Will MWI Ever Make Sense with Probability in Quantum Mechanics?

[Fredrik]

They're all essentially the same because they all start by throwing out the Born rule. That move is the cause of all their problems, but it's not what brings many worlds into the ontology. The many worlds are brought in by the assumption that QM describes a physical system. (Note that that's a stronger statement than to just say that QM makes predictions about results of experiments). So you can avoid the problems by keeping the Born rule, and still have many worlds.

Edit: On second thought...the assumption that QM describes reality may not be enough. Right now I'm thinking that we may have to assume specifically that it's the correlations between subsystems that describe reality, as in von Neumann measurement theory and David Mermin's "Ithaca" interpretation. (Mermin's definition of his interpretation looks a lot like how I would define a non-crazy MWI...but Mermin doesn't conclude that there are many worlds. He thinks that we can be saved from that obvious conclusion by...uh...mysterious and so far unknown properties of consciousness).

 

[ThisIsMyName]

Fredrik, isn't it funny how people just want to solve every problem with consciousness? :P
Dmitry67 (no offense) claims the Born Rule MWI problem can be solved simply by saying "A future theory of consciousness will explain why we percieve the born rule"... :P

I'll look into the Ithaca interpretation, name sounds familiar so maybe I've read about it before

 

[Fredrik]

Fredrik, isn't it funny how people just want to solve every problem with consciousness? :P

Yes, it is kind of funny.

I'll look into the Ithaca interpretation, name sounds familiar so maybe I've read about it before

The relevant links can be found in post #15 in this thread.

 

[Dmitry67]

It's obviously a better approach to the measurement problem than CI, but I doubt it's better than TI, dBB or a future interpretation.

Trying to catch up with the thread...
Just quick note: TI belongs to the same group of 'collapse' interpretations, and I believe is also a history. What is left: Ensemble + Non collapse interpretations: MWI and BM. Wavefunction is the same in MWI and BM.

Second note: while MWI has fundamental problems with Born rule, BM has fundamental problems with definition of reality, so I can't say that BM particles solve any problems, they just replace one problem with another.

 

[Demystifier]

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.

The Holland's book is an excellent book. You will find there almost everything you might want to know (except the results found after this book) on dBB. The most important part of the book is Chapter 8. You don't understand dBB until you understand Chapter 8.

 

[Maaneli]

Wavefunction is the same in MWI and BM.

Not quite. MWI assumes what Valentini calls 'eigenvalue realism', whereas deBB does not.

BM has fundamental problems with definition of reality

Please elaborate on why you think this.

 

[Demystifier]

Second note: while MWI has fundamental problems with Born rule, BM has fundamental problems with definition of reality, so I can't say that BM particles solve any problems, they just replace one problem with another.

Interesting view!
But I think my food analogy helps:
https://www.physicsforums.com/blog.php?b=6

 

[Demystifier]

Please elaborate on why you think this.

He has explained it in many other posts. Basically, if wave function is also real, then why empty waves are not real? This is what confuses him. And my answer has not satisfied him.

 

[Demystifier]

MWI assumes what Valentini calls 'eigenvalue realism', whereas deBB does not.

I don't think that MWI assumes eigenvalue realism, at least not the modern variant of MWI based on decoherence.

 

[Dmitry67]

1 Not quite. MWI assumes what Valentini calls 'eigenvalue realism', whereas deBB does not.

2 Please elaborate on why you think this.

1 In BM, wavefunction is real :) But check #2
2 Demistifier had already explained it a little bit.

In fact, the BM description of reality is confusing. n BM wavefunction is real (all braches). However, worlds without BM particles are not. If S.cat is dead, then wavefunction of alive cat is real, but the cat itself is not!

This problem is not fundamental, however, it is just how we use words (tags). In BM it is something like 'half-real wavefunction' + 'particles' = 'real reality'

The fundamental problem arises if we ask 'is half-real observer consious?' If it is, then the whole theory is not different from MWI. If it is not, then WHY?

It is not compatible with Strong AI hypotesis:
http://en.wikipedia.org/wiki/Chinese_room#Strong_AI
For me it is pure magic: BM particles, 'injected' into wavefunction, make it conscious, while the same wavefunction of a brain without BM particles is not! Note that the evolution of brain wavefunction does not depend on the BM particles... Pure magic...

