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> And so it doesn't matter what mathematical model you put underneath this unpredictability. It can be axiomatic, it can be chaotic, or it can be a cosmic Turin

> And so it doesn't matter what mathematical model you put underneath this unpredictability. It can be axiomatic, it can be chaotic, or it can be a cosmic Turing machine computing the digits of pi. I don't think this is correct. Each formal model will allow you degrees of freedom that are ruled out by other models because the axioms differ. This is why a quantum field theory for Bohmian mechanics has been much harder to formulate than it was for Copenhagen, for example. Unifying quantum mechanics with general relativity could actually be easier under a "fractal model" of quantum mechanics than it is with Copenhagen. Edit on your [update]: > [UPDATE] The general principle is that quantum experiments produce an unbounded amount of information That doesn't sound correct either. No experiment can produce an unbounded amount of information. I'm not sure where you're getting this idea.

lisper 4y ago
> Each formal model will allow you degrees of freedom that are ruled out by other models because the axioms differ. Nope. All QM interpretations produce the same predictions. They are formally equivalent in the same sense that lambda calculus and TMs are equivalent. The reason it is hard to unify Bohm and relativity to produce a Bohmian quantum field theory is that Bohm is committed to an intuitionistic metaphysics that requires there to be an answer to which measurement of an entangled system was performed first, and so it requires the imposition of an arbitrary foliation of space-time. This is a metaphysical requirement, not a physical one. That is what makes it hard to extend Bohm to a field theory. > No experiment can produce an unbounded amount of information. No single experiment can, but over time you can do an unbounded number of experiments. Note that I am deliberately using the term "unbounded" rather than "infinite". These are not the same. An unbounded quantity is finite at any given time, but it can keep growing without an upper bound. (In actual fact all of these numbers are probably finite and bounded because the observable universe is finite and the second law of thermodynamics puts a limit on how many experiments you can do.)
- naasking 4y ago
  > Nope. All QM interpretations produce the same predictions. Correction: the same observable predictions in the domains we've tested. They all have different metaphysical implications which impact the plausibility. > They are formally equivalent in the same sense that lambda calculus and TMs are equivalent. No, that's not strictly correct. Bohmian mechanics allows the existence of quantum non-equilibrium, as but one example. Isomorphism is fine as an informal analogy, but it's not strictly true. > This is a metaphysical requirement, not a physical one. That is what makes it hard to extend Bohm to a field theory. The axioms of every interpretation are metaphysical. The axioms are what let you make certain steps in one interpretation that cannot be done in another. This is why unifying GR with Bohmian mechanics is hard but isn't with Copenhagen, which is exactly what I said.
  - lisper 4y ago
    > Correction: the same observable predictions "Observable" is redundant. A prediction in science is understood to mean a prediction about the outcome of an experiment, i.e. a prediction about an observation. > in the domains we've tested. No. The predictions of all QM interpretations are the same, full stop. If this were not the case we would not be having this conversation at all, we could determine which interpretation was correct by doing an experiment. (There is one exception to this, and that is GRW collapse, which predicts that there is some macroscopic scale at which systems stop exhibiting quantum behavior because of internal spontaneous collapse. But so far all experiments have falsified this.) > The axioms of every interpretation are metaphysical. No, that's not true. Bohmian positions are physical. Collapse is physical. Multiple worlds are physical. The thing that makes Bohmian foliations metaphysical is not that they are unmeasurable, it is that they are arbitrary. You cannot tell which foliation is correct even in principle.
    - naasking 4y ago
      > If this were not the case we would not be having this conversation at all, we could determine which interpretation was correct by doing an experiment. No, that's not correct. Again, Bohmian mechanics allows for quantum non-equilibrium, but we're not yet sure how to create such a state. So it is does make observably different prediction, in principle. This prediction is just not within experimental reach at the moment. Most interpretations make equivalent predictions, but not all. Those predictions that differ are outside of domains we've tested. > No, that's not true. Bohmian positions are physical. Collapse is physical. Multiple worlds are physical. They are physical by virtue of metaphysical assertions about what does and does not exist, ie. the axioms. > The thing that makes Bohmian foliations metaphysical is not that they are unmeasurable, it is that they are arbitrary. You cannot tell which foliation is correct even in principle. A preferred foliation can be derived from the wave function in Bohmian mechanics. You can arguably do without one. Both references are cited here: https://link.springer.com/article/10.1007/s10955-015-1369-8 https://link.springer.com/article/10.1007/s10955-015-1369-8

