Why MWI cannot explain the Born rule

[jensa]

That is odd. I can view it just fine. What happens if you use this link:

http://books.google.com/books?id=6eTHcxeNxdUC&lpg=PP1&pg=PA175#v=onepage&q=&f=false

 

[Demystifier]

That is odd. I can view it just fine. What happens if you use this link:

http://books.google.com/books?id=6eTHcxeNxdUC&lpg=PP1&pg=PA175#v=onepage&q=&f=false

It gives me no more than 101 pages plus the back cover. How many pages can you see?

 

[jensa]

It gives me no more than 101 pages plus the back cover. How many pages can you see?

Oddly I can see pages 134-180 + the first few pages with table of contents etc + backcover. I am a little confused as to how the preview feature works...perhaps its either 101 first pages or part of a chapter of your choosing.

You could try amazon as well, at least I am able to look at that particular section (searching for page 175).

https://www.amazon.com/dp/3540003908/?tag=pfamazon01-20

 

[Demystifier]

Oddly I can see pages 134-180 + the first few pages with table of contents etc + backcover. I am a little confused as to how the preview feature works...perhaps its either 101 first pages or part of a chapter of your choosing.

Perhaps different pages are allowed in different countries?
It is the fact that some web pages have different appearance in different countries. For example, on the top of page of this Forum I often see an advertisement for an IQ test in CROATIAN language (I live in Croatia).

 

[Fredrik]

Google books uses cookies for something. (I'm not sure what). So I would at least try clearing out the cookies from the browser, and also make sure that it allows cookies from that site.

 

[Demystifier]

*) See the book "Decoherence and the appearance of a classical world in quantum theory" by Joos, Zeh, Kiefer, Giulini, Kupsch and Stamatescu in the section entitled "True, False and Fake decoherence". I personally prefer this book over Schlosshauer's.

Now I have noticed that Schlosshauer also explains the notions of true and fake decoherence, but does not mention false decoherence. Could you be so kind to explain to me (by your own words) what false decoherence is and what is the difference between false decoherence and fake decoherence?

 

[jensa]

Now I have noticed that Schlosshauer also explains the notions of true and fake decoherence, but does not mention false decoherence. Could you be so kind to explain to me (by your own words) what false decoherence is and what is the difference between false decoherence and fake decoherence?

Well, I hope I didn't give the impression that I am some kind of expert in decoherence, I'm certainly not. But I can try to explain what I understand from the the book. Joos describes false decoherence as when "Coherence is trivially lost if one of the required components [of the wavefunction] disappears". I'm not sure really how to interpret this sentence, but he gives two examples of such cases 1) Relaxation 2) When we are considering only a subset of all available states.

Let's start with what I think is the easiest one no. 2). It is sometimes convenient to use a truncated model to describe a system. For example, many qubit implementations are in fact multilevel systems although we choose only to consider the two lowest energy levels as an operational subspace. It is clear that there is a certain probability of "leakage" out of this subspace, this process also produces suppression of the off-diagonal elements of our density matrix, however it also does not conserve probability (within the subspace). Coherence is not really lost here, it's just a consequence of our truncated model.

As for Relaxation, it should originate from interaction with an environment (since energy is not conserved). So I suppose the point he is trying to make is that interaction with environment can produce "true decoherence" which is a pure quantum effect, as well as an exchange of energy which also occurs for classical systems. Relaxation, although it also suppresses the off-diagonal elements of the density matrix, should be distinguished from "true decoherence".



If you would like, I could scan the pages and send them to you. Would be nice to see what somebody else makes of it.

 

[Demystifier]

Thanks jensa, it was a quite clear explanation.

 

[Dmitry67]

Here is a radical view. What is Born rule does not need to be derived from MWI? What if Born rule is not objective but subjective?

Usually we look it from the inside (frogs perspective): I am looking at the world and I observe more frequent event than events with lower probability. How is it explained by MWI, while all possible outcomes exist in omnium? I think that this question is incorrect. We should ask an inversed question instead: We know that all branches exist, why there is “more” conscious observers with the higher “intensity of existence?”

I can give you another example. Say, we have a very powerful computer and we know TOE. So we were able to calculate the “wavefunction of the Universe” from moment 0 (initial conditions at BB) to, say, 1 second. Not just one “branch”, but omnium at whole, the global solution. There are no conscious observers, however. But do we need a Born rule as soon as we know the global solution?