 

[Maaneli]

I don't think that MWI assumes eigenvalue realism, at least not the modern variant of MWI based on decoherence.

You deny that MWI (including the modern variant based on decoherence) assigns an ontological status to the eigenvalues of linear operators acting on the wavefunction? If so, then how do you understand the ontology of MWI?

 

[Demystifier]

You deny that MWI (including the modern variant based on decoherence) assigns an ontological status to the eigenvalues of linear operators acting on the wavefunction? If so, then how do you understand the ontology of MWI?

Just the wave function, and nothing else. Perhaps the best way to explain it is through the tree analogy:
https://www.physicsforums.com/showpost.php?p=2330840&postcount=8
Different branches of the tree do not know about each other, but they are all there.

 

[Maaneli]

BM wavefunction is real (all braches). However, worlds without BM particles are not. If S.cat is dead, then wavefunction of alive cat is real, but the cat itself is not!

It sounds like you are using two different notions of 'real', and I think it would help to distinguish between the two. The empty waves are indeed ontological in deBB, just as much so as the non-empty waves. But in deBB, Schroedinger's cat (and all fermionic matter in general) is made up of the particles only. What then distinguishes between the empty and non-empty waves? They behave differently under certain classes of measurement operations, and have different classical limits.

Here is a concise discussion by Valentini (page 14) on how these measurement operations differ, and how, in light of this difference, one should interpret the empty wave in deBB:

... one might argue that each packet ψ1 and ψ2 behaves like a hydrogen atom, under operations defined by changes in the external potential V . Specifically, the motion of the empty packet ψ1 will respond to changes in V , in exactly the same way as will the motion of the occupied packet ψ2. One might then claim that, if one regards each packet as physically real, one may as well conclude that there really are two hydrogen atoms present. But this argument fails, because the similarity of behaviour of the two packets holds only under the said restricted class of operations (that is, modifying the classical potential V ). In pilot-wave theory, in principle, other experimental operations are possible, under which the behaviours of ψ1 and ψ2 will be quite different.

For example, suppose one first carries out an ideal subquantum measurement, which shows that the particle is in the packet ψ2. One may then carry out an additional experiment — say an ordinary quantum experiment, using a piece of macroscopic apparatus — designed to find out whether or not a given packet is occupied. One may predict that, in the second experiment, if the operation is performed on packet ψ1 the apparatus pointer will point to ‘unoccupied’, while if the operation is performed on ψ2 the pointer will point to ‘occupied’.11 It will then become operationally apparent that ψ1 consists solely of a bundle of the complex-valued ψ-field, whose centroid happens to be simulating the approximately classical motion of a hydrogen atom in an external field (under the said restricted class of operations).

It is of course hardly mysterious that in some circumstances one may have an ontological but empty ψ-packet whose motion approximately traces out the trajectory of a classical body — just as, in some circumstances, a localised classical electromagnetic pulse traveling through an appropriate medium (with variable refractive index) might trace out a trajectory similar to that of a moving body. In both cases, it would be clear from other experiments that the moving pulse is not really a moving body.

De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
Authors: Antony Valentini
http://arxiv.org/abs/0811.0810

It is not compatible with Strong AI hypotesis:
http://en.wikipedia.org/wiki/Chinese_room#Strong_AI
For me it is pure magic: BM particles, 'injected' into wavefunction, make it conscious, while the same wavefunction of a brain without BM particles is not! Note that the evolution of brain wavefunction does not depend on the BM particles... Pure magic...

First of all, there is very little evidence to support the notion that Strong AI is the correct approach to understanding human consciousness. Second, it is simply unnecessary to consider the complications and controversies of AI and consciousness when trying to understand the distinction between deBB and MWI.

 

[Maaneli]

Just the wave function, and nothing else. Perhaps the best way to explain it is through the tree analogy:
https://www.physicsforums.com/showpost.php?p=2330840&postcount=8
Different branches of the tree do not know about each other, but they are all there.

So let me see if I understand you. You agree that the decomposition of the wavefunction into a linear superposition of eigenstates is ontological in MWI, but you deny that the eigenvalues of each eigenstate are ontological? If so, then this sounds just like the interpretation of the wavefunction in deBB, but without the particle. And then I find it difficult to make sense of measurements and observables in MWI, since MWI does not have any means by which to prefer the position basis a priori.

