamental.

I repeat again that it is *this* locality which is required by relativity in order to avoid the paradox of receiving as a message, what will be my free choice later (so that I can make another choice and lead to a paradox). This is the reason why I stick to it. If it weren't for this property, I wouldn't give a damn about locality.

 

[ttn]

Ah we're home

Yes, I think so! How refreshing to have a high-level, rather heated discussion about an important and controversial issue, that actually ends with mutual understanding and agreement! Practically unprescedented!

You think of "collapse of the wavefunction". Well, let me tell you something: EVERYBODY AGREES that collapse of the wavefunction in this way would be bluntly non-local. So I fully agree with you that such a thing is just as ugly non-local as Bohm ! And it is one of the reasons many people don't like it. ( (There is also another reason that I find even more severe: that is that we don't know what physical process could ever lead to such a collapse)
But in an MWI-like view of QM THERE IS NO SUCH COLLAPSE AT A DISTANCE.
So if Bob "could locally look at your part of the wavefunction" nothing special would happen when Alice "looks at her part of the wavefunction"
And if they see the wavefunction, they wouldn't see any result of a measurement. It is only because of a property of observers that apparently they have to choose a result that they 1) obtain a result and 2) experience some randomness in that result. But the wavefunction itself nicely continues to evolve in all its splendor, whether you have looked or not (well, except for your OWN part of the wavefunction, which gets smoothly entangled, locally, with what you are measuring and of which you have to pick one branch).

I pretty much agree with all this. I think there are some difficult questions for the MWI type view regarding what exactly it would even mean to talk about "if they see the wavefunction..." Terms like "they" and "the wavefunction" start to get slippery when there are a bunch of parallel universe copies of everything (and a still-not-very-clear way of telling the difference between two distinct branches and one branch with a superposition in it). But it seems clear to me, and I'm happy to grant, that in some sense (i.e., in some way that perhaps still requires some polishing around the edges) MWI is able to maintain locality.

In the "internal information sense":

Bohm is non-local
Copenhagen QM is non-local
MWI QM is local

In the "external information sense"
Bohm is local
Copenhagen and MWI QM are local

In the "Bell local sense"
Bohm is nonlocal
Copenhagen and MWI QM are non local

Yes, exactly. I wish I had more to say, but you encapsulated it beautifully. So I'll just copy your statements for everyone to look at one more time.



cheers,
Patrick.[/QUOTE]

 

[ttn]

I do not object to applying Bell locality to stochastic theories, I tell you that it is a criterium *designed* on the basis of deterministic theories, and that stochastic theories that by coincidence obey it, can (that's exactly the MEANING of Bell Locality) simply be turned into deterministic local hidden variable theories, so that ALL the randomness comes about from the lack of knowledge of local variables, which, if we would know them, determine all outcomes with certainty.

Bell Locality is a criterion that says: from *this* theory, it is possible to make a local, deterministic hidden variable theory.

That's why I consider it as a too severe criterion to judge locality on.

That is very clarifying, thank you. I now understand what you've been saying.

I'm still not certain that this point is true, however. I think you are making a rather nontrivial claim here -- that any stochastic theory that satisfies Bell Locality can be "built" out of an underlying deterministic local theory. If true, I think that is a very interesting point. Do you have any sense of how/whether this could be rigorously proved? Or maybe (since I'm just now getting your point for the first time and haven't really thought about it a lot yet) it's more trivial than I am sensing, i.e., nothing so fancy as a formal proof is really needed. Thoughts?

 

[ttn]

Well, again, we've switched vocabulary, but Bell is wrong on this issue. "causal influence" in my book, corresponds to information transfer.

It's not that Bell is wrong, but merely that you prefer different terminology. When Bell says "causal influence" in that quote, he is not talking about (what he might call) "mere information transfer" but about Bell Locality -- which he regarded as a good test for causal influences (even ones that couldn't be used to build telephones).

It is because he cannot get rid of the old paradigm of deterministic theories in which of course ALL correlations between A and B are related to 1) direct causal influence or 2) indirect "common cause" causal influence.

I would say (and I suspect Bell would say the same thing, but who really knows) that the requirement for (persistent, lawlike) correlations to involve either direct causal connection or a common cause has nothing to do with determinism per se. Non-deterministic theories can still support causal connections and common causes, and Bell would be perfectly happy if one of these ended up being true. The issue, Bell says, is *local causality*, not determinism.

If your claim from the other post is true -- if any such Bell Local non-deterministic theory can be straightforwardly converted into a deterministic theory -- that would be an interesting twist here. But I'm not sure it would change anything -- Bell could still quite reasonably claim merely to be forbidding nonlocal causation, and if the only way nature can figure out to respect local causality is with deterministic theories, too bad for nature!

The reason for this, in a deterministic paradigm, is that we only know of one mechanism to have randomness, namely the lack of information we have of internal degrees of freedom. And then it is clear that upon the observation of correlations between the observed randomness of A and B, you have somehow to "transport these internal degrees of freedom", or, directly from A to B (1), or you had to transport them from a common origin C to A and to B (2). And Bell cannot get out of that view. (1) is non-local, and (2) is Bell Locality. He cannot conceive the possibility that these correlations "just are", and are not related to a lack of knowledge.

I don't think that's right, at least as a statement of Bell's motivation. What made him uncomfortable (as you say "he cannot conceive") was that the correlations couldn't be explained without requiring that events *here* depend on events *over there* in a way that can't be screened out by a common cause in the shared past. On its face, that is a requirement for *locality*, not determinism. If it turns out that only deterministic theories satisfy this locality requirement, I see that as in some sense an accident. Bell's primary intention was to require *local causality*, period.

But if you now switch to another paradigm, which is the one of fundamentally stochastic theories, "god does play dice" and the fundamental quantity this time is the probability distribution (the n-point correlation function ; usually in our examples 2-point correlations are sufficient) then you do not need to assume that all randomness is related to lack of knowledge of internal degrees of freedom. And thus you do not need anymore to conclude that correlations can only come about through 1) or through 2). It is by forcing such a fundamentally stochastic theory in the deterministic paradigm that you end up drawing conclusions about locality or about the age of your mother in law.

I don't think Bell had any strong objections to god playing dice. He just figured, given the empirical success of relativity theory, if god is going to be playing dice he evidently better roll separate dice independently at different locations -- the outcomes of his dice rolls shouldn't depend on, e.g., the color of the dice rolled, or the outcome, at space-like separated dice-rolling events.

I think this is a prima facie reasonable thing to impose on theories (stochastic or otherwise) if you take relativity's prohibition on superluminal causation seriously. It is not simply a way of "smuggling in" some pre-existing bias for determinism.

 

[DrChinese]

1. As I noted here earlier, Einstein did not write the EPR paper. Podolsky did. ...

2. Re: Bell, I suppose we will have to agree to disagree. I simply don't understand how you can claim that what he proved has nothing to do with (i.e., is not openly premised on) locality. The whole point of the theorem is that a theory in which the outcomes of measurements are pre-determined by some kind of "instruction set" in the particles -- AND THAT RESPECTS THE BELL LOCALITY CONDITION -- cannot agree with experiment. i.e., local hidden variable theories are ruled out.

3. BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

4. Perhaps you could explain why you believe the completeness doctrine. Bell's theorem is no argument in its favor, since QM itself is just as nonlocal as the hidden variable theories you'd want to dismiss on Bellian grounds. And if anything has come out very clearly in this thread, it's that Bohmian mechanics (a real honest to god hidden variable theory that reproduces all the predictions of QM) and regular QM are exactly parallel when it comes to their various senses of locality and nonlocality. So how could there possibly be a conclusive argument in favor of the completeness doctrine? I have never heard one, but I would certainly like to if it exists.

1. Einstein's name is on the paper and it is generally accepted in the literature. What else do I need to say? I provided the quotes and they speak for themselves. For anyone who wants to read the original paper, and see for themselves whether the formalism is about locality or reality: EPR, Bell and Aspect: The original references.

2. The entire question I am raising is: is there any evidence that there is independent reality to observations not actually made? (That would exactly correspond to EPR's (2) which is the non-communting operators) And the answer is NO, there is no such evidence whatsoever.

3. The question I have is: does BM state that there is independent reality of unmeasured observables? I don't think it says this, but perhaps we could discuss this in more detail. As I understand BM (which is woefully little), it specifies a mechanism by which the non-local effects can occur.

4. I simply believe the completeness doctrine because of the wall that has been bumped up against in attempting to locate a more complete specification of the system. I also believe that electrons have no internal structure. Do you think that is unjustified too?

I believe that theories which are indistinguishable in their predictions from other theories are "ad hoc" and therefore of no utility. Should that change, I would happily reconsider my position.

 

[vanesch]

Do you have any sense of how/whether this could be rigorously proved? Or maybe (since I'm just now getting your point for the first time and haven't really thought about it a lot yet) it's more trivial than I am sensing, i.e., nothing so fancy as a formal proof is really needed. Thoughts?

Let us give it a try. We assume Bell Locality, so:

Let "L" be the state in a stochastic theory describing the stochastic variables A and B such that we have:

P(( A,B) = (A1,B2) ;a,b,L) = P(A=A1;a,L) x P(B=B1; b,L)

So there are two functions p1(A1,a,L) giving the first factor and p2(A2,b,L) giving the second factor.
We will, for the sake of argument, assume that a and b can only take on a finite number of values, so a can be a1, a2, a3, a4... a26 and b can be b1, b2, b3, ... b87.

Let me now introduce two extra "hidden variable tuples" u(a) and v(b) which have an independent probability distribution given as follows:
P(u(a) = A1) = p1(A1,a,L)
and P(v(b) = B1) = p2(B1,b,L)

Note that u(a) stands for 26 different real random variables, and v(b) stands for 87 different real random variables, and that each individual component within a tupel is an independent random variable.

Next, let K be the state in a deterministic theory which is everything in L, plus u(a) and v(b), seen as extra hidden variables.
We haven't talked about the probability distribution of L, because we are taking each individual case of L separately. So we should now consider each individual case of u(a) and v(b).

We next define a new "probability law" for our new theory K. For a given complete state description K, (an L, plus a specific value of u(a) and v(b)) we define new probabilities:
P(A = A1 ; a, K) = 1 if u(a) == A1 and = 0 if not
P(B = B1 ; b, K) = 1 if v(b) == B1 and = 0 if not

Note that these probabilities are still "local": the right hand side, in the first case, only depends on a, A1 and K and in the second case only on b, B1 and K.

P( (A,B) = (A1,B1) ; a, b, K) = P(A = A1 ; a, K) x P(B = B1 ; b, K)

We impose Bell Locality here.

Now, if we lack knowledge of the value of u(a) and v(b), you can easily find out that if u(a) and v(b) are drawn according to the distributions we specified for them, the ensemble probabilities will fall back on those given by the stochastic "L" theory. So u(a) and v(b) in theory K, as hidden variables, with the given distributions, generate the stochastic theory L.
We also see that by definition, Bell Locality is satisfied.

And we see that all probabilities in K theory are 1 or 0, hence it is a deterministic theory.

Hence, Patrick's theorem: "A stochastic theory satisfying Bell Locality is equivalent to a deterministic hidden variable theory satisfying Bell Locality".

Hey, I didn't know the proof was that easy, I just felt it in my bones that it had to be that way

cheers,
Patrick.

 

[ttn]

So there's no point in saying that such a theory is possible. It is always possible.

This may be true, but even if it is always possible, I think one shouldn't minimize Bohm's achievement in actually creating such a thing. For one thing, people had allegedly (!) proved that this *wasn't* possible for QM, so Bohm deserves credit for (a) trying and (b) showing by construction of counterexample that the proofs were bogus. In addition, even if it is possible in principle always to construct such a theory, it seems unlikely that the theory so constructed would turn out to be so natural. Bohmian mechanics is. My point is just that, as a particular example of a way to fill out a nonlocal stochastic theory with an underlying deterministic nonlocal dynamics, Bohmian mechanics is far more *interesting* than the tone of your comment suggests.

What is more interesting is to do what Bell did: to prove that a certain stochastic theory (in casu QM) predicts probabilities that cannot be generated by deterministic local hidden variable theories, where local means local in the internal information sense, which, together with the deterministic part, leads to the Bell locality condition ; which leads to the Bell inequalities.

So the choice is between respect of the internal information locality or determinism.

This starts to sound suspiciously like the inconsistency I thought we agreed was bad. Sure, it's nice to know that the QM predictions can't be generated by a deterministic (or stochastic!) local hidden variable theory (w/ "local" = "internal info sense of local"). But to cast the resulting choice as between "respect of the internal info locality or determinism" is to imply that QM itself respects "internal info locality". But as we agreed previously, it doesn't. So (leaving aside MWI) one is forced to accept that viable theories cannot respect "internal info locality". There is no choice of interest there. There is also no choice of interest w.r.t. "signal locality" -- no theory on the table allows superluminal communication.

There *is* a genuine choice between stochastic and deterministic, e.g., between orthodox QM and Bohmian mechanics. But it is a choice without a price -- that is, it's not like choosing Bohmian mechanics means you have to give anything up.

So I truly don't understand why you would say that the choice is between "internal info locality" and "determinism".


Oh yeah, a couple of comments on why I said above that Bell's Theorem rules out both deterministic *and stochastic* hv theories that obey Bell Locality. (I still can't tell for sure if you disagree with this??) Leaving aside our discussion of whether Bell Locality is the appropriate way to impose "local causality" on a theory, and just taking for granted for the sake of this point that it is, I think it is clear that Bell's inequality applies to Bell-Local-Stochastic theories just as much as it applies to Bell-Local-Deterministic theories. After all, the whole derivation is in terms of probabilities like P(A|a,b,B,L), etc. In a deterministic theory, all these P's would be either zero or one (since we are conditionalizing on "L"). But this assumption is never made in the derivations of the inequality. That is, the inequality still holds even if the P's are just regular old probabilities, i.e., if the theory is genuinely stochastic (but still Bell Local). So there you go. Of course, you have claimed that any genuinely stochastic Bell Local theory can be trivially filled out by an underlying deterministic dynamics. Perhaps; I'm not convinced, but maybe that's true. But any way, regardless, Bell's Theorem as stated does surely apply to Bell-Local stochastic theories. So no such theory is empirically viable, given Aspect et al. So it is terribly misleading to suggest that the choice we face post-Bell is between (a) deterministic nonlocal theories and (b) stochastic local theories. That kind of statement would make Bell roll over in his grave!

Given the fact that a theory like QM is on the outside information-local, I prefer to sacrifice determinism, because I would consider sacrificing internal information-locality as a kind of conspiracy (why does the internal machinery not respect it, but does the outside user not notice it ?).

We've been here before. QM *also* suffers from this kind of "conspiracy" -- it is nonlocal in the Bell or "internal info" sense, but local "on the outside". It is exactly parallel to Bohmian mechanics on both counts. So why talk of "preferring to sacrifice determinism"? Nothing -- literally nothing -- is *saved* by making this sacrifice. That doesn't necessarily prove you ought to choose the deterministic theory, but surely it shows that there's no *reason* for rejecting the deterministic theory. And as I've said about a bajillion times now, that all I really want to argue for here.