In fact, once you look at the Universe from ‘bird’s view’, having the solution of the evolution of the omnium, there is no Born rule. We have a solution, that’s it. Born rule appear when we try to jump inside the Universe, converting from a single birds view to some arbitrary frog’s view. At the moment of the choice you already implicitly use the Born rule, choosing “more intensive” branch. In such case the Born rule – which is so obvious when we look around – is nothing more then an illusion, created by our consciousness, similar to so obvious flow of time

 

[Demystifier]

Dmitry, I don't see that this view explains the Born rule in any quantitative sense.

 

[Dmitry67]

Well, my idea was that it Born rule is just an illusion created by our consiousness.
It is a part of theory of consciousness, not a part of physics.

 

[Dmitry67]

Suppose, there are 2 outcomes of some experiment: (F)requent (90%) and (R)are 10%
We repeat this experiment 3 times.
Obviously, there are 8 branches, begiining from F-F-F to R-R-R
Why do we see F events more often then R events?

Check the picture.
There is no difference between F-F-F and R-R-R at the birds view.
In the frog's view (asking "what observer will see?") you must define the basis (a point on my diagram). So we chose (for some mysterious reason, I agree) the point showed by red cross and ask: why in the history of that observer there are more Fs then Rs?

So Born rule is not about physics, it is about how consicous observers are chosen.

 

[pellman]

So we chose (for some mysterious reason, I agree) the point showed by red cross and ask: why in the history of that observer there are more Fs then Rs?

The "mysterious reason" is the crux of the whole question.

Although the question "why in the history of that observer there are more Fs then Rs?" is somewhat troublesome. There are 8 potential observers. One of them sees F-F-F. And we chose to label that one with the X.

But what is special about that observer?

 

[Count Iblis]

In the bird's view there is one timeless multiverse. What we experience as time evolution is just a unitary mapping from one sector of the multiverse to another. At the level of the whole multiverse, time does not exist.

In this case you have some sector containing the initial observer |i>, which maps under the time evolution operator to a |F> + b |R>. It is this time evolution operator which is subjective to the observer. In the bird's view time does not exist and you could have considered any other unitary operator.

For the observer things are different. An observer is essentially an algorithm that processes information. To define the algorithm as it is in any particular computational state, you have to list the outputs for each possible input. This defines an operator which is essentially a sort of coarse grained Hamiltonian which generates the time evolution experienced by the observer.

You cannot just define an observer by looking at a sequence of the states it runs through, because you can then map that to the states of a clock which does not execute a nontrivial algorithm. You have include the information about counterfactual inputs and the corresponding counterfactual outputs, which will not be mapped correctly from the observer to the clock.

Note that the information about the correct Hamiltonian is not present in the bird's view, because if H is the "correct" Hamiltonian, the whole multiverse satisfies an equation like:

H|psi> = 0

There is then no way you can construct H back from|psi>. You can replace H by any other Hamiltonian that except for |psi> has different eigenvectors.

 

[Dmitry67]

The "mysterious reason" is the crux of the whole question.

Although the question "why in the history of that observer there are more Fs then Rs?" is somewhat troublesome. There are 8 potential observers. One of them sees F-F-F. And we chose to label that one with the X.

But what is special about that observer?

I can provide a part of an answer by giving another example:

the moment of "NOW"

This is also a big red cross, a moment very special to consciousness. But as we believe in block time, physically there is absolutely nothing special about NOW!

So if our consicouness can break symmetry on T axis, creating an illusion of a special moment 'NOW', then why it can't create another illusion on B-axis (Branch axis. Yes, I am aware that it is not an axis at all)

 

[Dmitry67]

You cannot just define an observer by looking at a sequence of the states it runs through, because you can then map that to the states of a clock which does not execute a nontrivial algorithm. You have include the information about counterfactual inputs and the corresponding counterfactual outputs, which will not be mapped correctly from the observer to the clock.

This sounds very interesting but I am lost at the part I quoted
Could you elaborate?

 

[Demystifier]

Well, my idea was that it Born rule is just an illusion created by our consiousness.
It is a part of theory of consciousness, not a part of physics.

Does this mean that such a theory does not need to have a quantitative form?

 

[Dmitry67]

Yes, but we can use Born rule for practical purposes. As a rule of thumb

For example, NOW we are 13.7 billion years from the BB, or 8.2*10^60 plank times from the Big Bang

Can you derive somehow this integer dimensionless number (8.2*10^60) from BM?

 

[Demystifier]

You can use the Born rule as a rule of thumb.
However, if it is the best that MWI can do about the Born rule, then BM is much more successfull than MWI because in BM the Born rule is much more than a rule of thumb.

