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The problem is about physics, not Turing machines. You don't need to make a random choice as part of your physical model, the model only makes predictions about
by Y_Y 2y ago
The problem is about physics, not Turing machines. You don't need to make a random choice as part of your physical model, the model only makes predictions about the distribution. You can't represent the continuous dynamical manifolds of classical or quantum mechanics on a TM either, but that's ok, because we have discrete models that work well.
- hackandthink 2y agoI am asking myself: Does a probabilistic Turing machines needs aleatory uncertainty? (would have called this ontological but (1) disagrees) Epistemic uncertainty would mean her: We don't know which deterministic Turing machine we are running. Right now, I see no way to use this in algorithms. (1) https://dictionary.helmholtz-uq.de/content/types_of_uncertainty.html https://dictionary.helmholtz-uq.de/content/types_of_uncertai...
- lisper 2y agoThe whole point of Turing Machines is to eliminate all of these different kinds of uncertainty. There is in point of actual physical fact no such thing as a Turing Machine. Digital computers are really analog under the hood, but they are constructed in such a way that their behavior corresponds to a deterministic model with extremely high fidelity. It turns out that this deterministic behavior can in turn be tweaked to correspond to the behavior of a wide range of real physical systems. Indeed, there is only one known exception: individual quantum measurements, which are non-deterministic at a very deep fundamental level. And that in turn also turns out to be useful in its own way, which is why quantum computing is a thing.
- 11101010001100 2y agoRight, the point is that we don't need a solution to the 'measurement problem' to have a quantum computer.
- lisper 2y agoWell, yeah, obviously. But my point is that you do need a solution to the measurement problem in order to model measurements in any way other than simply punting and introducing randomness as a postulate.
- 11101010001100 2y agoAnd is that solution required to be deterministic? If so, that is another postulate.
- lisper 2y agoYou have to either postulate randomness or describe how it arises from determinism. I don't see any other logical possibility. BTW, see this: https://arxiv.org/abs/quant-ph/9906015 https://arxiv.org/abs/quant-ph/9906015 for a valiant effort to extract randomness from determinism, and this: https://blog.rongarret.info/2019/07/the-trouble-with-many-worlds.html https://blog.rongarret.info/2019/07/the-trouble-with-many-wo... for my critique.
- lisper 2y ago> You don't need to make a random choice as part of your physical model You do if you want to model individual quantum measurements.
- 11101010001100 2y agoInteraction in quantum physics is something that remains abstract at a certain level. So long as conservation principles are satisfied (include probability summing to one), interactions are permitted (i.e., what is permitted is required).
- lisper 2y agoYes. So? What does that have to do with modeling measurements, i.e. the macroscopic process of humans doing experiments and observing the results?
- 11101010001100 2y agoWould you agree that measurement is considered an interaction?
- lisper 2y agoSure. So?