Many worlds interpretation, probability distribution

[chupe1123]

Where exactly do the probability distributions we observe come from under the many worlds interpretation? I know it has something to do with being the only stable configurations in Hilbert space but I don't understand why.

This is my attempt to explain it in my own way, please tell me if it makes sense:
If four dimensional universes are separated perpendicularly by a fifth spatial dimension then couldn't it be that particles persist through the parallel universes as a fifth dimensional string and that the points on the string closer to our four dimensional universe would be more likely to have an effect than further points?
It seems like if that were true that the probability spectrums would look something like what they do.

I'm not a physicist so please don't throw math at me, it's too scary.

Thanks!

 

[Ger]

you can state any answer to a problem as a plausible one, but have to find the maths proving your answer. Find a closed solution which does fit the answer. And then present a solution to a problem which can not be solved, or does solve an existing problem in an easy way. Must be observable. Sorry that is most of the time maths (which is nothing more as a kind of short notation of extreem logical reasoning based on as few axioms as needed)

 

[spoirier]

I think the only effective meaning one can give to the many worlds interpretation is this :

There is no such thing as probability. Probabilities would only be an appearance for the situation where existence is divided into several "possibilities" with their respective weights, that turn out to no more interfere with each other. For example when we have an experience whose prediction is (square root of 2 / 2) "probability" to get outcome A and the rest to get outcome B, then what we have at the end is that result A receives a quantity of existence equal to (√2 / 2) (times the quantity of existence of the initial conditions), while B receives the remaining quantity of existence.

So in my sense the problem here is not mathematical but metaphysical : it is mathematically consistent to conceive existence as a quantity that can be divided among several possibilities in irrational proportions, but it does not make metaphysical sense that fits what we feel "existence" should mean.
This is why I do not agree with the many worlds interpretation but I prefer the "Mind makes collapse" interpretation. See more details in my site (settheory.net), that includes an introduction to quantum physics with a simplified version of its mathematical core expressed in geometric terms.

 

[haael]

@chupe1123

The picture you have is not right. Many worlds interpretation is not about parallel universes, this is just a slogan invented by press. There is no fifth dimension that you can pass to travel to another universe. You could however imagine that there is a gigantic configuration space, each point of it is a separate universe. Alas, our normal distance dimenstions are something completely different to the configuration space dimensions. "Travelling" through the configuration space has nothing to do with a physical movement as we understand it.

Where exactly do the probability distributions we observe come from under the many worlds interpretation?

The many worlds interpretation has a problem with providing an accurate answer. One possible answer is that the most probable experiment outcome is the one where the observer remains alive. Suppose that a bunch of observers are performing a chain of experiments. Each experiment can give virtually any result - including a result that kills the observer. But dead observers can not publish the results they obtained, so only the living observers' reults do count.

One thing you get from this interpretation is that people should be immortal. This thought experiment is called the "quantum suicide" - try googling it.

I personally don't believe in these explanations, despite I believe in MWI.

 

[chupe1123]

Thanks guys!

@haael I'm familiar with quantum suicide but I don't see how the 'dead experimenters can't publish results' explanation accounts for something like the interference pattern in the double split experiment.
Maybe a fifth spatial dimension isn't the appropriate way to describe how universes are separated in hilbert space, I'll take your word for it. Is there any conception of a "distance" that would make sense?
@Ger, I know- I'm just asking if it sounds plausible to someone with experience in the field before I spend years investing in the necessary knowledge to prove it myself.
@spoirier- I'm curious- I will check out your site.

 

[mfb]

Maybe a fifth spatial dimension isn't the appropriate way to describe how universes are separated in hilbert space, I'll take your word for it. Is there any conception of a "distance" that would make sense?

The influences becomes extremely small extremely quick, assigning a "distance" would not give anything interesting I think.

In MWI, you always have observers which observe "probable" (in the sense of probabilistic interpretations (now: PIs)) events with a large amplitude and observers which observe "improbable" events with a small amplitude.
While this is not a theoretic problem, this gives no direct way to explore the amplitude distributions - we could not do interesting science with that. However, there is a flaw in this argument.

Let's look at PIs again: We could be unlucky and do not get an interference pattern in double slits at all. The probability is just incredibly low.
In the same way, you can perform science with MWI with correct result in all worlds with correspond to large probabilities in PIs.To make this a bit more formal:
Assume that the whole universe can be described as the evolution of a wave function. Develop some theory about the world which can describe the evolution of the wave function. Note that, given appropriate initial conditions, the wave function can split into a number of different parts, which are (in really good approximation) independent of each other. Each part is called a world.
Define a measure for worlds, which is just the integral over the amplitude squared over their region in phase space.
The evolution has to conserve the measure for all worlds (PI equivalent: probabilities always add up to 1). The theory now allows to predict how the wave function can split into several parts by things usually called "observation".