 

[vanesch]

This may be true, but even if it is always possible, I think one shouldn't minimize Bohm's achievement in actually creating such a thing. For one thing, people had allegedly (!) proved that this *wasn't* possible for QM, so Bohm deserves credit for (a) trying and (b) showing by construction of counterexample that the proofs were bogus. In addition, even if it is possible in principle always to construct such a theory, it seems unlikely that the theory so constructed would turn out to be so natural. Bohmian mechanics is. My point is just that, as a particular example of a way to fill out a nonlocal stochastic theory with an underlying deterministic nonlocal dynamics, Bohmian mechanics is far more *interesting* than the tone of your comment suggests.

I hope you understood that I am of the opinion that the only viable ways to view QM are:
1) as purely a generator of probabilities, and we shouldn't attach any physical meaning to the formalism (I'm not in favor of that because it brings your physical intuition to a grinding halt, but I have to admit it is a logical possibility)
2) an MWI like view which I favor.

I agree with you that Copenhagen QM is an ugly theory, which is not only ridden with a lot of internal inconsistencies, but is also bluntly non-local in its mechanism, except of course in its probability predictions.

I think in the building of a theory, one should more stick to general principles than to any other criterion. One such principle is information-locality ; it is the essential principle of SR combined with causality. Another one is the superposition principle ; it is the essential principle of QM. No great principle demands for determinism and it turns out that the first two make determinism impossible.

So we have a paradigm which is build upon information-locality and the superposition principle, and which will turn out to be essentially stochastic.

Within that paradigm, we try to set up a specific theory, and we do now what we want, but we do not infringe on the principles of the paradigm we are working in. So no bricolage in the internal mechanism of a theory that infringes on the principles we've set forth, even if we think of extra stuff to protect us from detecting it (such as *hidden* variables).

Copenhagen QM is bricolage of course, _except_ if we do not consider it as a theory in which the formalism corresponds to anything physical, but just as a generator of probabilities, in which case you don't have to take the collapse of the wavefunction seriously: it is just a mathematical trick to generate probability functions. There are so many things wrong with taking Copenhagen QM as a description of any reality that infringing on information locality in its internal workings is only one defect. It also infringes on the superposition principle ! So it does everything wrong if you take the wavefunction description as something "real". But it works just fine if you consider it as a tool that cranks out probability distributions.

Bohm is just as well bricolage because it wants to introduce (hidden ) determinism, but sacrifices one of the great principles, namely information locality, in its internal workings. It doesn't even consider the superposition principle. But it works just fine if you consider it as a tool that cranks out probability distributions.

However, MWI-like QM DO respect information locality and the superposition principle. That's why I think it is the natural view on quantum theory. It contains fundamentally stochastic elements (namely the imposed choices of the branch of the observer), but it sticks to the basic philosophy of the paradigm laid out.

This starts to sound suspiciously like the inconsistency I thought we agreed was bad. Sure, it's nice to know that the QM predictions can't be generated by a deterministic (or stochastic!) local hidden variable theory (w/ "local" = "internal info sense of local"). But to cast the resulting choice as between "respect of the internal info locality or determinism" is to imply that QM itself respects "internal info locality". But as we agreed previously, it doesn't. So (leaving aside MWI) one is forced to accept that viable theories cannot respect "internal info locality". There is no choice of interest there. There is also no choice of interest w.r.t. "signal locality" -- no theory on the table allows superluminal communication.

But why do you leave the only natural option, namely MWI, aside ?

EDIT:
Quantum theory seen as a stochastic theory of which we do not add any reality to the formalism, but just a calculational trick to let us obtain probabilities of outcomes of measurements, respects information locality. That is "external information locality" because there is no internal mechanism postulated so there's nothing to test "internal information locality" against.

Quantum theory, seen in an MWI formulation, where one DOES give a kind of reality to the wavefunction, also respects internal information locality.

The thing that does not, is when one assumes that measurements "collapse the wavefunction" and that this is some kind of physical phenomenon. In _that_ case, this internal mechanism doesn't respect "internal information locality". That's why one shouldn't do it.

There *is* a genuine choice between stochastic and deterministic, e.g., between orthodox QM and Bohmian mechanics. But it is a choice without a price -- that is, it's not like choosing Bohmian mechanics means you have to give anything up.

With Bohmian mechanics you construct a hybrid. You want determinism and then you have to hide it. So, determinism, IS it, or ISN'T it a fundamental principle on which you want to build your theory ? If it is, I don't know why we have to hide it, and if it isn't, I don't know why you try to put it inside.
Only, you HAVE to hide the determinism, because otherwise you CAN do FTL signalling. But what does it mean, hidden determinism ?
I'm not going to comment orthodox QM, I already told you it is just as ugly, EXCEPT as a generator of statistics. It is then on the same level as Bohm, and I don't see why you should even consider Bohm, given that you don't win anything (but I agree with you that you don't loose anything either: you've anyway lost everything else already in Copenhagen QM !). The two are viewed as two calculational procedures to arrive at the only physical quantities of interest: probabilities of measurement outcomes. Maybe some calculations are easier in Bohm's formulation than in the Hilbert state space formulation ; but I doubt that.

So I truly don't understand why you would say that the choice is between "internal info locality" and "determinism".

Well, because I think that information locality is one of the pillars of SR and QM. Determinism isn't. So if there is one thing I would like to stick to, it is information locality, and I can construct a quantum theory that respects that and does have a kind of description of reality (MWI approach) or one that just gives you probabilities (abstract probability calculation, with the calculational technique of your choice: Hilbert or Bohm, whichever leads to the result in the smallest amount of CPU time).

Oh yeah, a couple of comments on why I said above that Bell's Theorem rules out both deterministic *and stochastic* hv theories that obey Bell Locality. (I still can't tell for sure if you disagree with this??)

Sure, I agree with it.

Leaving aside our discussion of whether Bell Locality is the appropriate way to impose "local causality" on a theory, and just taking for granted for the sake of this point that it is, I think it is clear that Bell's inequality applies to Bell-Local-Stochastic theories just as much as it applies to Bell-Local-Deterministic theories. After all, the whole derivation is in terms of probabilities like P(A|a,b,B,L), etc. In a deterministic theory, all these P's would be either zero or one (since we are conditionalizing on "L"). But this assumption is never made in the derivations of the inequality. That is, the inequality still holds even if the P's are just regular old probabilities, i.e., if the theory is genuinely stochastic (but still Bell Local). So there you go. Of course, you have claimed that any genuinely stochastic Bell Local theory can be trivially filled out by an underlying deterministic dynamics. Perhaps; I'm not convinced, but maybe that's true. But any way, regardless, Bell's Theorem as stated does surely apply to Bell-Local stochastic theories. So no such theory is empirically viable, given Aspect et al. So it is terribly misleading to suggest that the choice we face post-Bell is between (a) deterministic nonlocal theories and (b) stochastic local theories. That kind of statement would make Bell roll over in his grave!

I agree with most of what you say, but I consider it not the right criterion, and I reiterate my claim that Bell's theorem is based upon Bell Locality, which is a condition that is INSPIRED by deterministic thinking, namely that in order to have a correlation, you need a direct causal influence, or an indirect "common cause" influence. This by itself comes from the fact that we consider that the ONLY randomness we're willing to accept is lack of knowledge of internal variables.
Part of my proof you already have: a stochastic theory satisfying Bell Locality is replacable by a deterministic theory satisfying Bell Locality.
So you can read this that we only allow for stochastic theories which can be deterministically explained by lack of knowledge of the complete state.

This is a reformulation that Bell Locality is the requirement that the only form of randomness allowed in a theory, is through incomplete knowledge of some parameters in a state description, which, if we would know them, would determine every outcome with certainty.

We've been here before. QM *also* suffers from this kind of "conspiracy" -- it is nonlocal in the Bell or "internal info" sense, but local "on the outside". It is exactly parallel to Bohmian mechanics on both counts. So why talk of "preferring to sacrifice determinism"? Nothing -- literally nothing -- is *saved* by making this sacrifice. That doesn't necessarily prove you ought to choose the deterministic theory, but surely it shows that there's no *reason* for rejecting the deterministic theory. And as I've said about a bajillion times now, that all I really want to argue for here.

That's because you're comparing to Copenhagen QM. But that's indeed a very ugly theory. Try to compare to MWI like QM. You'll be delighted

cheers,
Patrick.

 

[DrChinese]

Re: Bell, I suppose we will have to agree to disagree. I simply don't understand how you can claim that what he proved has nothing to do with (i.e., is not openly premised on) locality. The whole point of the theorem is that a theory in which the outcomes of measurements are pre-determined by some kind of "instruction set" in the particles -- AND THAT RESPECTS THE BELL LOCALITY CONDITION -- cannot agree with experiment. i.e., local hidden variable theories are ruled out.

BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

...

And the final piece: Bell states openly that, he thinks, nonlocality is a fact, period -- that it's *not* something which merely afflicts hv theories. As he says, you *cannot* dismiss the operations on one side as causal influences on the other. How can he believe this? What else would he need to have to believe to make this claim given the above paragraph? Obviously he would have to think that orthodox QM was *also* nonlocal. IF it wasn't, there'd be no grounds for claiming that all possible alternatives -- i.e., nature -- were nonlocal.

OK, I think I can come pretty close to a position that we can see eye to eye on. Repeating a portion of an argument made in an earlier post and adding a bit:

I. EPR proves: "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

II. Bell proves both cannot be true: (1) QM is incomplete (as represented by the \lambda in his formulas; and (2) the predictions of QM are correct. To quote: "The paradox of Einstein, Podolsky and Rosen was advanced as an argument that quantum mechanics was not complete but should be supplemented by additional parameters... In this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics."

III. Accepting both EPR and Bell as correct (as I do), as well as Aspect, you must conclude that:

a) Aspect et al proves that the predictions of QM are correct (please Cat stay out of this discussion as we are not interested in debating this).
b) If QM is correct, then Bell (2) is true; therefore Bell (1) is false.
c) If Bell (1) is false, then EPR (1) is also false as they are equivalent by design.
d) If EPR (1) is false, then EPR (2) is true.

I.e. my position, that "when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

IV. EPR also said that if relativistic causality (what maps, I believe, to your Bell locality condition) is assumed, then EPR (2) is false. (I don't see this stated too well in the paper itself, so I will see if I can locate some additional material which ties this loose end up as well as provide a quote.)

Bell locality -> Reality (of non-commuting observables)

If we agree that is a valid deduction of EPR, then the contranegative is also true:

~Reality -> ~Bell locality

Since we know from III.d. above that EPR (2) is in fact true (~Reality), then we deduce that relativistic causality cannot be true. Ergo, by your definition, non-locality is demonstrated.

 

[vanesch]

I would say (and I suspect Bell would say the same thing, but who really knows) that the requirement for (persistent, lawlike) correlations to involve either direct causal connection or a common cause has nothing to do with determinism per se. Non-deterministic theories can still support causal connections and common causes, and Bell would be perfectly happy if one of these ended up being true. The issue, Bell says, is *local causality*, not determinism.

Let us elaborate a bit because it is the essential point in our differences in viewpoint I think.

My claim is that causality only has a meaning as "information transfer". This can be "internal information transfer" also, even if we cannot perform real experiments in the lab because the internal quantity we're talking about is not directly accessible (such as a hidden variable) ; but one thing is necessary to be able to send information, and that is making free choices at the sending end. Upon my decision of acting at A, if something happens at B or not determines if there is information transfer and hence a causal link.
Some semantics: my "choice at A" _causes_ "an effect at B". In order to cause something, I have to have a choice in causing it, otherwise I just see it as a "description of what is happening" and not of "what causes what".
Let us call this view on causality "information - causality".
From "information - causality" follows then naturally "information - locality".
I told you why I think that is the right definition, it comes from a paradox you can obtain in SR if you don't stick to it.

You could also define a "correlation causality" and it leads to "Bell Locality".
"Correlation causality" states that you can only have statistical correlations if there is a direct dependence of the result at A on the result at B (in a statistical sense) or if they have both a common origin (state L). Bell Locality is the mathematical expression of this causality if we assume that the direct influence cannot take place ("locality"), that the only link between the two factors is through L (common cause).

But I don't see any requirement in special relativity to require Bell locality.

I will now try to find the link between "information locality" (required by SR) and Bell Locality (required by, eh, what ? We'll see :-).

My second claim is that "Bell Locality" is the above notion, applied to an underlying deterministic model ; that the notion that a "correlation implies a direct causal link or an indirect common cause link" finds its origin in a deterministic underlying model.
I think it is THIS point which is hard to get by, because THIS is the real paradigm shift needed to let go determinism. And I think it was this paradigm shift that Bell couldn't conceive, namely that you could have correlations which were NOT implying a direct causal link or an indirect common cause link.
I don't know what I can do more than reiterate Patrick's theorem
"Any stochastic theory satisfying Bell locality leads to a deterministic theory satisfying Bell locality".
I think it is a small step to show:
"From Bell locality follows information locality."

Indeed, the factorized form of P(A,B ; a,b) = P(A ; a) x P(B ; b) means that the choice of a cannot influence the probability of B.


I guess what I still should try to prove is that from information-local determinism follows Bell locality.

So now we have, from determinism, that P(A,B ; a,b,K) equals 1 or 0 ; so do the individual probabilities P(A ; a, b, K) and P(B ; a, b, K) ;
and from information locality follows that P(A ; a, K) and P(B ; b, K) do not depend on the "other" choices b and a respectively.

This means, in fact, that A = A(a) and B = B(b): for a given value (choice) of a, there is ONE A value that is the outcome, with certainty ; all other A values have probability 0.

So P(A(a), B(b) ; a,b,K) = 1 = P(A(a) ; a,K) x P(B(b) ; b,K)

So at least for the P=1 values, we can write the product form.
But this is also true for the P=0 values, because if A1 != A(a) OR B1 != B(b), then P(A1, B(b) ; a,b,K) = 0 = P(A1 ; a,K) x P(B(b) ; b, K) (namely 0 x 1)
and idem for the two other cases A(a), B1 and A1,B1.

So we have that determinism and information-locality leads to Bell locality.
So I came to a full circle:

(1)From Bell locality follows Bell local determinism. (Patrick's theorem)
(2) From Bell locality follows information locality
(3) From information locality and determinism follows Bell locality

Together:

BELL LOCALITY <===> information locality and determinism

QED

cheers,
Patrick.

 

[ttn]

Hey, I didn't know the proof was that easy, I just felt it in my bones that it had to be that way

Very good! I jusk skimmed the proof, but it looks like what you were saying was pretty trivial, now that I understand better what it actually meant. Basically, so long as a stochastic theory respects Bell-Locality, you can always just postulate new hidden variables which determine the outcomes: just pick the probability distribution over the outcome-determining hv's to match whatever the original stochastic theory said the probabilities were. Duh!

