# MWI and Born Rule

1. Jun 23, 2010

### ThisIsMyName

I've been thinking a lot about MWI and probability lately and I can't say desicion theory is very convincing.
Obviously if MWI can't derive at the Born Rule, it is falsified.

Do you feel that MWI will ever make sense with probabilities or do you believe we can put MWI in the trashcan and start working on something else?

2. Jun 24, 2010

### Demystifier

3. Jun 24, 2010

### Demystifier

My opinion is somewhere in the middle. I think that MWI is correct, but not complete. In other words, the main ideas of MWI should not be rejected, but these ideas should be supplemented with some additional axioms/assumptions needed for the completion. A prominent example of such a completion is the Bohmian interpretation.

4. Jun 24, 2010

### ThisIsMyName

Mainly because a lot of people seemed uncertain about their views, so I figured maybe they had made their minds up now.

5. Jun 24, 2010

### Dmitry67

My opinion: Born rule is an illusion, created by our consciousness. Like 'NOW' or 'Flow of time'. There is no 'NOW' in spacetime, and time does not 'move'. It is quite obvious in SR and GR, while our common sense reasoning is crying the opposite. But who believes in our 'common sense reasoning' after so many spectacular failures?

Note: How can you derive Born rule in MWI if Born rule can't be even formulated in MWI framework? Hint: MWI does not know the word 'probability'. To start talking about Born rule one need to provide good (observed dependent? what observer? in what branch?) definition of a probability.

6. Jun 24, 2010

### cesiumfrog

Is there a simple exposition of the decision theory argument someplace?

7. Jun 24, 2010

### Demystifier

http://arxiv.org/abs/0808.2415

In particular, the author clearly emphasizes the crucial (and controversial) assumption called "Equivalence assumption".

Last edited: Jun 24, 2010
8. Jun 24, 2010

### ThisIsMyName

Dmitry67, I think everybody that has ever thought about MWI and Probability has thought of something similar.
However this doesn't let MWI off the hook, the emperical evidence still flies in the face of MWI.
Even if you say probabilities are a illusion, observation still shows Born Rule, in MWI it wouldn't.

So saying probability is a illusion or a pink elephant doesn't change anything...
MWI is still falsified until it can account for emperical evidence.

9. Jun 25, 2010

### Dmitry67

Then SR and GR are falsified too, because they use the concept of 'Block time' (eternalism) while the 'emperical evidence' tells us the opposite.

10. Jun 25, 2010

### ThisIsMyName

Dmitry67, no.
Neither is a spherical earth falsified just because our senses tells us that the earth is flat.

Let's say you set up a experiment much like the Schroedingers Cat.
Except instead of having the cat die/live lets picture 2 light bulps.
1 Red and 1 Blue.
Probability for the red one lighting up 0.001 and 0.999 for the blue one.
Carry out this experiment 1000 times in a row, and you'll have 1 occurence of red light, and 999 of blue light.

In the MWI picture, you'd expect to see 50/50 of red and blue lights since the universe branch off into 2 results everytime.
1 blue light universe and 1 red light universe.

How you can say "well in the future we might discover some theory of consciousness that shows probability is a illusion" are supposed to solve this, is really not an answer.

You could just as easily say the same for any interpretation, that a "future theory of consciousness" will explain everything and that superposition is just a illusion created by our brains and that no such thing ever existed, and therefore we can refute all interpteation of quantum mechanics...

You don't see the problem with this approach?

11. Jun 25, 2010

### K^2

The problem of Borne Rule in MWI is the same as that of classical statistical weights with "random" chance.

Say you have a bag of marbles. 1/4 of them are white, and 3/4 are black. What are the odds, at random, of pulling a white marble? 1/4. Can you prove it?

MWI results in something very similar. You end up with a superposition of world-states with observer being entangled to these. You can think of it as continuum of possible states with there being more of some states than the others. The rest is just like pulling marbles at random. Sure, you end up in all of the future states, rather than just one, but you are currently experiencing just one state, and currently, your odds of experiencing one state over another are proportional to the number of states. Just like pulling a marble, only your experience of pulling the marble is also part of the marble.

