Will MWI Ever Make Sense with Probability in Quantum Mechanics?

[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 occurrence 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.