Why does nothing happen in MWI?

[Demystifier]

So your solution is that everything happens (in contrast to nothings happens). Then we just pick what we like.

Yes. More precisely, each possible decomposition of the vector in the Hilbert space counts as a different object, and each of them is simultaneously real. But they are not all equal. Some of those objects have a decohered structure in it, and for some reason (which might have something to do with consciousness, according to Tegmark) the world we see is a part of one of those decohered objects.

So it should not be called "many world interpretation". It should be called "many many world interpretation", because we have two levels of many-worldness. At the first level, each decomposition of a given vector in the Hilbert space counts as a different many-world object. At the second level, given a decomposition, each term in the decomposition can be counted as a different world.

 

[atyy]

Yes. More precisely, each possible decomposition of the vector in the Hilbert space counts as a different object, and each of them is simultaneously real. But they are not all equal. Some of those objects have a decohered structure in it, and for some reason (which might have something to do with consciousness, according to Tegmark) the world we see is a part of one of those decohered objects.

So it should not be called "many world interpretation". It should be called "many many world interpretation", because we have two levels of many-worldness. At the first level, each decomposition of a given vector in the Hilbert space counts as a different many-world object. At the second level, given a decomposition, each term in the decomposition can be counted as a different world.

To paraphrase some MWI proponents: MWI is just BM with no worlds picked out: Bohmian Many World (BMW) And as you point out, there are many BMs, depending on choice of hidden variable, dynamics, degree of solipsism etc, so it is BM^MMMW.

 

[tzimie]

But the point of MWI is to solve the measurement problem, so if MWI doesn't solve it, it fails.

Unless the measurement problem itself is formulated incorrectly in the MWI framework.

 

[tzimie]

The advantage is that it merges the measurement problem with the hard problem of consciousness.

I really like this.
And thank you for mentioning the "hard problem of consciousness"

 

[maline]

Let me get this straight: is the argument saying that MWI predicts an unchanging universe and is falsified by observation, or just that the factorisations we use aren't "preferred" by the hamiltonian since the "Nirvana basis" should be more "preferred"?

 

[Demystifier]

Let me get this straight: is the argument saying that MWI predicts an unchanging universe and is falsified by observation, or just that the factorisations we use aren't "preferred" by the hamiltonian since the "Nirvana basis" should be more "preferred"?

It's a kind of both, but the latter is more straightforward because it requires fewer assumptions.

 

[maline]

Please clarify. What are the assumptions that would lead to predicting a static universe?

A side point: does the solution you are proposing & disliking mean that there are infinitely many copies of the hilbert space, each with a built-in factorisation? If so, I don't think that's what Derek intends.

 

[Derek Potter]

It should be called "many many world interpretation"

Which is what I often have called it. But I also call it "The Too Many Worlds Interpretation" for obvious reasons.

 

[Derek Potter]

Please clarify. What are the assumptions that would lead to predicting a static universe?

A side point: does the solution you are proposing & disliking mean that there are infinitely many copies of the hilbert space, each with a built-in factorisation? If so, I don't think that's what Derek intends.

Well it's always dangerous to try to guess what I mean - seems like it takes 50 posts to get a measure of understanding.
I do not see why it is necessary to postulate copies of the Hilbert space. In fact I don't know what that would mean as the space is not a physical object it's just somewhere to put a vector. The plurality is in the ways we can factorize the space. The factorized spaces coexist in the sense that 3+4 = 7 coexists with 6+1 = 7. You don't need separate copies of "7".

 

[Derek Potter]

OK, it's good to know that now we understand each other.I would put it differently. He takes that assumption not because he likes it, but because he thought it is assumed by those who pursue MWI. And then he (correctly) shows that such an assumption is not consistent with the existence of physical objects. So at the very least, he has proved a no-go theorem which shows how MWI should not be understood: In MWI, the reality is not the vector in the Hilbert space.

He does not say what is the reality in MWI, but now the compact answer seems to be: the set of all possible decompositions of the vector in the Hilbert space.

So, what to say about such an interpretation of QM? First, I think it is logically and mathematically consistent. Second, I think it is very inelegant. So I don't reject it, but I also don't like it.

Hmm! What do you think is inelegant about it?