 

[Demystifier]

And then I find it difficult to make sense of measurements and observables in MWI, since MWI does not have any means by which to prefer the position basis a priori.

Not a priori, but yes a posteriori. The trick is in the theory of decoherence. Since all interactions between wave functions in nature are LOCAL, it turns out that, due to decoherence, the macroscopic branching always occurs in the position basis, or more precisely that detector wave functions do not overlap in the position basis. This fact does not depend on interpretation.

This fact is crucial for consistency of the Bohmian interpretation. It is less crucial for MWI, but in the MWI-context explains the emergence of a special role of the position basis.

 

[Dmitry67]

Maaneli, there is a hidden assumption in that explanation. Yes, of course you can tell experimantally 'empty' systems from the 'occupied' ones... but... but only assuming that the experimenter is REAL. Then there is a simple induction. REAL observer sees real things, which interact with other real things etc.

No matter how obvious that assumption is to our 'common sense reasoning', it is an assumption. Without that assumption that logic fails. Example: how an observer can (experimentally) detect is he/she is real or not if he is not sure :) ?

I claim that that assumtion can't be derived from anything, so it is a pure axiom in BM requivalent to 'only occupied systems can be consious'

 

[Demystifier]

Second, it is simply unnecessary to consider the complications and controversies of AI and consciousness when trying to understand the distinction between deBB and MWI.

I agree. But to understand the Dmitry's point of view, it seems that he does not merely want to have an interpretation of QM. Instead, he wants to have an interpretation of EVERYTHING, so he cannot simply disregard consciousness and AI as irrelevant. For him, an interpretation of QM that disregards consciousness and AI is incomplete, and therefore not completely satisfying.

 

[Demystifier]

I claim that that assumtion can't be derived from anything, so it is a pure axiom in BM requivalent to 'only occupied systems can be consious'

Yes, it is an axiom, and yes, this axiom can be questioned.

However, I do not think that this axiom is unreasonable. After all, one has a similar axiom in classical mechanics, and nobody complains about this axiom in classical mechanics.

In my tree and ant analogy, it is also not unreasonable to assume that only ants, and not the tree, are conscious. This assumption can (and should) be questioned, and yet it is not an unreasonable assumption.

 

[Dmitry67]

I agree. But to understand the Dmitry's point of view, it seems that he does not merely want to have an interpretation of QM. Instead, he wants to have an interpretation of EVERYTHING, so he cannot simply disregard consciousness and AI as irrelevant. For him, an interpretation of QM that disregards consciousness and AI is incomplete, and therefore not completely satisfying.

Well, based on Tegmarks MUH, TOE has null interpretation, so it can't have any additional non-mathematical axioms. That particular axiom is non mathematical.

 

[Tomsk]

Mermin's definition of his interpretation looks a lot like how I would define a non-crazy MWI...but Mermin doesn't conclude that there are many worlds.

Have you read of the relational interpretation by Carlo Rovelli? It seems to me to be quite similar to the Ithaca interpretation, but it doesn't prioritize consciousness, Rovelli specifically says any physical system can act as observer, not just conscious ones. He also says that QM is complete so I think it could be classed as a 'non-crazy MWI'. He also doesn't conclude that there are many worlds, but rather there is no such thing as an observer independent reality, which seems like a more sensible alternative the more I think about it!

 

[Demystifier]

I think the relational interpretation can be viewed as a compromise between Copenhagen and MWI. (Which does not necessarily make it better than Copenhagen or MWI. Sometimes compromises are even worse than the two extremal options.)

 

[ThisIsMyName]

This is another objection to MWI from a correspondent:

You (like many other nonphysicists who talk about MWI) seem to think solely in terms of splitting worlds - which is the idea you would get if you thought QM was based on localized randomness. A random thing happens, the world splits, and each possibility happens in a different child-world, and the processes repeats. But that is *not* how it works, because QM also involves convergence of probability streams, and furthermore, they can *cancel*, because the streams can have negative 'amplitude'. Thus in the double-slit experiment the dark patches are places where no photon arrives because the amplitudes for the two possibilities (travel via one slit, travel via the other slit) cancel at that point. How can you explain that in terms of worlds? That world doesn't happen because the two precursor worlds cancel? It very clearly doesn't make sense.

