So it’s not hard to get a Born rule—Everett did it nicely in his original paper. But in order to do so, he had to introduce the requirement that the probability measure of different observations should be defined for vectors in the Hilbert space of solutions to the Schroedinger equation. An extra law of physics, basically. Which is fine. But it means that many worlds isn’t necessarily simpler than other stuff.
To meet my challenge, you’d need to require the Born probabilities instead the naive probabilities using only the Schroedinger equation and a Hamiltonian, basically. By “the naive probabilities,” I mean assigning each eigenstate equal probability. Which isn’t what we observe. But if the Schroedinger equation alone isn’t enough, it would make sense that just using it gives us probabilities that aren’t what we would observe.
But in order to do so, he had to introduce the requirement that the probability measure of different observations should be defined for vectors in the Hilbert space of solutions to the Schroedinger equation. An extra law of physics, basically. Which is fine. But it means that many worlds isn’t necessarily simpler than other stuff.
What? No, seriously… what? The extra law of physics you just listed was, ‘The Schrodinger Equation determines physical reality’
Which is to say, it’s entirely redundant with the rest of quantum mechanics. This is not new information, here.
To meet my challenge, you’d need to require the Born probabilities instead the naive probabilities using only the Schroedinger equation and a Hamiltonian, basically. By “the naive probabilities,” I mean assigning each eigenstate equal probability. Which isn’t what we observe.
Did you even read the derivation? How much do you actually know about quantum mechanics anyway? Are you a physicist?
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.
So it’s not hard to get a Born rule—Everett did it nicely in his original paper. But in order to do so, he had to introduce the requirement that the probability measure of different observations should be defined for vectors in the Hilbert space of solutions to the Schroedinger equation. An extra law of physics, basically. Which is fine. But it means that many worlds isn’t necessarily simpler than other stuff.
To meet my challenge, you’d need to require the Born probabilities instead the naive probabilities using only the Schroedinger equation and a Hamiltonian, basically. By “the naive probabilities,” I mean assigning each eigenstate equal probability. Which isn’t what we observe. But if the Schroedinger equation alone isn’t enough, it would make sense that just using it gives us probabilities that aren’t what we would observe.
What? No, seriously… what? The extra law of physics you just listed was, ‘The Schrodinger Equation determines physical reality’
Which is to say, it’s entirely redundant with the rest of quantum mechanics. This is not new information, here.
Did you even read the derivation? How much do you actually know about quantum mechanics anyway? Are you a physicist?
Well, if you could say that in a way that isn’t also true for the naive probabilities that would be a good avenue to pursue. Yes. A fair bit. Yes.
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.