I still want to say this doesn't change anything, though. This argument shows that all Bell Local theories either are or can be made into deterministic theories. As you have made clear elsewhere, you think that part of what it means to really jettison the deterministic paradigm and accept deep, irreducible stochasticity in a theory, is to accept not only that specific local outcomes can't be explained by any previous state of the world but that, more generally, correlations between separated events also can't be explained by any previous state of the world. Something like: if you're going to accept outcomes just "popping" into existence, you should also accept *correlations* just popping into existence. Is that a fair statement of your position? (If so, it exactly matches what I remember Arthur Fine arguing in "Do Correlations Need to be Explained?", the article I mentioned a while back... Maybe you'd enjoy checking it out.)

I don't have any particularly clean argument against this; I concede it's an internally consistent position. But I still don't see how one can fail to be bothered by unexplained, lawlike correlations between distant events. You can talk all you want about god rolling dice, but as I said earlier, I don't think relativity theory ought to permit god to, in effect, roll the same dice simultaneously at two distant locations. Of course, he's god, so he can do whatever he wants -- but if he does this, I think we have to call a spade a spade and say that god is exerting a nonlocal (stochastic) causality, even if the nonlocality is "well hidden" or "washed out" or "behind the scenes" or "not useful for sending messages" or whatever.

But probably there is nothing else interesting to say about this. What matters is what we agreed on before: Copenhagen and Bohm are both non-local in the various stricter senses (Bell-Locality or "internal info locality") and both local in terms of "external info transfer". And to the extent that MWI makes sense and/or is well-defined it is probably more local than either of those other two alternatives.

 

[ttn]

I hope you understood that I am of the opinion that the only viable ways to view QM are:
1) as purely a generator of probabilities, and we shouldn't attach any physical meaning to the formalism (I'm not in favor of that because it brings your physical intuition to a grinding halt, but I have to admit it is a logical possibility)
2) an MWI like view which I favor.

I agree with you that Copenhagen QM is an ugly theory, which is not only ridden with a lot of internal inconsistencies, but is also bluntly non-local in its mechanism, except of course in its probability predictions.

and then later

Bohm is just as well bricolage because it wants to introduce (hidden ) determinism, but sacrifices one of the great principles, namely information locality, in its internal workings. It doesn't even consider the superposition principle. But it works just fine if you consider it as a tool that cranks out probability distributions.

I'm not sure what you mean by saying Bohm "doesn't even consider the superposition principle". Wave functions in Bohmian mechanics are solutions of Schroedinger's equation (or whatever), just like orthodox QM. Bohm doesn't forbid or jettison superpositions!

Also, a subtle equivocation has I think snuck into your comment here. You talk about "information locality" being one of the cornerstones of SR and hence a guiding principle for building theories/interpretations. From your comments elsewhere it is clear that what you actually mean by that is what you once clarified as "external info locality", i.e., no transmission of information superluminally. But when you criticize Bohm for sacrificing "information locality in its internal workings" this either equivocates on "info local" or just plain doesn't make sense. Bohm's theory is local in the "external info" sense but nonlocal in the "internal info" sense. Just like regular QM on both counts.

I think you understand this perfectly well, but a lot of people are terribly confused, so let me repeat it for the benefit of others who are reading. If what you mean by "local" is "information cannot be transferred superluminally" then orthodox QM and Bohmian mechanics are equally local. If, on the other hand, what you mean is "the internal guts of the theory obey Bell's local causality constraint" then both orthodox QM and Bohmian mechanics are nonlocal. And keeping that straight will, I think, help prevent dubious statements like "Unlike regular QM, Bohm's theory is nonlocal, which puts it in conflict with SR, which means we shouldn't really take it seriously." That argument just doesn't hold water unless you equivocate like mad about the meaning of "local" -- i.e., unless you cheat!

But why do you leave the only natural option, namely MWI, aside ?

As I think I said a long time ago in this thread, I just think MWI is too crazy to take seriously. You talk about faithfully respecting certain principles (superposition, relativity, ...) to guide one in interpreting or building theories. Well, one of the principles that is to me even more fundamental than the ones you mention is scientific realism. I just can't take seriously something claiming to be a theory of physics that is in fact a form of solipsism. I know others disagree, which is why I prefer to just leave that issue aside and focus on, say, Bohm vs. QM, which we can speak about without it turning into a pointless debate about philosophy.

With Bohmian mechanics you construct a hybrid. You want determinism and then you have to hide it. So, determinism, IS it, or ISN'T it a fundamental principle on which you want to build your theory ? If it is, I don't know why we have to hide it, and if it isn't, I don't know why you try to put it inside.
Only, you HAVE to hide the determinism, because otherwise you CAN do FTL signalling. But what does it mean, hidden determinism ?
I'm not going to comment orthodox QM, I already told you it is just as ugly, EXCEPT as a generator of statistics. It is then on the same level as Bohm, and I don't see why you should even consider Bohm, given that you don't win anything (but I agree with you that you don't loose anything either: you've anyway lost everything else already in Copenhagen QM !). The two are viewed as two calculational procedures to arrive at the only physical quantities of interest: probabilities of measurement outcomes. Maybe some calculations are easier in Bohm's formulation than in the Hilbert state space formulation ; but I doubt that.

You seem to have forgotten the main point in favor of Bohm -- that it gets rid of all the "unprofessional vagueness and ambiguity" of Copenhagen. In particular, there is no measurement problem in Bohm's theory. So, putting it a different way, Bohm's theory is actually well defined as a theory. Surely that counts in its favor relative to regular QM.

 

[ttn]

I. EPR proves: "...either (1) the quantum-mechanical description given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

I'm not really all that interested in arguing about this here. I think it says a lot that (1) Einstein didn't write the EPR paper you are quoting, (2) Einstein explicitly stated that he thought that paper had failed to make clear the real point that was important to him, and (3) Einstein later explicitly stated what he thought that real point was. If you disagree, so be it. I would just mention once again Arthur Fine's book "The Shaky Game" -- the first few chapters cover EPR and some of the surrounding history that Fine uncovered in great detail and are extremely clarifying re: understanding and untangling the bizarre structure of the actual EPR paper. Check it out!

 

[ttn]

So we have that determinism and information-locality leads to Bell locality.
So I came to a full circle:

(1)From Bell locality follows Bell local determinism. (Patrick's theorem)
(2) From Bell locality follows information locality
(3) From information locality and determinism follows Bell locality

Together:

BELL LOCALITY <===> information locality and determinism

OK... and what, in your opinion, is the significance of this? I think it was obvious before that Bell Locality was a stronger condition than "no signalling". So this clarifies exactly how it is stronger. I guess you'll want to say that this shows that Bell's error in thinking of locality as Bell Locality was that he was going beyond what was actually required by relativity (which you claim is "no signalling") and secretly smuggling in the additional requirement of determinism. And that, of course, is a bad thing since it merely reflects "classical bias" or an inability to drop the old paradigm and get with the times or whatever.

This is an interesting argument, and I think it is very cool to have shown that Bell Locality is equivalent to the conjunction of "no signalling" and "determinism."

However, your interpretation of this result hangs on a crucial premise: namely, "no signalling" is what relativity *really* requires. That is not obvious. Surely relativity requires something *at least as strong as* "no signalling" but many people believe it requires something more, something stronger. For example, Bell eloquently asked:

"Do we then have to fall back on 'no signalling' faster than light' as the expression of the fundamental causal structure of contemporary theoretical physics? That is hard for me to accept. ... ...the 'no signalling' notion rests on concepts which are desperately vague, or vaguely applicable. The assertion that 'we cannot signal faster than light' immediately provokes the question: Who do we think *we* are? ..."

Even if you disagree with this and believe that *all* relativity requires is that we not be able to transmit information faster than light, you surely must admit that Bell on pretty reasonable ground for raising these questions. Relativity is supposed to be about the fundamental structure of spacetime. It would be frankly bizarre if what it imposed on that structure was somehow intimately bound up with human activities like "signalling" and building telephones and whatnot. It seems like the requirements of relativity ought to be more fundamental -- it ought to forbid any kind of causal influence outside the light cone, even if (for whatever reason) it is one that can never be used by humans to transmit information. That just makes sense. And as soon as you start thinking that way, you will come to believe, like Bell, that "Bell Locality" is what relativity *really* requires, not merely "no signalling."

And that means that your parsing of Bell Locality into "no signalling" plus determinism doesn't have the kind of implications you are suggesting. It has, really, no implications... it merely bring out the fact that, in order to have a serious (i.e., non-MWI ) theory that is consistent with experiment, you have to back off significantly from the relativity-motivated idea of (strong) local causality, and retreat to something that is strange, vague, and extremely superficial. And I think, in such a situation, one ought to simply concede that relativity (taken *seriously* as a statement about the *fundamental* causal structure of spacetime) is just wrong. That is, one should begin to take seriously the possibility that there is more structure in spacetime than is attributed to it by relativity, e.g., the "foliations" introduced in the context of relativistic Bohmian theory.

(I'm sure that will get your blood boiling!...)

 

[vanesch]

I'm not sure what you mean by saying Bohm "doesn't even consider the superposition principle". Wave functions in Bohmian mechanics are solutions of Schroedinger's equation (or whatever), just like orthodox QM. Bohm doesn't forbid or jettison superpositions!

The superposition principle says:
if L1 is a "complete state of nature" and if L2 is "a complete state of nature", then there are infinitely many other "complete states of nature" described by a L1 + b L2. If I understand Bohm a bit, this only applies to the "wave function" part, but not to the "guiding wave" part, no ?

From your comments elsewhere it is clear that what you actually mean by that is what you once clarified as "external info locality", i.e., no transmission of information superluminally. But when you criticize Bohm for sacrificing "information locality in its internal workings" this either equivocates on "info local" or just plain doesn't make sense. Bohm's theory is local in the "external info" sense but nonlocal in the "internal info" sense. Just like regular QM on both counts.

How many times do I have to repeat this that MWI QM does not suffer from this problem ? It is only a problem for Copenhagen QM (which is in any case, when considered as describing something physical, wrong - yes, probably Bohm is not as ugly as Copenhagen QM, I agree with that, in the same way that Frankenstein is not as ugly as the Living Dead )

I think you understand this perfectly well, but a lot of people are terribly confused, so let me repeat it for the benefit of others who are reading. If what you mean by "local" is "information cannot be transferred superluminally" then orthodox QM and Bohmian mechanics are equally local. If, on the other hand, what you mean is "the internal guts of the theory obey Bell's local causality constraint" then both orthodox QM and Bohmian mechanics are nonlocal. And keeping that straight will, I think, help prevent dubious statements like "Unlike regular QM, Bohm's theory is nonlocal, which puts it in conflict with SR, which means we shouldn't really take it seriously." That argument just doesn't hold water unless you equivocate like mad about the meaning of "local" -- i.e., unless you cheat!

Absolutely !

As I think I said a long time ago in this thread, I just think MWI is too crazy to take seriously. You talk about faithfully respecting certain principles (superposition, relativity, ...) to guide one in interpreting or building theories. Well, one of the principles that is to me even more fundamental than the ones you mention is scientific realism. I just can't take seriously something claiming to be a theory of physics that is in fact a form of solipsism. I know others disagree, which is why I prefer to just leave that issue aside and focus on, say, Bohm vs. QM, which we can speak about without it turning into a pointless debate about philosophy.

I can understand that viewpoint but I think it is misguided. I don't know who said "we all agree that your theory is crazy. The debate is on if it is crazy enough".
The amount of solispsim in MWI is in fact rather modest, you know. It only relates to what *you* observe, and honestly, you should acknowledge that that is a very private affair. It doesn't deny the existence of others either. Only, the person you talked to yesterday is not "the same" as the one you're talking to today, but a clone with exactly the same memory and physical body, which has a new "I experience" (while the "I experience" of the person you saw yesterday is now somewhere else, forever separated: admit the romantic drama in all this ).

No, seriously, I went through a lot of effort to make you see what you intuitively call "scientific realism" is "underlying determinism", in that if you would know all the nitty gritty details nature is hiding for you, you would know everything with certainty. You might stop your theoretical description short of that, and allow for a so-called "essential stochastic process", but your requirements are such that it still allows for underlying determinism.

You seem to have forgotten the main point in favor of Bohm -- that it gets rid of all the "unprofessional vagueness and ambiguity" of Copenhagen. In particular, there is no measurement problem in Bohm's theory. So, putting it a different way, Bohm's theory is actually well defined as a theory. Surely that counts in its favor relative to regular QM.

Absolutely ! Copenhagen QM is a mess. But...
When you say that there is no measurement problem in Bohm, how does this happen then ? Because there IS an objective difference between Copenhagen QM and MWI for instance: it is the physical process that determines measurement. In Copenhagen QM, this system CANNOT be considered to be in a superposition,and in MWI that's what you do. So there is a difference _in principle_ because, with enough care and technology, you COULD make the measurement instrument interfere with itself in MWI, and not in Copenhagen. So on which side does Bohm then flip ? Could I, or could I not, in principle, make a measurement instrument interfere with itself ?
When is a physical process a measurement ? I don't know enough about Bohm to realize this.

cheers,
Patrick.

 

[vanesch]

I still want to say this doesn't change anything, though. This argument shows that all Bell Local theories either are or can be made into deterministic theories. As you have made clear elsewhere, you think that part of what it means to really jettison the deterministic paradigm and accept deep, irreducible stochasticity in a theory, is to accept not only that specific local outcomes can't be explained by any previous state of the world but that, more generally, correlations between separated events also can't be explained by any previous state of the world. Something like: if you're going to accept outcomes just "popping" into existence, you should also accept *correlations* just popping into existence. Is that a fair statement of your position?

I should let you talk to yourself. You explain my views better than I do myself.

But probably there is nothing else interesting to say about this. What matters is what we agreed on before: Copenhagen and Bohm are both non-local in the various stricter senses (Bell-Locality or "internal info locality") and both local in terms of "external info transfer". And to the extent that MWI makes sense and/or is well-defined it is probably more local than either of those other two alternatives.

yup

cheers,
Patrick.

 

[vanesch]

However, your interpretation of this result hangs on a crucial premise: namely, "no signalling" is what relativity *really* requires. That is not obvious. Surely relativity requires something *at least as strong as* "no signalling" but many people believe it requires something more, something stronger.

I agree with you that "relativity would look nicer" with Bell Locality. But Bell Locality is like diamonds for the girl. If you can have it, why not.
However, info locality is much more essential, because it leads to a paradox. Not a theoretical, unesthetic one, no, a real one.

Make a device that, upon receiving A, sends out not-A (you know, with a 74 series inverter). I hope I don't have to explain you in detail (because it is a bit long and technical) that if you have an FTL phone, you can build 2 of them, put one in a spaceship etc... and phone back to your past. So you can build it such that your device receives its output at 12PM and will send it at 12:03PM. You monitor with an oscilloscope: what will you see ?
Will you receive A or not-A at 12 PM ? Will you send out then not-A or A at 12:03PM ?

See, information locality is the bare necessity. So we cannot let it go.
Maybe you require more, but you require AT LEAST this. So this should be AT LEAST a great principle.

And this puts my equivalence: Bell locality <==> info locality and determinism
in another light. I would like to have Bell locality. But we know we can't have it. I desperately NEED info locality. So what's the deal ? Let go determinism !

