Will MWI Ever Make Sense with Probability in Quantum Mechanics?

[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.

 

[Demystifier]

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.

Neither did I. But have you seen them CLAIMING the eigenvalue realism? I haven't.

 

[Maaneli]

Neither did I. But have you seen them CLAIMING the eigenvalue realism? I haven't.

Not explicitly, but they could certainly be assuming it implicitly. And I think that that's what Valentini's argument against the motivation for the MWI shows.

 

[cesiumfrog]

How does one define probability in classical mechanics?

Classical mechanics was based on a deterministic flow over a symplectic manifold or some such, so there was no probabilities: it was entirely certain what the outcome of any given coin toss would be. A way an observer could introduce probability into their predictions would be by postulating a probability distribution for aspects of the environment that the observer is ignorant of. (Likewise, I'd be surprised if the Born rule can't be derived in MWI after presuming a probability distribution over pointer states in the environment or similar.) Throughout classical mechanics there are statements like the independence of subsequent coin tosses, the statistical equipartition of energy among degrees of freedom, the equiprobability of microstates (is this even basis-independent?)... is the justification for probability in CM really any better than the arguments for it in MWI?

 

[mitchell porter]

http://www.youtube.com/watch?v=MvaQKtVQzk4"

 

[hamster143]

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

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

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

There are 2^1000 outcomes with different light histories, and 1001 outcomes with different light counts. Each of these outcomes has a different amplitude. You're choosing to associate "universes" with light histories, which is a fairly arbitrary choice.

It is not very intuitive what "amplitude" means. This term is best treated mathematically, not intuitively. However, try to think of it this way. Suppose your system rolls a 1000-sided dice and the red light lights up only when the dice shows 1. At each step, there are 1000 "internal" outcomes, but the information about the internal outcome is lost. So, external observers think that there are only two possible outcomes. Furthermore, a naive observer might say "but wait, you expect to see 50/50 of red and blue lights, because there are only two universes at each step!" And this is obviously wrong.

You really have to think big (or small, Planck-scale small). For any splitting that you can "touch and feel" (like in this case, red light vs blue light) there are myriads of splittings and joinings occurring every 10^-43 seconds in every point, and they all create a nice-looking continuous picture if we wash over most of the details.

The question that needs to be asked is not so much the Born rule itself, but rather, "why do we expect to find ourselves in a universe with a high amplitude"? (Note the vague wording - you can't even formulate that kind of question properly!) And I believe it can be demonstrated (as I said in the other thread) that you can derive the Born rule from the axiom that universe-wide probability is monotonously related to the norm of the amplitude.

We probably need a complete QG theory to make sense of everything. Maybe there's a finite, discrete number of universes, and low-amplitude universes die off at some point. That's really an implementation detail.

 

[Dmitry67]

http://www.youtube.com/watch?v=MvaQKtVQzk4"

:)
... but now it is a Dead rule

 

[ThisIsMyName]

Dmitry67, just because your pet theory can't make sense of born rule it's a dead rule and doesn't matter?
Your religious...

Hamster, will get back to you later today

 

[Dmitry67]

The question that needs to be asked is not so much the Born rule itself, but rather, "why do we expect to find ourselves in a universe with a high amplitude"?

Yes, it was also my point, about unfair sampling.

BTW, I am not sure that we really are in the universe with a high amplitude.

I see anthropic principle (AP) as severe violaton of the Born rule. I suspect that probability of life is say 10^-200. But no matter how tiny is it, something will be observed in MWI. It is possible that life can exist only in the narrow range of the parameters of the Standard Model (if they are determined at BB). Finally, we (as observers) never appear at 1s after BB, or in the core of neitron star, or in the middle of nowhere between the galaxies. Isnt it obvious how special is our choice of the observed location in space, time, and branch?

 

[Demystifier]

And I believe it can be demonstrated (as I said in the other thread) that you can derive the Born rule from the axiom that universe-wide probability is monotonously related to the norm of the amplitude.

Of course you can derive it that way, it is trivial. But of course, the problem is to justify this axiom.

 

[hamster143]

Of course you can derive it that way, it is trivial. But of course, the problem is to justify this axiom.

Justification: we live in a probabilistic universe, in which there are likely events and unlikely events. Likely events are more likely than unlikely events. There should be something in underlying physics that differentiates them.

Mechanism of action: we know from experience that likely events tend to have more pathways leading to them than unlikely events: for example, there's one pathway towards winning the jack pot at Mega Millions for every 175 million pathways towards losing. MWI quantum amplitudes and numbers of pathways are both multiplicative. We could, therefore, presume that the amplitude reflects some kind of internal "pathway count", or a count of identical copies of each universe, with a twist (namely, that each state has an imaginary phase associated with it, and relative phases matter during evolution, dictating whether pathways add or subtract.) The specific implementation of the mechanism could come from QG.