Problems with Many Worlds Interpretation

[Demystifier]

Exactly! But one story is special for you, because of your consciousness.
So we have a constructive disagreement - our axioms are different, I assume a special role of consciousness aka 'qualia'.

I don't have a problem with your axioms, indeed they seem viable to me. My point is that your additional consciousness axiom makes the total axiomatic system more complicated than typical MWI-believers would like. So you are a not-typical MWI-believer, which I think is good.

 

[Dmitry67]

Thank you. Minor question about BM: say, there are 2 observers in 2 different inertial frames. Do they agree on the 'trajectories' of BM 'particles'? (Of course, they can't observe these trajectories because they are hidden, but observers can calculate them).

Probably they would agree in BM flavor with hidden special rest frame, but what's about flavor without special hidden rest frame?

 

[Ilja]

Of course I understand it - you had probably misunderstood my post.
But I've heard that BM has a special rest frame, is it true?

Yes it has. Some people try to get rid of it, but I don't think it is a good idea (sorry, Demystifier).

But to have a preferred frame in cosmology does not mean that there has to be a hidden center of the universe. It is simply a preferred foliation in the GR sense, not an inertial frame in the SR sense.

Trajectories in different frames are trajectories with completely different initial values and there is no reason at all to suspect that they have something in common. But observers will not think that their own rest frame, based on the quite arbitrary Einstein synchronization, has some relation with the hidden preferred rest frame. So I think they will agree that the CMB frame is the closest candidate for the hidden preferred frame and use it, independend of their own speed, for computations.

 

[Demystifier]

Thank you. Minor question about BM: say, there are 2 observers in 2 different inertial frames. Do they agree on the 'trajectories' of BM 'particles'? (Of course, they can't observe these trajectories because they are hidden, but observers can calculate them).

Probably they would agree in BM flavor with hidden special rest frame, but what's about flavor without special hidden rest frame?

The two observers agree on the trajectories, both with and without special hidden rest frame.

 

[Dmitry67]

Ilja, thank you for understanding correctly and answering my question about BM vs cosmology.

Trajectories in different frames are trajectories with completely different initial values and there is no reason at all to suspect that they have something in common.

But if different observers don't agree on the trajectories, can you call BM particles 'real'? BM insists that in some sense, 'particles' are what makes otherwise empty Universe wavefunction 'real' in some branches?

Related question, if trajectories are different, what guarantees that different observers agree on the outcomes of the experiments? If for Bob cat is dead, what guarantees that for Alice flying at 0.99c, particles also fall into the 'dead cat' branch, making it real?

UPD: answers from Ilja and Demystifier are different, I'll wait for the clarification

 

[Hurkyl]

He discusses that issue as well. What matters in MWI is not the Hamiltonian (with its symmetries), but the wave function (as a function of time). If you know the wave function, you don't need the Hamiltonian. A wave function is a particular solution, and in general it does not have any symmetries which the Hamiltonian does.

A wave function doesn't have the symmetries of Hilbert space either.

The objection is to the claim that "all wave functions look the same". This can only make sense if you forget the laws of physics. But the 'brilliant analogies' you lauded earlier demonstrate quite clearly that if you forget about the laws of physics, you can't discern what information is meaningful.


But it strikes me that there's another way to respond that makes the emptiness of this line of reasoning more obvious. Yes, a point in state space is not enough to describe a physical system. You need something more. That 'something more' is the laws of physics.

Nobody worth their salt should have ever claimed that MWI considers a state vector to be a complete description of the universe. Instead, the description is the triple

(state vector, Hamiltonian, Schrödinger equation)​

(or some equivalent formulation).

The last component is nearly always left implicit, and the middle one usually so. But if you're going to start talking about symmetry groups and consider two descriptions in the same orbit as equivalent systems, it is a terrible mistake to forget about them.

 

[Demystifier]

The statement by Ilja quoted by Dmitry makes no sense to me. So I'll also wait for Ilja's clarification.

 

[Demystifier]

But it strikes me that there's another way to respond that makes the emptiness of this line of reasoning more obvious. Yes, a point in state space is not enough to describe a physical system. You need something more. That 'something more' is the laws of physics.

Yes, but the claim is that a TRAJECTORY in phase space should be enough. Namely, if you know the trajectory, the laws of physics seem superfluous.

