5 ms·

One theorem that gets little discussion is John Conway's Free Will Theorem https://en.wikipedia.org/wiki/Free_will_theorem https://en.wikipedia.org/wiki/Free_wi

by meroes 5y ago

One theorem that gets little discussion is John Conway's Free Will Theorem https://en.wikipedia.org/wiki/Free_will_theorem https://en.wikipedia.org/wiki/Free_will_theorem IF our choices and actions are free, quantum particles' behavior is free in the exact same sense, assuming three postulates, FIN, SPIN, and TWIN. Neither random nor deterministic, but free. I take its lack of being discussed by the usual heavy-hitters in quantum physics as a sign it is not well received, but there is still a lack of discussion for being a theorem developed by Conway and Kochen, both very highly regarded. "Free choice" is so visceral, and it is hard to imagine how experimental outcomes would be determined in heavily contrived ways such as the 9182nd word in a some book chosen by some other contrived way, and so on and so on to choose which spin axis to measure. And all done after the particles are spacelike separated

breuleux 5y ago
> Neither random nor deterministic, but free. What does that mean, though? It seems to me that a mixture of randomness and determinism covers all logically possible systems. I don't understand what "free" is supposed to represent at all. The Free Will Theorem is about certain events not being a function of the past, but does it exclude randomness? How does it do that?
- nahuel0x 5y ago
  That's the crux of it. Free will is an elusive concept who sits over randomness and determinism, being neither of them. We stick to it because it reflects our internal sensation, "I'm choosing this", and because is related to the consciousness/subjective problem ("I feel this"), not mentioning historical baggage.
  - breuleux 5y ago
    Isn't a simpler explanation that we're just... wrong about what we're feeling? My thought about this is that the feeling of free choice that we have stems from a form of irreducible epistemic uncertainty: we can't know what we are going to do before we do it, because our knowledge would influence our action. Furthermore, when choosing between A and B, we may use our self-concept to simulate our choices, meaning that by necessity our self-model is non-deterministic: it indeed performs several different choices during deliberation. I think our error is that we mistake epistemological uncertainty for metaphysical uncertainty, and the non-determinism of our self-model for the non-determinism of our real self.
    - meroes 5y ago
      Absolutely, free will may be a feeling and largely due to incomplete knowledge and not fundamental. But is it the simpler explanation? That is hard to answer. On the one hand Many Worlds is "simple" and deterministic, on the other hand the complexity of the universe is so much greater. A stochastic model like GRW is also simple in the sense there is only one world, and all particles have a regular chance of random collapse. Also Many Words doesn't just provide the (classical picture)*(number of worlds), so it isn't even that "simple". There is nonlocal structure to the global wavefunction. The worlds don't split into any possible worlds; if one splits one way the others have to split into the other possible choices. These global correlations are nonlocal AFAIK - I know the MWI is nonlocal but I have a hard time understanding David Wallace, Lev Vaidman, and Tim Maudlin who all say it is nonlocal. The precise nature of the nonlocality is hard to understand (for me), but it is nonlocal!
      - breuleux 5y ago
        My general philosophy about interpretations of quantum mechanics is that insofar that there is an infinity of possible interpretations that are all mathematically equivalent, the probability that we would think of, let alone find the correct one is for all intents and purposes zero. I don't see any objective criterion that would let us rank them either, so even though it's a fun debate, it is also a pointless one (as long as there are no experiments to differentiate them). > The worlds don't split into any possible worlds; if one splits one way the others have to split into the other possible choices. My (possibly flawed) understanding of MWI is that there isn't really any splitting. There is just a quantum superposition of all possible worlds, and the amplitude corresponding to each one fluctuates over time. A "split" from A to possibilities B and C would just correspond to the amplitude of A draining to 0, half going to B, the other half going to C, but the branches might have had nonzero amplitudes to begin with (they already existed, but now they are "stronger"). Different "branches" may also pour amplitude into the same other "branch" (i.e. they join rather than split). In other words, every moment of possible universe has always existed and will always exist, but over time they switch from "off" (amplitude 0) to various degrees of "on", or to off again, and so on, accordingly to the wavefunction. It's nonlocal in the same way that quantum entanglement is nonlocal in any interpretation, it's just that now we're working on the gargantuan quantum entanglement of every possible state of the entire universe. MWI is arguably the simplest interpretation from the standpoint of rule simplicity: it doesn't involve a notion of collapse, so it has less rules than other interpretations. It is less simple if you look at the sheer mass of what exists according to it, but I find that notion of simplicity less compelling than rule simplicity. Either way, I don't think it matters so I'm noncommittal.
- meroes 5y ago
  I think a definition of Conway's is that there is no mathematical function possible in principle, assuming his three axioms SPIN, TWIN, and FIN, that predicts a free outcome.

