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Do you know if these efforts also only limit the formula describing these Qbit to computable reals? I think it's a quite interesting crossroad. Either reals d
by j-pb 6y ago
Do you know if these efforts also only limit the formula describing these Qbit to computable reals?
I think it's a quite interesting crossroad.
Either reals don't exist, and everything is at most turing complete, in which case the universe is detemernistic and predictable, yet there are very hard boundaries to what can be known and proven.
Or reals DO exist in which case the church turing thesis is false, as the universe (with it's operations on reals) is a reified example of a super turing system, in which case we can know a lot more things than in the discrete case, but some of that knowledge can only be grasped intuitively, because the moment you try to articulate it into formulas, it's discretized and thus limited to your sub-universe/brain powerfull turing machine.
- GoblinSlayer 6y agoReals are a digital model of analog reality. Is just a model enough for your definition of existence?
- j-pb 6y agoThere are whole books writen about mathematical objects that turned out to not have existed. Non-computable reals are also perfectly capable of modeling "analog reality" (because for all intents and purposes, reality could be discrete and finitely describable very small scales).
- defterGoose 6y ago>analog reality. Quantization would like a word with you.
- abdullahkhalids 6y agoIt has been claimed that "we can simulate a BQP machine using efficiently computable entries from the set {−1, −4/5 , − 3/5 , 0, 3/5 , 4/5 , 1}" [1]. So any part of reality that you can reduce to an efficient computation on a quantum computer, admits a description using the rationals only. But I might be out of my depth here. [1] https://arxiv.org/abs/quant-ph/0003035 https://arxiv.org/abs/quant-ph/0003035