1,083 reputation
418
bio website scottaaronson.com
location Cambridge, MA
age 33
visits member for 2 years, 5 months
seen Sep 4 at 21:38

Jul
2
awarded  Curious
Apr
29
awarded  Yearling
Feb
18
awarded  Nice Answer
Feb
6
comment Does natural unit of information and entropy, nat, play special role in the freebit picture?
I don't understand why you're calculating the entropy S by averaging over all x in the interval [0,1]. If you really take seriously that this is Knightian uncertainty, then you ONLY know that x is in [a,b]: you don't even have probabilistic information beyond that, and you certainly don't know that x is uniform. So, not knowing where your formula came from, it's hard to say whether it's "just a neat mathematical coincidence" or whether it has some operational meaning.
Nov
18
comment Quantum version of the Galton Board
Well, I think you can at least get a pretty good approximation in closed form, if you're willing to count special functions as "closed form."
Nov
18
revised Quantum version of the Galton Board
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Nov
1
revised Quantum version of the Galton Board
added 1575 characters in body
Nov
1
answered Quantum version of the Galton Board
Sep
28
comment Is the firewall paradox really a paradox?
By "actual" I meant "referring to the real world, not to a particular approximate method of calculation." You seemed to be suggesting that one can resolve the information-loss problem by saying that information IS lost in a semiclassical approximation, but isn't lost when you sum over all topologies. I was explaining why I don't think that answers the question: because one can state what's "hard to swallow" here or an apparent challenge to locality, without ever needing to make assumptions that come from the semiclassical approximation.
Sep
28
comment Is the firewall paradox really a paradox?
Well, suppose the external observer applies a unitary transformation to the early Hawking radiation, that lets the infalling observer easily see that the early radiation is entangled with the radiation just coming out. Then by monogamy of entanglement, the radiation just coming out can't ALSO be entangled with the modes just inside the horizon. But if they're not entangled, then the infalling observer won't experience a smooth QFT vacuum. That's pretty much the content of AMPS.
Sep
27
answered Is the firewall paradox really a paradox?
Apr
29
awarded  Yearling
Apr
13
awarded  Nice Question
Mar
29
answered Does quantum computing rely on particular interpretations of quantum mechanics?
Mar
19
awarded  Necromancer
Jan
3
comment If the ground states of interacting QFTs are so complicated, how did Nature find them?
dmckee: You seem to be answering a much easier question than the one I asked! I know there's an algorithm to efficiently simulate at least special QFTs on a quantum computer, since JLP showed it (check out their paper if you haven't yet). And yes, certainly you can describe such an algorithm in path-integral language. My question was about the step in their algorithm where you need to adiabatically prepare the interacting vacuum state. Can you avoid that step? If so how? If not, how does Nature do that step? (John Preskill has now partly answered this question; see below.)
Jan
3
comment If the ground states of interacting QFTs are so complicated, how did Nature find them?
@Hugh: This is off-topic, but I think that's completely wrong. If it were correct, then why shouldn't MWI believers simply shoot themselves with (very fast and effective) guns hooked up to quantum random number generators? Since they can never observe the gun being fired, obviously it will seem never to do so! ;-D Yet I don't see them lining up to try it (nor can I blame them, since I don't see anything in MWI that says we get to condition on remaining alive).
Jan
3
awarded  Nice Question
Jan
3
revised If the ground states of interacting QFTs are so complicated, how did Nature find them?
added 29 characters in body
Jan
3
comment If the ground states of interacting QFTs are so complicated, how did Nature find them?
BTW, I suppose we'd better HOPE that the early universe found the correct QCD ground state! I'd never quite put together that, if the known universe gets destroyed via tunneling to a lower-energy vacuum state, the Earth incinerated by a bubble expanding outward at the speed of light, then we ought to blame the failure of the quantum adiabatic algorithm to efficiently find global optima to NP- and QMA-hard optimization problems. :-)