 

[mfb]

But there is a basis in which it does not move around. The basis in which only the phase changes.

Perhaps it is easier to understand it in a classical analog:

Consider a 3-dimensional universe containing nothing but one classical pointlike particle moving around. Does anything happen in such a universe? You can consider the system in coordinates (the classical analog of basis) comoving with the particle. In these coordinates the particle does not move. So nothing happens in the universe with one particle.

How about the 3-dimensional universe with two particles? Now there is relative motion of two particles, so one may think that something really happens in the case of two particles. However, the mathematics of two particles in 3 dimensions is the same as mathematics of one particle in 6 dimensions. So mathematically, we may say that we still have one particle, only in 6 dimensions. So from that point of view nothing happens even with two particles, because they are mathematically equivalent to one particle.

How to avoid the conclusion that nothing happens in a universe with two particles? Only by saying that physically we really do have two particles (in 3 dimensions) and not one particle (in 6 dimensions). But we cannot say that only from the mathematical structure of classical mechanics. There must be some additional structure involved, something which tells us that two particles in 3 dimensions is not the same as one particle in 6 dimensions. So pure classical mechanics cannot explain why something happens.

Likewise, pure quantum mechanics (the Schrodinger equation and nothing else) also cannot explain why something happens.

The one particle in 6 dimensions would accelerate with the usual coordinate system, but you can find coordinates where the 6-dimensional particle is at rest. Those coordinates have to be quite special, and designed to make the particle resting. So I think you are hiding the "something happens" in the coordinates. That applies to classical mechanics and quantum mechanics with MWI in the same way.
I made an example for a pendulum in a previous thread.

Either nothing happens in classical mechanics (and I disagree with that view), or something happens in MWI as well.

 

[Derek Potter]

I really like this.
And thank you for mentioning the "hard problem of consciousness"

Well, atyy is making a bit of a stretch there. The best approach is that although the HP is unsolved and (say some) unsolvable, we can safely assume that one's mental state supervenes on the state of the brain and thus, in part, on the physical state of our sense organs. Add consciousness to taste.

 

[Derek Potter]

The one particle in 6 dimensions would accelerate with the usual coordinate system, but you can find coordinates where the 6-dimensional particle is at rest. Those coordinates have to be quite special, and designed to make the particle resting. So I think you are hiding the "something happens" in the coordinates. That applies to classical mechanics and quantum mechanics with MWI in the same way.
I made an example for a pendulum in a previous thread.
Either nothing happens in classical mechanics (and I disagree with that view), or something happens in MWI as well.

If I am a chicken laying an egg I can always pretend to be doing nothing at all, it's just the rest of universe doing crazy things around me. That would appear to confirm that nothing happens in classical mechanics. I think this is what Ilja is saying. However I am not sure what we should make of this. We don't want to insist on a preferred basis/frame unless it's forced upon us. Perhaps we should say that the idea of something happening needs to be refined - what does it mean to lay an egg if some pathological coordinate system sees me as a full orchestra playing Beethoven's Fifth? Schwindt talks about the system being nice or unpleasant according to the frame used but there has to be a better criterion than Schwindt's personal likes and dislikes.

 

[Ilja]

If I am a chicken laying an egg I can always pretend to be doing nothing at all, it's just the rest of universe doing crazy things around me. That would appear to confirm that nothing happens in classical mechanics. I think this is what Ilja is saying.

?
What I'm saying was completely different. Classical mechanics in general does not specify the particular configuration space and the particular Lagrangian, but it specifies that a complete classical theory specifies a configuration space, a Lagrangian, and then everything else, in particular the evolution equation, is fixed. Then, the evolution of our particular universe is defined by the initial values. And the theory also specifies what is the form of these initial values - an initial configuration q(t) and its first time derivative. And once all this is fixed, one cannot pretend that there is no evolution if there is evolution.

The only thing one can pretend to get rid of motion is that one has not correctly identified what is at rest an what not, thus, that one has made an error in the definition of $\dot{q}(t)$ which should have been $\dot{q}(t)-v$. This is relevant only for positivists, who want to be able to identify everything based on observation, a stupid but popular philosophical idea. For everybody else this is quite irrelevant.