12. Jun 25, 2010

### Dmitry67

Yes, there are both branches, no matter how low is the probability of the 'rare' event.
MWI predicts that both branches exist.
It predicts, that in 'normal' branch experimenter would say - you see, Born rule works!
In weird branches it predicts that experimenter would say - WTF???
Exactly what is happening.

Lets look again at your experiment. You make the experiment 1000 times, and with 2 outcomes you get 2^1000 branches. To simplify, lets assume that you make it only 3 times and (as expected) always get the 'frequent' outcome: FFF. There are other branches like R(are)FF, FFR and even RRR.

So what you are doing from the god/birds view? You are doing the unfair sampling. You put your finger on the point of the Unverse wavefunction where FFF is true and ask: why Born rule is valid here?
Next question: But why our consicousness appear on the most frequent branches?[/]
Answer: It must be studied by the theory of consiousness

13. Jun 25, 2010

### ThisIsMyName

So Dmitry67, after several failed attempts by Wallace, Greaves, Deutsch and a few others, instead of thinking... gee maybe there is something wrong with this interpretation, you choose to "postpone" the problem to the future where it MAY somehow make sense in a theory of consciousness?

I am a firm believer that consciousness is nothing special, but hwat you are suggesting is very special, so this would be like a new axiom, hence the "elegance" of MWI is out the window.
Atleast until you have this theory of consciousness, and you have once again managed to put consciousness in the middle of the measurement problem.
Exactly what MWI tries to avoid.

14. Jun 25, 2010

### Fredrik

Staff Emeritus
People have tried to do such things, but failed miserably. Kent's article "Against many-worlds" has comments about some of them.

This is incorrect. No MWI that I've heard of predicts violations of the Born rule.

I don't think consciousness is anything more than physical interactions in a system that's also interacting with its environment, but I still think consciousness has a role to play in a more straightforward MWI (...one that doesn't throw away the Born rule). Something like...when a subsystem of the universe (e.g. an atom) interacts with its environment (which includes a measuring device and a physicist), there are many ways to decompose the universe into "worlds", but there's only one decomposition that produces worlds where the subsystem's environment can contain stable records (e.g. memories in a human brain) of the result of its interaction with the subsystem. So "consciousness" isn't actively changing anything, but the "branches" would be defined by the only decomposition into "worlds" that describes worlds were information can be stored...and those are the only ones that can contain conscious observers.

15. Jun 25, 2010

### GeorgCantor

Alternatively, one could give up dreaming of a theory of everything.

16. Jun 25, 2010

### Dmitry67

No, I dont suggest to give up or postpone, I am just thinking that the question is much deeper than one expects. Trying to 'explain' Born rule in its current form is nothing more like a desperate "brute force attack" (it terms of computer science). Born rule must be reformulated before we can try to 'explain' it.

And yes, consciousness (closely related to AP) is special. For example, we are now 13.7Gy away from Big Bang. But no observers can observe anything before say 10^6 years. Do you agree? This is another example of unfair sampling.

17. Jun 25, 2010

### ThisIsMyName

18. Jun 25, 2010

### Demystifier

Then you have not heard enough.
See e.g. the contribution of Graham in the book
B.S. DeWitt and N. Graham (eds.), The Many-Worlds Interpretation of Quantum Mechanics

19. Jun 25, 2010

### ThisIsMyName

Any of the proponents actually read the papers or seen/heard the talks by people like David Albert, Adrian Kent, Huw Price, Tim Maudlin, Roderich Tumulka etc.?
These present pretty clearly the problems of MWI.
Even proponents of MWI have accepted that MWI is hanging by a very thin thread, check out Jacques Mallah www.onqm.blogspot.com
He goes through each argument and debunks it and present a last resort, which too have major problems.

20. Jun 26, 2010

### Fredrik

Staff Emeritus
I think we briefly talked about that article before. I haven't really tried to understand it. It didn't look good to me, and it gets thoroughly trashed in Kent's article. (That whole book looks pretty bad).