Define a test as a series of measurements in some way. Sort the possible results in two groups: One with a large measure (and preferably, but not necessarily, a small set of different measurement results) and one with all other results with a small sum of amplitude squares. Publish that you will perform this test (that is good scientific practice!) and that the test is a success in all worlds which are part of the group with large measure. Perform the test.
Now, some worlds will see a success and some will not. But here is the trick: If the theory was right, most of the measure will see a success. If not (in a significant way), a large part of the measure will see a failure.
With more and more tests, every theory which is wrong gets discarded in worlds containing a measure of ~1*. A correct theory will see a lot of confirmations and kept in worlds containing a measure of ~1*. A lot of worlds will come to wrong scientific conclusions, but their total measure goes to 0.

Comparison to PIs: There are many ways how experiments can go wrong, but the probability of all experiments going wrong tends to 0.*strictly speaking, human scientists do not exist in all worlds, but this does not matter. It can be scaled to the fraction of the world with humans inside.

 

[haael]

I don't see how the 'dead experimenters can't publish results' explanation accounts for something like the interference pattern in the double split experiment.

Photons behave just as they do. If they did differently, the universe would be harder to live in. Maybe the double slit pattern is the consequence of the very same thing that allows us to live, i.e. electrons sitting on their orbits or molecules hanging together.

When everything is possible, we see only what allows us to exist. Do you get the idea?

Note that this is not a well-accepted explanation and MWI doesn't really answer what you asked.

 

[malreux]

“Where exactly do the probability distributions we observe come from under the many worlds interpretation? I know it has something to do with being the only stable configurations in Hilbert space but I don't understand why.”
The answer to your question is actually pretty involved, but let me initially side step it and offer some motivation for (a) that there is some problem of probability peculiar to many worlds and (b) some resolution to such.
(My answer borrows heavily from David Wallace’s new book ‘The Emergent Multiverse’ – the relevant places to look are chapters 4 -6.)
It’s often claimed there is a huge problem or puzzle regarding probability in the Everett interpretation. The most common argument (in conversation, if not in papers) goes something like this:
“Probability enters physics in one of two ways: either, as in classical statistical mechanics, it represents our ignorance of the microstate of the system, or probability represents the fact the system under investigation isn’t deterministic. In the former case, if we knew everything there is to know about the microstate, and had sufficient computing power, we could eliminate probabilities. In the latter case, even if we did know everything about the microstate, that wouldn’t be sufficient to determine it at later times. (Early hidden variable theories tended towards the former, and most dynamical collapse theories tend towards the latter).
Neither of these apply to the Everett interpretation. The Schrodinger equation is deterministic, and though knowing the exact microstate is unrealistic, normally we know enough about the microstate to calculate what the branching structure will be including what weights should be attached to each branch.
Further, in both the ignorance case and the stochastic case the probabilities can be taken as labelling *alternative probabilities* - we can’t understand the weights in the Everett interpretation that way: all the branches are actually there!
So, whatever these ‘weights’ may be, they aren’t probabilities. And since our empirical evidence for QM is entirely composed of its probabilistic predictions, that makes the Everett interpretation empirically inadequate.”
The usual Everettian reply is something like:
“OK, let’s just forget about finding out about the ‘nature’ of probability. Mathematically, how does it enter physical theory? Any theory, stripped down to its mathematical core, consists of a space of instantaneous configurations, together with a rule stating which paths through space – which histories of the system – are dynamically possible (satisfy the laws of physics). In a deterministic theory, that rule is all-or-nothing: some paths are allowed, some are not, and for each initial segment of a path (i.e. for each path specified up to some time t) there is at most one path which has that segment as its initial segment.
Stochastic theories relax that rule: for a given initial segment, the theory places a probability measure over all histories which have that segment as their initial segment. Again, never mind what that measure is conceptually: mathematically, it’s just a function from sets of histories to positive real numbers, additive over disjoint sets of histories, and such that the set of all histories with the given segment as initial segment gets probsbility one.
Now, at the *fundamental* level, the Everett interpretation is deterministic, not stochastic. The configuration space is Hilbert space, and the Schrodinger equation picks out exactly one dynamically allowed trajectory through every point in the space.
Recall that there is an *emergent* branching structure realized by the underlying unitary dynamics. In that emergent theory, the configuration space can be taken to be the space of instantaneous decoherence-selected projectors discussed in the above reference (chapter 3). The emergent dynamics assign a weight to each history, and thus a relative weight to each history relative to each of its initial segments. And because of decoherence, these weights obey the axioms of a probability measure (at least within the degree of precision at which the emergent description itself is valid) – see Greaves (2004), Greaves & Myrvold (2010) and Greaves & Wallace (2006).
So, mathematically, formally, the branching structure of the Everett interpretation (‘many worlds’) *is* a stochastic dynamical theory. ‘Nuff said.”
Whilst I sympathise with this common reply, one has to admit that the criticism has some bite. What the reply does demonstrate is that this problem is a higher-level philosophical problem.
As to the nitty-gritty re cashing out a many worlds solution, I’d recommend the above references.

 

[malreux]

PS In case it wasn't clear in my reply, I'm using 'many worlds' and 'the Everett interpretation' interchangeably, to at least describe the same family of 'interpretations'. Note that not all authors would agree with this usage (including me!)...

 

[chupe1123]

Thanks malreux, I'm a little closer to understanding what "the probability distribution" is in many worlds. I think I'll check out Wallace's book.