 

[Demystifier]

Dmitry67, today appeared a new paper that might interest you:
"The role of the observer in the Everett interpretation"
http://arxiv.org/abs/1211.0196

Also, I have a question for you. If, except the wave function, one also needs consciousness, then does this consciousness needs a preferred (Lorentz) frame? Of course, it is difficult to answer this question without an explicit mathematical model of consciousness (which is the reason why I prefer Bohmian trajectories over consciousness as an additional structure needed in MWI), but perhaps the question still makes sense to you.

 

[Hurkyl]

Yes, but the claim is that a TRAJECTORY in phase space should be enough. Namely, if you know the trajectory, the laws of physics seem superfluous.

Anyone who makes that claim without implicitly assuming the laws of physics are fixed (or believes the structure of the state space includes the laws of physics) is either being very silly, or hasn't fully thought things through yet.

I'm sure there are people who would make the claim without this assumption, or haven't yet realized its importance. These people are wrong.

 

[Dmitry67]

Thanks, I'll take a look.

Regarding your question, I suppose consciousness resides in some Lorentz frame - the frame where consciousness holder (brain) is located. Don't ask me what if brain is made of relativistic components - I don't know :)

This answer is on the surface, deeper analysis requires an understanding what consciousness is. For example, I can't answer the following question:

In infinite Universe, there are infinitely many physical copies of myself in identical states, even very very far from each other. Are these exact copies share the same consciousness or not? I don't know how '=' is defined for consciousness.

 

[Demystifier]

Dmitry, thanks for the honest answer!

 

[Ilja]

But if different observers don't agree on the trajectories, can you call BM particles 'real'? BM insists that in some sense, 'particles' are what makes otherwise empty Universe wavefunction 'real' in some branches?

I do not say that different observers don't agree.

If different observers agree about the hypothesis that the CMBR frame is the preferred one, then they will compute the same trajectories. The hypothesis about the CMBR frame as the preferred one is a reasonable one, the hypothesis that the own frame obtained by Einstein synchronization is a preferred one seems, instread, quite stupid.

Related question, if trajectories are different, what guarantees that different observers agree on the outcomes of the experiments? If for Bob cat is dead, what guarantees that for Alice flying at 0.99c, particles also fall into the 'dead cat' branch, making it real?

This is a completely different question. That different observers agree on the outcomes is caused in BM by the simple fact that the trajectory of the configuration is the same. It has to be computed in the true prefferred frame.

If you fail to make the correct hypothesis about which frame is the preferred one, you compute some stupid meaningless trajectories which have nothing in common with reality. But, because the probabilities in quantum equilibrium will not depend on this error, it usually does not matter.

 

[Ilja]

The two observers agree on the trajectories, both with and without special hidden rest frame.

And this does not make sense to me.

Somewhere Valentini has made the point that outside the quantum equilibrium you have no problem of sending FTL messages in BM. And these messages of course define a preferred frame. (At least if you want to preserve a world with causality but without causal loops.)

 

[Demystifier]

Somewhere Valentini has made the point that outside the quantum equilibrium you have no problem of sending FTL messages in BM. And these messages of course define a preferred frame. (At least if you don't want to preserve a world with causality but without causal loops.)

I guess you wanted to say "... if you want to preserve a world with causality but without causal loops."

 

[Ilja]

I guess you wanted to say "... if you want to preserve a world with causality but without causal loops."

Indeed. Corrected.

 

[Demystifier]

Indeed. Corrected.

OK. Then I would like to add that my covariant BM does NOT preserve causality. Or more precisely, it does not preserve the usual relativistic causality, but replaces it with a more general notion of causality.

 

[Ilja]

OK. Then I would like to add that my covariant BM does NOT preserve causality. Or more precisely, it does not preserve the usual relativistic causality, but replaces it with a more general notion of causality.

Of course, relativistic causality cannot be preserved, but classical causality of an absolute time (preferred frame) without causal loops can be preserved, and this is the usual version of causality of dBB theory, non-relativistic or relativistic.

Relativistic causality in the weak sense (only about information transfer, not about reality) one obtains in quantum equilibrium.

 

[kith]

Indeed, the title of section starting at page 20 is "Is the world a mathematical structure?". He correctly points out that if it is, then Bohmian mechanics also has a problem. But so has classical mechanics in configuration or phase space. Yet this is not really a problem for Bohmians, or for classical physicists, because they typically don't think that "the world is a mathematical structure". Such thinking is more typical for many-world people.

So why do (some?) many-worlds people think that the world is a mathematical structure if this isn't even a meaningful concept in classical mechanics?