Then, there remains to be the final freedom - where we are in this particular solution. For this, in classical mechanics a particular event (where I am now) has to be specified.

In general, every physical theory should follow a similar scheme. The general scheme should define what has to be defined to define a particular physical theory. Given these additional data, which define the particular physical theory, the theory should define the set of additional information which is required to specify the particular universe (or multiverse, whatever this means). And, then, finally, it should be clear what has to be specified to identify my own position in this uni- or multiverse. If some general scheme does not clarify these points, it should be rejected as unphysical.

Quantum mechanics in its Copenhagen as well as its dBB variant does all this. The particular theory has to specify a configuration space Q. The state is specified by a wave function on the configuration space and a particular configuration. In the Copenhagen variant, there is some strange subdivision of the configuration space into a classical and a quantum part, where the wave function is defined only on the quantum part and the configuration only on the classical part. Then, there is a Hamiltonian operator which defines the evolution of the wave function, and the evolution of the configuration is defined by the guiding equation, in Copenhagen by a classical evolution equation on the classical part. And where we are ourself is also well-defined, in the same way as in classical mechanics, as a part of the configuration near a given event defined by its space coordinate at a given moment of time.

Thus, a complete quantum theory also specifies a configuration space, and defines what is a changing of the configuration in time. The positivistic problem of identifying absolute rest exists too, and is irrelevant for a realistic understanding too, as well for the question which is discussed here - if we see some motion in our world, it is impossible to uses this Galilean symmetry to get rid of the motion.

To accept MWI as a reasonable interpretation of quantum physics I require a similar scheme. But it is not given. The wave function, together with some abstract unitary evolution, is clearly not sufficient to specify the physics.

 

[Derek Potter]

?
What I'm saying was completely different.

I am still not sure whether I understand you. How exactly does classical mechanics specify that a classical theory must specify a particular configuration space? edit - Why shouldn't a theory consider different spaces and develop transforms to go from one to another? In QM, polarization states do not have a unique "configuration space", i.e. basis. Yet it's easy to say *this* state (suitably prepared) is a|A>+ b|B> in one basis and |c|C>+d|D> in another. Why is it non-physical to talk of the photon state as being different things in different configuration spaces? I don't see why you should reject MWI as unphysical because it accommodates talking about circular polarization and linear polarization at the same time.

 

[Ilja]

I am still not sure whether I understand you. How exactly does classical mechanics specify that a classical theory must specify a particular configuration space? edit - Why shouldn't a theory consider different spaces and develop transforms to go from one to another? In QM, polarization states do not have a unique "configuration space", i.e. basis. Yet it's easy to say *this* state (suitably prepared) is a|A>+ b|B> in one basis and |c|C>+d|D> in another. Why is it non-physical to talk of the photon state as being different things in different configuration spaces? I don't see why you should reject MWI as unphysical because it accommodates talking about circular polarization and linear polarization at the same time.

I think this is the simplest, and, therefore, preferable way - to specify one particular configuration space, one particular evolution equation and so on.

Your proposal to allow for different configuration spaces, which may be transformed into each other, but leave all physical observables unchanged, is a variant, which appears automatically, in a quite natural way, if one observes that all the observable things are not sufficient to specify the configuration space completely. For a realist (and, let's not forget, MWI claims to be a realistic interpretation, thus, justified or not, it has to follow the general principles of realistic theories) this is an unimportant complication caused by the unfortunate fact that we cannot observe everything. But this is unimportant, because, if we would have the ability to observe everything, we would have no problem to identify the correct choice. And, moreover, it would not be problematic at all if we make the wrong choice - the observables would be the same.

So, note, this allowance for different but equivalent descriptions does not change any physical prediction - we allow these different description only because these observable things are not changed.

MWI is rejected because the Nirvana frame does not reproduce the visible changing universe, but predicts an obviously different, statical universe. Or, in my variant, because different choices of the operator q lead to different physics, even if the Hamilton operator h is the same.

 

[Demystifier]

What do you think is inelegant about it?

It is mathematically and physically natural to consider the same vector represented in different basis as the same object. So it is un-natural and in-elegant not to consider so.

