Prompted by Mitchell Porter, I asked on Physics StackExchange about the accuracy of the physics in the Quantum Physics sequence:
What errors would one learn from Eliezer Yudkowsky's introduction to quantum physics?
Eliezer Yudkowsky wrote an introduction to quantum physics from a strictly realist standpoint. However, he has no qualifications in the subject and it is not his specialty. Does it paint an accurate picture overall? What mistaken ideas about QM might someone who read only this introduction come away with?
I've had some interesting answers so far, including one from a friend that seems to point up a definite error, though AFAICT not a very consequential one: in Configurations and Amplitude, a multiplication factor of i is used for the mirrors where -1 is correct.
Physics StackExchange: What errors would one learn from Eliezer Yudkowsky's introduction to quantum physics?
So, let me see if I can restate what you're saying, building up a bit of the background:
1) Suppose you've got a Hamiltonian. Then the SE constrains the world to a specific set of vectors (forming some oddly-shaped manifold) in a Hilbert space on spacetime.
2) Any one of these vectors can be given an equal weight of probability.
There's more to it, but... I'd like to stop here for a moment anyway. See, these vectors are not instantaneous state vectors. Each vector is the history of a whole many-worlds universe, with all of the quantum branching included. Each vector includes ALL of the branches, all of the weights, everything.
The different vectors, here, are just the cases where different initial conditions (or boundary or other conditions, if you want to really seriously demote time) are taken.
If I'm right about this interpretation, then this isn't what the Born Probabilities are talking about. Maybe they all are real, with equal weights. No observation we could make would contradict that. Meanwhile, the Born Probabilities are, as you indicated above, highly experimentally testable.