 

[martinbn]

Later in the paper he explains that only the wave function is what matters, in the sense that if wave function at all times is given, then the Hamiltonian is irrelevant. The Hamiltonian only serves to determine wave function at all times for the case when it is not already known.

Ok, but I still don't understand. Given the wave function for all times i.e. given a "curve" in the Hilbert space is not the same as just the Hilbert space. Vectors do not all look the same, some are on the curve and some are not, those on the curve are ordered and so on. The curve gives the Hamiltonian and its eignvectors are different in a way than the others and so on. Also my question why the factorization was not answered. At one point he says "let's ignor the why question and do the factorization anyway".

 

[mfb]

So why do (some?) many-worlds people think that the world is a mathematical structure if this isn't even a meaningful concept in classical mechanics?

You can fully define a classical system by the Hamiltonian and a vector (given for a specific time) in phase space. I think this is very similar to a mathematical structure. The existence of the system (if it corresponds to the universe) could be similar to the "existence" of the vector (1,5,2) in R³.

 

[kith]

You can fully define a classical system by the Hamiltonian and a vector (given for a specific time) in phase space.

You can't tell wether you have 3 particles moving in n dimensions or n particles moving in 3 dimensions from this. So you have to assume the division into subsystems.

 

[Dmitry67]

So why do (some?) many-worlds people think that the world is a mathematical structure if this isn't even a meaningful concept in classical mechanics?

http://arxiv.org/abs/0704.0646

 

[mfb]

You can't tell wether you have 3 particles moving in n dimensions or n particles moving in 3 dimensions from this.

So what? I do not care ;).

The Hamiltonian will be easier to write if you group those degrees of freedom in groups of 6.

 

[kith]

http://arxiv.org/abs/0704.0646

Thanks, I will read this when I have the time

So what? I do not care ;)

That's certainly a valid point of view, if you are willing to accept that the time evolution in our world of experience is only due to the choice of coordinates.

 

[Ilja]

So why do (some?) many-worlds people think that the world is a mathematical structure if this isn't even a meaningful concept in classical mechanics?

I think the very idea to interpret the world as a mathematical structure is an implicit consequence of the positivistic rejection of interpretations, metaphysics, and philosophy.

The point is that there is a natural and justified wish to consider interpretation, metaphysics and philosophy. So those who officially, ideologically accept this rejection, in fact want to consider them. So what to do them? They try the most innocent (from the positivistic point of view) metaphysics. Which metaphysics is the most innocent one, from point of view of those who reject metaphysics? It is the metaphysics which does not add any new methaphysical structure, which, does not openly argue for additional structure except the one which is given by the mathematics of the theory.

So, one takes the mathematics of the given theory, does not accept anything in contradiction with these mathematics. And tries to interpret the mathematics metaphysically.

That means, one rejects preferred frames (addtional structure), ether interpretations of fields (additional structure), Bohmian trajectories (addtional structure) but accepts spacetime interpretations (four-dimensional mathematics instead of 3D reality) despite closed causal loops, nontrivial topologies and singularities (they are holy as part of mathematics) frequency interpretation (mathematics of probability theory as part of nature) instead of Bayesian interpretation (where the same mathematics is only used to describe incomplete human information) and wave function realism (also no new mathematics).

So the mystification of the mathematics of the actual physical theories seems to me a quite natural consequence of the antimetaphysical prejudices of the last century, which have not played an important role in classical physics.

 

[Dmitry67]

dBB is in fact incompatible with MUH, but not because of the preferred frame. Incompatibility with MUH is not about having additional structures, no matter how ugly they are, it is about having something that can't be defined as formula in principle.

 

[Ilja]

dBB is in fact incompatible with MUH, but not because of the preferred frame. Incompatibility with MUH is not about having additional structures, no matter how ugly they are, it is about having something that can't be defined as formula in principle.

I would not care about such a compatibility. But there is nothing in dBB which cannot be expressed in formulas. It is the interpretation where all the mysticism of the other interpretations is replaced by clear and simple precise mathematics. The guiding equation, the equation which defines the evolution of a subsystem in terms of the larger system and the configuration of the environment, which replaces all the mystery about collapse - simple mathematics.

