When a quantum coin-flip happens at A the universe splits everywhere at the same time.
If you believe in relativity, that can't be true. And in fact some MWI people speak explicitly of splitting as starting locally and then spreading along the lightcone. But I don't think anyone has a working description of this, because those secondary, tertiary... quantum coin-flips would be happening and that means that the splitting light-cone has to develop new propagating splits of its own.
The union of relativity and quantum mechanics is an amazingly challenging subject, and the extension of MWI to the relativistic domain even more so. Since you don't have absolute time, you don't have a unique wavefunction of the universe evolving in time, and you can't reduce everything to a unique flow of amplitudes through configuration space. The prototypical QFT calculation is a sum over histories, in which whole relativistic histories get amplitudes, not just static, instantaneous spacelike configurations. It almost suggests a new MWI in which there's no splitting, just a stack of self-contained histories, but as usual, I don't see how to independently justify a phenomenological Born rule from this.
Also, the actual practice of QFT contains so many other hacks - complexified variables, analytic continuations - and so many bizarre transformations and re-representations of the math have been discovered in recent years (the twistor renaissance, the Hopf algebra of diagrams, AdS/CFT duality) that I expect the final answer to be something very different to what anyone imagines.
I agree that the problem of extending MWI (and for that matter, any interpretation of QM) to quantum field theory is a very difficult one. There is good reason to think that one of the central tenets of MWI -- wavefunction realism -- will not survive the transition. I said in a response to Villam's question that the fundamental ontology of the MWI is a universal wavefunction on configuration space. This is the view promoted by Eliezer in his QM sequence. It's an elegant view, but unfortunately its appeal falls apart when you start looking at QFT.
Part of th...
Today's post, Spooky Action at a Distance: The No-Communication Theorem was originally published on 05 May 2008. A summary (taken from the LW wiki):
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