if i understand it correctly (i may not!), scott aaronson argues that hidden variable theories (such as bohmian / pilot wave) imply hypercomputation (which should count as an evidence against them): https://www.scottaaronson.com/papers/npcomplete.pdf
If hypercomputation is defined as computing the uncomputable, then that’s not his idea. It’s just a quantum speedup better than the usual quantum speedup (defining a quantum complexity class DQP that is a little bigger than BQP). Also, Scott’s Bohmian speedup requires access to what the hidden variables were doing at arbitrary times. But in Bohmian mechanics, measuring an observable perturbs complementary observables (i.e. observables that are in some kind of “uncertainty relation” to the first) in exactly the same way as in ordinary quantum mechanics.
There is a way (in both Bohmian mechanics and standard quantum mechanics) to get at this kind of trajectory information, without overly perturbing the system evolution—“weak measurements”. But weak measurements only provide weak information about the measured observable—that’s the price of not violating the uncertainty principle. A weak measuring device is correlated with the physical property it is measuring, but only weakly.
if i understand it correctly (i may not!), scott aaronson argues that hidden variable theories (such as bohmian / pilot wave) imply hypercomputation (which should count as an evidence against them): https://www.scottaaronson.com/papers/npcomplete.pdf
If hypercomputation is defined as computing the uncomputable, then that’s not his idea. It’s just a quantum speedup better than the usual quantum speedup (defining a quantum complexity class DQP that is a little bigger than BQP). Also, Scott’s Bohmian speedup requires access to what the hidden variables were doing at arbitrary times. But in Bohmian mechanics, measuring an observable perturbs complementary observables (i.e. observables that are in some kind of “uncertainty relation” to the first) in exactly the same way as in ordinary quantum mechanics.
There is a way (in both Bohmian mechanics and standard quantum mechanics) to get at this kind of trajectory information, without overly perturbing the system evolution—“weak measurements”. But weak measurements only provide weak information about the measured observable—that’s the price of not violating the uncertainty principle. A weak measuring device is correlated with the physical property it is measuring, but only weakly.
I mention this because someone ought to see how it affects Scott’s Bohmian speedup, if you get the history information using weak measurements. (Also because weak measurements may have an obscure yet fundamental relationship to Bohmian mechanics.) Is the resulting complexity class DQP, BQP, P, something else? I do not know.