atyy said:
A brain state S must be defined with respect to a framework.
That doesn't seem at all correct to me.
Let's ridiculously oversimplify and assume that there are a discrete set of things that a person could be thinking about: subject 1, subject 2, etc. There are corresponding brain states S_1 in which the person is thinking about subject 1, S_2 in which he is thinking about subject 2, etc.
Then there might be an observable, the brain state, which corresponds to an operator \hat{S} that has eigenvalues \lambda_1, \lambda_2, ... and satisfies the
equation:
\hat{S} | S_j \rangle = \lambda_j |S_j \rangle
Now, we could make up another operator, \hat{T} that mixes brain states. For example, suppose it works like this:
\hat{T} |S_j \rangle = \alpha_j |S_{j+1} \rangle + \beta_j |S_{j-1} \rangle
for some complex constants \alpha_j and \beta_j
A framework consists of a choice of observables at particular times. So to simplify, let's consider a single moment of time. So there might be framework \mathcal{F}_1 which uses observable \hat{S} at that moment, and framework \mathcal{F}_2 which uses observable \hat{T}.
So let's consider a brain that is thinking about framework \mathcal{F}_1. Maybe that corresponds to brain state |S_1\rangle. Maybe a brain that is thinking about framework \mathcal{F}_2 is brain state |S_2\rangle
So a person in brain state S_1 would use framework \mathcal{F}_1 and compute such and such a probability that \hat{S} = \lambda_1 and would compute such and such a probability that \hat{S}= \lambda_2. So within framework \mathcal{F}_1, you can analyze the probability that you might have chosen framework \mathcal{F}_2 to think about.
The framework does not determine which brain state you are in. The framework determines which observables have definite values. It doesn't determine what those values are.
So there are two different levels of "worlds" in CH: The choice of which framework, and the choice of which history within a framework.
In which framework is your brain in state S1 in which you are computing probabilities according to framework 1?
Well, the way I defined things above, brain states have definite values only in framework \mathcal{F}_1. Within that framework, the brain could be in states |S_1\rangle, |S_2\rangle, |S_3\rangle, etc.. But the brain cannot be in the state
\alpha |S_1\rangle + \beta |S_2\rangle
because the framework \mathcal{F}_1 makes brain states definite.
Can your brain be in state S2 in framework 2
The way I've set things up, brain states only have definite values in framework \mathcal{F}_1. So it doesn't make sense to talk about having state |S_2\rangle in framework \mathcal{F}_2. You can talk about being in some superposition of states,though.
in which you are calculating things using framework 1?
The way I've set things up, having a definite value for the question of "which framework are you using" means having a definite brain state. Only in framework \mathcal{F}_1 do you have a definite brain state. So only within framework \mathcal{F}_1 can you calculate probabilities according to framework \mathcal{F}_2 (or \mathcal{F}_3, etc.)