 

[Fredrik]

Max Tegmark made a poll on preferred interpretation of QM during a conference Fundamental Problems in Quantum Theory, 1997, and got:

Copenhagen 13
Many Worlds 8
Bohm 4
Consistent Histories 4
Modified dynamics (GRW/DRM) 1
None of the above/undecided 18

http://arxiv.org/abs/quant-ph/9709032v1

I think polls like this are kind of pointless, mainly for these two reasons:

1. There are no standard definitions of these interpretations. In fact, it's hard to find two people who mean the same thing by "the CI" or "the MWI". There isn't even a standard definition of the term "interpretation of QM", so different people have different ideas about what sort of things an interpretation should say.

2. A lot of physicists haven't thought enough about interpretations to have an informed opinion. So anyone's guess is as good as theirs.

Edit: I didn't even realize that this post was on the first page. I thought I was I was replying to a comment made recently.

 

[Dmitry67]

I would not care about such a compatibility. But there is nothing in dBB which cannot be expressed in formulas. It is the interpretation where all the mysticism of the other interpretations is replaced by clear and simple precise mathematics. The guiding equation, the equation which defines the evolution of a subsystem in terms of the larger system and the configuration of the environment, which replaces all the mystery about collapse - simple mathematics.

As you remember, Universe wavefunction in dBB is exactly the same as in MWI (this fact is well known as "dBB is MWI in chronic denial"). As unavoidable consequence of MUH is that empty dBB branches are real.

The word "real" is confusing, but it is fair to say that in dBB some branches are empty, while one is "tagged" with "particles" (dBB people tend to say that "it is real, while empty branches are not" - but you can't say it under MUH - they are just different, but both "real")

Evolution of the wavefunction branch with a dead cat, or better, poor experimenter slowly dying from poison, is controlled by the same laws as the 'tagged' one - dBB particles don't affect the wavefunction. In empty branch, neurons in experimenter's brain are sending panic signals... Vision becomes blurry, pain grows stronger and...

Now comes the pure magic. dBB says: don't worry about him. Yes, it looks almost exactly as 'real', but it is empty. He does not feel any pain. That experimenter is not conscious at all! But why if wavefunction of his brain is the same? Because there are no particles inside! But these particles don't affect the wavefunction! Still, they are the undetectable but they are the most important part of the consciousness!

So here is a non-physical axiom of dBB (with the assumption of MUH): while all branches are real, non-tagged branches are somehow... ehhh... existence-challenged :) Earth in empty branch is populated with perfect examples of http://en.wikipedia.org/wiki/Philosophical_zombie

 

[Quantumental]

As you remember, Universe wavefunction in dBB is exactly the same as in MWI (this fact is well known as "dBB is MWI in chronic denial"). As unavoidable consequence of MUH is that empty dBB branches are real.

Well the thing is, quite a lot of Bohmians view the pilot wave as nomological instead of ontological.
And as we can see now, "pure WF" doesn't have any structure, so there are definitely no worlds in the empty pilot waves, only the particles will give rise to anything.
This is sort of the point of this paper.


So now we know that: Many Worlds cannot make sense of Born Rule and it can't even get structure out of it's hypothesis.
So the only way to save this (i don't see any reason why you'd want to) would be to postulate some structure and then hope it fits Born Rule and all other observed phenomena.
This would inevitably be way worse than Bohm

 

[bohm2]

Well the thing is, quite a lot of Bohmians view the pilot wave as nomological instead of ontological.

But there are problems with treating the wave function as nomological (e.g. denoting a law of nature) because as has been pointed out by many:

laws aren’t supposed to be dynamical objects, (as) they aren’t supposed to change with time, but the wave function of a system typically does...(since), we can in (a) sense control the wave function of a system. But we don’t control a law of nature. This makes it a bit difficult to regard the wave function as nomological.

I believe this is one of the reasons why not only Wallace but even Bohmians like Valentini/Hiley doesn't buy that view. Unfortunately Valentini's approach has also problems:

Next, Valentini claims that his interpretation of ψ as a ‘guiding field of information’ is “free of complications”. In claiming this, he evidently does not see the irreducibly multi-dimensional character of ψ as a “complication”. This point brings out an internal tension in his guidance view. He wants to interpret ψ (via the pilot wave S) in realistic terms as representing a physically real causal entity, yet he never expressly takes a stand regarding the status of the configuration space in which ψ exists. He introduces further ambiguity by equivocating upon the real physical status of ψ itself. While in one place he takes the view that “The pilot-wave theory is much better regarded in terms of an abstract ‘guiding field’ (pilot-wave) in configuration space...” , in another he states that “The quantum mechanical wave function ψ(x, t) is interpreted as an objectively existing ‘guiding field’ (or pilot-wave wave) in configuration space...”. Is ψ a concrete entity existing in a physically real space or is it only an abstract entity existing in a mathematical space? Valentini does, though, somewhat clarify his view elsewhere by stating that “the pilot wave ψ should be interpreted as a new causal agent, more abstract than forces or ordinary fields. This causal agent is grounded in configuration space...” .