Thoughts?

 

[Hurkyl]

Thoughts?

It sounds like he's foisting an a priori idea of what he thinks "world" means onto the mathematics, rather than letting the mathematics tell him what a "world" ought to be.

 

[Tomsk]

I think the relational interpretation can be viewed as a compromise between Copenhagen and MWI. (Which does not necessarily make it better than Copenhagen or MWI. Sometimes compromises are even worse than the two extremal options.)

Maybe... personally I think it's better than both put together.

 

[Demystifier]

Maybe... personally I think it's better than both put together.

Maybe ...
But for me, the ONLY problem with MWI is the Born rule, and such an approach does not help in it.
If the reality is relational, why some relations have a larger probability than the others?

 

[Fredrik]

Have you read of the relational interpretation by Carlo Rovelli? It seems to me to be quite similar to the Ithaca interpretation, but it doesn't prioritize consciousness, Rovelli specifically says any physical system can act as observer, not just conscious ones. He also says that QM is complete so I think it could be classed as a 'non-crazy MWI'. He also doesn't conclude that there are many worlds, but rather there is no such thing as an observer independent reality, which seems like a more sensible alternative the more I think about it!

I'm familiar with it. I read the article a few years ago, before I understood MWI stuff as well as I do now. I remember thinking that he was making the sort of statements that I would expect from a clarification of what a MWI is really saying. But I didn't study the article carefully. I will probably read it again some time, but not today.

 

[Dmitry67]

This is another objection to MWI from a correspondent:

You (like many other nonphysicists who talk about MWI) seem to think solely in terms of splitting worlds - which is the idea you would get if you thought QM was based on localized randomness. A random thing happens, the world splits, and each possibility happens in a different child-world, and the processes repeats. But that is *not* how it works, because QM also involves convergence of probability streams, and furthermore, they can *cancel*, because the streams can have negative 'amplitude'. Thus in the double-slit experiment the dark patches are places where no photon arrives because the amplitudes for the two possibilities (travel via one slit, travel via the other slit) cancel at that point. How can you explain that in terms of worlds? That world doesn't happen because the two precursor worlds cancel? It very clearly doesn't make sense.

Thoughts?

The cancelling is predicted by QM and MWI.
What we call a 'branch' appears only after the measurement=decoherence.
So as soon as you do it there are no dark spots (which-way information destroys interference)

Branches never merge. You can see merging and cancelling only if you carefully preserve system with decohering with the environment, preserving the world from 'splitting'

 

[Maaneli]

Maaneli, there is a hidden assumption in that explanation. Yes, of course you can tell experimantally 'empty' systems from the 'occupied' ones... but... but only assuming that the experimenter is REAL. Then there is a simple induction. REAL observer sees real things, which interact with other real things etc.

You don't even need to necessarily appeal to experimenters. Suppose that during the Big Bang, some proportion of matter was born initially into a quantum nonequilibrium state, and some other proportion was born into a quantum equilibrium state. And suppose that these two matter distributions started interacting (e.g. mixing by Gibbs stirring). Then the nonequilibrium particles will still interact differently with non-empty branches of the equilibrium matter, than they will with the empty branches produced by the equilibrium matter.

Example: how an observer can (experimentally) detect is he/she is real or not if he is not sure :) ?

This question makes no sense to me.

I claim that that assumtion can't be derived from anything, so it is a pure axiom in BM requivalent to 'only occupied systems can be consious'

I think one could argue that the assumption is reasonable because the dynamics of the empty branches in the classical limit are not robust enough to serve as a representation of stable classical matter configurations. Again, I refer you to the following passage from Valentini's paper (the essential points are highlighted):

... it is interesting to ask if it is possible to have localised ontological packets (‘built out of Ψ’) whose motions execute alternative classical histories: that is, it is interesting to ask if the ‘strong form’ of the Claim discussed above — which in any case fails, but is still rather intriguing — could ever occur in practice in realistic models. The answer, again, is no.