It would be frankly bizarre if what it imposed on that structure was somehow intimately bound up with human activities like "signalling" and building telephones and whatnot. It seems like the requirements of relativity ought to be more fundamental -- it ought to forbid any kind of causal influence outside the light cone, even if (for whatever reason) it is one that can never be used by humans to transmit information. That just makes sense. And as soon as you start thinking that way, you will come to believe, like Bell, that "Bell Locality" is what relativity *really* requires, not merely "no signalling."

As I said, all this is nice. But we CAN'T have it. So do we throw out determinism, or do we throw out relativity ?

Note that info-locality has nothing to do with humans per se. It means that one can conceive physical structures leading to a paradox, such as my inverter gate. If it needs a certain sophistication to arrive at such paradoxal physical situations doesn't matter. It is as if a physical theory didn't allow for poles of 25.3 meter because then they would also be only 3 m long, and you were arguing that that is not a problem, because poles of 25.3 meter are not found in nature, you need humans to think of that. I'd say that your theory then has a very serious problem.

 

[ttn]

The superposition principle says:
if L1 is a "complete state of nature" and if L2 is "a complete state of nature", then there are infinitely many other "complete states of nature" described by a L1 + b L2. If I understand Bohm a bit, this only applies to the "wave function" part, but not to the "guiding wave" part, no ?

Yes, that's right. The wf would be a superposition, but the particle would be definitely in one or the other localized (in config space) "part" of the wf.

The amount of solispsim in MWI is in fact rather modest, you know. It only relates to what *you* observe, ...

That is the funniest thing I have read for a long time!

and honestly, you should acknowledge that that is a very private affair. It doesn't deny the existence of others either. Only, the person you talked to yesterday is not "the same" as the one you're talking to today, but a clone with exactly the same memory and physical body, which has a new "I experience" (while the "I experience" of the person you saw yesterday is now somewhere else, forever separated: admit the romantic drama in all this ).

Maybe you could explain how you understand QM's predictions for measurement probabilities in MWI. For example, if I prepare a bunch of spin 1/2 particle in the +z state and then measure their y-spin one after the other, how come I typically find about half +y and half -y?

When you say that there is no measurement problem in Bohm, how does this happen then ? Because there IS an objective difference between Copenhagen QM and MWI for instance: it is the physical process that determines measurement. In Copenhagen QM, this system CANNOT be considered to be in a superposition,and in MWI that's what you do. So there is a difference _in principle_ because, with enough care and technology, you COULD make the measurement instrument interfere with itself in MWI, and not in Copenhagen. So on which side does Bohm then flip ? Could I, or could I not, in principle, make a measurement instrument interfere with itself ?
When is a physical process a measurement ? I don't know enough about Bohm to realize this.

Yes, according to Bohm, in principle you could get something macro to interfere. The other branches of the wf continue to exist, only they are "empty", not containing the "particle" (i.e., actual configuration space point) and hence not (presently) affecting the particle's trajectory. But in principle, if you could arrange for one of those empty lumps of wf to overlap with the active lump, it would affect the particle, i.e., you'd see interference.



cheers,
Patrick.[/QUOTE]

 

[ttn]

I agree with you that "relativity would look nicer" with Bell Locality. But Bell Locality is like diamonds for the girl. If you can have it, why not.
However, info locality is much more essential, because it leads to a paradox. Not a theoretical, unesthetic one, no, a real one.

Make a device that, upon receiving A, sends out not-A (you know, with a 74 series inverter). I hope I don't have to explain you in detail (because it is a bit long and technical) that if you have an FTL phone, you can build 2 of them, put one in a spaceship etc... and phone back to your past. So you can build it such that your device receives its output at 12PM and will send it at 12:03PM. You monitor with an oscilloscope: what will you see ?
Will you receive A or not-A at 12 PM ? Will you send out then not-A or A at 12:03PM ?

See, information locality is the bare necessity. So we cannot let it go.
Maybe you require more, but you require AT LEAST this. So this should be AT LEAST a great principle.

Sure, but info locality is so superficial, you can keep it while having a theory whose guts is rather blatantly at odds with relativity. I say: if you're stuck with something which is fundamentally opposed to the principle of relativity (but rather magically obeys signal locality nevertheless) you should seriously consider that the principle of relativity is wrong or doesn't mean what we thought it meant or something. In effect, that *is* what you're doing when you admit that you have to give up Bell Locality (which "would look nicer") and comfort yourself with mere info locality. You're saying: I thought relativity actually prohibited nonlocal action at a distance, but evidently it doesn't. It merely prohibits something very high-level, something almost suspiciously human. Anyway, my point is just: don't pretent this is the same relativity you wanted or thought you had before. The fact that Bell Locality is violated means relativity is "less right" than we expected; we should face up to that squarely and not sweep it under the rug.

And this puts my equivalence: Bell locality <==> info locality and determinism
in another light. I would like to have Bell locality. But we know we can't have it. I desperately NEED info locality. So what's the deal ? Let go determinism !

I see. But I interpret it differently: I would like to have Bell locality, because I see relativity as requiring it. But we know we can't have it. So, too bad for relativity. (And note: you only "desperately NEED info locality" for relativistic reasons. If we've been thinking about relativity incorrectly all this time, e.g., maybe there really is a preferred frame in which collapse occurs or whatever, then that provides a whole slew of totally different possible ways of eluding the causal paradoxes you claim to NEED info locality for!)

As I said, all this is nice. But we CAN'T have it. So do we throw out determinism, or do we throw out relativity ?

Bell stated that, for him, the upshot of all this was that we needed to seriously rethink the idea of fundamental lorentz invariance. I think that means he wanted to "throw out relativity". I personally feel the same way. But I feel this way based on the reasoning above, not merely based on some obsessive attachment to deterministic theories.

 

[vanesch]

Maybe you could explain how you understand QM's predictions for measurement probabilities in MWI. For example, if I prepare a bunch of spin 1/2 particle in the +z state and then measure their y-spin one after the other, how come I typically find about half +y and half -y?

I'll do it for 3 particles, ok ? And let us say that it is Alice who does the measurements, then comes to tell me.

Beginstate:
|ignorant-me> |ignorant-Alice>|1z+> |2z+> |3z+>

Alice "measures" first particle:

(u = sqrt(2))

|ignorant-me> (1/u|Alice+>|1x+>+1/u|Alice->|1x->) |2z+> |3z+>

Both Alice states measure second particle:

|ignorant-me> (1/2|Alice++>|1x+>|2x+>+1/2|Alice+->|1x+>|2x->+
1/2|Alice-+>|1x->|2+>+1/2|Alice-->|1x->|2->) |3z+>

The 4 Alice states measure the third particle:
|ignorant-me>
(1/2u |Alice+++>|1x+>|2x+>|3x+> + 1/2u|Alice+-+>|1x+>|2x->|3x+> +
1/2u|Alice-++>|1x->|2x+>|3x+> + 1/2u|Alice--+>|1x->|2x->|3x+> +
1/2u |Alice++->|1x+>|2x+>|3x-> + 1/2u|Alice+-->|1x+>|2x->|3x+> +
1/2u|Alice-+->|1x->|2+>|3z+> + 1/2u|Alice--->|1x->|2->|3x+>)

Now, Alice comes to me and tells me her result. In doing so, I become entangled with her because of her telling me (which is a physical interaction):

1/2u |me+++>|Alice+++>|1x+>|2x+>|3x+> + 1/2u|me+-+>|Alice+-+>|1x+>|2x->|3x+> +
1/2u|me-++>|Alice-++>|1x->|2x+>|3x+> + 1/2u|me--+>|Alice--+>|1x->|2x->|3x+> +
1/2u|me++->|Alice++->|1x+>|2x+>|3x-> + 1/2u|me+-->|Alice+-->|1x+>|2x->|3x+> +
1/2u|me-+->|Alice-+->|1x->|2+>|3z+> + 1/2u|me--->|Alice--->|1x->|2->|3x+>

But now the "Born rule of my consciousness" has to be applied which means that the "I experience" in my "|ignorant-me>" state has to choose between all these different entangled me-states, in order to pick one, with probability equal to the coefficient ||^2 (as the Born rule prescribes). Here, all have probability 1/8.

So my "I experience" will go into one and exactly one of these "body states", say, the third one (with probability 1/8). All the other "body states" will acquire a new "I experience" as if it were an exact copy of myself at that moment (except for the different information from Alice), and I will never hear of them again.

So now, my continued I experience has seen a transition from a body in the "ignorant me" state into the state |me-++> and is in a product state with an Alice body state which is also in an |Alice-++> state (so we will both remember that the first particle was seen in the x- state, the second in an x+ state and the third one in an x+ state).

For all what matters now, we only need to work with this branch which corresponds to my "I experience". So it is *as if* I applied a projection postulate into the state |me-++>|Alice-++>|1x->|2x+>|3x+>.

Note that in all interactions of alice and the particles, there has only been a "local" interaction: when Alice was measuring particle 1, only those parts of the state description which had to do with Alice and with particle 1 were affected, the rest remained in a product state.

You can also analyse this way, EPR and quantum eraser experiments ; I put some of my posts on that in my journal.

From Alice's point of view, of course, each time she did a measurement, she became entangled, so up to the point where she has a consciousness (that's not sure of course, how can I know) her "I" experience had to choose. These choices do not have to be the same as mine. So it is very well possible that the "I experience" of the ignorant Alice, which I knew well, ended up in |Alice+-->. But I will not know, whatever I do with Alice, because the Alice state I can still interact with, namely |Alice-++>, will have EXACTLY the same bodystates, ideas, passions, in the past, and she will have a new "I experience", a clone, say, of the Alice I knew.

cheers,
Patrick.

 

[vanesch]

And note: you only "desperately NEED info locality" for relativistic reasons. If we've been thinking about relativity incorrectly all this time, e.g., maybe there really is a preferred frame in which collapse occurs or whatever, then that provides a whole slew of totally different possible ways of eluding the causal paradoxes you claim to NEED info locality for!

Well, I would think that relativity (SR) was experimentally verified to the extend that there had to be no doubt about these paradoxes, no ? I would think that the aspects you need to get to that paradox are not so very complicated. Once time dilatation and so on have been verified (and I would think they are), I'd think it is obvious that FTL signalling comes down to signalling in the past, no? I'm not talking here about "the spacetime structure of the universe" or something, just about almost feasible experiments ?
So whatever you will replace SR with, you'll be stuck with that paradox (in the same way as we will be stuck with Aspect-like results) ?

cheers,
Patrick.

EDIT: an important remark: in all this stuff, I try to stick to SR and QM predictions. If you want to propose a new *physics* theory, then this changes the tone of the discussion, because then the first thing to do is not to sit down and talk, but to propose discriminating experiments.
So once you talk about a "preferred frame" the best thing to do is to design an experiment that could show us that preferred frame, not to talk about how this could be nice if it were true.

 

[ttn]

Well, I would think that relativity (SR) was experimentally verified to the extend that there had to be no doubt about these paradoxes, no ?

Sure, it was completely reasonable to think that -- up until the point it became clear that Bell Locality was violated in nature!

I would think that the aspects you need to get to that paradox are not so very complicated. Once time dilatation and so on have been verified (and I would think they are), I'd think it is obvious that FTL signalling comes down to signalling in the past, no? I'm not talking here about "the spacetime structure of the universe" or something, just about almost feasible experiments ?

Actually, no. There exist possible theories with more spacetime structure than relativity (e.g., a preferred frame/foliation) but which also contain time dilation and all the other usual relativistic effects and in fact agree completely with relativity at the level of actual observation. The most obvious example is the old Lorentz type theory, which Bell wrote about in his beautiful paper "How to Teach Special Relativity." In a theory like this, you can have FTL signalling without any causal paradoxes.

So whatever you will replace SR with, you'll be stuck with that paradox (in the same way as we will be stuck with Aspect-like results) ?

Not true.

EDIT: an important remark: in all this stuff, I try to stick to SR and QM predictions. If you want to propose a new *physics* theory, then this changes the tone of the discussion, because then the first thing to do is not to sit down and talk, but to propose discriminating experiments.
So once you talk about a "preferred frame" the best thing to do is to design an experiment that could show us that preferred frame, not to talk about how this could be nice if it were true.

Yes, I agree, it would be good to do this. Of course, you already know it's going to be hard -- all the pre-Bell stuff that people (justifiably) took as strong evidence against the existence of a preferred frame, presumably means that if there is a preferred frame, it's well hidden. After Bell, one can say that it is hidden by quantum randomness/uncertainty, which is an interesting twist. So perhaps if Bohm's theory is true and someday some clever person figures a way around the uncertainty principle, we could use Bohm's nonlocal correlations to actually detect the preferred frame (in which presumably those nonlocal "signals" propagate). This has been pointed out many times, but, as you suggest, it's all talk until there's some serious suggestion for how to actually do it.

 

[ttn]

But now the "Born rule of my consciousness" has to be applied which means...

Yes, yes. But I was asking specifically about *probabilities*. You mentioned the Born rule here, which usually goes something like this: "the probability of a particular outcome is equal to ..." You are of course talking about something slightly different, and that's what I want to understand clearly. Is there a probability involved at all? It seems there isn't since, with certainty, all possible "outcomes" (or "experiences" if you want to talk in terms of your own solipsistic consciousness...) in fact occur. So there is nothing for probability to mean. Perhaps you want to say that the Born rule probabilities give the probability that "the current you" will find yourself in the next moment experiencing some particular thing. But I don't see how that makes any sense. The current you will, with certainty, find yourself in the next moment experience *all* the possible things, period. What is the probability supposed to be a probability *for*??

that the "I experience" in my "|ignorant-me>" state has to choose between all these different entangled me-states, in order to pick one, with probability equal to the coefficient ||^2 (as the Born rule prescribes). Here, all have probability 1/8.

It's the "in order to pick one" part that I don't understand. In what sense exactly is one picked? It seems to me that the rest of your story commits you to the notion that they're all picked, i.e., there's no "picking" going on at all, i.e., there's nothing for the Born rule probabilities to be probabilities *of*.

So my "I experience" will go into one and exactly one of these "body states", say, the third one (with probability 1/8). All the other "body states" will acquire a new "I experience" as if it were an exact copy of myself at that moment (except for the different information from Alice), and I will never hear of them again.

This seems to trade on equivocations about the meaning of "I". If "all the other 'body states' ... acquire a new 'I experience'" in exactly the same way as one another, how do you pick one out uniquely as "the real later you"? Aren't they all equally real, equal claimants to the title of "the real later you"? After all, it's essential to the whole MWI perspective that there is no collapse, i.e., that all branches of the wf continue to really exist, period. So what are the Born rule probabilities supposed to be probabilities for? The whole evolutionary story told by the theory is entirely, 100% deterministic.

Looked at another way, in standard QM, Born's rule only applies at the moment that the wave function collapses. You want to get rid of the collapse and have only the unitary evolution. So don't you get rid of any talk of Born rule probabilities in the process? It seems so, but if that's right, then I don't see how MWI can constitute a valid interpretation of QM, an essential part of which is *predictions for relative frequencies of various outcomes*.

