Problems with Many Worlds Interpretation

[mfb]

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.

In collapse interpretations and several other interpretations, you observe Born-like probabilities in the possible measurement results with probability ~1. It is possible, but very unlikely that you observe a serious deviation from them.
In MWI, you observe Born-like "probabilities" in worlds with measure ~1. It happens that you observe a serious deviation from them, but the total measure of those worlds is ~0.

I don't see the fundamental difference.

 

[Dmitry67]

So now we know that: Many Worlds cannot make sense of Born Rule

I also recommend this: http://arxiv.org/abs/1008.1066
Max Tegmark - again - suggested an explanation of Born rule. This article is very elegant, and there are also 2 nontrivial ideas behind it:

MWI indirectly implies infinite universe;
In infinite universe Bayesian probability approach is equivalent to the frequentist one.

 

[Dmitry67]

1 For being real they have to be defined in a sufficiently certain way.
2 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.

1 In MUH, it is enough that it is defined mathematically
2 Again, you are using the word "real" in some special sense, probably common for dBB people, but definitely not in MUH sense.

And I take it as a proof that dBB is not compatible with MUH, as you can't make a small step in dBB without saying "empty branches are not real" :)

 

[bohm2]

as you can't make a small step in dBB without saying "empty branches are not real" :)

I think that is a problem for the Bohmian model, more so than the action-reaction violation between wave and particle. As an aside, Bohm and Hiley did acknowledge this difficulty and offered a possible solution:

In these cases we need to ensure we have some way of 'killing off' the effects of the `empty' wave-packets for `ever'. We spent a whole chapter in "The Undivided Universe" discussing this problem. We concluded that this would happen, provided you allowed some coupling to the environment. The coupling that we propose is different from the coupling that is assumed in the usual discussions of decoherence. Our argument is that if the particle interacted with the environment, it would produce further separated wave-packets in which only one would be occupied. This scattered particle would then collide with an other particle which would be scattered, occupying yet another separating wave packet and so on. Interference would only return if at least one each of the empty scattered wave packets could be returned to overlap. Since the scattering of the environmental particles was random, the chances of this happening would be remote. Thus the QP (quantum potential) would never return spontaneously to its original form and interference would not reappear. Of course it may be possible, in principle, to exactly reverse everything but such a possibility is very hard to achieve so the system will behave as if the wave packet has collapsed, but no collapse has actually taken place. This argument is supported by Anton Zeilinger's interference experiment with hot bucky-balls [20]. Thus in our view, it is not new physics that destroys interference. It is the fact that you cannot in practice reverse all the particle positions in such a way as to restore interference.

The Bohm Approach Re-assessed
http://www.bbk.ac.uk/tpru/BasilHiley/BohmReassed1.pdf

 

[Hurkyl]

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.

The difference is artificial.

If I have a collection of mathematical statements that represent properties of the real world, then the real world is something that satisfies those mathematical statements.

Conversely, if the real world is something that satisfies a collection of mathematical statements, then those mathematical statements represent properties of the real world.

 

[Ilja]

1 In MUH, it is enough that it is defined mathematically
2 Again, you are using the word "real" in some special sense, probably common for dBB people, but definitely not in MUH sense.

And I take it as a proof that dBB is not compatible with MUH, as you can't make a small step in dBB without saying "empty branches are not real" :)

Sorry, but you have started with a meaning of "real" which does not have much in common with an abstract mathematical realism:

Yes, it looks almost exactly as 'real', but it is empty. He does not feel any pain.

I have criticized and rejected the confusion between a function on a space of possible configurations (real or not) with the configuration itself. It is a part of the configuration which can feel pain, not the function on states where something feels pain which can feel pain.

And, of course, I also criticize that such ill-defined parts of functions as branches are used as if they are well-defined.

But to accept that the wave function itself is real is not a problem at all for dBB. I would say that it is the dBB mainstream.

Just to clarify these distinctions with an example: I have a program on the computer with adds all the bits in a file and tells if the sum is odd or even. This function is well-defined an real - implemented in my computer memory.

Now you can apply it to pictures and videos of people feeling pain. But, clearly, the really existing program does not feel any such pain, and it also does not show pictures of people feeling pain.

You can define a branch of this function - a variant which gives 0 for all files except sadistic jpg files, and works in the same way as the original program on these files. No problem, but it nonetheless does not feel any pain, nor does it show pictures of people feeling pain. And, moreover, if the original program really exists, it does not follow that a program restricted to sadistic jpg files and giving 0 else really exists. In fact, the original is easy to implement and does not need much memory, while its branch needs much more abilities, some variant of artificial intelligence, so that it even cannot exist on an old and small computer.

Last but not least: MUH itself is something in my opinion completely unreasonable in itself. So it would certainly not be an argument at all against dBB if it would be incompatible with MUH - that would only be yet another argument against the MUH.