For an elementary non-chaotic system, one can obtain a narrow ‘Wigner packet’ Wred(q,p,t) approximating a classical trajectory, and one could also have a superposition of two or more such packets (with macroscopic separations). One might then argue that, since Wred is built out of Ψ, we have (in a realistic setting, with decoherence) something like the ‘strong form’ of the Claim discussed above. However, the models usually involve a mixture of Ψ’s, of which Wred is not a local functional. So the ontological status of a narrow packet Wred is far from clear. But even glossing over this, having a narrow packet Wred following an approximately classical path is in any case unrealistic in a world containing chaos, where, as we have already stated, one can show only that Wred — an approximately non-negative function, with a large spread over phase space — has a time evolution that approximately agrees with the time evolution of a classical (delocalised) phase-space distribution; that is, Wred follows an approximately Hamiltonian or Liouville flow (with a diffusive contri- bution). Again, one cannot obtain anything like ‘localised ontological Ψ-stuff’ (or something locally derived therefrom) executing an approximately classical trajectory — not even for one particle in a chaotic potential, and certainly not for a realistic world containing turbulent fluid flow, double pendulums, people, wars, and so on.

One can obtain localised trajectories from a quantum description of a chaotic system, if the system is continuously measured — which in practice involves an experimenter continuously monitoring an apparatus or environment that is interacting with the system (Bhattacharya et al. 2000). Such trajectories for the Earth and its contents might in principle be obtained by monitoring the environment (the interstellar medium, the cosmic microwave background, etc.), but in the absence of an experimenter performing the required measurements it is difficult to see how this could be relevant to our discussion. And in any case, in a pilot-wave treatment, there is no reason why such a procedure would yield ‘localised ontological Ψ-stuff’ executing the said trajectories.
In a realistic quantum-theoretical model, then, the outcome is a highly de-localised distribution Wred(q,p,t) on phase space, obeying an approximately Hamiltonian or Liouville evolution (with a diffusive contribution). As in the unrealistic WKB example above, in pilot-wave theory there will be one trajectory for each system. And, while different initial conditions will yield different trajectories, there is no reason to ascribe anything other than mathematical status to these alternatives — just as in the analogous classical case of a test particle moving in an external field or background geometry. Once again, the alternative trajectories are mathematical, not ontological.

Of course, given such a distribution Wred(q,p,t), if one wishes one may identify the flow with a set of trajectories representing parallel (approximately classical) worlds, as in the decoherence-based approach to many worlds of Saunders and Wallace. This is fair enough from a many-worlds point of view. But if we start from pilot-wave theory understood on its own terms, there is no motivation for doing so: such a step would amount to a reification of mathematical structure (assigning reality to all the trajectories associated with the velocity field at all points in phase space). If one does so reify, one has constructed a different physical theory, with a different ontology; one may do so if one wishes, but from a pilot-wave perspective there is no special reason to take this step.

Finally, decoherence and the emergence of the classical limit has also been studied using the decoherent histories formulation of quantum theory.15 In these treatments, there will still be no discernible ‘localised ontological Ψ-stuff’ following alternative classical trajectories, for realistic models containing chaos. Therefore, again, the ‘strong form’ of the Claim (which in any case fails by virtue of subquantum measurement) could never occur in practice.

 

[Maaneli]

it turns out that, due to decoherence, the macroscopic branching always occurs in the position basis, or more precisely that detector wave functions do not overlap in the position basis. This fact does not depend on interpretation.

Yes, I am aware of this. But it is not clear to me that this is sufficient to provide a robust ontology for MWI in the classical limit. Also, I have not seen proponents of MWI, such as Wallace, Brown, Saunders, or even Deustch deny the assumption of eigenvalue realism, even after Valentini gave his talk at the Everett at 50 conference.

 

[Tomsk]

Maybe ...
But for me, the ONLY problem with MWI is the Born rule, and such an approach does not help in it.
If the reality is relational, why some relations have a larger probability than the others?

I'm not sure how to answer that directly but I will say that wavefunctions do collapse in RQM, so I think the frequentist approach works.

The catch is that wavefunction collapse is observer dependent - while one observer may see a wavefunction collapse, another may see entanglement created between the first observer and the system. In RQM, that is all wavefunction collapse is- the creation of a correlation between an observer and system. It represent an exchange of information between system and observer.