Perhaps I'm attacking a bit of a straw man at this point, and should give you a chance to clarify your view before I say anything more. Hopefully my comments will at least give you a sense of the direction of my attack so you can defend yourself appropriately.

 

[vanesch]

So don't you get rid of any talk of Born rule probabilities in the process? It seems so, but if that's right, then I don't see how MWI can constitute a valid interpretation of QM, an essential part of which is *predictions for relative frequencies of various outcomes*.

Well, I'm not a real MWI-er. What you write (get rid of the Born rule) is indeed part of the program of MWI, and I think I have found a mathematical proof that this cannot work, which I hope to publish soon.
I think that there is some real need for the Born rule. On the other hand, I want to get rid of the projection postulate, and up to there, I follow MWI.

Imagine yourself, and imagine that we cut your body in 2 pieces, and restituate the missing half so that we now have 2 exact copies of your original body. (I think that this cannot really be done, but no matter).
When you guys both wake up after the operation, one of you will be in the left bed, and the other one in the right. But I can imagine that your *I experience* now is in one of both. Surely you don't experience a "body doubling" do you ? If I put a needle in one of the new bodies, YOU will feel pain in one case, and nothing at all in the other case, because it is in "the other copy's body" that I pick a needle.
Why are you in "the left bed" and not "in the right bed" ?

Next, imagine that I can scan your body up to subatomic scale and reproduce it completely. I now have an exact copy of your body, and that new body remembers exactly everything you know, etc... but I can assume that you still are yourself, and that, if I didn't even tell you that I made a copy of you, you wouldn't even know. Your *I* experience is still in your old body, but your new copy has a new *I* experience, with exactly the same memories as you do. If I put a needle in the copy's body, you won't feel anything.

Well, I postulate that exactly the same happens with these entangled states of your body: that ONE of these states inherits your "I" experience as a continuation of what happened before, and that the others are "new copies", but starting out with (almost, because of the different observations) identical personalities, mindsets, memories etc... To all external observers, you cannot make any difference between the you with your "old I experience" and the new copies because they behave in exactly the same way.
But to you, as a subjective experience, it makes of course all the difference in the world, if you are in one copy or in another.
And I claim that the fundamental physics of "I experiences" is the Born rule, which decides probabilistically in which of the copies your subjective I experience will now be.

There. You don't believe a word of it, do you

cheers,
Patrick.

 

[vanesch]

Imagine yourself, and imagine that we cut your body in 2 pieces, and restituate the missing half so that we now have 2 exact copies of your original body. (I think that this cannot really be done, but no matter).
When you guys both wake up after the operation, one of you will be in the left bed, and the other one in the right. But I can imagine that your *I experience* now is in one of both. Surely you don't experience a "body doubling" do you ? If I put a needle in one of the new bodies, YOU will feel pain in one case, and nothing at all in the other case, because it is in "the other copy's body" that I pick a needle.
Why are you in "the left bed" and not "in the right bed" ?

To make it more dramatic, imagine I'm explaining you the procedure, and I let you choose which of the two copies, the one in the left bed, or the one in the right bed, will be tortured atrociously, while the other copy will be made rich.

Don't you think it is 1 chance out of 2 that you will be lucky and 1 out of two that you will doom yourself ?

cheers,
Patrick.

 

[ttn]

Imagine yourself, and imagine that we cut your body in 2 pieces, and restituate the missing half so that we now have 2 exact copies of your original body. (I think that this cannot really be done, but no matter).
When you guys both wake up after the operation, one of you will be in the left bed, and the other one in the right. But I can imagine that your *I experience* now is in one of both. Surely you don't experience a "body doubling" do you ? If I put a needle in one of the new bodies, YOU will feel pain in one case, and nothing at all in the other case, because it is in "the other copy's body" that I pick a needle.
Why are you in "the left bed" and not "in the right bed" ?

OK, good example. Can we give names to the 3 people involved here, just to make it easier to refer to them? Say Albert is the guy that walks into the doctor's office, and Bob and Bill are the two guys on the two beds at the end of the day. Fair? If I read you correctly, you want to say that one of the two, either Bob or Bill, is somehow "more really the same person as" Albert. Yes? But I don't understand what could possibly underwrite that claim. Presumably if Bill, say, inherits all of Albert's memories from before the operation, then, by symmetry so does Bob. So, sure, if you ask Bob: "are you Albert?" he'll say "You bet I am! I remember being at home this morning eating breakfast and my wife called me Albert, etc..." But if you ask Bill the same question, he'll give the same response. Right?

So there seems no basis (either in terms of bodies or minds) to pick one or the other of the two copies (Bob or Bill) as "special", as "really Albert".

Next, imagine that I can scan your body up to subatomic scale and reproduce it completely. I now have an exact copy of your body, and that new body remembers exactly everything you know, etc... but I can assume that you still are yourself, and that, if I didn't even tell you that I made a copy of you, you wouldn't even know.

OK...

Your *I* experience is still in your old body, but your new copy has a new *I* experience, with exactly the same memories as you do. If I put a needle in the copy's body, you won't feel anything.

Yes, that's my understanding. But I think you run the risk of getting confused when you refer to putting a needle "in the copy's body." For I see no objective basis for claiming that one is *really* the copy. There are just two people who are like identical twins (in terms of sharing body structure, etc., but having their own individual consciousnesses) but who happen to share a memory history. Won't each legitimately regard the other one as "a copy of me", and legitimately believe themself to be "the real Albert."

Well, I postulate that exactly the same happens with these entangled states of your body: that ONE of these states inherits your "I" experience as a continuation of what happened before, and that the others are "new copies", but starting out with (almost, because of the different observations) identical personalities, mindsets, memories etc...

That makes no sense to me. If they all inherit my memories, then what picks out "ONE" as special, as the one that "inherits my 'I experience' as a continuation of what happened before"? They *all* do that!

To all external observers, you cannot make any difference between the you with your "old I experience" and the new copies because they behave in exactly the same way.
But to you, as a subjective experience, it makes of course all the difference in the world, if you are in one copy or in another.

The word "you" in this last sentence seems ambiguous. Are you referring to Albert here, or Bob, or Bill, or what? Surely it matters to Bob that he is a real person with memories and a mind and all that. But it matters equally much to Bill. Does it matter to Bob that he isn't Bill, that, for him, Bill is some other person? Sure. But it is symmetrical: it matters equally much to Bill that he isn't Bob, etc...

When you write that it matters "if you are in one copy or in another", I can only assume that the "you" is referring to Albert. It matters to Albert that one of the copies is "really him" and the other one isn't. Well, I don't think that's true; I don't think there's any way it could possibly be true since there is, by construction, no difference between Bob and Bill.


Now, people usually want to try to get out of this problem by saying that the evolution along the branching structure picks out one of the branches as "special" -- e.g., there really is some fact of the matter as to whether Bob or Bill is "the real Albert", the continuation-forward-in-time of Albert's "I experience". That solves this problem, but at the price of bringing back in everything that is wrong with Copenhagen. Because then you just have some extra law (Born's rule) for picking one of the branches at random as "real" and then you throw the others away as "empty" or "unreal" or "full of mere mindless hulks" or whatever. Well, you might as well just collapse wave functions and forget all the (then pointless) "many worlds" stuff...

 

[ttn]

To make it more dramatic, imagine I'm explaining you the procedure, and I let you choose which of the two copies, the one in the left bed, or the one in the right bed, will be tortured atrociously, while the other copy will be made rich.

Don't you think it is 1 chance out of 2 that you will be lucky and 1 out of two that you will doom yourself ?

Ah, good, this makes my objection clearer. You're asking "me" which of the two guys in the bed to torture. But who is "me"? There is no presently-existing third person who represents the "real me". There are just the two guys in the bed. If you ask Bill, I'm sure he'd prefer you torture Bob. And if you ask Bob, he'll likely prefer you torture Bill.

I think there is a 100% chance that one of the guys will end up happy and the other in pain. There is a 100% chance that "you will be lucky" -- for some value of "you" (either you=Bob or you=Bill). Talking about a probability of 50% that "you will be lucky" seems to presuppose that one of the two guys is "really me", and I don't know how you can claim any such thing without bringing in some new dynamics (other than the unitary evolution) that will confer privileged status on one of the two copies.

So much for getting rid of the projection postulate...

 

[vanesch]

I will try to give another example that should hopefully illustrate better what I'm at.

Imagine the following situation:
Somebody proposes the following deal:
You come to his office, and - staying awake and everything - your body will be scanned by a zargon ray scanner, which allows one to make an exact copy of you, with all of your memory content and everything. That copy will then be tortured slowly to death, and you will get a lot of money for it. Do you accept the deal or not ?

I can tell you, I do.

Now, somebody else proposes you another deal:
You will again be scanned, but now *YOU* will be tortured to death, while your copy gets a lot of money. Will you accept the deal ?

I can tell you, I won't.

Nevertheless, AFTER the copying, both you and the copy in the lab next doors are *identical*. But one of them is you, and the other one is a copy, and your *I* experience stayed (I assume) in your body.

To prove this, a final deal:

A copy will again be made, but this time, both of you will walk into a room with 500 different doors. The first one who will go through the 32nd door will get the money, and the other one will be tortured. Do you accept ?

I won't because of course my copy will know the deal too. So there will be a fight to get through this door and it is not sure I'm going to win against my copy and I don't like money that much that I want to risk to be tortured (but I don't give a damn about my copy).

Well, it is the same with the Born rule. I will be the one, selected randomly via the Born rule, in one of the states, and the others will be copies.

Does this clarify more what I want to say ?

cheers,
patrick.

EDIT: to add something here: in all these examples, the copy will of course know it is the copy, because it has had a strange experience: at one moment it was standing in the doctor's office in the scanner, and suddenly it blinked its eyes in a humming cylinder. Of course, the first thing is just a memory of something it never did.
But we could add more drama by making the inside of the scanner and of the humming "building" cylinder look identical, and placed symmetrically in a room. In that case, both the original you and your copy will have an identical experience.
You could then even accept the third deal: your copy is the one who will start to count the doors on the wrong side (and will think of you the same). Surprise when your copy will open the bad door, thinking he will be rich.
But, but... you might be a bit scared during that period that, well, maybe you are not the original, after all...

 

[ttn]

I will try to give another example that should hopefully illustrate better what I'm at.

Imagine the following situation:
Somebody proposes the following deal:
You come to his office, and - staying awake and everything - your body will be scanned by a zargon ray scanner, which allows one to make an exact copy of you, with all of your memory content and everything. That copy will then be tortured slowly to death, and you will get a lot of money for it. Do you accept the deal or not ?

I can tell you, I do.

Now, somebody else proposes you another deal:
You will again be scanned, but now *YOU* will be tortured to death, while your copy gets a lot of money. Will you accept the deal ?

I can tell you, I won't.

Nevertheless, AFTER the copying, both you and the copy in the lab next doors are *identical*. But one of them is you, and the other one is a copy, and your *I* experience stayed (I assume) in your body.

A nice, disturbing example.

But isn't it equivalent to the Albert/Bob/Bill case, except now you're saying: Bob and Bill are laying on the two beds, the doctor comes in and sends Bob out of the room for a minute, at which point he offers Bill lots of money if he'll consent to Bob getting tortured. Well, sure, I suppose Bill will consent to this. As would Bob, had it been Bill that was sent out into the hallway. It's like I said earlier: by construction there seems to be nothing to pick out one of the two as "really the same person as" the original guy, Albert.

Now you seem to want to get around this by assuming the operation (zargon ray scanner or whatever ) is such that the copy is produced in a different place than the original, the next room, say. And that does indeed suggest a way to identify "the real Albert" -- if Bob is the one in the next room over, then he's the copy and Bill is Albert.

That's fine as far as it goes. But then I think you're going to have a problem mapping that onto the quantum/MWI context. Because there, if I understand correctly, there is not supposed to be anyone of the copies that is in any way dynamically special. It's not like when the universal wave function splits, one of the new branches "exists in the next room over", whatever the heck that would mean. They all exist in the same (huge) configuration space of the universe. So either the analogy breaks down, or you bring in something to break the symmetry and pick one of the branches (and that will end up being equivalent to the collapse postulate, with all the badness that entails ).

To prove this, a final deal:

A copy will again be made, but this time, both of you will walk into a room with 500 different doors. The first one who will go through the 32nd door will get the money, and the other one will be tortured. Do you accept ?

I won't because of course my copy will know the deal too. So there will be a fight to get through this door and it is not sure I'm going to win against my copy and I don't like money that much that I want to risk to be tortured (but I don't give a damn about my copy).

Well, it is the same with the Born rule. I will be the one, selected randomly via the Born rule, in one of the states, and the others will be copies.

I don't follow you here. What is it that picks you out as, well, you? Is it that the copy was zargon-generated in the next room over? If so, then it's the same problem as above. But if you're intending to gloss over that (or have something less obviously asymmetrical, like the earlier example of cutting Albert in half down the middle and zargon-regenerating the two missing halves) then I see no basis at all for identifying one of the two as "really you".


Here's my problem in a nutshell. When the wf "branches", either one of the several branches is picked out as somehow special, or they're all equivalent. If they're all equivalent, there's no meaning to talking about probabilities and hence no place for the Born rule. If one of the branches is picked out as special, you could probably (ha ha) have a stochastic law so that which branch is picked is governed by the Born rule. But then I fail to see how the theory is any better than Copenhagen -- it will suffer from the same measurement problem, etc...

 

[vanesch]

Now you seem to want to get around this by assuming the operation (zargon ray scanner or whatever ) is such that the copy is produced in a different place than the original, the next room, say. And that does indeed suggest a way to identify "the real Albert" -- if Bob is the one in the next room over, then he's the copy and Bill is Albert.

In the Bob and Bill case, the doctor will not be able to know which one actually has the "continuation of I experience" and which one only thinks he has it, but whose *I experience* just came into being. There is no way to know this from the outside, or from any physical aspect because both will behave in exactly the same way, in all possible circumstances. But - it is strange that I cannot make you see this ; it is almost as if I'm talking to a copy of you - can't you conceive that, if YOU were undergoing this operation, your experiences are as follows:
you come in the doctor's office, you lie down on the operation table, you sleep under anesthesy, and... you wake up in the LEFT bed, with a thing which terribly looks like yourself in the bed to the right of you ? And that thing looks at you, and tells you: Hi, I'm Albert ! And you now realize that there is NO WAY IN THE WORLD you are going to be able to convince the doctor that you are the real Albert ?
You will tell me that the "guy in the right bed" will of course have exactly the same reaction. But that's not the point. That only makes both indistinguishable from the outside. Your subjective experience, I hope, will continue to exist in ONE of the copies.

If we go back to the other story (with the zargon scanner), I took that story not for the doctor to be able to make the difference, or an external observer to make the difference, but to try to make you see where your "continued I experience" attaches to one and only one body, and one could imagine that a zargon scanner doesn't affect you that much that your "I experience" flips over to the copy: you remain "yourself", in that your experience is: you walk into the doctor's office, stand on a metal plate, you hear "zmmmm" while you're still looking at the doctor, you step down, and get a big cheque, while you hear screaming in the room next door. In the same way you would have gone to the dentist, opened your mouth, had an intervention, and went home again. Imagine now a weird dentist who installed a zargon scanner on his chair and makes copies of you without you even noticing. It doesn't make a difference for you, does it ?