by meroes 5y ago

breuleux 5y ago

> Neither random nor deterministic, but free. What does that mean, though? It seems to me that a mixture of randomness and determinism covers all logically possible systems. I don't understand what "free" is supposed to represent at all. The Free Will Theorem is about certain events not being a function of the past, but does it exclude randomness? How does it do that?

nahuel0x 5y ago
That's the crux of it. Free will is an elusive concept who sits over randomness and determinism, being neither of them. We stick to it because it reflects our internal sensation, "I'm choosing this", and because is related to the consciousness/subjective problem ("I feel this"), not mentioning historical baggage.
- breuleux 5y ago
  Isn't a simpler explanation that we're just... wrong about what we're feeling? My thought about this is that the feeling of free choice that we have stems from a form of irreducible epistemic uncertainty: we can't know what we are going to do before we do it, because our knowledge would influence our action. Furthermore, when choosing between A and B, we may use our self-concept to simulate our choices, meaning that by necessity our self-model is non-deterministic: it indeed performs several different choices during deliberation. I think our error is that we mistake epistemological uncertainty for metaphysical uncertainty, and the non-determinism of our self-model for the non-determinism of our real self.
  - meroes 5y ago
    Absolutely, free will may be a feeling and largely due to incomplete knowledge and not fundamental. But is it the simpler explanation? That is hard to answer. On the one hand Many Worlds is "simple" and deterministic, on the other hand the complexity of the universe is so much greater. A stochastic model like GRW is also simple in the sense there is only one world, and all particles have a regular chance of random collapse. Also Many Words doesn't just provide the (classical picture)*(number of worlds), so it isn't even that "simple". There is nonlocal structure to the global wavefunction. The worlds don't split into any possible worlds; if one splits one way the others have to split into the other possible choices. These global correlations are nonlocal AFAIK - I know the MWI is nonlocal but I have a hard time understanding David Wallace, Lev Vaidman, and Tim Maudlin who all say it is nonlocal. The precise nature of the nonlocality is hard to understand (for me), but it is nonlocal!
    - breuleux 5y ago
      My general philosophy about interpretations of quantum mechanics is that insofar that there is an infinity of possible interpretations that are all mathematically equivalent, the probability that we would think of, let alone find the correct one is for all intents and purposes zero. I don't see any objective criterion that would let us rank them either, so even though it's a fun debate, it is also a pointless one (as long as there are no experiments to differentiate them). > The worlds don't split into any possible worlds; if one splits one way the others have to split into the other possible choices. My (possibly flawed) understanding of MWI is that there isn't really any splitting. There is just a quantum superposition of all possible worlds, and the amplitude corresponding to each one fluctuates over time. A "split" from A to possibilities B and C would just correspond to the amplitude of A draining to 0, half going to B, the other half going to C, but the branches might have had nonzero amplitudes to begin with (they already existed, but now they are "stronger"). Different "branches" may also pour amplitude into the same other "branch" (i.e. they join rather than split). In other words, every moment of possible universe has always existed and will always exist, but over time they switch from "off" (amplitude 0) to various degrees of "on", or to off again, and so on, accordingly to the wavefunction. It's nonlocal in the same way that quantum entanglement is nonlocal in any interpretation, it's just that now we're working on the gargantuan quantum entanglement of every possible state of the entire universe. MWI is arguably the simplest interpretation from the standpoint of rule simplicity: it doesn't involve a notion of collapse, so it has less rules than other interpretations. It is less simple if you look at the sheer mass of what exists according to it, but I find that notion of simplicity less compelling than rule simplicity. Either way, I don't think it matters so I'm noncommittal.
meroes 5y ago
I think a definition of Conway's is that there is no mathematical function possible in principle, assuming his three axioms SPIN, TWIN, and FIN, that predicts a free outcome.