lisper 4y ago

> Each formal model will allow you degrees of freedom that are ruled out by other models because the axioms differ. Nope. All QM interpretations produce the same predictions. They are formally equivalent in the same sense that lambda calculus and TMs are equivalent. The reason it is hard to unify Bohm and relativity to produce a Bohmian quantum field theory is that Bohm is committed to an intuitionistic metaphysics that requires there to be an answer to which measurement of an entangled system was performed first, and so it requires the imposition of an arbitrary foliation of space-time. This is a metaphysical requirement, not a physical one. That is what makes it hard to extend Bohm to a field theory. > No experiment can produce an unbounded amount of information. No single experiment can, but over time you can do an unbounded number of experiments. Note that I am deliberately using the term "unbounded" rather than "infinite". These are not the same. An unbounded quantity is finite at any given time, but it can keep growing without an upper bound. (In actual fact all of these numbers are probably finite and bounded because the observable universe is finite and the second law of thermodynamics puts a limit on how many experiments you can do.)

naasking 4y ago
> Nope. All QM interpretations produce the same predictions. Correction: the same observable predictions in the domains we've tested. They all have different metaphysical implications which impact the plausibility. > They are formally equivalent in the same sense that lambda calculus and TMs are equivalent. No, that's not strictly correct. Bohmian mechanics allows the existence of quantum non-equilibrium, as but one example. Isomorphism is fine as an informal analogy, but it's not strictly true. > This is a metaphysical requirement, not a physical one. That is what makes it hard to extend Bohm to a field theory. The axioms of every interpretation are metaphysical. The axioms are what let you make certain steps in one interpretation that cannot be done in another. This is why unifying GR with Bohmian mechanics is hard but isn't with Copenhagen, which is exactly what I said.
- lisper 4y ago
  > Correction: the same observable predictions "Observable" is redundant. A prediction in science is understood to mean a prediction about the outcome of an experiment, i.e. a prediction about an observation. > in the domains we've tested. No. The predictions of all QM interpretations are the same, full stop. If this were not the case we would not be having this conversation at all, we could determine which interpretation was correct by doing an experiment. (There is one exception to this, and that is GRW collapse, which predicts that there is some macroscopic scale at which systems stop exhibiting quantum behavior because of internal spontaneous collapse. But so far all experiments have falsified this.) > The axioms of every interpretation are metaphysical. No, that's not true. Bohmian positions are physical. Collapse is physical. Multiple worlds are physical. The thing that makes Bohmian foliations metaphysical is not that they are unmeasurable, it is that they are arbitrary. You cannot tell which foliation is correct even in principle.
  - naasking 4y ago
    > If this were not the case we would not be having this conversation at all, we could determine which interpretation was correct by doing an experiment. No, that's not correct. Again, Bohmian mechanics allows for quantum non-equilibrium, but we're not yet sure how to create such a state. So it is does make observably different prediction, in principle. This prediction is just not within experimental reach at the moment. Most interpretations make equivalent predictions, but not all. Those predictions that differ are outside of domains we've tested. > No, that's not true. Bohmian positions are physical. Collapse is physical. Multiple worlds are physical. They are physical by virtue of metaphysical assertions about what does and does not exist, ie. the axioms. > The thing that makes Bohmian foliations metaphysical is not that they are unmeasurable, it is that they are arbitrary. You cannot tell which foliation is correct even in principle. A preferred foliation can be derived from the wave function in Bohmian mechanics. You can arguably do without one. Both references are cited here: https://link.springer.com/article/10.1007/s10955-015-1369-8 https://link.springer.com/article/10.1007/s10955-015-1369-8