But now, let us imagine that there has been a technical improvement in zargon ray scanners, with zargon II rays.
Again, you go as usual to your dentist, go lie on the chair, open your mouth... and suddenly, you find yourself in a strange room, you look out of the window and... you see yourself walking home from the dentists, next door ! zargon II rays transport ALSO your *I experience* ! But for the dentist, nothing unusual, he knows that his copies are screaming, and try to convince him that they are the real you ; he already had that with his old zargon scanner.

BTW, for a "beam me up Scotty" transporter, I'd prefer a zargon II scanner with build-in meat grinder !

cheers,
Patrick.

 

[ttn]

In the Bob and Bill case, the doctor will not be able to know which one actually has the "continuation of I experience" and which one only thinks he has it, but whose *I experience* just came into being.

Yes, the doctor won't be able to tell. What's not clear to me is whether there is any fact of the matter at all. (I am thinking here of the original chainsaw-in-half-and-regenerate case, not the zargon-ray-in-the-next-room case.) If there is a perfect symmetry -- Bob and Bill each get exactly half of Albert's brain, etc. -- how is there any basis *in fact* (not merely in some particular person's knowledge) for saying that one of the half-copies is the "real" forward-continuation of Albert, but the other is a mere copy? Any fact which you point to as arguing for, say, Bill as the forward-continuation of Albert, I will say: yes, but that same fact applies equally to Bob, so where's the difference?

it is strange that I cannot make you see this ; it is almost as if I'm talking to a copy of you

I am admittedly a bit of a mindless hulk...

- can't you conceive that, if YOU were undergoing this operation, your experiences are as follows:
you come in the doctor's office, you lie down on the operation table, you sleep under anesthesy, and... you wake up in the LEFT bed, with a thing which terribly looks like yourself in the bed to the right of you ? And that thing looks at you, and tells you: Hi, I'm Albert ! And you now realize that there is NO WAY IN THE WORLD you are going to be able to convince the doctor that you are the real Albert ?

Yes, I think that is exactly what "I" would experience. But you are forgetting that this other guy would experience something very similar, except he'd wake up with "me" on his left. My point is, not only could I never convince the doctor that I'm the real Albert -- I could never convince the guy in the other bed that I'm the real Albert. Any argument I tried to make for that claim ("but I remember coming in here this morning and my wife said 'goodbye Albert' before I left home!") wouldn't work, because the other guy would be able to make precisely the same argument.

My point is that the natural grammar here is misleading. You write: "you lie down on the table, you sleep under anesthesy, and... you wake up...". I think it is grammar, and grammar only, that makes you believe there is some natural or obvious connection between the person referred to by "you" in the first two occurrences of that word, and the third occurrence of it. Of course, Bill will believe that he is Albert -- he has a more or less continuous memory of Albert evolving continuously forward in time *into him*. So he naturally believes he is Albert. But Bob has exactly that same continuous sense. So literally , when you say "...and then *you* wake up" I don't know who/what you are referring to by the word "you". The grammar suggests you are, in some sense, referring to the same thing that word meant earlier in the sentence (Albert), and if we don't think too carefully we will just assume that one or the other of Bob/Bill is the forward-continuation of Albert. Why do we think this? I guess because we are used to believing that one person cannot become two, so "obviously" if Albert becomes two, one is real and one is a mere copy. But the whole point of the example is to deny that very intuition -- one person, by hypothesis here, *can* become two. So there is no *unique* forward-continuation-of-Albert. There are two.

Now, I must confess to being a bit lost as to how any of this is supposed to relate to QM. If it would help move the argument forward, I'd be happy to just concede, for the sake of argument, that one or the other of Bob/Bill is somehow picked out as metaphysically special -- the "real" forward-continuation of Albert (because of some continuity of "I experience" or because the other loser was born 5 minutes ago in the next room or whatever). So... if I just admit that, what happens next?

I guess you want to say the splitting of universes is just like that -- the universal wf splits into several branches at some moment, and this generates a bunch of "copies" of Albert, one of which is picked out as special in the sense of being the "real" forward-continuation of Albert. Yes?

And then I will point out: there is nothing in the unitary dynamics that can *perform* this job of picking out one of the copies as special. If you want one to be special, you need to add something to the unitary dynamics -- something that starts to smell suspiciously like the Born rule and an associated wave function collapse...

You will tell me that the "guy in the right bed" will of course have exactly the same reaction. But that's not the point. That only makes both indistinguishable from the outside. Your subjective experience, I hope, will continue to exist in ONE of the copies.

"My" subjective experience? I don't know what you mean. Bob's experience will exist in only one of the copies. Bill's experience will exist in only one of the copies. Which one is really the forward continuation of Albert? You tell me.

Anyway, whatever. Maybe conscious "I experience" really does work the way you assume. I have no idea, really. So I'm happy to grant whatever you want for the sake of bringing the discussion back to QM and MWI. I still don't see how any of this justifies talk of probabilities there...

 

[vanesch]

So I'm happy to grant whatever you want for the sake of bringing the discussion back to QM and MWI. I still don't see how any of this justifies talk of probabilities there...

You might be surprised, but it is extremely related.

Remember my "|ignorant-me>" body state, which was related to my "I experience. After talking to Alice, my body got into a superposition of states, namely |me+++>, |me-++> ...
Now, if you accept, for a moment, that there is a continuation of my "I experience" from the body state "ignorant me" into ONE of these |mexxx> states, with a probability given by the Born rule, then I have 1/8th chance to end up, in, say, the |me+--> state. AND I DON'T KNOW ANYTHING ABOUT ALL THE OTHERS. So my old "I experience" is now related to the body state |me+-->, and as I'm entangled with the Alice+-- state, when I will later talk to Alice we will both agree that we had first a + state, then a - state, and then again a - state. I am also entangled with the |1x+> state, so if I'm going to do an experiment on the first particle, everything will seem to me as if it was in a pure |1x+> state.
So for all practical matters, I can now continue with the state of the universe being |alice+-->|1x+> |2x-> |3x->.
So it is AS IF I applied the projection postulate ! I will never know anymore about all these other states.
If I do now a new quantum experiment, say, with Bob having done 4 measurements, my "old" I experience is now in |me+--> and after Bob tells me his results, my body state (starting out from this |me+--> state) will entangle with Bobs and his particles, and again, because my "I experience" cannot stand being entangled, chooses, according to the Born rule, ONE of these new body states to "live in" while the others are again "copies".

So my (I-experience-wise) new state will now be |me+--AACB> or something, which has been assigned to me, I recall, again by choosing randomly one of the possible states, with probabilities according to the Born rule.
As such, my "I experience" accumulates different experiences, results of measurements etc... and when you do statistical tests on these results, they are conform with the Born rule (that's maybe not so obvious, but it can be shown). More ! I only end up in a product state with bodystates of other people who ALSO have that experience of the correctness of the Born rule. So we end up writing theories about it, call them "quantum mechanics" and believe in the validity of the Born rule.

True Everettians come close to this view, but they refuse the "assignment by fiat" through the Born rule, and hope they can somehow find a logical argument on why it must be so. A recent argument by Deutsch goes even as far as saying that these probabilities must be given by the Born rule, because (in situations such as money/torture choices) these are the only reasonable probabilities a rational gambler would assign to his later becoming Bob or Bill based on symmetry arguments and so on ; and then goes on defining what a rational gambler is (and I think I found where in this definition he smuggled in the Born rule!). I think I know that this cannot work in general, so I just plug in the Born rule by fiat, as a postulate ; "the god of the Born rule re-assigns the souls of the observers to the new body states by playing dice according to the Born rule" ! Einstein would get sick of it !

In all of this, you might object: "yes, but what happens to the copies then ?". My answer is: I don't know, I will never know, because I have only one I-experience. A bit like if you were continuously being copied by aliens right now, flying over your house with zargon ray machines. You'll never know about those copies. The Born rule is what singles out one body state (and this is the essentially probabilistic part of the theory) to be your new body state in which your I experience will now live on. And it has as a consequence (and that is important!) that this succession of body states will accumulate experience and memory in agreement with statistics of the Born rule as if the projection postulate were true, and more, it will be in a product state with other people's body states who also accumulated such an agreement with the Born rule experience.
The scary thing in all this is that those "other people's body states" are probably not those in which *their* original I experience is now travelling, and they are probably now in contact with one of your copies. But you (being external to them) will never notice anything about that, the behaviour of their copy being identical.

cheers,
Patrick.

 

[vanesch]

I guess you want to say the splitting of universes is just like that -- the universal wf splits into several branches at some moment, and this generates a bunch of "copies" of Albert, one of which is picked out as special in the sense of being the "real" forward-continuation of Albert. Yes?

And then I will point out: there is nothing in the unitary dynamics that can *perform* this job of picking out one of the copies as special. If you want one to be special, you need to add something to the unitary dynamics -- something that starts to smell suspiciously like the Born rule and an associated wave function collapse...

This is true. But the nice thing about it is that somehow, maybe, you can assume that "I experiences" are, as you call it, metaphysical, and do not have to obey the rules of material physical objects.

As I said, I want to stick as closely as possible to the existing formalism (QM and SR). Everettians think they can get rid of that ugly Born rule, but I think that's wrong. So I hide it there where it doesn't harm physics per se: in my subjective experiences. That's not something physical, so I cannot write "the hamiltonian of my subjective experiences". I can write the Hamiltonian of my body and brain, so that's still physics. But as far as my subjective experiences themselves go, I can make the case that they do not belong to physics, and hence do not obey some unitary dynamics. Instead, they obey the Born rule.

And now off the record: if you ask me whether I really believe that that is how nature works ? No, of course not I have to say I don't know how nature "really" works, and I'm even convinced we will never know. But this is just, IMHO, a nice story that can go perfectly well with the current formalism of QM and SR. In fact, after thinking a long time about it, I have never found any OTHER story that goes with it and strictly sticks to the formalism...

cheers,
Patrick.

 

[selfAdjoint]

And now off the record: if you ask me whether I really believe that that is how nature works ? No, of course not I have to say I don't know how nature "really" works, and I'm even convinced we will never know. But this is just, IMHO, a nice story that can go perfectly well with the current formalism of QM and SR. In fact, after thinking a long time about it, I have never found any OTHER story that goes with it and strictly sticks to the formalism...

Aaah, Patrick, I can't tell you how much better that statement makes me feel! I personally would almost give up the formalism to avoid having to take MWI seriously, with all its implications. Shut up and calculate does OK for me (but then you know I am not much good at calculating! Or shutting up, for that matter. )

 

[ttn]

Remember my "|ignorant-me>" body state, which was related to my "I experience. After talking to Alice, my body got into a superposition of states, namely |me+++>, |me-++> ...
Now, if you accept, for a moment, that there is a continuation of my "I experience" from the body state "ignorant me" into ONE of these |mexxx> states, with a probability given by the Born rule, then I have 1/8th chance to end up, in, say, the |me+--> state. AND I DON'T KNOW ANYTHING ABOUT ALL THE OTHERS. So my old "I experience" is now related to the body state |me+-->, and as I'm entangled with the Alice+-- state, when I will later talk to Alice we will both agree that we had first a + state, then a - state, and then again a - state. I am also entangled with the |1x+> state, so if I'm going to do an experiment on the first particle, everything will seem to me as if it was in a pure |1x+> state.
So for all practical matters, I can now continue with the state of the universe being |alice+-->|1x+> |2x-> |3x->.
So it is AS IF I applied the projection postulate ! I will never know anymore about all these other states.
If I do now a new quantum experiment, say, with Bob having done 4 measurements, my "old" I experience is now in |me+--> and after Bob tells me his results, my body state (starting out from this |me+--> state) will entangle with Bobs and his particles, and again, because my "I experience" cannot stand being entangled, chooses, according to the Born rule, ONE of these new body states to "live in" while the others are again "copies".

OK, I understand all of this; it is more or less what I thought you thought, but it's nice to get it out here in black and white.

Remind me once again why I should take any of this seriously? Oh, right, because this story allows me to elude what would otherwise be an in-eludable violation of Bell Locality in my theory. So the calculus is: retaining belief that relativity is really fundamental (as opposed to merely emergent or somehow otherwise not the final story in spacetime) outweighs belief in basic, common-sense "realism" including, say, the idea that our best theories (including QM) are telling us something reliable about the world (remember, under MWI, we are deluded into thinking that experimental outcomes are governed by the Born rule, etc.), that our best friends are actually conscious beings on par with us, and so forth.

I admit there is a choice to be made here, but I frankly don't understand why anyone would give up so much merely to save something so little.

True Everettians come close to this view, but they refuse the "assignment by fiat" through the Born rule, and hope they can somehow find a logical argument on why it must be so. A recent argument by Deutsch goes even as far as saying that these probabilities must be given by the Born rule, because (in situations such as money/torture choices) these are the only reasonable probabilities a rational gambler would assign to his later becoming Bob or Bill based on symmetry arguments and so on ; and then goes on defining what a rational gambler is (and I think I found where in this definition he smuggled in the Born rule!).

Yes, I've heard Deutsch's argument. I'm sure you're right that it smuggles in the Born rule somehow, since you can't get statements about probability out of thin air from a complete deterministic theory. But it would be interesting to see specifically how this sneaks in. Kudos to you for having the, ahem, courage to take Deutsch's arguments seriously enough to give them careful scrutiny.

I think I know that this cannot work in general, so I just plug in the Born rule by fiat, as a postulate ; "the god of the Born rule re-assigns the souls of the observers to the new body states by playing dice according to the Born rule" ! Einstein would get sick of it !

Probably, but I doubt it would be the dice-rolling part that would mostly bother him.

In all of this, you might object: "yes, but what happens to the copies then ?". My answer is: I don't know, I will never know, because I have only one I-experience. A bit like if you were continuously being copied by aliens right now, flying over your house with zargon ray machines. You'll never know about those copies. The Born rule is what singles out one body state (and this is the essentially probabilistic part of the theory) to be your new body state in which your I experience will now live on. And it has as a consequence (and that is important!) that this succession of body states will accumulate experience and memory in agreement with statistics of the Born rule as if the projection postulate were true, and more, it will be in a product state with other people's body states who also accumulated such an agreement with the Born rule experience.
The scary thing in all this is that those "other people's body states" are probably not those in which *their* original I experience is now travelling, and they are probably now in contact with one of your copies. But you (being external to them) will never notice anything about that, the behaviour of their copy being identical.

Yes, this is precisely the point that led (I believe) David Albert to coin the term "mindless hulks" to describe all those people out there in our worlds which we think are people but are really mindless hulks.


By the way, do you believe that each individual person "lives" in some one particular branch at each moment, so (from god's perspective) there really are several billion distinct conscious people on Earth right now? Or would you say, instead: this view commits me to believing that it is overwhelmingly like that everyone I've ever seen and taken to be a conscious person was in fact merely a mindless hulk; hence I have no evidence whatsoever for believing in the existence of other conscious people; hence I assume I am the only one.

