I was reading a book from the philosopher Robert Nozick (Invariances: The Structure of the Objective World), and there was something that confused me.
Around page 159 he argues that every logically possible world exists, and to do that, as he says, he uses a modified Feynman's path integration (specifically, he uses a "vast generalization" of it). The thing is that I don't understand why this is a generalization. I am having difficulties to see how did he modify Feynman's theory:
At page 159, he says:
(…) We can find an example of an SEP that is not at the end of a special dimension but smack in the center, in analogue of Richard Feynman's formulation of quantum mechanics. According to that path-integration formulation, all possible ways that something can happen, all ways that are given positive probability in the wave function, affect the result that does occur. The analogue of Feynman's procedure would be to hold that the framework of all physical possibilities, set by the laws of the actual world, or (alternatively) the wave function of the actual world, is simply the average of all logical possibilities. Our world might not be a special world at the end of salient dimension, but simply an average world.
The sum over all possibilities offers a structural and general criterion of actuality, which is an advantage. The form of the theory is that the actual world is some function (in this case the average) of all possible worlds. This is a desirably neutral form, less arbitrary than starting with given initial conditions
And later, at page 167, he writes:
(…) Earlier we considered a vast generalization of Feynman's path-integral approach by treating the actual worlds as an average world, the average of all possibilities
I think that the main problem is that I do not fully understand what Nozick did when he said:
hold that the framework of all physical possibilities, set by the laws of the actual world, or (alternatively) the wave function of the actual world, is simply the average of all logical possibilities
So, my question basically is: Why is this exactly a "vast generalization" of Feynman's theory? What does this modified Feynman's path integration have that the original form of the theory does not?