Thus, the pilot wave or ‘guiding field’, while being more abstract than forces or classical fields, in the sense of being further removed conceptually from ordinary experience-the concept of ‘guiding field’ is achieved by abstracting the notion of ‘force’ from the classical concept of ‘field’, is nonetheless an objectively existing causal entity. But, that such an entity is grounded in configuration space implies that configuration space itself must be taken to be physically real in some sense. Whereas Albert takes an unequivocal (though perhaps incoherent) stand on this, Valentini leaves us without a clear idea of in what sense configuration space is to be regarded as physically real. Is configuration space itself the only physical reality? Or are both configuration space and ordinary space physically real? And, if so, are they real in the same physical sense? These questions remain to be answered for any interpretation of Bohmian mechanics that would postulate entities in configuration space.

Formalism, Ontology and Methodology in Bohmian Mechanics
http://www.ingentaconnect.com/content/klu/foda/2003/00000008/00000002/05119217

 

[Ilja]

As unavoidable consequence of MUH is that empty dBB branches are real.

For being real they have to be defined in a sufficiently certain way.

Then, a function on a space of nonexisting nonsense may be existing and nontrivial. As the opinions in my mind about how interesting are various types of unicorns. I think white unicorns are boring, but the invisible pink unicorn is a really good idea. That's a nontrivial, really existing function, once my brain is real, it changes in time following some evolution equation.

A similar example would be the evolution of a Bayesian probability density following the Liouville equation of classical mechanics. Nobody cares about the pain of the empty branches.

Now comes the pure magic. dBB says: don't worry about him. Yes, it looks almost exactly as 'real', but it is empty. He does not feel any pain. That experimenter is not conscious at all! But why if wavefunction of his brain is the same?

But nobody cares about the pains of functions. Nor about empty branches, nor about the nonempty. All one has to care about is the real configuration itself, not about the wave function branch containing it.

Because there are no particles inside! But these particles don't affect the wavefunction! Still, they are the undetectable but they are the most important part of the consciousness!

They are not only not undetectable, they are all what we see.

So here is a non-physical axiom of dBB (with the assumption of MUH): while all branches are real, non-tagged branches are somehow... ehhh... existence-challenged :)

The subdivision of the wave function into branches is existence-challenged, it is mystical (non-mathematical). And the connection of a function on the space of imaginable configurations with a real configuration is also a mystical one. It would be mystical even if the function itself would be highly localized, so to say a "branch".

 

[kith]

So now we know that: Many Worlds cannot make sense of Born Rule and it can't even get structure out of it's hypothesis.

That's false. Provided that his proof is correct, Schwindt has "only" shown that you can't derive the factorization of the universal state into states of our world of experience from only knowing the universal state at all times.

If you think about it, this is not surprising because the same is true already for classical mechanics. Schwindt's argument is against taking the mathematical structure for the real thing and not about the MWI per se. Everett's initial paper for example is not touched by it.

So the only way to save this (i don't see any reason why you'd want to) would be to postulate some structure and then hope it fits Born Rule and all other observed phenomena. This would inevitably be way worse than Bohm.

This is not worse, because Bohmian mechanics has to postulate exactly the same structure. If the Born rule can be derived from the unitarian dynamics for a given division into subsystems, it is simply a matter of philosophical preference wether a realist chooses hidden variables or many worlds. (I am aware that this hasn't been done yet in a universally accepted manner)

 

[kith]

So, one takes the mathematics of the given theory, does not accept anything in contradiction with these mathematics. And tries to interpret the mathematics metaphysically.

Thanks for your explanations. What I have destilled from the last few pages here is that there are two kinds if realists: people who are realist about physical systems and people who are realist about mathematical structures. It seems kind of obvious that these two groups can't have a fruitful discussion. While the first group thinks that the mathematics must reproduce a representation of our specific world, the second group thinks that our world is one out of many possible representations of a specific mathematical structure.

I think both positions are compatible with the MWI. At least, Everett's initial paper takes a collection of physical systems as given.