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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?

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    For 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. – user9166 Aug 29 '19 at 3:31
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    I'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 Aug 29 '19 at 4:13
  • @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 Aug 29 '19 at 21:23
  • You are missing the point. You can follow the possible paths of the particle or focal object through the rest of the world to see how it will respond next. If you are following the world through 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. – user9166 Aug 29 '19 at 21:32
  • Feynman 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. – user9166 Aug 29 '19 at 21:35
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Giving Nozick the benefit of the doubt, he's just making up analogies between unrelated fields and name-dropping a Nobel prize-winner to justify them.

This has been a popular game played by philosophers for years. See Sokal and Bricmont's book, Fashionable Nonsense, for a particularly thorough inventory of examples that are at least as breathtaking in their inanity as this one from Nozick.

Regarding the actual physics, if you want to play this game at Feynman's level, then at the very least you better be able to pick up a pencil and write down a sum-over-histories expression for the system you are studying. It's not at all clear that you could possibly do that for a planet, or even a baseball for that matter. Does Nozick take pencil in hand and deliver? No? Well then, that's all you need to know.

  • Why couldn't we do a sum-over-histories for a planet or a baseball ball? I mean, in what cases we could not do that? Also, why is Nozick's idea so unrelated to Feynman's original "path integration"? What does he claim that is so separated from what Feynman thought? @nielsnielsen – Maribel Aug 29 '19 at 21:26
  • @Maribel, a sum-over-histories approach is used to predict the outcome of an event like a single photon, or two photons, passing through an optical slit, or for an electron passing close by an atom. This works for single particles but is useless in the case of a baseball, which has about 10^23 atoms in it (one with 23 zeros after it), and hence impossible to use on a planet or a human being. More in the next comment. – niels nielsen Aug 29 '19 at 22:01
  • @Maribel, Nozick's idea contains no math at all whereas the sum-over-histories or path integral method is a precise mathematical procedure used in the field of quantum electrodynamics to predict the outcomes of experiments involving photons and charged particles. As such, the analogy is an absurd misuse of physics in support of a psychological or sociological assertion. – niels nielsen Aug 29 '19 at 22:06
  • @nielsnielsen Is there a reason beyond complexity that it works at the level of photons but not baseballs? It seems like it could equivalent to this: assuming determinism we could, in principle, predict every event in the next hundred years by tracking the movements of every particle this second. No one denies this consequence because we can't jot down the sum. Why is this a refutation of Nozick here then? it looks a weak argument, but i'm sceptical that our inability to compute particle behaviour past a certain scale shows the math doesn't apply to particles past a certain scale. – Daniel Prendergast Sep 1 '19 at 22:34
  • Math applies to large collections of gas particles as well; this is known as statistical mechanics and forms the basis of the science of thermodynamics which allows precise computation of collective particle behavior up to the scale of stars and galaxies. Feynman's formalism was neither designed nor intended to do that. Nozick is refuted by his invocation (but not actual use) of mathematical tools in a completely nonmathematical context. more in next comment. – niels nielsen Sep 2 '19 at 1:21
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I totally agree with the scepticism already expressed by others about what Nozick is trying to say. However, I would like to take a guess at what he is driving it.

He is really saying, the world we find might be the average outcome, or only averagely variant from that. So if the universe ran from some uniform initial condition like a symmetrical big bang, on average we would expect this - fundamental particles like this, forces like so, stable atoms, occasional black holes etc. It's a solution to the fine tuning problem without using the anthropic principle.

Without more context on what purpose he is putting this woolly argument he makes, it's hard to say more than that about his intentions behind the passage. To clarify the physics problem with what he says though: Feynman's sum-over-histories solved a problem by correcting quantum probabilities, to account not just for the most likely things to have been happening between observations, nor the least likely, but the average. So, when a light ray is travelling along there is some probability of it splitting into all the particle-antiparticle pairs, and creating all the things a photon can - whatever it's energy, though the probabilities get much higher with greater energy. So, in a sense this makes all the things that could have happened between observations, part of what did happen. The opposite of Nozick's idea, where he seems to think unlikely universes couldn't have come to be, only the average. Thr existence of unlikely universes would have to have real, impactful consequences - in a sense this universe would have to show traces of not being average, for Nozick to be right.

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