Why MWI cannot explain the Born rule

Dmitry67

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

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

Dmitry67

So are you saying that some properties visible in the frog's view cant be derived mathematically, even in principle, from birds view? So even when we have an ultimate TOE equation, we cant explain everyhting we observe?

Demystifier

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

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

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

toho

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 cant 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.

toho

Well, the MWI is only deterministic to an outside observer who is able to observe the wave function. An observer - a brain - in the universe is described by the wave function just as everything else. The state of that brain can be entangled with the outcome of an event, just as two spins can be entangled.

My point is, according to the MWI, our perception of the outcome of a future event is uncertain. If we want to use probabilities to describe the likelihood of (our perception of) the outcome, there is only one sensible probability measure (i.e. there is only one way to assign the probabilities). That is the Born rule. If I understand your interpretation of MWI, you believe that it is possible to assign probabilities in a way so that events that are exceedingly rare according to the Born rule will have much larger probabilities. I don't think that is possible to do in a systematic way without violating the axioms of probability.

That is essentially what I am saying (you would need regularity conditions, I guess). But I don't see it as a weak form of the Born rule. If the universe is uniquely determined by the wave function, then any probability measure must surely be derived from the wave function as well. Otherwise there is additional information outside of the wave function.

Dmitry67

1 Yes, so called "birds view" (c) Max Tegmark

2 Well, lets forget about our expectations of the future. How do you explain Born rule as statistics of the past events? Say, I have a substance with half decay time of 1 minute. I take 1'000 atoms and wait 1 minute. 500 (or 498 or 501 atoms) decay. But it is very unlikely the ALL of them decayed or NONE of them.

But in MWI where are 2**1000 branches (if we assign number to every atom and register everything) and all of them equally valid.

So how do you explain that?
So lets talk about frequentist probability, not ignorance (bayesian) probability

3 In general, no. With some exceptions (I can give clarifications)

4 Yes, I believe it is called officially "measure of existence". I agree on that, so letas return to the main issue - issue #2

BTW I found the article I menationed:
http://plato.stanford.edu/entries/qm-manyworlds/#6.3

toho

Explain what exactly? You have 2^1000 branches. In any probabilistic interpretation of physics where you would assign an equal probability to each sequence, then the sequence that you actually observed had a probability of 1/2^1000. The same very low probability as that of observing 1000 decays in a row. Any outcome observed will have been exceedingly improbable before the fact.

As soon as you start computing statistics you are in probability land, and then there is only one way to assign probabilities in MWI that makes sense - Born. Any other rule for assigning probabilities is unphysical in the sense that it would place you - your conscious, your brain - in a favoured position in the universe. If the same rule for assigning probabilities shall apply to the entire universe, then Born it is.

Of course, you can drop the probabilistic interpretation, but then the problem goes away. You just accept that you are in a branch that has 501 decays, conclude that it is consistent with QM and MWI and go to the beach.

toho

Thanks for the link. I will read as soon as I find time.

Dmitry67

So we agreed that we can't use frequentists approach over the set of branches, because it gives incorrect results (like having 50% change to win in any lottery because there are 2 branches - where I win and where I dont)

But the part marked Bold looks as axiom. I agree with that sentence (so we have almost agreed), but you are just introducing a Born rule as axiom. FAPP it works, but I just wanted to dig deeper, so let me play devils advocate.

Returning to the toy example I provided many pages ago. There are 2 outcomes Frequent (90%) and Rare (10%). I do 3 tries, I get 8 branches from FFF (72.7 %) to RRR (0.1%).

Now we are both Gods, using the Bird's view, looking at the wavefunction from the outside. As God, I also have a magic monitor: I doubleclick on the desired branch and monitor shows how that branch looks like. I click on RRR and I hear the words of experimenter "What the hell? Is it mulfunctioning?" I click on FRF and I hear "As expected... Boooring..."

Now I ask - what does the probability means from that point of view? Can "Gods" talk about the Born rule?

toho

No, I am not introducing it as an axiom. I mean that sentence in the context of the conjecture before (and you provided a link that says there is indeed a theorem saying more or less the same thing). There is only one set of probabilities that are sensible (in a mathematically precise way). That happens to be the Born rule. Thus, there is a way to derive the Born rule from first principles. You may (probably will) need more axioms than the two posted at the beginning of this thread, or at least you would need to make them more precise, but you don't need to postulate the Born rule. It can be derived.

You can use probability theory whenever there is incomplete information, but the result of your calculations depend on the probability measure you are using. Usually, there is no favoured probability measure, such as when calculating the probability of future stock market moves. Sometimes you can use statistics to fix probabilities. Sometimes you can use symmetry arguments to fix probabilities, and that allows you to make much more precise calculations. But in MWI there is no freedom with regards to the probability measure.

Using probability is a choice. It is a way to mathematically treat a system where you don't have complete information. So, sure, we as Gods can use probability theory, if only to calculate probabilities of outcomes that the actors in the world we are observing should reasonably expect with the information available to them.

Because of Bell's theorem, I guess many physicists tend to look at probability in QM as something fundamentally different from probability in deterministic games of chance with incomplete information, such as coin flipping. But I think that is really just a mystics position. Probability is probability. It is a way to calculate, and it follows from a few simple axioms. Nothing more, nothing less.

Dmitry67

Well, I tried to explain but apparently my explanation was confusing.

So let me continue playing the devil's advocate, to take my logic to extreme and to deny the Born rule. In the toy example above, I claim that F and R have the same probability. Here is a logic:

There are 8 branches: RRR, RRF, RFR, RFF, FRR, FRF, FFR, FFF
I incarnate myself in all of them and count the number of times I see F and R
I get 12 R and 12 F. Hence I have 50% chance to observe R and F.
Prove that I am wrong :)

Now you say: but wait, more often we appear in the more probable branches, like FFFFRFFFFRFFFFF..., not like RRRRRRRRRRRRRR... So this is what you do: you get all branches, then you prepare some artificial subset of them based on the Born rule (thinking: I have more chances to appear in the ..FFFF.. branch), then you say: look, the number of Fs and Rs obey the Borns rule! So it is cyclical.

Born rule is encoded not when you count the number of F's and R's in some branch, but when you select that branch.