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Source-"fabric of reality"- author d. deutsch - his contention, as I understand it, is that quantum interference is caused by "almost, but not identical quite quantum entities" , e.g. electrons, from the multiverse causing this interference.

His book is, by it's very nature, written as popular science, so it's not in any way mathematically (or even physically) rigorous on many points regarding wave interference.

does this necessarily imply that there is a commonality, (perhaps even identical quantum electron fields in all universes) between every one of the separate electron fields?

otherwise, to my knowledge, this interference would not occur, as relative phase difference is all that I can conjecture that could produce this interference effect?

If the electron fields between universes were not identical, is there any other mechanism that could produce this intererence effect?

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Many-worlds ideologues like Deutsch never had an exact mathematical model of how the different universes interact, or even of what parts of the wavefunction are the universes. By the way, I regret the inflammatory term "ideologue", but neutered terms like "believer" or "advocate" are not strong enough for me. People like Deutsch combine aggressive advocacy for the correctness of the many-worlds interpretation (MWI), while not having a rigorous concept of what a "world" is.

A layperson hearing about quantum mechanics, through all the homely examples like the cat that is dead and alive at the same time, will naturally think that wavefunctions or quantum states naturally consist of a weighted sum of world #1 plus world #2 plus world #3... but it's not that simple. Partly it comes back to the uncertainty principle, e.g. the trade-off between knowledge of position and knowledge of momentum (which is mass times velocity).

To go from a general wavefunction, to position probabilities, you can break the wavefunction down into a sum of position "eigenstates" - simpler wavefunctions which correspond to the particle(s) having definite positions. But to get momentum predictions, you break it down into a different sum, a sum of momentum eigenstates. (In terms of waveforms, the difference between a position eigenstate and a momentum eigenstate is the difference between a waveform which is peaked at one point and which is zero everywhere else - that's a position eigenstate - and a waveform which extends everywhere and consists of waves of constant wavelength - that's a momentum eigenstate.)

The more general rule, is that to get predictions for some observable property, you break the wavefunction into a sum of eigenstates or eigenfunctions for that particular observable property. The eigenstate is a state where that property definitely has a particular value - with 100% probability. A sum of eigenstates with different eigenvalues corresponds to some probability for one value, and some probability for the other value. And there are definite rules or patterns for what sort of waveforms / functions / quantum states, are the eigenstates for a particular observable property like position, momentum, energy, etc.

The essence of the many worlds approach, is to say that the wavefunction is a real thing, the fundamental thing in nature, and the eigenstates that it contains, are the many worlds. But there are multiple ways to decompose a wavefunction; which one, if any, is the correct one? Common sense would probably favor the position eigenstates, because they most resemble the world of common sense. But the preference among many-world believers is to say that no particular choice of eigenstates is preferred. They think they can do without a "preferred basis" (as it is called), just as relativity does without an objective universal time coordinate.

However, this has never been turned into a coherent ontology or picture of reality. So at bottom, many worlds just consists of orthodox quantum mechanics, plus rhetoric and vague intuitions about multiple worlds. It does not consist of a mathematically exact model in which there are definite worlds that interact in an exactly specified way. In the last few years, that sort of theory has finally been defined mathematically, under the name "many interacting worlds" (MIW). But it is a modification of quantum mechanics, a modification made precisely so as to specify which eigenstates are the worlds, and to have definite laws of inter-world interaction. Back when Deutsch wrote The Fabric of Reality, no such theory existed - his remarks about the double slit experiment being explained by the interaction of photons in our world with "shadow photons" in other worlds are pure rhetoric.

So it's a little hard to answer your question within the MWI framework, because that framework only exists in a vague way. Someone working on MIW might be able to answer it in exact terms.

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The Many Worlds Interpretation is not designed to make any different predictions than any other interpretation, as such you can use any mathematics from any other interpretation and it works fine.