At some point you admitted that your view was solipsistic -- so I'm just trying to understand which of these versions of solipsism you subscribe to.


PS -- I'm glad that MWI fans don't watch old zombie movies where the good guys have to go around killing all the zombies. Or if they do watch them, I hope they don't get any ideas...

 

[ttn]

As I said, I want to stick as closely as possible to the existing formalism (QM and SR). Everettians think they can get rid of that ugly Born rule, but I think that's wrong. So I hide it there where it doesn't harm physics per se: in my subjective experiences. That's not something physical, so I cannot write "the hamiltonian of my subjective experiences". I can write the Hamiltonian of my body and brain, so that's still physics. But as far as my subjective experiences themselves go, I can make the case that they do not belong to physics, and hence do not obey some unitary dynamics. Instead, they obey the Born rule.

You seriously think it "doesn't harm physics" to bring all this blatantly non-physics loony business *into* physics? I think it does tremendous harm.

And now off the record: if you ask me whether I really believe that that is how nature works ? No, of course not I have to say I don't know how nature "really" works, and I'm even convinced we will never know. But this is just, IMHO, a nice story that can go perfectly well with the current formalism of QM and SR. In fact, after thinking a long time about it, I have never found any OTHER story that goes with it and strictly sticks to the formalism...

Hmmm... If you really honestly don't believe any of this (because deep down you're a sane person and no sane person could take this stuff seriously!) then why advocate it as if you did believe it, as if it was a serious physics theory? If you're convinced "we will never know" how nature really works, then by all means don't spend your time trying to figure it out. But some people are not convinced of that; we are trying to find out how nature works. Personally I don't think "trying to figure out how nature works" is something that physicists should have to *apologize* for! We should be trying to do it, and we should be doing so proudly.

This is why I think, contrary to what you implied above, it does harm physics to take MWI seriously or to pretend that you do. It makes others feel embarrassed that they *can't* take that seriously, or that they believe physics should be taken seriously, etc. In short, it sends off a vibe into the rest of the physics community that "physics isn't serious", or "physics can never really figure out how nature works, so we just make up stupid stories that we don't really take seriously anyway", or "physics is all a big inside joke, but don't tell the government or they'll stop funding us", or god knows what. Well, as someone who has a lot of respect for people like Newton and Maxwell and Boltzmann and Einstein and Bell -- people who did take physics seriously and didn't think it was doomed to become a failure or a joke -- I don't think it's good to be spreading this kind of attitude. It will cause future Newtons and Boltzmanns and Bells to go into a field that does take itself seriously like, oh god, cultural studies, or basket weaving, or who knows what.

 

[DrChinese]

1. BUT NONLOCAL HIDDEN VARIBLE THEORIES ARE NOT RULED OUT. That is why the existence of Bohmian mechanics doesn't cause the universe to disappear in a puff of logic.

2. Then you must be confused about what Bell proved. Bell's theorem shows that, if you try to "complete" QM by adding local hidden variables, the theory you get cannot both respect the Bell Locality condition and agree with experiment. So, as lots of people say, if you want a local theory, you'd better stick with QM and its completeness doctrine, and not go down the hidden variables road. But that strategy obviously presupposes that QM itself is local -- otherwise, saying "you should stick with QM and not pursue hidden variable theories, on pain of nonlocality" just makes no sense.

3. And the final piece: Bell states openly that, he thinks, nonlocality is a fact, period -- that it's *not* something which merely afflicts hv theories. As he says, you *cannot* dismiss the operations on one side as causal influences on the other. How can he believe this? What else would he need to have to believe to make this claim given the above paragraph? Obviously he would have to think that orthodox QM was *also* nonlocal. IF it wasn't, there'd be no grounds for claiming that all possible alternatives -- i.e., nature -- were nonlocal.

1. I have reviewed Goldstein's summary of BM at http://plato.stanford.edu/entries/qm-bohm/. Now I am more confused than ever! I just don't see where there are hidden variables at time t=0. He mentions that contextuality is assumed and is no big deal. Yet nowhere is the simultaneous reality of non-commuting observables asserted.

2. You see Locality as the essential assumption, and I see the "reality" of A, B and C as the essential assumption.

3. I think all of the QM interpretations somehow violate "local causality" which I define as: causes must precede effects, and there is no FTL propagation of causes.

 

[vanesch]

You seriously think it "doesn't harm physics" to bring all this blatantly non-physics loony business *into* physics? I think it does tremendous harm.

I guess what you call "loony business" are concepts which you would rather classify as philosophical or spiritual, and not as materialistic science. But it is a long standing tradition that concepts which "didn't have their place in science" came into science when science grew sophisticated enough to deal with it. The human body was something beyond scientific investigation ; organic chemistry was something beyond scientific investigation ; the fact that humans could decend from apes and in the end from bacteria was something unheard of ; the movement of the heavens was beyond scientific investigation. All these domains have now been "invaded" by science. So why not the concepts of consciousness, "I experience" etc... ?
After all, if something like MWI *is* an approximate description of reality, that would then be the first time that such "unheard of" concepts are integrated into the scientific machinery, all be it very coarsely.
So I don't accept the argument that this "loony business" has nothing to do with science, because I put it on the same level as saying that human blood has nothing to do with chemistry.

Hmmm... If you really honestly don't believe any of this (because deep down you're a sane person and no sane person could take this stuff seriously!) then why advocate it as if you did believe it, as if it was a serious physics theory?

You understood my statement "on the wrong side of its meaning" (like I knew a professor who told somebody that he "almost got zero". When the student asked how much he had, the professor said: "minus five" .)

When I say that I "don't take this seriously" I only mean that this stuff is still too speculative and naive. After all, we don't even have all of *material physics* into a theory. So there are still many changes to be accepted, and I think that something like MWI is only the beginning ! Probably nature is way way more weird than this simplistic view in MWI ; I didn't mean that we would get "back to good old positivism". In fact, if science is to progress, I really think that one day it will have to tackle issues which, for me, seem currently out of its scope, such as consciousness (and I'm not talking about the brain processes that are at its basis). So maybe, just maybe, quantum theory is our first indication of it.

If you're convinced "we will never know" how nature really works, then by all means don't spend your time trying to figure it out. But some people are not convinced of that; we are trying to find out how nature works. Personally I don't think "trying to figure out how nature works" is something that physicists should have to *apologize* for! We should be trying to do it, and we should be doing so proudly.

This is why I think, contrary to what you implied above, it does harm physics to take MWI seriously or to pretend that you do. It makes others feel embarrassed that they *can't* take that seriously, or that they believe physics should be taken seriously, etc. In short, it sends off a vibe into the rest of the physics community that "physics isn't serious", or "physics can never really figure out how nature works, so we just make up stupid stories that we don't really take seriously anyway", or "physics is all a big inside joke, but don't tell the government or they'll stop funding us", or god knows what.

Well, you misunderstood me, clearly. When I say that we will never know exactly what reality is about, I really believe that, because we had to change our views already a few times very profoundly, so we will have to do that again in the future, implying that at any moment, we are only in an approximative scheme (having given up, or not, to continue).
As such, I think that Newtonian physics is farther from reality than say, Maxwell's classical field view. And Maxwell's classical field view is farther from reality, than, say, general relativity. Or farther from reality than QM, with its MWI viewpoint. And MWI is farther from reality than *fill in our next paradigm*. I think however, that MWI is much closer to reality than Newton's viewpoint, for instance. But I'm aware that it will still change many times, and it is probably still too early to get it out of the speculative realm. In fact, as long as we don't have a serious theory of quantum gravity, I think it is too early to know. However, if the theory of quantum gravity DOES still adhere to the superposition principle, I think you cannot get by without MWI. So all string theorists and (I think) all loop quantum gravitists must be somehow "MWI" inspired. Superstrings makes no sense without MWI. But I'm very attentive to positions such as Penrose's, who thinks that gravity will play a crucial role in the measurement process in QM.

Well, as someone who has a lot of respect for people like Newton and Maxwell and Boltzmann and Einstein and Bell -- people who did take physics seriously and didn't think it was doomed to become a failure or a joke -- I don't think it's good to be spreading this kind of attitude. It will cause future Newtons and Boltzmanns and Bells to go into a field that does take itself seriously like, oh god, cultural studies, or basket weaving, or who knows what.

I'm affraid you could say the same about people trying to apply chemistry to organic materials, which were supposed to be "outside of the scope of science" at a certain point, and try to tell them to stick to minerals, if serious people were supposed to take chemistry serious in the future.
I really don't see why bringing in ideas such as subjective experience are blasphemy to physics. After all, one day, we will have to find out ! Before being able to make zargon ray machines of the second generation !
However, it might be that we are still far from that achievement, and that you 're right, that quantum theory as it stands, today, doesn't touch upon it yet, and we need a few more millennia of "positivist materialist science" before we get there. Nevertheless, I think it is funny that if you take QM very literally, you almost naturally arrive at MWI like situations.

However, this discussion showed me something. I think I really should learn more about Bohm's theory. All I know about it is in fact the 1-particle description.

So if you're willing, you can teach me some Bohmian mechanics ! Then I'm the guy making the nasty remarks, and you're the guy who has to explain and justify :-)

cheers,
Patrick.

 

[DrChinese]

So if you're willing, you can teach me some Bohmian mechanics !

I am interested in knowing more about how BM applies to EPR too.

As to the "paradigm" each of us uses... Who is to say what is best, really? I have seen this point argued ad infinitum in plenty of areas of science, and the answer is always inconclusive.

The fact is, any model (map) can serve a purpose. And a good idea can come from anywhere, even the most unexpected place. So there is not a lot of point to argue that one model is "better" or "more promising" because that can't really be objectively agreed upon.

For example, in the early sixties, who would have thought that the next big thing would emerge from a little city in England called Liverpool? Or that a Swiss clerk would emerge as the most powerful force in theoretical physics?

 

[vanesch]

I am interested in knowing more about how BM applies to EPR too.

As to the "paradigm" each of us uses... Who is to say what is best, really? I have seen this point argued ad infinitum in plenty of areas of science, and the answer is always inconclusive.

The fact is, any model (map) can serve a purpose. And a good idea can come from anywhere, even the most unexpected place. So there is not a lot of point to argue that one model is "better" or "more promising" because that can't really be objectively agreed upon.

This is true. I think the only thing that is not acceptable are logically inconsistent views: you know, things that give a different answer according to the way you arrive at it.

That's why I think that Copenhagen QM has a problem if we take it that the wave function is something "real". And the reason for that is that we arbitrarily have to decide which physical processes are measurements (which induce a collapse), and which physical processes are interactions (which evolve unitarily), and that we can in fact, choose between both for a great many of them, leading to different behaviours of our "real" wavefunction.

However, Copenhagen QM is perfectly all right if we see it as an abstract mathematical machinery out of which come predictions of probability (the "shut-up-and-calculate" approach). In this case, we take physical theories just to be epistemological: they just allow us to know answers, but they don't describe what is "really there". However, there is a danger that we apply the Born rule too early: we have to apply it only at the end, when we are really extracting probabilities that will be compared to experimental relative frequencies.

Nevertheless, a more ontological approach to a physical theory seems to be desirable: you would like to map things of the formalism to "things out there".
The question then is for how much deviation you allow from the existing formalism, and what principles you use in order to guide you to a formalism that IS ontologically mappable.

I would then think that an MWI like approach is what comes closest to the existing formalism: you take 2 basic principles which are at the basis of the theory (namely locality (in its minimalistic version: information locality), and the superposition principle) for "real" in that the machinery has to apply it too.
However, the result sounds "crazy" and you arrive at the use of "loony business" such as talk about subjective experience and so on.

If you give yourself more liberty with the formalism, I guess you can arrive at Bohmian mechanics. I have to say that this discussion gave me some incentive to learn more about it ; for instance, I was of the opinion that Bohmian mechanics had a serious problem with QFT ; but this may not be the case, I don't know. This is then a question if Bohmian mechanics is formally equivalent with any Hilbert state description or not. If it is not, then we're actually talking about 2 different theories, which will probably make different predictions for certain cases, and not about 2 different ways of viewing the same theory (namely quantum mechanics).

Whatever way you take, I suppose, as you say, that it is a matter of preference, as long as it is compatible with established results and is internally consistent.

cheers,
Patrick.

EDIT: Although predicting things is difficult, especially if it concerns the future, and - as you say - that inspiration can come from the most unexpected view, I would nevertheless allow myself to poder whether, say, if Bohm's view had been predominant, and not von Neumann's, whether one would have arrived at anything like quantum field theory...

 

[ttn]

I guess what you call "loony business" are concepts which you would rather classify as philosophical or spiritual, and not as materialistic science. But it is a long standing tradition that concepts which "didn't have their place in science" came into science when science grew sophisticated enough to deal with it. The human body was something beyond scientific investigation ; organic chemistry was something beyond scientific investigation ; the fact that humans could decend from apes and in the end from bacteria was something unheard of ; the movement of the heavens was beyond scientific investigation. All these domains have now been "invaded" by science. So why not the concepts of consciousness, "I experience" etc... ?

Oh, I have nothing against bringing new concepts into science. I guess I got the impression from your earlier comment that the point of bringing consciousness in the way you want to in MWI, however, wasn't really to clarify or build any new science, but, rather, merely because it was a convenient and safe place to "hide" the Born rule where it couldn't be refuted because it didn't make any contact with actual physics (i.e., physical objects). I think that is a pretty bad motive for bringing in new concepts into physics; so it's not that I'm against doing so per se, but only against doing it for what seems like really fishy, unscientific reasons.

So if you're willing, you can teach me some Bohmian mechanics ! Then I'm the guy making the nasty remarks, and you're the guy who has to explain and justify :-)

Well, maybe, but it really is easier to wear the critic's hat...

 

[ttn]

This is true. I think the only thing that is not acceptable are logically inconsistent views: you know, things that give a different answer according to the way you arrive at it.

I don't really want to get into a big debate over pure philosophy here, but I'm not sure I agree with this. In particular, I think you are using a too-narrow definition of "logical consistency" to mean merely narrowly-conceived internal consistency. I believe in scientific realism, part of which is the idea that the physical world we perceive is more or less real -- there really is a world that "looks" that way. Or putting it negatively, we aren't massively deluded (e.g., brains in vats) about everything we rationally believe. But MWI requires us to believe that we are massively deluded about pretty much everything we ever thought we believed. So why shouldn't I count *that* as a violation of "logical consistency"? To say that the only bad theory is one that makes two different predictions for the same one event, is, I think, to have a way-too-open mind about theories. How exactly to sniff out quality theories is a notoriously difficult quesiton; but there must be some sort of standards that go beyond mere blatant internal contradictions. If there aren't, then it's going to be impossible, e.g., to argue against the persistent "local realism" crowd who wants to suppose weird conspiracy theory type explanations for why 17 different experiments don't *really* prove that Bell's inequalities are violated... (not to mention a lot of other *way crazier* or even way more insidious junk.)