 

[Demystifier]

Can you derive somehow this integer dimensionless number (8.2*10^60) from BM?

Of course I can't. If you give me a theory that can, I will accept that theory immediately. Moreover, if that theory turns out to be incompatible with BM, I will reject BM as well. But in the meantime, I will keep BM as the most attractive possibility currently known.

 

[Dmitry67]

You can use the Born rule as a rule of thumb.
However, if it is the best that MWI can do about the Born rule, then BM is much more successfull than MWI because in BM the Born rule is much more than a rule of thumb.

Yes, there is some advantage, but it is too weak.
Observer is point is some space, and history is a curve.
While BM limits the number of curves to 1, it does not limit the curve to a single point. So I think the claim 'MWI does not explain what is observed now' is to the full extent applicable to BM. It just slightly limits the number of degrees of freedom, where we can put that red cross.

 

[Dmitry67]

Of course I can't. If you give me a theory that can, I will accept that theory immediately. Moreover, if that theory turns out to be incompatible with BM, I will reject BM as well. But in the meantime, I will keep BM as the most attractive possibility currently known.

Hm. Do you think that symmetry breaking (NOW vs not-NOW) must be explained by physical theiry? It sounds very Smolin-like.

 

[Dmitry67]

Note that the information about the correct Hamiltonian is not present in the bird's view, because if H is the "correct" Hamiltonian, the whole multiverse satisfies an equation like:

So are you saying that some properties visible in the frog's view can't be derived mathematically, even in principle, from birds view? So even when we have an ultimate TOE equation, we can't explain everyhting we observe?

 

[Demystifier]

Hm. Do you think that symmetry breaking (NOW vs not-NOW) must be explained by physical theiry?

Maybe yes, maybe not.

 

[toho]

Regarding deriving the Born rule from the MWI, here is a conjecture:

The Born rule is the only probability measure, Q, consistent with the criteria that
i) P(A)=0 iff L2-norm of psi over A = 0, for every A in the limit as time -> infinity
ii) Q is a function of psi, for any psi consistent with QM

I.e. if you want a probabilistic interpretation of the MWI interpretation of QM, it has got to be the Born rule. (It think it would be possible to relax the t->inf critera, btw)

 

[Dmitry67]

I.e. if you want a probabilistic interpretation of the MWI interpretation of QM, it has got to be the Born rule. (It think it would be possible to relax the t->inf critera, btw)

Yes, if you want to use MWI practically, you need to add Born rule as new axiom
That axiom is not purely mathematical (as MWI is deterministic and does not know the word "probability")
Also, sometimes Born rule is violated (Anthropic principle)

On the deeper level Born rule can not and should not be explained by MWI, but rather by a future theory of conciousness.

 

[Count Iblis]

So are you saying that some properties visible in the frog's view can't be derived mathematically, even in principle, from birds view? So even when we have an ultimate TOE equation, we can't explain everyhting we observe?

I believe you can explain in principle everything, however the predictions may be dependent on the specification of the frog.

 

[toho]

Yes, if you want to use MWI practically, you need to add Born rule as new axiom

On the deeper level Born rule can not and should not be explained by MWI, but rather by a future theory of conciousness.

No, my point is that you don't need to add the Born rule as a new axiom. (Provided that the conjecture is correct, which I am pretty sure it is. You do have to accept the axioms of probability theory, though.) The Born rule is the only sensible probabilistic interpretation of the wave function.

I don't think the Born rule has anything to do with conciousness at all. If you accept MWI, you will also have to accept that there are multiple versions of your conciousness in orthogonal branches of the universe.

A probabilistic interpretation is indeed practical in many situations, analogous to how a probablistic interpretation of a determistic but unpredictable outcome, such as a coin flip, can be practical.

(I edited the conjecture after your posting, by the way. It wasn't very clear as originally stated.)

 

[Dmitry67]

Ok, so you have an explanation, so I will challenge you.

What is Born rule in MWI? MWI is deterministic. So Born rule in MWI is not about what we see, but it is about how we chose the preferred basis for the consciousness In another words, it is about brid->frog transition, or about how particular frog is chosen

As "measure of existences" never fades to 0, there are all sorts of weird branches where all sorts of weird things happen (and one of such things is life). We should see all of them, then why FAPP we expect to see frequent events?

So I ask clarification on your waords about how we can use a probability interpretation in MWI. I think the root of the problem is there.

 

[Dmitry67]

P.S.
I can't find it right now but I am sure I have seen it somewhere, some form of "weak" Born rule: so if we assume that probability is some function of wavefunction, then we can derive the Born rule.