Inés - again after many delays, I'm responding to your note above.
>> Out of the many branches of the wavefunction, the ones that progress are the ones that give rise to a world that can still progress. Or, if we want to link it with Marc's idea, to a world that still contains the observer that was observing the universe an instant before.
That's an interesting way of putting it, and does capture the point I wanted to make. I developed the analogy with biological evolution a bit further in a previous essay. I certainly agree that for these ideas to be useful, we need to show that they entail many of the specific features of quantum mechanics. We evidently live in a world where each observer's viewpoint and local context keeps getting carried forward very reliably, from moment to moment, always with small changes reflecting its interaction with other viewpoints. Ideally we could demonstrate that to do this, the universe needs to have the kind of complex and finely-tuned physics that our world in fact has, at the quantum level.
>> I do understand the part that the outcome of the random choice has to be compatible for both sides of the system. That's what entanglement is about, right? Once an interaction develops, subsystems become coupled. Now, how do you derive Born's rule from here? I always thought it was a starting point, not something to be derived.
Entanglement means that when two systems interact, their quantum states become coupled, so that a subsequent measurement made on one of them constrains the results of a measurement made on the other. Such interactions don't "collapse" the wave function of either system. In fact, the big mystery of QM is how this "collapse" happens at all. Every interaction described by the theory just entangles things, so it's very unclear under what circumstances what we call a "measurement" can take place.
Born's rule is usually presented as a basic postulate of QM, as you say. But apparently it's possible to describe QM mathematically in different ways, and Born's rule is sometimes derived from other axioms. For example, you could look at this paper and this one. But these arguments are way over my head - you're much better equipped to follow them than I am.
Here's what I think I understand about this, though. Ordinary statistics assigns probabilities to various outcomes that together sum to 1. Quantum statistics are different, in that the various outcomes have "probability amplitudes" that sum to 1. No one really knows what that means, but to get the actual probability of an outcome when a measurement is made, you basically square the amplitude.
Now the thought I offered so cryptically in my comment in Marc's thread is that this squared amplitude is just the probability that (a) the measured system selects a particular outcome at random, and (b) the observing system also happens to select that same outcome at random.
In effect, the results of a measurement in QM are "doubly random" - that is, a measurement only happens when both the object and the observer accidentally make the same choice.
In classical physics, by contrast, when we measure something, the observed information was already there to begin with. The measured object had definite properties all along, and this information just gets copied over to the observer. But in QM the information only comes to exist in the course of the measurement, through a kind of accidental agreement between object and observer. I'm trying to understand this as a kind of natural selection.
There is an interpretation of QM that explains the Born rule just this way, called the "Transactional Interpretation". Ruth Kastner has done a remarkable job developing it - she has an interesting website and a couple of books - the more recent one is a popularization (that I haven't read), the earlier one a more technical treatment. This treats every interaction as a mutual agreement between an "emitter" and an "absorber", through a theory involving time-reversed action. It's a fairly well-accepted interpretation, though largely ignored in the physics community, though I don't know why time-reversed action should be considered any less reasonable than the more popular many-worlds interpretation, for example.
My own feeling is that the somewhat cumbersome mechanics of this theory isn't really needed. Kastner is a self-described "realist", and her work is useful to me mainly as confirmation that my thoughts about the Born rule work out at a technical level. But in the conversation with you and Marc, we're imagining reality as somehow "co-emerging" in processes that evolve meaningful information between "agents" and "observers", and I'm not sure the underpinnings of Ruth's theory are relevant here.
I've been trying to work out my intuitions about all this through several FQXi essays, hoping to pull it all together into some more coherent presentation. But that's as much clarification as I can manage at the moment!
With thanks and best wishes -- Conrad