I would then think that an MWI like approach is what comes closest to the existing formalism:

The quantum formalism has two parts: unitary evolution and measurement/collapse. When you say MWI stays close to the existing formalism, you are already making a judgment call about which parts of that existing formalism are important and which aren't. But remember the reason for the collapse postulate -- without it, QM cannot predict the experimental outcomes which are actually *observed* and on which basis we believe in QM in the first place! So it wouldn't be all that crazy to think that *that* was the more important of the two aspects of QM. Of course, that doesn't leave you with much of a theory of anything (there being nothing to apply the collapse postulate *to* if you dump wave functions evolving unitarily...). But my point is broader: looked at from a "forest" perspective, wave functions and superpositions are the *least familiar*, most strange and new and suspicious looking parts of QM. The part that says "the probability of this needle pointing left is 50%" is by contrast very grounded, very familiar, very easy to understand. So I think one perspective on what MWI is doing is to dump the most familiar/intuitive/grounded aspects of QM and raise up in importance just those aspects that are least well understood and most unfamiliar. Again, maybe there's no blatant internal contradiction involved in doing this, but it's the kind of move which wouldn't be taken very seriously in other branches of science. That is, it would only be taken seriously if/when some other more obvious, better grounded moves had first been tried and found to fail.

If you give yourself more liberty with the formalism, I guess you can arrive at Bohmian mechanics.

I'm not sure what liberty you need. Basically, if you say, "QM is a theory about particles like electrons" -- and then you take that *seriously* and start to think about how the theory might be attached to a particle ontology -- you get Bohmian mechanics. I think it's far less "liberal" to believe that QM is about particles (if one knows the historical origins of QM especially!) than to think "hey maybe all those experimental results we thought argued for QM actually didn't have outcomes at all!"

I have to say that this discussion gave me some incentive to learn more about it ; for instance, I was of the opinion that Bohmian mechanics had a serious problem with QFT ; but this may not be the case, I don't know.

There are some problems, if you want to call them that. First, there have only been a handful of people working with Bohm's theory for 50 years. So obviously it hasn't been developed *nearly* as much as the standard approach. But several versions of Bohm-type QFT's exist, and I don't think there is any serious obstacle here. The second point is that people will often say that Bohm-type QFT's and such are "obviously wrong" since they are nonlocal and hence seem to violate relativity. But this objection is very wrong-headed. Really, it's just the same old debate about nonlocality from nonrelativistic QM all over again. Yes, Bohmian theories are rather obviously nonlocal (in the Bell locality sense...) and this remains true in the context of relativistic theories (Dirac equation, or QFT). But (drumroll please) so are all the *orthodox* relativistic theories, if you take them seriously, collapse postulate and all. And if all you mean is that regular QFT is *information local*, well, so are the "obviously nonlocal" Bohmian versions. So anyway, one has to be very careful here and keep an open mind about things like extra space-time structure like preferred frames, etc.

 

[vanesch]

I believe in scientific realism, part of which is the idea that the physical world we perceive is more or less real -- there really is a world that "looks" that way. Or putting it negatively, we aren't massively deluded (e.g., brains in vats) about everything we rationally believe. But MWI requires us to believe that we are massively deluded about pretty much everything we ever thought we believed. So why shouldn't I count *that* as a violation of "logical consistency"? To say that the only bad theory is one that makes two different predictions for the same one event, is, I think, to have a way-too-open mind about theories.

I didn't say that every logically consistent theory is a good theory ! I said that a good theory needs at LEAST this, and that the rest is open to debate, taste etc... I think it is a good idea to be very open minded a priori. And about being deluded not a right thing to do: hey, I believed in Santa Claus until I was 8 years old ! So I have the habit of being deluded. Nothing special about it.

How exactly to sniff out quality theories is a notoriously difficult quesiton; but there must be some sort of standards that go beyond mere blatant internal contradictions.

But all other standards are open to debate. You'll see that I have different standards.

If there aren't, then it's going to be impossible, e.g., to argue against the persistent "local realism" crowd who wants to suppose weird conspiracy theory type explanations for why 17 different experiments don't *really* prove that Bell's inequalities are violated... (not to mention a lot of other *way crazier* or even way more insidious junk.)

I agree with you that you need other criteria ; only, it is open to debate which criteria. If you allow to impose FIRST some criteria, then the LR crowd can put forward local realism as an unviolable criterium. You're closer to the LR crowd with your viewpoint than you think! Your viewpoint is that we cannot be "deluded" ; I guess this means: A theory that EXPLAINS correctly all results, but which has an underlying ontology which seems to differ with the intuitive picture you have of it, is a bad theory ? The problem is that this is so much dependent on what you can consider as your intuition that it is a dangerous viewpoint. The LR crowd cannot accept the violation of Bell locality ; it is against their intuition too. So if those 17 experiments have to go, and QM has to go, so be it, in order to stick to their intuition. In your case, if SR has to go, then so be it, in order to stick to your intuition.

My criteria is that one should look for fundamental principles which are at the base of the formalism and then stick to it at all costs. In (relativistic) quantum theory, these are the superposition principle and lorentz invariance (from which follows the need for information locality).
All my reserves come from the fact that another great principle, namely general covariance (of general relativity) has a serious clash with the superposition principle. So I expect a serious review of the fundamental principles when we will have a quantum theory of gravity. Such a revision will then imply a fundamental revision of all one can deduce, including MWI and everything. But usually, in such a paradigm shift, things only get weirder, not "more intuitive".

The quantum formalism has two parts: unitary evolution and measurement/collapse. When you say MWI stays close to the existing formalism, you are already making a judgment call about which parts of that existing formalism are important and which aren't. But remember the reason for the collapse postulate -- without it, QM cannot predict the experimental outcomes which are actually *observed* and on which basis we believe in QM in the first place! So it wouldn't be all that crazy to think that *that* was the more important of the two aspects of QM. Of course, that doesn't leave you with much of a theory of anything (there being nothing to apply the collapse postulate *to* if you dump wave functions evolving unitarily...). But my point is broader: looked at from a "forest" perspective, wave functions and superpositions are the *least familiar*, most strange and new and suspicious looking parts of QM. The part that says "the probability of this needle pointing left is 50%" is by contrast very grounded, very familiar, very easy to understand. So I think one perspective on what MWI is doing is to dump the most familiar/intuitive/grounded aspects of QM and raise up in importance just those aspects that are least well understood and most unfamiliar. Again, maybe there's no blatant internal contradiction involved in doing this, but it's the kind of move which wouldn't be taken very seriously in other branches of science. That is, it would only be taken seriously if/when some other more obvious, better grounded moves had first been tried and found to fail.

Well, as far as I know, they have failed as long as we stick to something that looks like special relativity !

I'm not sure what liberty you need. Basically, if you say, "QM is a theory about particles like electrons" -- and then you take that *seriously* and start to think about how the theory might be attached to a particle ontology -- you get Bohmian mechanics. I think it's far less "liberal" to believe that QM is about particles (if one knows the historical origins of QM especially!) than to think "hey maybe all those experimental results we thought argued for QM actually didn't have outcomes at all!"

I'm not denying this. But to me, basically QM is NOT a theory about particles like electrons. To me, QM is the formalism that goes with the superposition principle, and together with special relativity, it gives rise to things like quantum fields, which "look sometimes like particles".

But ok, if Bohmian theory also works for QFT, I'm interested to look at it...
Let's continue in the other thread then !

cheers,
Patrick.

 

[straycat]

Born rule and MWI

Hey Patrick,

I read the very interesting discussion that you had with Travis (hey Travis! ) back in Feb, and I have a question for you regarding how the Born rule fits into the MWI.

In your journal, you wrote:

The problem is that MOST of these "yous" will accumulate experiences which are NOT in agreement with the statistics of the Born rule. It is the problem MWI proponents never could solve (although they give a lot of "plausibility arguments"), and that's because they left out explicitly the Born rule.

This, I think, is a very interesting topic. Here's one way I might flesh it out with an example. Suppose we have N identically prepared spin 1/2 particles, prepared so that a spin measurement along the x-axis will yield spin up with, say, probability = p. (So we get spin down with probability 1-p.) If we measure the spins of each of these N particles, then we end up with 2^N worlds. At the end of these N measurements, the observer plans to calculate p by simply counting the number of particles that were observed to be spin up and dividing by N. The difficulty, as you point out, is that if p is not equal to 0.5, a significant number of these worlds will contain observers who conclude that the Born rule is incorrect! In fact, as N gets larger, the percentage of worlds such that the observed p deviates from the Born-rule prediction by some arbitrary cutoff (at least I think this is true -- I haven't actually shown this rigorously) just gets larger.

iiuc, Everett addresses this situation by defining a "probability measure" to each world which is, simply enough, prescribed by the Born rule. The conceptual difficulty here is that, in keeping with the "spirit" of the MWI, each individual world should be thought of as being on an "equal footing," so to speak. So what we have here are, in a sense, two different ways of counting worlds: by one method, we simply count the number of worlds via treating each distinct experimental outcome as one distinct world, so that, in the above example, we get 2^N worlds; by the other method, we give each of these worlds a "weighting" which is proportional to its Born-prescribed probability. The former method is in keeping with the "spirit" of the MWI by putting each physically distinct world on an equal footing, but suffers from the difficulty that most observers will think the Born rule to be false. In latter method, the set of worlds in which the Born rule is violated is of measure zero (as Everett, Hartle, and others have shown); however, we are in a way breaking with the "spirit" of the MWI.

If we want to rescue Everett's notion of attaching a probability measure to each experimental outcome, one thing we could do would be to say that -- to take a single spin measurement as an example -- instead of splitting into TWO worlds, we instead split into P_tot = P_up + P_down worlds, where p = P_up/ P_tot is the Born-rule given probability of observing spin up. P_tot, P_up, and P_down would, according to this scenario, be integers. And since in general, p can take on any value between 0 and 1, p_up and p_down would typically be expected to be able to be extremely large integers! In fact we can already see a problem here: if we assume P_up and P_tot to be integers, then we are effectively saying p must be an element of the rationals (ie, it cannot be any real-valued number in [0,1].)

A second problem is that, in the simplest scenario at least, there is no PHYSICAL distinction between one observer who ended up in one of the P_up worlds, and another observer who ended up in another of the P_up worlds. Now there is no strong reason to object to this scheme -- it's just that it seems, well, ill-motivated. Why should one observer split into P different directions, when all of them that split into the P_up direction are physically identical? It seems so unfrugal. (Is that a word? )

This is about as far as I have gotten in thinking about this particular topic. So let me turn to my question for you. Earlier you wrote:

Well, I'm not a real MWI-er. What you write (get rid of the Born rule) is indeed part of the program of MWI, and I think I have found a mathematical proof that this cannot work, which I hope to publish soon.
I think that there is some real need for the Born rule. On the other hand, I want to get rid of the projection postulate, and up to there, I follow MWI.

I've been doing a little background reading on the MWI -- for instance, I managed to get a hold of Everett's original dissertation from amazon -- but I have not yet run across anyone trying to "get rid of the Born rule." What does this mean, exactly? And what is your argument that "this cannot work?" I am intrigued.

straycat

PS The book that I got from amazon has a very interesting (not published elsewhere, afaict) decades-old article by Neill Graham, one of Bryce DeWitt's former students, addressing this very topic. He lays out the basic issue very nicely, I think, although I'll admit that I cannot follow his "solution."

 

[vanesch]

iiuc, Everett addresses this situation by defining a "probability measure" to each world which is, simply enough, prescribed by the Born rule.

But there is a problem in doing so. Indeed, in order to be able to apply a Born rule, you have to choose a preferred basis (the measurement basis). It is different if you apply the Born rule for "position" or for "momentum". It is different if you apply the Born rule in the z-spin basis, or in the x-spin basis. The only thing that distinguishes the measurement basis from any other basis, from an observer's point of view, is that in the measurement basis, he appears in a Schmidt decomposition (sum of |observer state> |system "measurement" state> components) while this is not the case in other basis states. But that's of course observer-related! So you can only define that measure AFTER having choosen already a basis. Honestly, you're then just applying the projection postulate.

The conceptual difficulty here is that, in keeping with the "spirit" of the MWI, each individual world should be thought of as being on an "equal footing," so to speak. So what we have here are, in a sense, two different ways of counting worlds: by one method, we simply count the number of worlds via treating each distinct experimental outcome as one distinct world, so that, in the above example, we get 2^N worlds; by the other method, we give each of these worlds a "weighting" which is proportional to its Born-prescribed probability.

The problem with this statement (which I endorse !) is that MWI says:
i d/dt psi = H psi AND THAT'S ALL. The original program (as I understood it) was that we could then derive all physical consequences from it, also the "observed" probabilities by observers. This was in a reaction to the Projection Postulate, which has a lot of problems, namely distinguishing "measurements" from "physical processes".

So when do we assign this "measure" to different terms in the wave function ? This is bluntly introducing the Born rule again!

Let us look at an example:
Imagine that I've been measuring the z-component of an electron spin ; so now the wavefunction is:

|psi> = Sqrt[0.9] |me+> |z+> + Sqrt[0.1] |me-> |z->

In an MWI setting, the idea somehow is that "a real me" only observes ONE of these branches. So there must be some kind of splitting of "me", so that there is now a "me" that will "have measured" the plus component, and that will now work in the first branch and a "me" that will have measured the minus component and will now work in the second branch.
There are NO PROBABILITIES involved in this game. BOTH happen.
What *I* am claiming is that in order for probabilities to arise (namely that I have 90% chance to be me+ and 10% chance to be me-), you HAVE TO MAKE AN EXTRA ASSUMPTION, and that extra assumption amounts to the Born rule: I explicitly consider this a "measurement process" and assign probabilities to the outcomes according to the Born rule. The way I prefer to do it (as I tried to explain in my journal), is by saying that although there are now 2 different body states (nothing surprising, there are also 2 different electron spin states), my "consciousness" has TO CHOOSE, ACCORDING TO THE BORN MEASURE, which body state it will live in. So I put the "measurement process" into the "inhabiting of a body state by my consciousness". But then we get easily into metaphysical discussions, and I don't want to here again. Say that it is some shortcut to make the picture work.

Remember, in a true MWI view, ALL "branches" or "worlds" (simply, Schmidt decomposition terms in the wave function and a choice of a system which is the "observer") "happen" (because simply all terms are present in the wave function), and there is no a priori probability of anything. It is very difficult to assign probabilities to terms in the wavefunction without introducing (again) a distinction between a "physical process" (you don't assign probabilities) and a "measurement" (you assign probabilities). And this was the difference (measurement/process) Everett wanted to get rid off in the first place.
The only way to introduce probabilities in a natural way is by "inhabiting" these terms with observers, according to a kind of probability measure, and the whole point of MWI, as I understood it, was that this probability measure would emerge "naturally" (by counting of something, say). Clearly, simply counting the terms doesn't work, so you can think of more complicated schemes: but then you have to POSTULATE these schemes somehow, and this postulate usually comes down to the Born rule.

cheers,
patrick.

 

[ZapperZ]

Hey Patrick,

I read the very interesting discussion that you had with Travis (hey Travis! ) back in Feb, and I have a question for you regarding how the Born rule fits into the MWI.

Well it's about TIME you join in the fun, straycat! Took you long enough! :)

Zz.