Timeline for Does the wave function/density state actually exist?
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9 events
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| Apr 3, 2013 at 6:54 | comment | added | Mitchell Porter | @wnoise It's ultimately a question of quantum computational complexity and not proven. But all the known speedups obtained by quantum computers (e.g. in Shor's algorithm) are at best sub-exponential, suggesting that this is the true increment of complexity involved in passing from classical to quantum. | |
| Dec 2, 2011 at 1:07 | comment | added | wnoise | @Mitchell Porter: do you have a citation for the non-local portion of the force being sub-exponential? Because I flatly refuse to believe it. If it were true, quantum problems would be efficiently simulatable classically, which no one should believe. | |
| Dec 1, 2011 at 20:52 | comment | added | Peter Shor | There is absolutely no reason to believe that the universe is being computed on some computer living in some hyperverse. In fact, if you take this view (as you seem to), you are left with the question of what is doing the computation that runs this hyperverse. Also, the absence of observations of "bugs" in the laws of physics argues strongly against this possibility. | |
| Nov 21, 2011 at 18:18 | comment | added | Ron Maimon | @Mitchell:you can repeat, you are still wrong. Just to specify the initial wavefunction, you need a function on 3N dimensions, which requires 10 to the 3N values even for only positions on a 10 cubed grid. The idea that the force only needs to be computed at the particle positions is seductive, but wrong in principle, because the wavefunction diffused around based on its own wave equation. You can calculate the wavefunction by summing over all paths, but there are exponentially many paths. | |
| Nov 21, 2011 at 0:05 | comment | added | Mitchell Porter | So I repeat, you do not need an exponentially large beable. You can have a polynomially large beable with a sub-exponentially complex self-interaction. | |
| Nov 21, 2011 at 0:03 | comment | added | Mitchell Porter | Ron, in nomological Bohmian mechanics you can get rid of the wavefunction entirely. You can go backwards from the Hamilton-Jacobi picture and just think of the net force which you calculate as the gradient of the phase, and then that force breaks into two parts as I described. Quantum dynamics then arises from the nonlocal part in the equations of motion for the classical beables. | |
| Nov 19, 2011 at 7:12 | comment | added | Ron Maimon | @Mitchell Porter: If you write a simulation of Bohmian mechanics, you still need a ton of RAM to store the wavefunction data, and there is no reduction in the amount of necessary data from the particle positions. The particle positions are just extra baggage. From a computation perspective, Bohm is worse than quantum mechanics, and the words you use like "nomological" don't make any difference to the computational heft of the wavefunction. | |
| Nov 19, 2011 at 6:42 | comment | added | Mitchell Porter | Have you ever heard of "nomological Bohmian mechanics"? The wavefunction is not treated as a thing, instead it is absorbed into the equation of motion of the classical configuration. That equation of motion can be reduced to local classical forces and a nonlocal quantum force whose specific form depends on the specific wavefunction that you started with. The point is that you do not need an exponentially large beable in order to get quantum dynamics. | |
| Nov 19, 2011 at 6:29 | history | answered | Ribok | CC BY-SA 3.0 |