I think they're good arguments against Everett's MWI, which isn't so much of an interpretation of QM as a redefinition of QM. But I would also say that if you just postulate that QM (as defined by the standard axioms) actually describes a physical system, you have actually defined a MWI that can't be debunked.

Max Tegmark mentioned Kent's "Against many-worlds interpretations" in his "Many worlds or many words". He dismissed it in a way that I find rather interesting. He just said that "...most of its claims were subsequently shown to result from misconceptions[31]". That reference [31] looks pretty bad to me, and as far as I can tell, it hasn't been published anywhere. It's interesting that a peer-reviewed article can dismiss another peer-reviewed article as useless nonsense simply by referencing something unpublished that probably is useless. Makes me wonder how much peer review really means.

Last edited: Jun 26, 2010
21. Jun 26, 2010

### ThisIsMyName

Sure it can't be "debunked" as ghosts can't be debunked, because you can always move the goal post "nono but the ghosts are invisible so by definition you can't prove them, but they DO exist".
It's that kind of pathetic logic.

Then again NO interpretation that fits the standarf formalism can be debunked in anyway...
However when MWI can't make sense of probability, has problems with SR and more problems you can say it's debunked.

I'll look into Tegmarks criticism, but remember that "against MWI" paper was from 1990, Adrian Kent has published a lot more papers after that showing how MWI struggles.
Not to mention his talks you can see here: http://pirsa.org/index.php?p=speaker&name=Adrian_Kent

Also lets not forget that Tegmark is the multiverse mania guy, he doesn't just believe in other universes out of some rational conclusion, he WANTS there to be other universes, he has like 4 different levels of multiverses without any proof.
So obviously he'll dismiss any criticism out of emotional response, not logic or rational thinking.

I agree that peer reviewing is biased, if the reviers prefer MWI, they'll publish it, if they don't they may point out errors.

What interpretation do you adhere to?

Also, even if you take the wavefunction to be physically real and represent everything you doesn't inevitably end up with a many worlds picture, you can just as easily end up with a single world picture which select a random world in accordance with Born's rule, as Adrian Kent suggested as a toy model.

Last edited: Jun 26, 2010
22. Jun 26, 2010

### Fredrik

Staff Emeritus
I didn't intend for this post to be so long, but I couldn't find a short way of saying it. This is why I've been trying to stay out of discussions about interpretations lately. They take too much time.

I agree about the ghosts, but I don't think it's an appropriate analogy.

I think the stuff he wrote about parallel universe is really good, and certainly not a reason to expect him to be irrational.

I need to say a few things about "interpretations" in general before I answer that.

The way I see it, a theory is defined by a set of axioms that tells us how to interpret some piece of mathematics as predictions about results of experiments. So a theory already includes one kind of "interpretation". An interpretation of a theory of physics must be something very different, because the theory already includes an interpretation of the first kind. The only thing it can be that makes any sense to me, is an answer to the question "What is the theory telling us about what actually happens to the physical system that the theory is making predictions about?

In other words, an interpretation of the first kind turns a piece of mathematics into a theory, and an interpretation of the second kind is either a claim that the theory doesn't describe reality, or an attempt to turn the theory into a "description of what actually happens". Note that all theories before QM had an obvious interpretation. There was never any debate about what the theory says is actually happening. For example, Newton's theory of gravity makes predictions about what results you will get if you measure the position of the Moon, and everyone agrees that those predictions describe (approximately) what's actually happening to the system even if no measurement is made. The Moon is there even when nobody looks.

Since I consider QM to be a theory of physics, and since I consider a theory to be defined by its axioms, I have to choose some specific list of axioms to define what I mean by "QM". I choose the standard axioms about Hilbert space and the Born rule, not because I think they must be the best, but because that's the set of axioms that most people are familiar with (and the ones I'm the most familiar with).