 

[Demystifier]

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 don't know. Perhaps they don't take classical mechanics seriously.

 

[Demystifier]

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

Yes, I am also one of them.

Concerning the objection that "laws are not supposed to depend on time", in
http://arxiv.org/abs/1209.5196
I explain how fundamental nomological wave function may be time-INdependent, while the time-dependent wave function is the conditional wave function defined by Bohmian particle trajectories.

 

[Dmitry67]

Sorry, but you have started with a meaning of "real" which does not have much in common with an abstract mathematical realism:
>Yes, it looks almost exactly as 'real', but it is empty. He does not feel any pain.

It was a sarcastic parody on dBB proponents :)

 

[Ilja]

It was a sarcastic parody on dBB proponents :)

I have to acknowledge that my sarcasm detection doesn't work when arguing about MWI. My common sense sarcasm detector does not work - it identifies the whole MWI as pure sarcasm one should not take seriously, so I cannot use it there.

 

[Dmitry67]

I have to acknowledge that my sarcasm detection doesn't work when arguing about MWI. My common sense sarcasm detector does not work - it identifies the whole MWI as pure sarcasm one should not take seriously, so I cannot use it there.

Lol...
But seriously, returning to your

But, clearly, the really existing program does not feel any such pain, and it also does not show pictures of people feeling pain

it is because the copy on a videotape or even inside the computer is ridiculously oversimplified. But do you believe in "mind upload"? http://en.wikipedia.org/wiki/Mind_uploading
If copy is exact (in some sense), does it feel any paint in it's virtual world?

If you answer "Yes" (functionalism), then wavefunction in empty brain is very accurate emulation of the wavefunction in the non-empty branch, so people there must feel pain.

If you answer "No", then you assign some magic properties to consciousness, which is OK, but it should be remembered as non-MUH axiom.

 

[Ilja]

it is because the copy on a videotape or even inside the computer is ridiculously oversimplified. But do you believe in "mind upload"? http://en.wikipedia.org/wiki/Mind_uploading
If copy is exact (in some sense), does it feel any paint in it's virtual world?

If you answer "Yes" (functionalism), then wavefunction in empty brain is very accurate emulation of the wavefunction in the non-empty branch, so people there must feel pain.

If you answer "No", then you assign some magic properties to consciousness, which is OK, but it should be remembered as non-MUH axiom.

I'm agnostic about some other things like souls, so I say Yes.

And I have no problem in acknowledging that the wave function on nonexisting brains may be a quite close copy of the wave function on an existing brain. But above are only functions on possibly existing configurations. So above do not feel any pain. It is only the existing configuration which can feel pain.

I do not assign special properties to some consciousness, but to the real configuration. In comparison with functions on the space of all imaginable configurations. Such functions may also really exist, but they are simply another, completely different type of entity.

 

[Dmitry67]

It is only the existing configuration which can feel pain.

They are both "existing" or "real" in terms of MUH
Of course, one has "particles" inside and one not, but that fact is not enough to call one "more real" than another, you can do it only using special non-mathematical axiom.

So you are denying MUH explicitly, which is OK, we just have different set of axioms.

 

[Ilja]

They are both "existing" or "real" in terms of MUH
Of course, one has "particles" inside and one not, but that fact is not enough to call one "more real" than another, you can do it only using special non-mathematical axiom.

So you are denying MUH explicitly, which is OK, we just have different set of axioms.

Please read again - I do NOT name one branch more real than another one. Above branches are branches. ABOVE branches may be real. Or may be not - that's a different question. But ABOVE have THE SAME degree of reality.

The difference is between above branches - which are FUNCTIONS on configuration space, and the CONFIGURATION (or, as you prefer to name them, the particles) which is an element of this space. These are clear and trivial mathematical differences. And even if the functions do exist, these are qualitatively very different entities.

 

[bohm2]

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

I'm not sure if you read this post by Maaneli but I thought he/she gave a pretty good argument against the nomological model:

There is a very serious and obvious problem with their interpretation; in claiming that the wavefunction is nomological (a law-like entity like the Hamiltonian as you said), and because they want to claim deBB is a fundamentally complete formulation of QM, they also claim that there are no underlying physical fields/variables/mediums in 3-space that the wavefunction is only a mathematical approximation to (unlike in classical mechanics where that is the case with the Hamiltonian or even statistical mechanics where that is the case with the transition probability solution to the N-particle diffusion equation). For these reasons, they either refuse to answer the question of what physical field/variable/entity is causing the physically real particles in the world to move with a velocity field so accurately prescribed by this strictly mathematical wavefunction, or, when pressed on this issue (I have discussed this issue before with DGZ), they simply deny that this question is meaningful. The only possiblity on their view then is that the particles, being the only physically real things in the world (along with their mass and charge properties of course), just somehow spontaneously move on their own in such a way that this law-like wavefunction perfectly prescribes via the guiding equation. This is totally unconvincing, in addition to being quite a bizarre view of physics, in my opinion, and is counter to all the evidence that the equations and dynamics from deBB theory are suggesting, namely that the wavefunction is either a physically real field on its own or is a mathematical approximation to an underlying and physically real sort of field/variable/medium, such as in a stochastic mechanical type of theory.