 

[Quantumental]

Happy to see this topic getting some serious discussion, as it deserves.
My question for you Derek Potter with regards to the Many-Many worlds you seem to be a proponent of, is how you get the probabilities correct?

 

[mfb]

We don't want to insist on a preferred basis/frame unless it's forced upon us.

Exactly. Something happens in most bases/frames. Only very special ones have a trivial time-evolution.

 

[atyy]

Happy to see this topic getting some serious discussion, as it deserves.
My question for you Derek Potter with regards to the Many-Many worlds you seem to be a proponent of, is how you get the probabilities correct?

I think one way to see the probabilities are right is to use Bohmian Mechanics as a form of MWI. So if BM is right, MWI is right. To paraphrase some MWI proponents: MWI is simply BM with no worlds picked out :p

So the only debate seems to be over what counts as "extra structure". For example, how is the factorization problem seen to be solved in BM? The factorization problem is: how do we know that what is "observable" is independent of the definition of subsystems? BM solves this by constructing a finest subsystem, and saying that all systems are made up of are composed from these finest subsystems, and we have strong heuristic arguments and we can see explicitly (although I don't know a general proof) that we recover common sense reality in all test cases known to date.

But how about crazy factorizations? Can they solve the nonlocality problem? In fact, amazingly to me, BM again shows how MWI solves the nonlocality problem - by denying that the Bell inequalities are violated at spacelike separation - making obvious what the Many-Minds people have been saying - they are brains in a vat! http://arxiv.org/abs/1112.2034: "Finally note that our result that different observers may live in different branches of the wave function is very similar to the many-world interpretation [16, 17], briefly discussed in Sec. 2.2. Yet, there is one crucial difference. In the many-world interpretation, there is a copy of each observer in any of the branches. In our solipsistic interpretation, for each observer there is only one copy living in only one of the branches."

Returning to "extra structure" - are all factorizations, no matter how crazy, discontinuous etc ok? If they are not, and something like BM's factorization are needed to rule those out, then one might argue that BMW (Bohmian Many Worlds) does have extra structure. If the crazy non-workable factorizations are harmless or obviously crazy, then one may say that's an obvious assumption, so it isn't "extra".

If we accept BMW, then one way to answer the question of extra structure is: what is the widest class of BM that is possible? What hidden variables are allowed or not allowed? What dynamics are allowed or not allowed? If the hidden variables or dynamics that are not allowed is non-trivial, then one can argue that these constitute "extra structure". The issue is commented on by http://arxiv.org/abs/quant-ph/9704021 and http://arxiv.org/abs/1112.2034.

 

[Derek Potter]

Happy to see this topic getting some serious discussion, as it deserves.
My question for you Derek Potter with regards to the Many-Many worlds you seem to be a proponent of, is how you get the probabilities correct?

I am not sure what you are asking. Probabilities emerge in MMWI in exactly the same way as they do in MWI. Of course the probabilities in one factorization are not the same as those in another - they do not even refer to the same (edited -) set of possible outcomes.

 

[bhobba]

is how you get the probabilities correct?

Gleason's Theorem. Contextuality does not make sense in MW.

Added Later:
In particular its the requirement for neutrality and equivalence.

All Wallaces proof is is a different route to the same result with the same assumptions ie a rational agent would naturally require neutrality and equivalence so that's why he does it.

Even Later Addition:
I managed to dig up the following that examines it:
http://users.ox.ac.uk/~mert2255/papers/pitei.pdf

Note - and this is VERY important:
Just because something is controversial does not mean its been proven wrong. It simply means issues need to be sorted out before final judgement is passed. That some do not agree with the approach MW adherents take does not prove them wrong - that is a much higher standard than some have issues with it.

Thanks
Bill

 

[atyy]

Another way to see how MWI saves BM and CI with a real collapse from Bell's theorem is that if we have many worlds, we can simply assume that all Lorentz ether frames are real, so that the theory has full Lorentz invariance. So BMW and CMW are something like spontaneously broken Lorentz invariance.

 

[Derek Potter]

Happy to see this topic getting some serious discussion, as it deserves.
My question for you Derek Potter with regards to the Many-Many worlds you seem to be a proponent of, is how you get the probabilities correct?