That's because an interpretation is fundamentally just a story you put on top of your experimental predictions. If your story has more things in it than another interpretation (both particles and fields, for instance) then you might need more equations or math than someone else to tell your story, but in the end the math that you end up actually using to make your actual experimental predictions must/has-to-be equivalent to the other person's math for their interpretation that they use to make actual predictions or else they aren't different interpretations they are different theories.

Some interpretations have a collapse, and the many world interpretation simply replaces each instance where there would have been a collapse (in a theory that has a collapse) into a branching of a world into a plurality of worlds, one for each eigenvalue of the observable that would have caused a collapse (in a theory that has a collapse). It basically replaces a prediction that one eigenvalue is observed with a prediction that one eigenvalue is observed per world. And that prediction is experimentally indistinguishable. Since the interpretations with a collapse don't have any math whatsoever to explain how an outcome develops or is picked, the many worlds interpretation also isn't required to model that. But since there are interpretations that have no collapse, the many worlds interpretation can use any of that math (or any new math it wants), and can just refers to those disjoint post-measurement outcomes as worlds (or anything one-to-one correlated with distinct worlds). The only requirement on an interpretation is that the experimental predictions match.

OK. So, if a world is just a name for a post-measurement result (or something 100% correlated to that), then why is it involved in a story about pre-measurement explanation? Well, after the measurement there is an eigenvalue/eigenspace/anything-100%-correlated-to-that, but before the measurement that current wavefunction can be written in terms of combinations of eignvectors in those eigenspaces. So the words are available if you want to describe things in terms of that. But your wavefunction might already be one of those eigenvectors, in which case it evolves the way it does without there being any other eigenvectors. And there might not be a branch if there is only one eigenvalue in the wave. So attributing the dynamics to a plurality of eigenvalues when there is sometimes a monolithic eigenvalue is misleading as a completely general explanation, but it could be fine for a specific situation or explaining some aspect of the process. However, I don't think it is related to your question.

You question deals with identity, and while you use some terminology that I personally would restrict to quantum field theory, I think you are still talking about quantum mechanics. In quantum mechanics, you deal with configuration space, which is where you specify the position or momentum of every single particle in the entire universe. Two points in configuration space are not close unless the entire configuration is close, just one particle being far away from where it is in the other configuration means you are far away in configuration space. There is a symmetry in the wave about how it deals with identical particles, but the wave depends-on/determines the configuration, so it is 100% not some wave in a 3D space (or 4D spacetime)

Interference is a name for a combination of waves (at the same point in configuration space) that can have a length of the sum that is different than the sum of the lengths, this is a common thing with vectors, so it just says that the wave is vector valued, in this case, that it is complex-valued (so 2d vector valued). Since it is only points in the exact same point in configuration space that interfere, interference only happens if (there is a nonzero amplitude for) every single particle in the entire universe to be in the exact same spot. Every single one. So it definitely better be an electron or a muon, no coyness allowed, since a configuration with an electron there is totally different than one with no electron there and a muon instead.

There is a completely different theory called Many Interacting Worlds that is actually a different theory (not just a different interpretation), but it has different classical worlds that interact between worlds in a way where they collectively act like there was something like a wavefunction. As the number of worlds gets large, the predictions approach standard quantum mechanics. However this is different than Many Worlds Interpretation where the number of worlds changes, and a MIW world is a classical configuration, whereas a MWI world is a post measurement eigenvalue/eigenspace/something-100%-correlated-to-that thing that post measurement has no effect on other worlds. So, they are entirely different things.

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  • $\begingroup$ thank you very much for your considered and helpful response... i AM talking about quantum mechanics in the question above because I do not yet (if ever!) have the the experience of much else. My problem is that I (wrongly) repeatedly attempt to put my questions in Q.M or (worse yet) classical terms because that's all I know to date. A common theme of my questions so far is that there are far more subtleties to them that I ever realised before posing them, so in future I will try to look at them from as many different angles as possible before I post them. $\endgroup$ – user74893 Mar 13 '15 at 21:57

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