0

0

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?

2For one thing. Feynman's procedure ends up with a probability distribution, for a single interaction, not a world. If you somehow did the path integrals including everything, you still wouldn't get a world, you would get the superimposed probability profile for a world. You would get something like Everett's map of alll the possible worlds. And it would be largely useless. – None – 2019-08-29T03:31:43.877

1I'm quite curious to what degree Nozick knew what he was talking about when citing Feynman. I have a cynical suspicion that was Nozick is writing about would be considered nonsense by a theoretical physicist, but I do not know one way or the other. – Chelonian – 2019-08-29T04:13:05.430

@jobermark What is the exact difference between Everett's worlds and Feynman "multiple histories"? And also, you say we could get a "map" of all Everett's possible worlds, but, as far as I know, Everett's worlds would only be based in our laws of physics while in Feynman's "path integral" we could get all logically possible universes (even ones with completely and radically different fundamental constants and laws of physics). So, wouldn't we get much more worlds than Everett's interpretation? – Maribel – 2019-08-29T21:23:53.103

You are missing the point. You can follow the possible paths of the particle or focal object through

the rest of the worldto see how it will respond next. If you are following theworldthrough the "rest of the world" you are not making tons of sense. And no, all possible worlds are all possible worlds, if variations in basic constants exist, they are part of the superposition. – None – 2019-08-29T21:32:19.903Feynman and Everett have to be equivalent at base because they are both formal interpretations equivalent to the Copenhagen and QFT formalisms. But Everett's version is useless for anything other than science fiction shows. Without isolating a focus, the notion of all possible states of all possible worlds does not gain us anything. It certainly does not present an 'average world', just a catalog of options. And the options are not separable. That is why as ingenious as it is Everett's model very seldom makes a prominent, meaningful entry into genuine science. – None – 2019-08-29T21:35:09.830