Ahem, just because I seem to be a proponent of something doesn't mean it's wrong.

 

[Demystifier]

Ahem, just because I seem to be a proponent of something does not mean it's wrong.

Just because MWI is not (even) wrong does not mean that one does not need to answer how the correct probabilities emerge from it.

 

[Derek Potter]

Just because MWI is not wrong does not mean that one does not need to answer how the correct probabilities emerge from it.

The question posed by Quantumental was about MMWI, not MWI.

For MWI, I think bhobba's answer - before he added to it :) - is sufficient: Gleason's Theorem.

There is no controversy that the BR gives the correct probabilities. All the argument is about how to justify applying a theorem about probability measures to a model which denies probability. But that's not what Quantumental asked about.

 

[bhobba]

The question posed by Quantumental was about MMWI, not MWI.

It was about MWI.

The issue is, as I posted, neutrality and equivalence, which is based on reasonableness arguments. To understand it you need to read the link I gave where a number of alternative ways of assigning probability are explored and shown to not be reasonable, and only a measure that is basis independent is what a rational agent would say is valid. Via Gleason that, basically (there are a few other assumptions like the strong superposition principle), means you have the Born rule.

The key point to understand is within the axioms assumed by MW adherents (ie its use of probability based on decision theoretic axioms) Born's rule does follow. The argument is if that's a valid way to define it within this context. It's logically equivalent to the Kolmogorov axioms so can't be faulted on logic alone. Basically its an argument about the meaning of probability - which believe it or not - is what most interpretations of QM is actually about:
http://math.ucr.edu/home/baez/bayes.html

Thanks
Bill

 

[Demystifier]

... only a measure that is basis independent is what a rational agent would say is valid

In classical phenomena, the probability measure is often not basis independent. Consider, for instance, the probability measure of coin flipping.

 

[Derek Potter]

It was about MWI.

"My question for you Derek Potter with regards to the Many-Many worlds..."
I assume, perhaps rashly, that when someone says "Many-Many worlds", they do mean "Many-Many worlds" and not merely "Many worlds". Regrettably I cannot cite a theorem that people mean what they say.

 

[Derek Potter]

In classical phenomena, the probability measure is often not basis independent. Consider, for instance, the probability measure of coin flipping.

Could you expand on that please?

 

[Demystifier]

Could you expand on that please?

For coin flipping, the basis {head,tail} is the preferred basis. (The probability of head+tail or head-tail is always zero.) Since there is a preferred basis, the probability measure is not basis independent.

That's the rough idea, for a more formal treatment see e.g.
http://lanl.arxiv.org/abs/quant-ph/0609163 [Found.Phys.37:1563-1611,2007]
Secs. 5.2 and 5.3.

 

[bhobba]

In classical phenomena, the probability measure is often not basis independent. Consider, for instance, the probability measure of coin flipping.

Sure. But from the axioms of decision theory in MW it's the only one that makes sense.

Consider for example the obvious one of assigning equal probability to each outcome of a two outcome observation. Then consider a combined observation with three outcomes where one of the outcomes feeds into another two outcome observation. What is each outcome - is it 1/3 1/3 1/3 or 1/2 1/4 1/4? Rationally you can't decide so you reject it. Its that sort of thing - only one assignment seems to be free of issues like that - the Born rule.

Thanks
Bill

 

[maline]

It is mathematically and physically natural to consider the same vector represented in different basis as the same object. So it is un-natural and in-elegant not to consider so.

Please help me understand: how can it matter whether we "consider" the representations to be the same object? If there is one valid basis according to which the vector contains us and our classical observations, then isn't that fact a property of the overall vector?

 

[Demystifier]

But from the axioms of decision theory in MW it's the only one that makes sense.

Yes, but those axioms are chosen in such a way to get what one wants to get. This is nicely explained in
http://lanl.arxiv.org/abs/0808.2415
especially in 2) at page 4.

 

[bhobba]

Yes, but those axioms are chosen in such a way to get what one wants to get.

That's part of the argument about it isn't it. They look pretty natural to me though.

As it says, and I pointed out above:
'The ‘Equivalence’ assumption is what does the real work, and it is the main point of controversy with the approach.'

Thanks
Bill