Dear Heinrich Päs,
I enjoyed your essay, since it tries to squeeze out as much information as possible out of the assumption that there is a global wave function governing all of reality (‚the universe').
I want to point you to the fact that the many-worlds-interpretation, means the assumption of a psi-ontic global wave function is a logical trickster in the following sense.
The MWI allows one to use the principle of non-contradiction together with its assumed 'complement' - the principle of contradiction.
It does so by assigning a probabilistic as well as a strictly deterministic ontology to one and the same events.
Consider for example me, obsvering a particle's spin up in a measurement. In a branched universe another individual (although totally identical with me - but nonetheless *another* individual) observes spin down for 'the same' particle.
Since such a branching, such a splitting is thought of as happening deterministically, the question remains why the individual should see the 'complementary' result of my measurement and not vice versa. One can only deny this dichotomy by assuming that 'spin up' and 'spin down' are only observer-relative due to decoherence. But one cannot deny that nature must assign a certain well-defined value in my universe.
Since I am distinct from the other individual for which nature has assigned another value (the complementary value for example), I can't even in the bird's view answer the question why it should be me and not the other individual that observes the measurement value I observe.
Since the other individual is thought of as identical with me at the moment the measurement outcome is fixed - but only as far as its thoughts and its body is concerned, but *not* in the sense that it has the exact same location within the wave function - the other individual will exactly conclude what I conclude: there is no cause in nature (at least not within a global wave function alone!) that could assign the measurement outcome that I observed. Hence there is also no cause in nature that the other individual should observe its 'complementary' measurement outcome.
If there is no cause in nature that assigns a specific event in my world or in the world of the other individual, the global wave function cannot be psi-ontic or must have some additional features.
What the MWI does here is that it mimicks a kind of 'coincidentia oppositorum', al melting of mutually exclusive concepts. It mimicks the coincidentia oppositorum of a probabilistic and a strictly deterministic version of natural behaviour for the same event. It can do so, because from a frog's view, it seems that both individuals in both branches are one and the same - with just a tiny difference in their environment (and finally in their brains where the measurement results are realized!).
Since everything is identical, even the particle before the measurement, this kind of coincidencia opppositorum seems like the mystical enlightenment of the real fundament of all there is. The price to pay is that we have married two mutually exclusive concepts by the very means we started from: namely by the superposition principle. This principle intertwines the law of non-contradiction with its 'complement', the principle of deductive explosion.
It may well be that nature is regularily confronted (before an arbitrary measurement takes place) with a multitude of possibilities that the principle of explosion represents, but the MWI does not resolve the presence of the principle of explosion. Moreover, the MWI does shift the problem of this principle from superpositions to branching in a deterministically manner, but cannot get rid of the probabilistic part, since within the formalism of quantum mechanics, there is nothing that could assign the well-defined measurement value that I will see when I make my next measurement. In this sense, the outcome must remain 'random', albeit this randomness is surely restricted by the probabilistic part of the formalism.
In conclusion, no individual in any part of the multitude of different branches within the MWI can predict the next outcome of a probabilistic quantum measurement. Since this seems to be true for me, I conclude that the MWI only mimicks a consistent interpretation. It does so to the price of eliminating an observer-independent world by claiming that it is perfectly observer-independent. Stated differently: the frog's and the bird's view cannot be complementary, since logically they have to be understood as mutually exclusive. They only can be made complementary by adding the principle of explosion.
One now may argue that the principle of explosion wasn't added at all, since it is a natural element of the formalism, means the superposition principle. This may be true, but does not eliminate the fact that the principle of explosion is present in the MWI together with the law of non-contradiction. The latter has is expression in the branching and its implication that branched universes cannot anymore communicate or causally interact with each other (unless one doesn't introduce a special kind of recoherence). The former is a consequence of the formalism itself, namely the superposition principle.
In summary, what the bird's view perceives as a kind of 'coincidencia oppositorum' is true, but it is the interwining of the principle of explosion with the principle of non-contradiction. Therefore it is no wonder that the MWI can 'deduce' all kinds of things for different branches - as long as the probability for these things to occur is not exactly zero. Or stated otherwise, as long as these things are not impossible in-principle. Since the main principle in this consideration is the formalism of quantum mechanics, the MWI and its multitude of worlds is a direct consequence of the principle of explosion.
But there is one thing the principle of explosion cannot handle. This is the fact that there are at all observers that can facilitate different interpretations of quantum mechanics. Since the formalism of quantum mechanics does not show the slightest signs that it should enable some self-reflection (in the form of observers), this formalism seems for me to not capture the universe as a whole (unless one interprets the timeless wave function as being fundamentally conscious and able to split this consciousness in some mysterious manner by its own branching).
Don't bother about my long comment, I like to make my thoughts as tracable as possible for the sake of exchange of viewpoints and arguments.
Hope the formatting problem of the fqxi-editor is now solved... :-)
Best wishes,
Stefan Weckbach