http://74.86.200.109/showthread.php?t=247367&page=2

Belousek makes a similar argument here:

On the DGZ view, then, the guidance equation allows for only the prediction of particle trajectories. And while correct numerical prediction via mathematical deduction is constitutive of a good physical explanation, it is not by itself exhaustive thereof, for equations are themselves 'causes' (in some sense) of only their mathematical-logical consequences and not of the phenomena they predict. So we are left with just particles and their trajectories as the basis within the DGZ view of Bohmian mechanics. But, again, are particle trajectories by themselves sufficient to explain quantum phenomena? Or, rather are particle trajectories, considered from the point of view of Bohmian mechanics itself, as much a part of the quantum phenomena that needs to be explained?...the mere existence of those trajectories is by itself insufficient for explanation. For example, to simply specify correctly the motion of a body with a certain mass and distance from the sun in terms of elliptical space-time orbit is not to explain the Earth's revolving around the sun but rather to redescribe that state of affairs in a mathematically precise way. What remains to be explained is how it is that the Earth revolves around the sun in that way, and within classical mechanics, Newton's law of universal gravitation and second law provide that explanation.

https://springerlink3.metapress.com...efs4l0jqe1yciritzpw3w&sh=www.springerlink.com

 

[Ilja]

I do not think that it is that easy to reject the nomological interpretation of the wave function in dBB.

The main point is that we know nothing about the wave function of the universe. In fact, what we use is a simple replacement: For a large enough system, containing all preparation devices, we use trivial product initial values. Then we consider (in fact we don't - this is usually omitted) the preparation phase, and after this we can use the observed values of the preparation measurement devices $a$ to compute the effective wave function $\psi(q)=\Psi(q,a)$ of the prepared object $q$.

So, all what distinguishs the wave functions of the prepared devices are, in fact, values of the configuration of the environment used to prepare the state. It is not something which depends on the wave function of the universe - which is an unknown animal.

And all we do successfully in science does not depend on this unknown animal. Else, scientific predictions would simply fail. We use some trivial independence assumptions for this animal, if we mention its existence at all.

So there is no evidence at all that this animal is rather complex - as complex as an arbitrary function on the gigantic space of all imaginable states of the whole universe.

Another point: I think it is quite a bad idea to consider quantum theory as fundamental. The fundamental theory will not have any infinities, but dBB velocities become infinite near the zeros of the wave function. This is evidence enough that quantum theory becomes wrong for sufficiently small $\psi$.
But a function on the space of possible states of something else is an ideal candidate for being simply a description of something different which influences somehow these states. The mentioned formula for the effective wave function defines one source of this "something different" - the configuration of the environment. This may be already sufficient. If not, ok, there may be other things. But there is no reason at all to assume that we need such a large space of additional things which influence our configurations.

 

[bohm2]

I do not think that it is that easy to reject the nomological interpretation of the wave function in dBB. The main point is that we know nothing about the wave function of the universe.

Yes, this is DGZ's argument. I hope I'm not misunderstanding you but both Wallace/Brown and Valentini offered some arguments against this position. First Wallace/Brown:

Such a strategy has been advocated by Goldstein and co-workers, taking its motivation from quantum cosmology. They suppose that the wavefunction of the Universe (regarded as the solution of some Wheeler-deWitt-type equation) may turn out to be both unique and time-independent, and that this will make it appropriate to regard it more as a physical law than as a physical object. Two comments should be made about this research program. Firstly, it is a research programme. Bohmian quantum cosmology, as with all other proposals for quantum cosmology, is at present purely speculative, beset with technical and conceptual problems, and quite disconnected from experiment... As such, the existence right now of a Bohmian solution of the measurement problem based on ideas from quantum cosmology is as implausible as the notion that Penrose’s speculative suggestions about gravitation-induced collapse mean that the measurement problem is now solved. Secondly, and perhaps more importantly, even given a technically satisfactory Bohmian cosmology, it is by no means clear that we should not reify that cosmology’s wavefunction. We identified earlier three features of the wavefunction which distinguish it from the Newtonian potential: it is dynamical; it is contingent; and it is extremely richly structured. Of these, it is at best very unclear that any of them fail in a cosmological context. As far as dynamics are concerned, though the cosmological wavefunction is usually taken to be time independent, the notion of time is so controversial in quantum cosmology that we would be reluctant to jump too quickly from this time-independence to any claim about dynamics. As for contingency, it is at most an article of faith with some physicists that the Wheeler-de Witt equation has a unique solution. And as for complexity (in our view perhaps the most important criterion) the structure encoded in the cosmological wavefunction will if anything be richer than that encoded in the non-relativistic wavefunction.