Now that I have defined what I mean by an interpretation of a theory of physics, and what I mean by QM, I'm finally ready to start talking about interpretations of QM. The way I see it, there are only two! Either QM describes reality or it doesn't. The claim that it doesn't is what people call the "ensemble interpretation" these days. The claim that it does is what I would take as the definition of a new many-worlds interpretation. (I don't consider Everett's MWI an interpretation of QM. It's nothing more than a failed attempt to find a different way to turn the underlying mathematics into a theory of physics. It was never intended to be what I would consider an interpretation of a theory).

It's funny that if you ask the most aggressive MWI-haters which of these two options they prefer, they usually say that the first option (QM describes reality...which I take as the definition of a MWI) is obviously true and that the second one (QM doesn't describe reality) is crazy nonsense. They dismiss the second one because it suggests that reality either isn't described by mathematics, or that there's a more fundamental theory than QM in which the variables are "unobservables" or observables with weird properties (e.g. non-local or contextual observables). They don't even want to think about the possibility of a "weird" fundamental theory as long as there are no experiments that contradict the predictions of QM. And most of them think it's self-evidently true that a theory that makes good predictions about reality must also be a good description of reality.

So which interpretation of QM do I prefer? I actually don't have a clue which one of the two I should think is more plausible. Two years ago, I would have said that I definitely prefer the ensemble interpretation. Now that I understand that there is a MWI that isn't fundamentally flawed like Everett's MWI, I'm torn between the two options. One thing that could tip the balance toward this MWI is if it turns out to have a wider range of applicability than the ensemble interpretation. For example, if it's neutral about whether entropy is increasing or decreasing with time, but identifies the branches where entropy is increasing with the branches that can contain conscious observers, we might have an anthropic argument that solves (or rather eliminates) the mystery of why the universe started out in a low-entropy state. For the moment, I'm leaning towards thinking that such arguments can be made.

I don't understand any of the other "interpretations" as well as these two (so I could be wrong about what I'm saying here), but it seems to me that most of them are just loosely stated ideas about what reality is really like. Such speculations are of no interest to me, and I don't think they should be called "interpretations". A few others seems reasonably well-defined at least, e.g. de Broglie-Bohm, transactional and consistent histories, but have the first two even successfully replicated all the predictions of QM? I'd be surprised if the answer is yes. (Doesn't dBB have problems with SR, and isn't transactional specifically for electromagnetic interactions?) And the last one just looks like a many-worlds interpretation of a slightly different but equivalent theory. (I consider two theories to be different if their axioms are different, and equivalent if they make the same predictions).

I disagree. I think that requires an additional axiom, which says explicitly that exactly one of the "worlds" is real. I don't mean that this makes that idea wrong, but it means that this single-world interpretation isn't an interpretation of QM, but an interpretation of the theory defined by the axioms of QM and this additional axiom that has no effect on the predictions.

Last edited: Jun 26, 2010
23. Jun 26, 2010

### Count Iblis

I find the good old thought experiment by Deutsch the most convincing argument for the MWI. Here one imagines an observer who is completely isolated from the environment (in practice that would likely mean implementing the observer in a virtual environment using a quantum computer)

The observer prepares an electron in the spin up state in the x-direction and then measures the z-component. The evolution from the initial state before the measurement is made to the final state is described by a unitary transformation. There exists a unitary transformation that will evolve the spin back to its initial state while erasing the memory record of the outcome of the measurement, but such that a record in the memory about the measurement having been performed, is kept.

It is easy to see that if only one outcome of the measurement really exists, the spin does not return to its original state.

24. Jun 27, 2010

### Demystifier

For your information, dBB replicated all predictions of QM. But I will not explain you how, unless you specifically ask (because otherwise you will probably not even read what I write). I will only say that the trick is in the fact that dBB is very similar to MWI (which, of course, does reproduce all predictions of QM, provided that the Born rule is postulated).

25. Jun 27, 2010

### Fredrik

Staff Emeritus
I appreciate the input. This is the right approach. I still intend to study dBB some time, but it's not at the top of my priorities right now. Perhaps you can just tell me if this is explained in Holland's book (which I bought some time ago but still haven't read), or if I'll have to read something else as well.