Solving the measurement problem: de Broglie-Bohm loses out to Everett
http://philsci-archive.pitt.edu/1659/1/Cushing.pdf

Valentini argues similarily:

Could ψ instead be regarded as `fictitious', that is, as a merely mathematical field appearing in the law of motion for q? As already mentioned, this does not seem reasonable, at least not for the theory in its present form, where-like the electromagnetic field –ψ contains a lot of independent and contingent structure, and is therefore best regarded as part of the state of the world. Valentini (1992, p. 13) considered the possibility that ψ might merely provide a convenient mathematical summary of the motion q(t); to this end, he drew an analogy between ψ and physical laws such as Maxwell's equations, which also provide a convenient mathematical summary of the behaviour of physical systems. On this view, `the world consists purely of the evolving variables X(t), whose time evolution may be summarised mathematically by ψ' (ibid., p. 13). But Valentini argued further (p. 17) that such a view did not do justice to the physical information stored in ψ, and he concluded instead that ψ was a new kind of causal agent acting in configuration space (a view that the author still takes today). The former view, that ψ is law-like, was adopted by Durr et al. They proposed further that the time dependence and contingency of ψ-properties that argue for it to be ontological-may be illusions, as the wave function for the whole universe is (so they claim) expected to be static and unique. However, the present situation in quantum gravity indicates that solutions for ψ (satisfying the Wheeler-DeWitt equation and other constraints) are far from unique, and display the same kind of contingency (for example in cosmological models) that we are used to for quantum states elsewhere in physics (Rovelli 2004). Should the universal wave function be static-and the notorious `problem of time' in quantum gravity urges caution here-this alone is not enough to establish that it should be law-like: contingency, or under-determination by physical law, is the more important feature. Therefore, current theoretical evidence speaks against the idea. And in any case, our task here is to consider the theory we have now, not ideas for theories that we may have in the future: in the present form of pilot-wave theory, the time-dependence and (especially) the contingency of ψ makes it best regarded as ontological.

De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
http://www.tcm.phy.cam.ac.uk/~mdt26/local_papers/valentini_2008_denial.pdf

 

[mitchell porter]

The logical development of the nomological interpretation of Bohmian mechanics is to get rid of the wavefunction entirely and replace it with a nonlocal potential. The implications are easiest to understand if you work downwards from cosmology. At the cosmological level, this means that theory-building is not about choosing a wavefunction of the universe, it is about choosing a specific nonlocal potential in the universe's equations of motion. It also means that in order to model individual quantum systems, you have to be concerned with the restriction of the nonlocal potential to the relevant local degrees of freedom. There's also the question of what the usual Bohmian probability axiom corresponds to, in this picture.

But it must work in the sense that, for any particular Bohmian system, there must be an equivalent formulation which uses a nonlocal potential rather than a pilot wave. It's curious that this path has not been explored.

 

[Ilja]

First Wallace/Brown:

As such, the existence right now of a Bohmian solution of the measurement problem based on ideas from quantum cosmology is as implausible as ...

Sorry but there is no animal like a measurement problem in dBB theory. The collapse is nicely described in dBB by the Schrödinger evolution of system + measurement device and reduction to the effective wave function of the system.

Of course, to refer to canonical quantum gravity is of course not a good idea. I would never do it.

But the point is much easier and completely dBB-internal: The global wave function does not have to have a nontrivial evolution to cause a nontrivial evolution of the global configuration. All one needs is that it is not completely real. And a nontrivial evolution of the global configuration leads to a nontrivial evolution of the effective wave function of all the small subsystems we are able to consider. So the physical character as well as the nontrivial evolution of the wave functions of small subsystems can be easily explained without any physical character and nontrivial evolution of the wave function of the whole universe.

even given a technically satisfactory Bohmian cosmology, it is by no means clear that we should not reify that cosmology’s wavefunction. We identified earlier three features of the wavefunction which distinguish it from the Newtonian potential: it is dynamical; it is contingent; and it is extremely richly structured. Of these, it is at best very unclear that any of them fail in a cosmological context.

In $\psi(q)=\Psi(q,q_{env}(t))$ the effective wave function obtains its dynamics, its contingency and its rich structure automatically from $q_{env}(t)$. So, if we take Ockham's razor seriously, we should not introduce yet another dynamic, contingent and extremely rich entity without necessity. So I don't see a good justification for reifying it.